Finite Group Databasebeta

← C2×D11×#553 #15660769

Subgroups — C2×D11×#553 #15660769

Order 2816.

8798 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623226C211yesmaximal, characteristic, complemented
2C2×#10623149C211yesmaximal, characteristic, complemented
3C2×#10623240C212yesmaximal, complemented
4C2×#10623089C211yesmaximal, characteristic, complemented
5C2×#10623071C212yesmaximal, complemented
6C2×#10623045C211yesmaximal, characteristic, complemented
7C2×#10623145C211yesmaximal, characteristic, complemented
8C2×#10623096C211yesmaximal, characteristic, complemented
9C2×#10623192C212yesmaximal, complemented
10C2×#10623061C211yesmaximal, characteristic, complemented
11C2×#10623132C212yesmaximal, complemented
12D11×#553C2132yesmaximal, direct product factor
13C2×D11×#126C212yesmaximal, complemented
14C2×D11×#125C211yesmaximal, characteristic, complemented
15C2×D11×#123C212yesmaximal, complemented
16C2×D11×#121C211yesmaximal, characteristic, complemented
17C2×D11×#121C212yesmaximal, complemented
18C2×D11×#121C211yesmaximal, characteristic, complemented
19C2×C4×D4×D11C211yesmaximal, characteristic, complemented
20C2×C4×D4×D11C211yesmaximal, characteristic, complemented
21C2×C4×D4×D11C212yesmaximal, complemented
22C2×D11×#117C211yesmaximal, characteristic, complemented
23C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
24C2×C11×#553C211yesmaximal, characteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C22×D4×D11C2212yes—
27C22×D4×D11C2211yescharacteristic
28C22×D4×D11C2212yes—
29C23×C4×D11C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×C4×D11C2212yes—
32C23×C4×D11C2212yes—
33C11×#553C22116yescomplemented
34C2×C11×#126C2212yescomplemented
35C2×C11×#125C2211yescharacteristic, complemented
36C2×C11×#123C2212yescomplemented
37C2×C11×#121C2212yescomplemented
38C2×C11×#121C2211yescharacteristic, complemented
39C2×C11×#121C2211yescharacteristic, complemented
40C2×C4×D4×C11C2211yescharacteristic, complemented
41C2×C4×D4×C11C2212yescomplemented
42C2×C4×D4×C11C2211yescharacteristic, complemented
43C2×C11×#117C2211yescharacteristic, complemented
44C22×C11×C4⋊C4C2211yescharacteristic, complemented
45C2×#66992C2212yescomplemented
46C2×#66992C2212yescomplemented
47C2×#66992C2212yescomplemented
48C2×#66992C2212yescomplemented
49C2×#66991C2212yescomplemented
50C2×#66991C2211yescharacteristic, complemented
51C2×#66991C2211yescharacteristic, complemented
52C2×#66988C2212yescomplemented
53C2×D4×Dic11C2211yescharacteristic, complemented
54C2×D4×Dic11C2212yescomplemented
55C2×D4×Dic11C2211yescharacteristic, complemented
56C2×#66983C2211yescharacteristic, complemented
57C2×#66983C2211yescharacteristic, complemented
58C2×#66983C2212yescomplemented
59C2×#66982C2212yescomplemented
60C2×C4×C22⋊D11C2212yescomplemented
61C2×C4×C22⋊D11C2211yescharacteristic, complemented
62C2×C4×C22⋊D11C2212yescomplemented
63C2×C4×C22⋊D11C2212yescomplemented
64C2×C4×C22⋊D11C2211yescharacteristic, complemented
65C2×#66979C2211yescharacteristic, complemented
66C22×C4⋊Dic11C2211yescharacteristic, complemented
67C22×Dic11⋊C4C2212yescomplemented
68#10623240C22132yescomplemented
69D11×#126C22132yescomplemented
70#10623226C22116yescomplemented
71D11×#125C22116yescomplemented
72#10623192C22132yescomplemented
73D11×#123C22132yescomplemented
74#10623149C22116yescomplemented
75#10623145C22116yescomplemented
76D11×#121C22116yescomplemented
77D11×#121C22132yescomplemented
78D11×#121C22116yescomplemented
79#10623132C22132yescomplemented
80#10623096C22116yescomplemented
81#10623089C22116yescomplemented
82C4×D4×D11C22132yescomplemented
83C4×D4×D11C22116yescomplemented
84C4×D4×D11C22116yescomplemented
85#10623071C22132yescomplemented
86#10623061C22116yescomplemented
87D11×#117C22116yescomplemented
88#10623045C22116yescomplemented
89C2×#66951C2212yescomplemented
90C2×#66951C2212yescomplemented
91C2×#66951C2212yescomplemented
92C2×#66948C2211yescharacteristic, complemented
93C2×#66948C2211yescharacteristic, complemented
94C2×#66948C2212yescomplemented
95C2×#66947C2212yescomplemented
96C2×#66947C2212yescomplemented
97C2×#66946C2211yescharacteristic, complemented
98C2×#66946C2212yescomplemented
99C2×#66946C2211yescharacteristic, complemented
100C2×#66945C2211yescharacteristic, complemented
101C2×#66945C2211yescharacteristic, complemented
102C2×C4⋊C4×D11C2212yes—
103C2×C4⋊C4×D11C2211yescharacteristic
104C2×C4⋊C4×D11C2211yescharacteristic
105C2×C4⋊C4×D11C2212yes—
106C2×C4⋊C4×D11C2211yescharacteristic
107C2×C4⋊C4×D11C2212yes—
108C2×C4⋊C4×D11C2211yescharacteristic
109C2×C4⋊C4×D11C22116yescomplemented
110C2×C4⋊C4×D11C2211yescharacteristic, complemented
111C2×C4⋊C4×D11C2212yescomplemented
112C2×C4⋊C4×D11C2211yescharacteristic, complemented
113C2×#66943C2211yescharacteristic, complemented
114C2×#66943C2211yescharacteristic, complemented
115C2×#66942C2212yescomplemented
116C2×#66942C2212yescomplemented
117C2×#66939C2212yescomplemented
118C2×#66937C2212yescomplemented
119C2×#66937C2212yescomplemented
120C2×#66937C2212yescomplemented
121C2×#66937C2212yescomplemented
122C2×#66936C2212yescomplemented
123C2×#66936C2212yescomplemented
124C2×(C22⋊D11)⋊C4C2212yescomplemented
125C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
126C2×(C22⋊D11)⋊C4C2212yescomplemented
127C2×(C22⋊D11)⋊C4C2212yescomplemented
128C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
129C2×C22⋊C4×D11C2212yes—
130C2×C22⋊C4×D11C2212yes—
131C2×C22⋊C4×D11C2212yes—
132C2×C22⋊C4×D11C2212yes—
133C2×C22⋊C4×D11C2211yescharacteristic
134C2×C22⋊C4×D11C2211yescharacteristic
135C2×#66932C2212yescomplemented
136C2×#66932C2212yescomplemented
137C2×#66932C2212yescomplemented
138C2×#66930C2212yescomplemented
139C2×#66929C2212yescomplemented
140C2×C4×D44C2212yescomplemented
141C2×C4×D44C2211yescharacteristic, complemented
142C2×C4×D44C2211yescharacteristic, complemented
143C2×#66925C2212yescomplemented
144C2×C42×D11C2211yescharacteristic
145C2×C42×D11C2212yes—
146C2×#66923C2211yescharacteristic, complemented
147C24×D11C2311yescharacteristic
148C24×D11C2312yes—
149C24×D11C2311yescharacteristic
150C22×D4×C11C2311yescharacteristic
151C22×D4×C11C2311yescharacteristic
152C22×D4×C11C2312yes—
153C22×D4×C11C2312yes—
154C23×C4×C11C2311yescharacteristic
155C23×C4×C11C2311yescharacteristic
156C23×C4×C11C2312yes—
157C23×C4×C11C2312yes—
158C22×C22⋊D11C2311yescharacteristic
159C22×C22⋊D11C2312yes—
160C22×C22⋊D11C2312yes—
161C22×C22⋊D11C2312yes—
162C22×C22⋊D11C2311yescharacteristic
163C22×C22⋊D11C2312yes—
164C22×C22⋊D11C2312yes—
165C23×Dic11C2311yescharacteristic
166C23×Dic11C2311yescharacteristic
167C23×Dic11C2312yes—
168C23×Dic11C2312yes—
169C2×D4×D11—28no—
170C2×D4×D11—216no—
171C2×D4×D11—28no—
172C2×D4×D11—48no—
173C2×D4×D11C23116yes—
174C2×D4×D11C2318yes—
175C2×D4×D11C2318yes—
176C2×D4×D11C23116yes—
177C22×D44C2312yes—
178C22×D44C2311yescharacteristic
179C22×D44C2311yescharacteristic
180C22×D44C2312yes—
181C22×C4×D11—28no—
182C22×C4×D11—28no—
183C22×C4×D11—48no—
184C22×C4×D11—48no—
185C22×C4×D11C2311yescharacteristic
186C22×C4×D11C2311yescharacteristic
187C22×C4×D11C2312yes—
188C22×C4×D11C2311yescharacteristic
189C22×C4×D11C2312yes—
190C22×C4×D11C2311yescharacteristic
191C22×C4×D11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C22×C4×D11C2311yescharacteristic
194C22×C4×D11C2312yes—
195C22×C4×D11C2311yescharacteristic
196C22×C4×D11C2318yes—
197C22×C4×D11C2318yes—
198C22×C4×D11C2312yes—
199C22×C4×D11C2312yes—
200C22×C4×D11C2312yes—
201C22×C4×D11C2312yes—
202C22×C4×D11C23116yes—
203C22×C4×D11C23116yes—
204C22×C4×D11C2311yescharacteristic
205C11×#126C23116yescomplemented
206C11×#125C2318yescomplemented
207C11×#123C23116yescomplemented
208C11×#121C23116yescomplemented
209C11×#121C2318yescomplemented
210C11×#121C2318yescomplemented
211C4×D4×C11C23116yescomplemented
212C4×D4×C11C2318yescomplemented
213C4×D4×C11C2318yescomplemented
214C11×#117C2318yescomplemented
215C2×C11×C4⋊C4C2312yes—
216C2×C11×C4⋊C4C2312yes—
217C2×C11×C4⋊C4C2311yescharacteristic
218C2×C11×C4⋊C4C2311yescharacteristic
219C2×C11×C4⋊C4C2311yescharacteristic
220C2×C11×C4⋊C4C2312yes—
221C2×C11×C4⋊C4C2311yescharacteristic
222C2×C11×C4⋊C4C2318yescomplemented
223C2×C11×C22⋊C4C2312yes—
224C2×C11×C22⋊C4C2312yes—
225C2×C11×C22⋊C4C2312yes—
226C2×C11×C22⋊C4C2312yes—
227C2×C11×C22⋊C4C2311yescharacteristic
228C2×C11×C22⋊C4C2311yescharacteristic
229C2×C42×C11C2311yescharacteristic
230C2×C42×C11C2312yes—
231C2×C22⋊Dic11C2312yes—
232C2×C22⋊Dic11C2312yes—
233C2×C22⋊Dic11C2312yes—
234C2×C22⋊Dic11C2312yes—
235C2×C22⋊Dic11C2311yescharacteristic
236C2×C22⋊Dic11C2311yescharacteristic
237#66992C23116yescomplemented
238#66992C23116yescomplemented
239#66992C23116yescomplemented
240#66992C23116yescomplemented
241#66991C2318yescomplemented
242#66991C2318yescomplemented
243#66991C23116yescomplemented
244#66988C23116yescomplemented
245D4×Dic11C2318yescomplemented
246D4×Dic11C23116yescomplemented
247D4×Dic11C2318yescomplemented
248#66983C23116yescomplemented
249#66983C2318yescomplemented
250#66983C2318yescomplemented
251#66982C23116yescomplemented
252C4×C22⋊D11C23116yescomplemented
253C4×C22⋊D11C2318yescomplemented
254C4×C22⋊D11C2318yescomplemented
255C4×C22⋊D11C23116yescomplemented
256C4×C22⋊D11C23116yescomplemented
257C2×(C2×D11)⋊C4C2312yes—
258C2×(C2×D11)⋊C4C2312yes—
259C2×(C2×D11)⋊C4C2311yescharacteristic
260C2×(C2×D11)⋊C4C2312yes—
261C2×(C2×D11)⋊C4C2311yescharacteristic
262C2×(C2×D11)⋊C4C2311yescharacteristic
263C2×(C2×D11)⋊C4C2312yes—
264C2×(C2×D11)⋊C4C2312yes—
265C2×(C2×D11)⋊C4C2312yes—
266C2×(C2×D11)⋊C4C2312yes—
267C2×(C2×D11)⋊C4C2311yescharacteristic
268C2×(C2×D11)⋊C4C2312yes—
269#66979C2318yescomplemented
270C2×C4⋊Dic11C2311yescharacteristic
271C2×C4⋊Dic11C2311yescharacteristic
272C2×C4⋊Dic11C2311yescharacteristic
273C2×C4⋊Dic11C2312yes—
274C2×C4⋊Dic11C2311yescharacteristic
275C2×C4⋊Dic11C2312yes—
276C2×C4⋊Dic11C2312yes—
277C2×C4⋊Dic11C2318yescomplemented
278C2×Dic11⋊C4C2312yes—
279C2×Dic11⋊C4C2312yes—
280C2×Dic11⋊C4C2312yes—
281C2×Dic11⋊C4C2312yes—
282C2×Dic11⋊C4C2311yescharacteristic
283C2×Dic11⋊C4C2312yes—
284C2×Dic11⋊C4C2312yes—
285C2×Dic11⋊C4C2311yescharacteristic
286C2×Dic11⋊C4C2312yes—
287C2×Dic11⋊C4C2312yes—
288C2×Dic11⋊C4C2312yes—
289C2×Dic11⋊C4C23116yescomplemented
290C2×C4×Dic11C2312yes—
291C2×C4×Dic11C2312yes—
292C2×C4×Dic11C2312yes—
293C2×C4×Dic11C2311yescharacteristic
294C2×C4×Dic11C2311yescharacteristic
295C2×C4×Dic11C2311yescharacteristic
296#66951C23116yescomplemented
297#66951C23116yescomplemented
298#66951C23116yescomplemented
299#66948C23116yescomplemented
300#66948C2318yescomplemented
301#66948C2318yescomplemented
302#66947C23116yescomplemented
303#66947C23116yescomplemented
304#66946C2318yescomplemented
305#66946C2318yescomplemented
306#66946C23116yescomplemented
307#66945C2318yescomplemented
308#66945C2318yescomplemented
309C4⋊C4×D11C2318yes—
310C4⋊C4×D11C23116yes—
311C4⋊C4×D11C23116yes—
312C4⋊C4×D11C2318yes—
313C4⋊C4×D11C2318yes—
314C4⋊C4×D11C2318yes—
315C4⋊C4×D11C23116yes—
316C4⋊C4×D11C23116yescomplemented
317C4⋊C4×D11C2318yescomplemented
318C4⋊C4×D11C2318yescomplemented
319#66943C2318yescomplemented
320#66943C2318yescomplemented
321#66942C23116yescomplemented
322#66942C23116yescomplemented
323#66939C23116yescomplemented
324#66937C23116yescomplemented
325#66937C23116yescomplemented
326#66937C23116yescomplemented
327#66937C23116yescomplemented
328#66936C23116yescomplemented
329#66936C23116yescomplemented
330(C22⋊D11)⋊C4C23116yescomplemented
331(C22⋊D11)⋊C4C23116yescomplemented
332(C22⋊D11)⋊C4C2318yescomplemented
333(C22⋊D11)⋊C4C23116yescomplemented
334(C22⋊D11)⋊C4C2318yescomplemented
335C22⋊C4×D11C23116yes—
336C22⋊C4×D11C23116yes—
337C22⋊C4×D11C23116yes—
338C22⋊C4×D11C23116yes—
339C22⋊C4×D11C2318yes—
340C22⋊C4×D11C2318yes—
341#66932C23116yescomplemented
342#66932C23116yescomplemented
343#66932C23116yescomplemented
344#66930C23116yescomplemented
345#66929C23116yescomplemented
346C4×D44C23116yescomplemented
347C4×D44C2318yescomplemented
348C4×D44C2318yescomplemented
349#66925C23116yescomplemented
350C42×D11C23116yes—
351C42×D11C2318yes—
352#66923C2318yescomplemented
353C22×#553—111nomaximal, Sylow
354C24×C11C2411yescharacteristic
355C24×C11C2412yes—
356C24×C11C2411yescharacteristic
357C23×D11—24no—
358C23×D11—24no—
359C23×D11—24no—
360C23×D11—24no—
361C23×D11—28no—
362C23×D11—28no—
363C23×D11—28no—
364C23×D11—24no—
365C23×D11#4118yes—
366C23×D11C2414yes—
367C23×D11C2418yes—
368C23×D11C2411yescharacteristic
369C23×D11C2412yes—
370C23×D11C2414yes—
371C23×D11C2411yescharacteristic
372C23×D11C2411yescharacteristic
373C2×D4×C11—24no—
374C2×D4×C11—28no—
375C2×D4×C11—24no—
376C2×D4×C11—44no—
377C2×D4×C11C2414yes—
378C2×D4×C11C2414yes—
379C2×D4×C11C2418yes—
380C2×D4×C11C2418yes—
381C22×C4×C11—24no—
382C22×C4×C11—24no—
383C22×C4×C11—44no—
384C22×C4×C11—44no—
385C22×C4×C11C2411yescharacteristic
386C22×C4×C11C2412yes—
387C22×C4×C11C2411yescharacteristic
388C22×C4×C11C2412yes—
389C22×C4×C11C2411yescharacteristic
390C22×C4×C11C2412yes—
391C22×C4×C11C2411yescharacteristic
392C22×C4×C11C2414yes—
393C22×C4×C11C2414yes—
394C22×C4×C11C2418yes—
395C22×C4×C11C2418yes—
396C22×C4×C11C2411yescharacteristic
397C2×C22⋊D11—28no—
398C2×C22⋊D11—28no—
399C2×C22⋊D11—24no—
400C2×C22⋊D11—24no—
401C2×C22⋊D11—28no—
402C2×C22⋊D11—44no—
403C2×C22⋊D11—44no—
404C2×C22⋊D11C2418yes—
405C2×C22⋊D11C2414yes—
406C2×C22⋊D11C2418yes—
407C2×C22⋊D11C2414yes—
408C2×C22⋊D11C2418yes—
409C2×C22⋊D11C2418yes—
410C2×C22⋊D11C2418yes—
411C22×Dic11—24no—
412C22×Dic11—24no—
413C22×Dic11—44no—
414C22×Dic11—44no—
415C22×Dic11C2414yes—
416C22×Dic11C2414yes—
417C22×Dic11C2411yescharacteristic
418C22×Dic11C2412yes—
419C22×Dic11C2411yescharacteristic
420C22×Dic11C2412yes—
421C22×Dic11C2411yescharacteristic
422C22×Dic11C2412yes—
423C22×Dic11C2411yescharacteristic
424C22×Dic11C2418yes—
425C22×Dic11C2418yes—
426C22×Dic11C2411yescharacteristic
427D4×D11—232no—
428D4×D11—232no—
429D4×D11—264no—
430D4×D11—432no—
431C2×D44—28no—
432C2×D44—24no—
433C2×D44—24no—
434C2×D44—44no—
435C2×D44C2418yes—
436C2×D44C2414yes—
437C2×D44C2414yes—
438C2×D44C2418yes—
439C2×C4×D11—24no—
440C2×C4×D11—24no—
441C2×C4×D11—232no—
442C2×C4×D11—232no—
443C2×C4×D11—24no—
444C2×C4×D11—24no—
445C2×C4×D11—24no—
446C2×C4×D11—28no—
447C2×C4×D11—24no—
448C2×C4×D11—28no—
449C2×C4×D11—28no—
450C2×C4×D11—24no—
451C2×C4×D11—24no—
452C2×C4×D11—44no—
453C2×C4×D11—44no—
454C2×C4×D11—44no—
455C2×C4×D11—44no—
456C2×C4×D11—432no—
457C2×C4×D11—432no—
458C2×C4×D11#4118yes—
459C2×C4×D11C2414yes—
460C2×C4×D11C2418yes—
461C2×C4×D11C2414yes—
462C2×C4×D11C2418yes—
463C2×C4×D11C2414yes—
464C2×C4×D11C2414yes—
465C2×C4×D11C2414yes—
466C2×C4×D11C2414yes—
467C2×C4×D11C2414yes—
468C2×C4×D11C2418yes—
469C2×C4×D11C2414yes—
470C2×C4×D11C2418yes—
471C2×C4×D11C2418yes—
472C2×C4×D11C2418yes—
473C2×C4×D11C2418yes—
474C2×C4×D11C2414yes—
475C11×C4⋊C4C2418yes—
476C11×C4⋊C4C2418yes—
477C11×C4⋊C4C2414yes—
478C11×C4⋊C4C2414yes—
479C11×C4⋊C4C2414yes—
480C11×C4⋊C4C2418yes—
481C11×C4⋊C4C2414yes—
482C11×C22⋊C4C2418yes—
483C11×C22⋊C4C2418yes—
484C11×C22⋊C4C2418yes—
485C11×C22⋊C4C2418yes—
486C11×C22⋊C4C2414yes—
487C11×C22⋊C4C2414yes—
488C42×C11C2414yes—
489C42×C11C2418yes—
490C22⋊Dic11C2418yes—
491C22⋊Dic11C2418yes—
492C22⋊Dic11C2418yes—
493C22⋊Dic11C2418yes—
494C22⋊Dic11C2414yes—
495C22⋊Dic11C2414yes—
496(C2×D11)⋊C4C2418yes—
497(C2×D11)⋊C4C2418yes—
498(C2×D11)⋊C4C2414yes—
499(C2×D11)⋊C4C2418yes—
500(C2×D11)⋊C4C2414yes—
501(C2×D11)⋊C4C2414yes—
502(C2×D11)⋊C4C2418yes—
503(C2×D11)⋊C4C2418yes—
504(C2×D11)⋊C4C2418yes—
505(C2×D11)⋊C4C2418yes—
506(C2×D11)⋊C4C2414yes—
507(C2×D11)⋊C4C2418yes—
508C4⋊Dic11C2414yes—
509C4⋊Dic11C2414yes—
510C4⋊Dic11C2414yes—
511C4⋊Dic11C2418yes—
512C4⋊Dic11C2414yes—
513C4⋊Dic11C2418yes—
514C4⋊Dic11C2418yes—
515Dic11⋊C4C2418yes—
516Dic11⋊C4C2418yes—
517Dic11⋊C4C2418yes—
518Dic11⋊C4C2418yes—
519Dic11⋊C4C2414yes—
520Dic11⋊C4C2418yes—
521Dic11⋊C4C2418yes—
522Dic11⋊C4C2414yes—
523Dic11⋊C4C2418yes—
524Dic11⋊C4C2418yes—
525Dic11⋊C4C2418yes—
526C4×Dic11C2418yes—
527C4×Dic11C2418yes—
528C4×Dic11C2418yes—
529C4×Dic11C2414yes—
530C4×Dic11C2414yes—
531C4×Dic11C2414yes—
532C2×#553—1132no—
533C2×#553—112no—
534C2×#553—111no—
535C2×#553—112no—
536C2×#553—112no—
537C2×#553—111no—
538C2×#553—111no—
539C2×#553—111no—
540C2×#553—112no—
541C2×#553—111no—
542C2×#553—111no—
543C2×#553—111no—
544C2×#553D1111yescharacteristic, direct product factor
545C22×#126—112no—
546C22×#125—111no—
547C22×#123—112no—
548C22×#121—112no—
549C22×#121—111no—
550C22×#121—111no—
551C22×C4×D4—112no—
552C22×C4×D4—111no—
553C22×C4×D4—111no—
554C22×#117—111no—
555C23×C4⋊C4—111no—
556C23×C11—22no—
557C23×C11—22no—
558C23×C11—22no—
559C23×C11—22no—
560C23×C11—24no—
561C23×C11—24no—
562C23×C11—24no—
563C23×C11—22no—
564C23×C11C2×#4114yes—
565C23×C11C2512yes—
566C23×C11C2514yes—
567C23×C11C2512yes—
568C23×C11C2511yescharacteristic
569C22×D11—22no—
570C22×D11—22no—
571C22×D11—232no—
572C22×D11—28no—
573C22×D11—28no—
574C22×D11—22no—
575C22×D11—22no—
576C22×D11—24no—
577C22×D11—24no—
578C22×D11—24no—
579C22×D11—22no—
580C22×D11—28no—
581C22×D11—216no—
582C22×D11—28no—
583C22×D11—216no—
584C22×D11—216no—
585C22×D11—28no—
586C22×D11—416no—
587C22×D11—432no—
588C22×D11C2×#4114yes—
589C22×D11C2×#41116yes—
590C22×D11C2×#4114yes—
591C22×D11C2×#4114yes—
592C22×D11H(5,𝔽2)14yes—
593C22×D11C2512yes—
594C22×D11C2514yes—
595C22×D11C2512yes—
596C22×D11C2512yes—
597D4×C11—28no—
598D4×C11—216no—
599D4×C11—28no—
600D4×C11—48no—
601C2×C4×C11—22no—
602C2×C4×C11—22no—
603C2×C4×C11—24no—
604C2×C4×C11—22no—
605C2×C4×C11—24no—
606C2×C4×C11—22no—
607C2×C4×C11—24no—
608C2×C4×C11—28no—
609C2×C4×C11—28no—
610C2×C4×C11—48no—
611C2×C4×C11—48no—
612C2×C4×C11C2×#4114yes—
613C2×C4×C11C2512yes—
614C2×C4×C11C2514yes—
615C2×C4×C11C2512yes—
616C2×C4×C11C2514yes—
617C2×C4×C11C2512yes—
618C2×C4×C11C2514yes—
619C2×C4×C11C2512yes—
620C2×C4×C11C2512yes—
621C22⋊D11—28no—
622C22⋊D11—216no—
623C22⋊D11—216no—
624C22⋊D11—28no—
625C22⋊D11—216no—
626C22⋊D11—48no—
627C22⋊D11—48no—
628C2×Dic11—22no—
629C2×Dic11—22no—
630C2×Dic11—24no—
631C2×Dic11—22no—
632C2×Dic11—22no—
633C2×Dic11—24no—
634C2×Dic11—24no—
635C2×Dic11—28no—
636C2×Dic11—28no—
637C2×Dic11—48no—
638C2×Dic11—48no—
639C2×Dic11C2×#4114yes—
640C2×Dic11C2512yes—
641C2×Dic11C2514yes—
642C2×Dic11C2512yes—
643C2×Dic11C2514yes—
644C2×Dic11C2512yes—
645C2×Dic11C2514yes—
646C2×Dic11C2512yes—
647C2×Dic11C2512yes—
648D44—216no—
649D44—28no—
650D44—28no—
651D44—48no—
652C4×D11—28no—
653C4×D11—28no—
654C4×D11—216no—
655C4×D11—28no—
656C4×D11—216no—
657C4×D11—28no—
658C4×D11—216no—
659C4×D11—28no—
660C4×D11—28no—
661C4×D11—28no—
662C4×D11—28no—
663C4×D11—48no—
664C4×D11—48no—
665C4×D11—48no—
666C4×D11—48no—
667C4×D11C2×#41116yes—
668C23×D4—111no—
669C23×D4—112no—
670C23×D4—111no—
671C23×D4—112no—
672C24×C4—111no—
673C24×C4—111no—
674C24×C4—112no—
675C24×C4—112no—
676#553—1132no—
677#553—1116no—
678#553—1132no—
679#553—1132no—
680#553—1116no—
681#553—1116no—
682#553—1132no—
683#553—1116no—
684#553—1116no—
685#553—1116no—
686#553—1116no—
687#553C2×D11116yesdirect product factor
688C2×#126—1132no—
689C2×#126—112no—
690C2×#126—112no—
691C2×#126—112no—
692C2×#126—112no—
693C2×#126—112no—
694C2×#126—112no—
695C2×#126—112no—
696C2×#126C2×D1112yescomplemented
697C2×#125—1116no—
698C2×#125—112no—
699C2×#125—112no—
700C2×#125—111no—
701C2×#125—111no—
702C2×#125—111no—
703C2×#125C2×D1111yescharacteristic, complemented
704C2×#123—112no—
705C2×#123—112no—
706C2×#123—1132no—
707C2×#123—112no—
708C2×#123—112no—
709C2×#123—112no—
710C2×#123—112no—
711C2×#123—112no—
712C2×#123C2×D1112yescomplemented
713C2×#121—112no—
714C2×#121—111no—
715C2×#121—111no—
716C2×#121—112no—
717C2×#121—112no—
718C2×#121—112no—
719C2×#121—112no—
720C2×#121—112no—
721C2×#121—111no—
722C2×#121—111no—
723C2×#121—1132no—
724C2×#121—1116no—
725C2×#121—1116no—
726C2×#121—112no—
727C2×#121—111no—
728C2×#121—111no—
729C2×#121—112no—
730C2×#121—112no—
731C2×#121—112no—
732C2×#121—112no—
733C2×#121C2×D1112yescomplemented
734C2×#121C2×D1111yescharacteristic, complemented
735C2×#121C2×D1111yescharacteristic, complemented
736C2×C4×D4—112no—
737C2×C4×D4—111no—
738C2×C4×D4—111no—
739C2×C4×D4—112no—
740C2×C4×D4—112no—
741C2×C4×D4—111no—
742C2×C4×D4—112no—
743C2×C4×D4—111no—
744C2×C4×D4—1132no—
745C2×C4×D4—1116no—
746C2×C4×D4—1116no—
747C2×C4×D4—112no—
748C2×C4×D4—111no—
749C2×C4×D4—111no—
750C2×C4×D4—112no—
751C2×C4×D4—112no—
752C2×C4×D4—111no—
753C2×C4×D4—112no—
754C2×C4×D4—111no—
755C2×C4×D4—112no—
756C2×C4×D4—111no—
757C2×C4×D4—111no—
758C2×C4×D4C2×D1112yescomplemented
759C2×C4×D4C2×D1111yescharacteristic, complemented
760C2×C4×D4C2×D1111yescharacteristic, complemented
761C2×#117—111no—
762C2×#117—1116no—
763C2×#117—111no—
764C2×#117—111no—
765C2×#117—112no—
766C2×#117—112no—
767C2×#117C2×D1111yescharacteristic, complemented
768C22×C4⋊C4—112no—
769C22×C4⋊C4—111no—
770C22×C4⋊C4—111no—
771C22×C4⋊C4—111no—
772C22×C4⋊C4—112no—
773C22×C4⋊C4—111no—
774C22×C4⋊C4—112no—
775C22×C4⋊C4—111no—
776C22×C4⋊C4—112no—
777C22×C4⋊C4—112no—
778C22×C4⋊C4—111no—
779C22×C4⋊C4—111no—
780C22×C4⋊C4—1116no—
781C22×C4⋊C4C2×D1111yescharacteristic, complemented
782C22×C22⋊C4—112no—
783C22×C22⋊C4—111no—
784C22×C22⋊C4—112no—
785C22×C22⋊C4—112no—
786C22×C22⋊C4—111no—
787C22×C22⋊C4—112no—
788C22×C42—112no—
789C22×C42—111no—
790C22×C11—22no—
791C22×C11—22no—
792C22×C11—28no—
793C22×C11—22no—
794C22×C11—22no—
795C22×C11—24no—
796C22×C11—24no—
797C22×C11—24no—
798C22×C11—22no—
799C22×C11—44no—
800C22×C11—48no—
801C22×C11C22×#4114yes—
802C22×C11C22×#4112yes—
803C22×C11C22×#4112yes—
804C22×C11C2×H(5,𝔽2)12yes—
805C22×C11C2611yescharacteristic
806C2×D11—22no—
807C2×D11—22no—
808C2×D11—28no—
809C2×D11—232no—
810C2×D11—22no—
811C2×D11—22no—
812C2×D11—24no—
813C2×D11—24no—
814C2×D11—24no—
815C2×D11—22no—
816C2×D11—44no—
817C2×D11—48no—
818C2×D11—416no—
819C2×D11—432no—
820C2×D11#553116yesdirect product factor
821C2×D11C22×#4114yes—
822C2×D11C22×#4114yes—
823C2×D11C22×#4114yes—
824C2×D11C2×H(5,𝔽2)14yes—
825C4×C11—22no—
826C4×C11—22no—
827C4×C11—24no—
828C4×C11—22no—
829C4×C11—22no—
830C4×C11—24no—
831C4×C11—24no—
832C4×C11C22×#4114yes—
833Dic11—22no—
834Dic11—22no—
835Dic11—24no—
836Dic11—22no—
837Dic11—22no—
838Dic11—24no—
839Dic11—24no—
840Dic11C22×#4114yes—
841C25—111no—
842C25—111no—
843C25—112no—
844C22×D4—112no—
845C22×D4—112no—
846C22×D4—111no—
847C22×D4—112no—
848C22×D4—111no—
849C22×D4—112no—
850C22×D4—112no—
851C22×D4—118no—
852C22×D4—1116no—
853C22×D4—118no—
854C22×D4—1116no—
855C22×D4—112no—
856C22×D4—111no—
857C22×D4—111no—
858C22×D4—112no—
859C22×D4—228no—
860C22×D4—2216no—
861C22×D4—228no—
862C22×D4—448no—
863C22×D4C22×D1112yes—
864C22×D4C22×D1111yescharacteristic
865C22×D4C22×D1111yescharacteristic
866C22×D4C22×D1112yes—
867C23×C4—111no—
868C23×C4—111no—
869C23×C4—111no—
870C23×C4—112no—
871C23×C4—112no—
872C23×C4—111no—
873C23×C4—111no—
874C23×C4—112no—
875C23×C4—111no—
876C23×C4—112no—
877C23×C4—111no—
878C23×C4—112no—
879C23×C4—111no—
880C23×C4—118no—
881C23×C4—111no—
882C23×C4—111no—
883C23×C4—118no—
884C23×C4—111no—
885C23×C4—112no—
886C23×C4—112no—
887C23×C4—1116no—
888C23×C4—112no—
889C23×C4—112no—
890C23×C4—1116no—
891C23×C4—228no—
892C23×C4—228no—
893C23×C4—448no—
894C23×C4—448no—
895C23×C4C22×D1111yescharacteristic
896C23×C4C22×D1111yescharacteristic
897C23×C4C22×D1112yes—
898C23×C4C22×D1112yes—
899#126—1116no—
900#126—1116no—
901#126—1116no—
902#126—1116no—
903#126—1116no—
904#126—1116no—
905#126—1116no—
906#126C22×D11116yescomplemented
907#125—1116no—
908#125—1116no—
909#125—118no—
910#125—118no—
911#125—118no—
912#125C22×D1118yescomplemented
913#123—1116no—
914#123—1116no—
915#123—1116no—
916#123—1116no—
917#123—1116no—
918#123—1116no—
919#123—1116no—
920#123C22×D11116yescomplemented
921#121—1116no—
922#121—118no—
923#121—118no—
924#121—1116no—
925#121—1116no—
926#121—1116no—
927#121—1116no—
928#121—1116no—
929#121—118no—
930#121—118no—
931#121—1116no—
932#121—118no—
933#121—118no—
934#121—1116no—
935#121—1116no—
936#121—1116no—
937#121—1116no—
938#121C22×D11116yescomplemented
939#121C22×D1118yescomplemented
940#121C22×D1118yescomplemented
941C4×D4—1116no—
942C4×D4—118no—
943C4×D4—118no—
944C4×D4—1116no—
945C4×D4—1116no—
946C4×D4—118no—
947C4×D4—1116no—
948C4×D4—118no—
949C4×D4—1116no—
950C4×D4—118no—
951C4×D4—118no—
952C4×D4—1116no—
953C4×D4—1116no—
954C4×D4—118no—
955C4×D4—1116no—
956C4×D4—118no—
957C4×D4—1116no—
958C4×D4—118no—
959C4×D4—118no—
960C4×D4C22×D11116yescomplemented
961C4×D4C22×D1118yescomplemented
962C4×D4C22×D1118yescomplemented
963#117—118no—
964#117—118no—
965#117—118no—
966#117—1116no—
967#117—1116no—
968#117C22×D1118yescomplemented
969C2×C4⋊C4—112no—
970C2×C4⋊C4—111no—
971C2×C4⋊C4—112no—
972C2×C4⋊C4—111no—
973C2×C4⋊C4—112no—
974C2×C4⋊C4—112no—
975C2×C4⋊C4—112no—
976C2×C4⋊C4—1116no—
977C2×C4⋊C4—118no—
978C2×C4⋊C4—112no—
979C2×C4⋊C4—111no—
980C2×C4⋊C4—112no—
981C2×C4⋊C4—112no—
982C2×C4⋊C4—112no—
983C2×C4⋊C4—111no—
984C2×C4⋊C4—111no—
985C2×C4⋊C4—111no—
986C2×C4⋊C4—112no—
987C2×C4⋊C4—112no—
988C2×C4⋊C4—112no—
989C2×C4⋊C4—118no—
990C2×C4⋊C4—118no—
991C2×C4⋊C4—1116no—
992C2×C4⋊C4—1116no—
993C2×C4⋊C4—118no—
994C2×C4⋊C4—118no—
995C2×C4⋊C4—118no—
996C2×C4⋊C4—1116no—
997C2×C4⋊C4—118no—
998C2×C4⋊C4—1116no—
999C2×C4⋊C4C22×D1111yescharacteristic
1000C2×C4⋊C4C22×D1111yescharacteristic
1001C2×C4⋊C4C22×D1112yes—
1002C2×C4⋊C4C22×D1111yescharacteristic
1003C2×C4⋊C4C22×D1112yes—
1004C2×C4⋊C4C22×D1111yescharacteristic
1005C2×C4⋊C4C22×D1112yes—
1006C2×C4⋊C4C22×D1118yescomplemented
1007C2×C22⋊C4—112no—
1008C2×C22⋊C4—111no—
1009C2×C22⋊C4—112no—
1010C2×C22⋊C4—112no—
1011C2×C22⋊C4—111no—
1012C2×C22⋊C4—112no—
1013C2×C22⋊C4—112no—
1014C2×C22⋊C4—112no—
1015C2×C22⋊C4—111no—
1016C2×C22⋊C4—111no—
1017C2×C22⋊C4—112no—
1018C2×C22⋊C4—112no—
1019C2×C22⋊C4—112no—
1020C2×C22⋊C4—112no—
1021C2×C22⋊C4—111no—
1022C2×C22⋊C4—111no—
1023C2×C22⋊C4—112no—
1024C2×C22⋊C4—112no—
1025C2×C22⋊C4—1116no—
1026C2×C22⋊C4—118no—
1027C2×C22⋊C4—1116no—
1028C2×C22⋊C4—1116no—
1029C2×C22⋊C4—118no—
1030C2×C22⋊C4—1116no—
1031C2×C22⋊C4C22×D1112yes—
1032C2×C22⋊C4C22×D1111yescharacteristic
1033C2×C22⋊C4C22×D1112yes—
1034C2×C22⋊C4C22×D1112yes—
1035C2×C22⋊C4C22×D1111yescharacteristic
1036C2×C22⋊C4C22×D1112yes—
1037C2×C42—112no—
1038C2×C42—112no—
1039C2×C42—112no—
1040C2×C42—111no—
1041C2×C42—111no—
1042C2×C42—111no—
1043C2×C42—1116no—
1044C2×C42—118no—
1045C2×C42C22×D1112yes—
1046C2×C42C22×D1111yescharacteristic
1047C2×C11—24no—
1048C2×C11—42no—
1049C2×C11—44no—
1050C2×C11C2×#55314yescomplemented
1051C2×C11C23×#4111yescharacteristic
1052C2×C11C23×#4111yescharacteristic
1053C2×C11C22×H(5,𝔽2)11yescharacteristic
1054D11—24no—
1055D11—42no—
1056D11—44no—
1057D11C2×#55318yesdirect product factor
1058C24—111no—
1059C24—118no—
1060C24—114no—
1061C24—111no—
1062C24—114no—
1063C24—118no—
1064C24—111no—
1065C24—112no—
1066C24—224no—
1067C24—224no—
1068C24—224no—
1069C24—228no—
1070C24—228no—
1071C24—224no—
1072C24—228no—
1073C24—224no—
1074C24C23×D1111yescharacteristic
1075C24C23×D1112yes—
1076C24C23×D1111yescharacteristic
1077C2×D4—28no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—44no—
1081C2×D4—118no—
1082C2×D4—118no—
1083C2×D4—114no—
1084C2×D4—118no—
1085C2×D4—114no—
1086C2×D4—118no—
1087C2×D4—118no—
1088C2×D4—118no—
1089C2×D4—114no—
1090C2×D4—114no—
1091C2×D4—118no—
1092C2×D4—228no—
1093C2×D4—224no—
1094C2×D4—2232no—
1095C2×D4—228no—
1096C2×D4—2264no—
1097C2×D4—2232no—
1098C2×D4—228no—
1099C2×D4—224no—
1100C2×D4—228no—
1101C2×D4—224no—
1102C2×D4—224no—
1103C2×D4—444no—
1104C2×D4—4432no—
1105C2×D4—444no—
1106C2×D4—444no—
1107C2×D4C23×D1118yes—
1108C2×D4C23×D1114yes—
1109C2×D4C23×D1114yes—
1110C2×D4C23×D1118yes—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—111no—
1116C22×C4—118no—
1117C22×C4—114no—
1118C22×C4—114no—
1119C22×C4—114no—
1120C22×C4—111no—
1121C22×C4—112no—
1122C22×C4—111no—
1123C22×C4—112no—
1124C22×C4—111no—
1125C22×C4—111no—
1126C22×C4—112no—
1127C22×C4—118no—
1128C22×C4—118no—
1129C22×C4—114no—
1130C22×C4—118no—
1131C22×C4—114no—
1132C22×C4—118no—
1133C22×C4—114no—
1134C22×C4—114no—
1135C22×C4—118no—
1136C22×C4—114no—
1137C22×C4—114no—
1138C22×C4—114no—
1139C22×C4—114no—
1140C22×C4—118no—
1141C22×C4—118no—
1142C22×C4—118no—
1143C22×C4—118no—
1144C22×C4—224no—
1145C22×C4—224no—
1146C22×C4—2232no—
1147C22×C4—2232no—
1148C22×C4—224no—
1149C22×C4—224no—
1150C22×C4—228no—
1151C22×C4—224no—
1152C22×C4—228no—
1153C22×C4—228no—
1154C22×C4—224no—
1155C22×C4—224no—
1156C22×C4—224no—
1157C22×C4—224no—
1158C22×C4—224no—
1159C22×C4—444no—
1160C22×C4—444no—
1161C22×C4—444no—
1162C22×C4—444no—
1163C22×C4—4432no—
1164C22×C4—4432no—
1165C22×C4—444no—
1166C22×C4—444no—
1167C22×C4C23×D1114yes—
1168C22×C4C23×D1114yes—
1169C22×C4C23×D1111yescharacteristic
1170C22×C4C23×D1112yes—
1171C22×C4C23×D1111yescharacteristic
1172C22×C4C23×D1112yes—
1173C22×C4C23×D1111yescharacteristic
1174C22×C4C23×D1111yescharacteristic
1175C22×C4C23×D1112yes—
1176C22×C4C23×D1118yes—
1177C22×C4C23×D1118yes—
1178C22×C4C23×D1111yescharacteristic
1179C4⋊C4—118no—
1180C4⋊C4—114no—
1181C4⋊C4—118no—
1182C4⋊C4—114no—
1183C4⋊C4—118no—
1184C4⋊C4—118no—
1185C4⋊C4—118no—
1186C4⋊C4—118no—
1187C4⋊C4—114no—
1188C4⋊C4—118no—
1189C4⋊C4—118no—
1190C4⋊C4—118no—
1191C4⋊C4—114no—
1192C4⋊C4—114no—
1193C4⋊C4—114no—
1194C4⋊C4—118no—
1195C4⋊C4—118no—
1196C4⋊C4—118no—
1197C4⋊C4C23×D1114yes—
1198C4⋊C4C23×D1114yes—
1199C4⋊C4C23×D1118yes—
1200C4⋊C4C23×D1114yes—
1201C4⋊C4C23×D1118yes—
1202C4⋊C4C23×D1114yes—
1203C4⋊C4C23×D1118yes—
1204C22⋊C4—118no—
1205C22⋊C4—114no—
1206C22⋊C4—118no—
1207C22⋊C4—118no—
1208C22⋊C4—114no—
1209C22⋊C4—118no—
1210C22⋊C4—118no—
1211C22⋊C4—118no—
1212C22⋊C4—114no—
1213C22⋊C4—114no—
1214C22⋊C4—118no—
1215C22⋊C4—118no—
1216C22⋊C4—118no—
1217C22⋊C4—118no—
1218C22⋊C4—114no—
1219C22⋊C4—114no—
1220C22⋊C4—118no—
1221C22⋊C4—118no—
1222C22⋊C4C23×D1118yes—
1223C22⋊C4C23×D1114yes—
1224C22⋊C4C23×D1118yes—
1225C22⋊C4C23×D1118yes—
1226C22⋊C4C23×D1114yes—
1227C22⋊C4C23×D1118yes—
1228C42—118no—
1229C42—118no—
1230C42—118no—
1231C42—114no—
1232C42—114no—
1233C42—114no—
1234C42C23×D1118yes—
1235C42C23×D1114yes—
1236C11C22×#55311yescharacteristic, complemented, Sylow
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—22no—
1245C23—114no—
1246C23—114no—
1247C23—114no—
1248C23—112no—
1249C23—1116no—
1250C23—114no—
1251C23—112no—
1252C23—112no—
1253C23—114no—
1254C23—228no—
1255C23—228no—
1256C23—2232no—
1257C23—228no—
1258C23—2216no—
1259C23—2216no—
1260C23—228no—
1261C23—2216no—
1262C23—228no—
1263C23—222no—
1264C23—222no—
1265C23—222no—
1266C23—222no—
1267C23—224no—
1268C23—224no—
1269C23—224no—
1270C23—222no—
1271C23—4416no—
1272C23—4432no—
1273C23#41×D1114yes—
1274C23C24×D1112yes—
1275C23C24×D1114yes—
1276C23C24×D1112yes—
1277C23C24×D1111yescharacteristic
1278D4—216no—
1279D4—28no—
1280D4—28no—
1281D4—48no—
1282D4—2216no—
1283D4—228no—
1284D4—2216no—
1285D4—2216no—
1286D4—228no—
1287D4—2216no—
1288D4—228no—
1289D4—228no—
1290D4—448no—
1291D4—448no—
1292D4—448no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—28no—
1301C2×C4—28no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—114no—
1305C2×C4—112no—
1306C2×C4—1116no—
1307C2×C4—112no—
1308C2×C4—114no—
1309C2×C4—112no—
1310C2×C4—114no—
1311C2×C4—112no—
1312C2×C4—112no—
1313C2×C4—114no—
1314C2×C4—228no—
1315C2×C4—228no—
1316C2×C4—228no—
1317C2×C4—228no—
1318C2×C4—2216no—
1319C2×C4—228no—
1320C2×C4—2216no—
1321C2×C4—2216no—
1322C2×C4—228no—
1323C2×C4—228no—
1324C2×C4—228no—
1325C2×C4—222no—
1326C2×C4—222no—
1327C2×C4—224no—
1328C2×C4—222no—
1329C2×C4—224no—
1330C2×C4—222no—
1331C2×C4—224no—
1332C2×C4—228no—
1333C2×C4—228no—
1334C2×C4—448no—
1335C2×C4—448no—
1336C2×C4—448no—
1337C2×C4—448no—
1338C2×C4—448no—
1339C2×C4—448no—
1340C2×C4#41×D1114yes—
1341C2×C4C24×D1112yes—
1342C2×C4C24×D1114yes—
1343C2×C4C24×D1112yes—
1344C2×C4C24×D1114yes—
1345C2×C4C24×D1112yes—
1346C2×C4C24×D1112yes—
1347C2×C4C24×D1114yes—
1348C2×C4C24×D1112yes—
1349C22—28no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—24no—
1355C22—24no—
1356C22—24no—
1357C22—22no—
1358C22—44no—
1359C22—48no—
1360C22—1116no—
1361C22—114no—
1362C22—114no—
1363C22—114no—
1364C22—114no—
1365C22—2232no—
1366C22—228no—
1367C22—222no—
1368C22—222no—
1369C22—222no—
1370C22—222no—
1371C22—224no—
1372C22—224no—
1373C22—224no—
1374C22—222no—
1375C22—4416no—
1376C22—4432no—
1377C22—444no—
1378C22—448no—
1379C22C2×#41×D1114yes—
1380C22C2×#41×D1112yes—
1381C22C2×#41×D1112yes—
1382C22D11×H(5,𝔽2)12yes—
1383C22C25×D1111yescharacteristic
1384C4—22no—
1385C4—22no—
1386C4—24no—
1387C4—22no—
1388C4—22no—
1389C4—24no—
1390C4—24no—
1391C4—114no—
1392C4—222no—
1393C4—222no—
1394C4—224no—
1395C4—222no—
1396C4—224no—
1397C4—222no—
1398C4—224no—
1399C4C2×#41×D1114yes—
1400C2—24no—
1401C2—42no—
1402C2—44no—
1403C2—118no—
1404C2—224no—
1405C2—442no—
1406C2—444no—
1407C2D11×#55314yesdirect product factor
1408C2C22×#41×D1111yescharacteristic
1409C2C22×#41×D1111yescharacteristic
1410C2C2×D11×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#553C2
socleC23×C11C25
hypercenterC2×#553D11
hypocenterC11C22×#553
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#553

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623149C2semidirect
3. C2×#10623240C2semidirect
4. C2×#10623089C2semidirect
5. C2×#10623071C2semidirect
6. C2×#10623045C2semidirect
7. C2×#10623145C2semidirect
8. C2×#10623096C2semidirect
9. C2×#10623192C2semidirect
10. C2×#10623061C2semidirect
11. C2×#10623132C2semidirect
12. D11×#553C2direct (N × H)
13. C2×D11×#126C2semidirect
14. C2×D11×#125C2semidirect
15. C2×D11×#123C2semidirect
16. C2×D11×#121C2semidirect
17. C2×D11×#121C2semidirect
18. C2×D11×#121C2semidirect
19. C2×C4×D4×D11C2semidirect
20. C2×C4×D4×D11C2semidirect
21. C2×C4×D4×D11C2semidirect
22. C2×D11×#117C2semidirect
23. C22×C4⋊C4×D11C2semidirect
24. C2×C11×#553C2semidirect
33. C11×#553C22semidirect
34. C2×C11×#126C22semidirect
35. C2×C11×#125C22semidirect
36. C2×C11×#123C22semidirect
37. C2×C11×#121C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C11×#121C22semidirect
40. C2×C4×D4×C11C22semidirect
41. C2×C4×D4×C11C22semidirect
42. C2×C4×D4×C11C22semidirect
43. C2×C11×#117C22semidirect
44. C22×C11×C4⋊C4C22semidirect
45. C2×#66992C22semidirect
46. C2×#66992C22semidirect
47. C2×#66992C22semidirect
48. C2×#66992C22semidirect
49. C2×#66991C22semidirect
50. C2×#66991C22semidirect
51. C2×#66991C22semidirect
52. C2×#66988C22semidirect
53. C2×D4×Dic11C22semidirect
54. C2×D4×Dic11C22semidirect
55. C2×D4×Dic11C22semidirect
56. C2×#66983C22semidirect
57. C2×#66983C22semidirect
58. C2×#66983C22semidirect
59. C2×#66982C22semidirect
60. C2×C4×C22⋊D11C22semidirect
61. C2×C4×C22⋊D11C22semidirect
62. C2×C4×C22⋊D11C22semidirect
63. C2×C4×C22⋊D11C22semidirect
64. C2×C4×C22⋊D11C22semidirect
65. C2×#66979C22semidirect
66. C22×C4⋊Dic11C22semidirect
67. C22×Dic11⋊C4C22semidirect
68. #10623240C22semidirect
69. D11×#126C22semidirect
70. #10623226C22semidirect
71. D11×#125C22semidirect
72. #10623192C22semidirect
73. D11×#123C22semidirect
74. #10623149C22semidirect
75. #10623145C22semidirect
76. D11×#121C22semidirect
77. D11×#121C22semidirect
78. D11×#121C22semidirect
79. #10623132C22semidirect
80. #10623096C22semidirect
81. #10623089C22semidirect
82. C4×D4×D11C22semidirect
83. C4×D4×D11C22semidirect
84. C4×D4×D11C22semidirect
85. #10623071C22semidirect
86. #10623061C22semidirect
87. D11×#117C22semidirect
88. #10623045C22semidirect
89. C2×#66951C22semidirect
90. C2×#66951C22semidirect
91. C2×#66951C22semidirect
92. C2×#66948C22semidirect
93. C2×#66948C22semidirect
94. C2×#66948C22semidirect
95. C2×#66947C22semidirect
96. C2×#66947C22semidirect
97. C2×#66946C22semidirect
98. C2×#66946C22semidirect
99. C2×#66946C22semidirect
100. C2×#66945C22semidirect
101. C2×#66945C22semidirect
109. C2×C4⋊C4×D11C22semidirect
110. C2×C4⋊C4×D11C22semidirect
111. C2×C4⋊C4×D11C22semidirect
112. C2×C4⋊C4×D11C22semidirect
113. C2×#66943C22semidirect
114. C2×#66943C22semidirect
115. C2×#66942C22semidirect
116. C2×#66942C22semidirect
117. C2×#66939C22semidirect
118. C2×#66937C22semidirect
119. C2×#66937C22semidirect
120. C2×#66937C22semidirect
121. C2×#66937C22semidirect
122. C2×#66936C22semidirect
123. C2×#66936C22semidirect
124. C2×(C22⋊D11)⋊C4C22semidirect
125. C2×(C22⋊D11)⋊C4C22semidirect
126. C2×(C22⋊D11)⋊C4C22semidirect
127. C2×(C22⋊D11)⋊C4C22semidirect
128. C2×(C22⋊D11)⋊C4C22semidirect
135. C2×#66932C22semidirect
136. C2×#66932C22semidirect
137. C2×#66932C22semidirect
138. C2×#66930C22semidirect
139. C2×#66929C22semidirect
140. C2×C4×D44C22semidirect
141. C2×C4×D44C22semidirect
142. C2×C4×D44C22semidirect
143. C2×#66925C22semidirect
146. C2×#66923C22semidirect
205. C11×#126C23semidirect
206. C11×#125C23semidirect
207. C11×#123C23semidirect
208. C11×#121C23semidirect
209. C11×#121C23semidirect
210. C11×#121C23semidirect
211. C4×D4×C11C23semidirect
212. C4×D4×C11C23semidirect
213. C4×D4×C11C23semidirect
214. C11×#117C23semidirect
222. C2×C11×C4⋊C4C23semidirect
237. #66992C23semidirect
238. #66992C23semidirect
239. #66992C23semidirect
240. #66992C23semidirect
241. #66991C23semidirect
242. #66991C23semidirect
243. #66991C23semidirect
244. #66988C23semidirect
245. D4×Dic11C23semidirect
246. D4×Dic11C23semidirect
247. D4×Dic11C23semidirect
248. #66983C23semidirect
249. #66983C23semidirect
250. #66983C23semidirect
251. #66982C23semidirect
252. C4×C22⋊D11C23semidirect
253. C4×C22⋊D11C23semidirect
254. C4×C22⋊D11C23semidirect
255. C4×C22⋊D11C23semidirect
256. C4×C22⋊D11C23semidirect
269. #66979C23semidirect
277. C2×C4⋊Dic11C23semidirect
289. C2×Dic11⋊C4C23semidirect
296. #66951C23semidirect
297. #66951C23semidirect
298. #66951C23semidirect
299. #66948C23semidirect
300. #66948C23semidirect
301. #66948C23semidirect
302. #66947C23semidirect
303. #66947C23semidirect
304. #66946C23semidirect
305. #66946C23semidirect
306. #66946C23semidirect
307. #66945C23semidirect
308. #66945C23semidirect
316. C4⋊C4×D11C23semidirect
317. C4⋊C4×D11C23semidirect
318. C4⋊C4×D11C23semidirect
319. #66943C23semidirect
320. #66943C23semidirect
321. #66942C23semidirect
322. #66942C23semidirect
323. #66939C23semidirect
324. #66937C23semidirect
325. #66937C23semidirect
326. #66937C23semidirect
327. #66937C23semidirect
328. #66936C23semidirect
329. #66936C23semidirect
330. (C22⋊D11)⋊C4C23semidirect
331. (C22⋊D11)⋊C4C23semidirect
332. (C22⋊D11)⋊C4C23semidirect
333. (C22⋊D11)⋊C4C23semidirect
334. (C22⋊D11)⋊C4C23semidirect
341. #66932C23semidirect
342. #66932C23semidirect
343. #66932C23semidirect
344. #66930C23semidirect
345. #66929C23semidirect
346. C4×D44C23semidirect
347. C4×D44C23semidirect
348. C4×D44C23semidirect
349. #66925C23semidirect
352. #66923C23semidirect
544. C2×#553D11direct (N × H)
687. #553C2×D11direct (N × H)
696. C2×#126C2×D11semidirect
703. C2×#125C2×D11semidirect
712. C2×#123C2×D11semidirect
733. C2×#121C2×D11semidirect
734. C2×#121C2×D11semidirect
735. C2×#121C2×D11semidirect
758. C2×C4×D4C2×D11semidirect
759. C2×C4×D4C2×D11semidirect
760. C2×C4×D4C2×D11semidirect
767. C2×#117C2×D11semidirect
781. C22×C4⋊C4C2×D11semidirect
820. C2×D11#553direct (N × H)
906. #126C22×D11semidirect
912. #125C22×D11semidirect
920. #123C22×D11semidirect
938. #121C22×D11semidirect
939. #121C22×D11semidirect
940. #121C22×D11semidirect
960. C4×D4C22×D11semidirect
961. C4×D4C22×D11semidirect
962. C4×D4C22×D11semidirect
968. #117C22×D11semidirect
1006. C2×C4⋊C4C22×D11semidirect
1050. C2×C11C2×#553semidirect
1057. D11C2×#553direct (N × H)
1236. C11C22×#553semidirect
1407. C2D11×#553direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232262
C2×#106231492
C2×#106232402
C2×#106230892
C2×#106230712
C2×#106230452
C2×#106231452
C2×#106230962
C2×#106231922
C2×#106230612
C2×#106231322
D11×#5532
C2×D11×#1262
C2×D11×#1252
C2×D11×#1232
C2×D11×#1212
C2×C4×D4×D112
C2×D11×#1172
C22×C4⋊C4×D112
C2×C11×#5532
C22×#55311