Finite Group Databasebeta

← #14914109

Subgroups — #14914109

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C2×#10623017C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071655C212yesmaximal, complemented
5#13071649C212yesmaximal, complemented
6#13071635C212yesmaximal, complemented
7#13071629C212yesmaximal, complemented
8#13071466C211yesmaximal, characteristic, complemented
9#13071465C211yesmaximal, characteristic, complemented
10#13071458C211yesmaximal, characteristic, complemented
11C22⋊C4×D44C211yesmaximal, characteristic, complemented
12#13071436C211yesmaximal, characteristic, complemented
13C22⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
14#13071432C211yesmaximal, characteristic, complemented
15#13071308C212yesmaximal, complemented
16#13071304C212yesmaximal, complemented
17#13071233C211yesmaximal, characteristic, complemented
18#13071197C211yesmaximal, characteristic, complemented
19#13071128C212yesmaximal, complemented
20C4×#66937C212yesmaximal, complemented
21#13070996C211yesmaximal, characteristic, complemented
22#13070971C211yesmaximal, characteristic, complemented
23C11×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2212yescomplemented
33C2×C4×C22⋊D11C2212yescomplemented
34C2×C4×C22⋊D11C2212yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38D11×#117—28no—
39C2×#66946C2212yescomplemented
40C2×#66945C2212yescomplemented
41C2×C4⋊C4×D11C2212yescomplemented
42C2×#66937C4116yescomplemented
43C2×#66937C2211yescharacteristic
44C2×#66937C2211yescharacteristic
45C2×#66937C2211yescharacteristic
46C2×#66937C2211yescharacteristic
47C2×#66937C2211yescharacteristic
48C2×#66937C2211yescharacteristic
49C2×#66937C2211yescharacteristic
50C2×#66937C2211yescharacteristic
51#10623017—28no—
52C2×(C22⋊D11)⋊C4C2212yescomplemented
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic
58C2×C22⋊C4×D11C2211yescharacteristic
59C2×#66930C2211yescharacteristic
60C2×#66930C2211yescharacteristic
61C2×#66930C2211yescharacteristic
62C2×#66930C2211yescharacteristic
63C2×C4×D44C2212yescomplemented
64C2×#66925C2212yescomplemented
65C2×C42×D11C2212yescomplemented
66C11×#388C2212yescomplemented
67C11×#388C2212yescomplemented
68C11×#385C2212yescomplemented
69C11×#381C2211yescharacteristic
70C11×#380C2211yescharacteristic
71C11×#379C2211yescharacteristic
72C4×C11×C22⋊C4C2211yescharacteristic
73C4×C11×C22⋊C4C2212yescomplemented
74#10622860C2211yescharacteristic
75#10622826C2212yescomplemented
76#10622825C2211yescharacteristic
77#10622824C2211yescharacteristic
78C4×C22⋊Dic11C2211yescharacteristic
79#10622603C2212yescomplemented
80#10622602C2212yescomplemented
81#10622601C2212yescomplemented
82#10622585C2212yescomplemented
83#10622585C2212yescomplemented
84#10622571C2212yescomplemented
85#10622570C2212yescomplemented
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622568C2211yescharacteristic
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622568C2211yescharacteristic
97#10622564C2212yescomplemented
98#10622564C2212yescomplemented
99#10622563C2212yescomplemented
100#10622555C2211yescharacteristic
101#10622555C2211yescharacteristic
102C22⋊C4×Dic11C2211yescharacteristic
103C22⋊C4×Dic11C2211yescharacteristic
104C22⋊C4×Dic11C2212yescomplemented
105#10622553C2212yescomplemented
106#10622552C2212yescomplemented
107C4×(C2×D11)⋊C4C2212yescomplemented
108C4×Dic11⋊C4C2212yescomplemented
109C4×Dic11⋊C4C2212yescomplemented
110#10622283C2212yescomplemented
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622280C2212yescomplemented
114#10622280C2212yescomplemented
115#10622279C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622262C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125#10622260C2212yescomplemented
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11—24no—
133C22×C22⋊D11—24no—
134C22×C22⋊D11—44no—
135C22×C22⋊D11C2×C418yescomplemented
136C22×C22⋊D11C2×C418yescomplemented
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C23×Dic11C2312yes—
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C22×D44—44no—
149C22×D44C2×C418yescomplemented
150C22×D44C2311yescharacteristic
151C22×D44C2311yescharacteristic
152C22×D44C2311yescharacteristic
153C22×D44C2311yescharacteristic
154C22×C4×D11—24no—
155C22×C4×D11—24no—
156C22×C4×D11C2×C418yescomplemented
157C22×C4×D11C2312yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C11×#117—24no—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4—24no—
169C2×C11×C22⋊C4C2×C418yescomplemented
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C42×C11C2312yes—
182C2×C42×C11C2312yes—
183C2×C22⋊Dic11—24no—
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2311yescharacteristic
191C4×C22⋊D11—28no—
192C4×C22⋊D11—28no—
193C4×C22⋊D11—44no—
194C2×(C2×D11)⋊C4C2×C418yescomplemented
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2311yescharacteristic
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2311yescharacteristic
210C2×(C2×D11)⋊C4C2311yescharacteristic
211#66979—24no—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2312yes—
214C2×Dic11⋊C4C2×C418yescomplemented
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233#66946—44no—
234#66945—28no—
235C4⋊C4×D11—28no—
236#66937C2×C418yescomplemented
237#66937C2×C418yescomplemented
238#66937C2×C418yescomplemented
239#66937C2×C418yescomplemented
240#66937C2×C418yescomplemented
241#66937C2×C418yescomplemented
242#66937C2×C418yescomplemented
243#66937C2×C418yescomplemented
244(C22⋊D11)⋊C4—28no—
245(C22⋊D11)⋊C4—28no—
246(C22⋊D11)⋊C4—44no—
247C22⋊C4×D11—24no—
248C22⋊C4×D11—24no—
249C22⋊C4×D11—24no—
250C22⋊C4×D11—24no—
251#66930—24no—
252#66930—24no—
253#66930—24no—
254#66930D418yescomplemented
255C4×D44—44no—
256#66925—28no—
257C42×D11—28no—
258C11×#95C2312yes—
259C11×#95C2312yes—
260C11×#95C2312yes—
261C11×#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270#34204—111nomaximal, Sylow
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—42no—
274C24×C11—42no—
275C24×C11C22×C414yes—
276C24×C11C2411yescharacteristic
277C24×C11C2411yescharacteristic
278C24×C11C2411yescharacteristic
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—22no—
282C23×D11—22no—
283C23×D11—24no—
284C23×D11—42no—
285C23×D11—42no—
286C23×D11—42no—
287C23×D11C22×C414yes—
288C23×D11C22×C414yes—
289C23×D11C2411yescharacteristic
290C23×D11C2411yescharacteristic
291C23×D11C2411yescharacteristic
292C23×D11C2411yescharacteristic
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—24no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11C22×C414yes—
300C22×C4×C11C22×C414yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C2×C22⋊D11—232no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—416no—
323C2×C22⋊D11C22×C414yes—
324C2×C22⋊D11C22×C414yes—
325C2×C22⋊D11C22×C414yes—
326C2×C22⋊D11C22×C414yes—
327C2×C22⋊D11C22×C414yes—
328C2×C22⋊D11C22×C414yes—
329C2×C22⋊D11C22×C414yes—
330C2×C22⋊D11C22×C414yes—
331C22×Dic11—24no—
332C22×Dic11—42no—
333C22×Dic11—42no—
334C22×Dic11—42no—
335C22×Dic11C22×C414yes—
336C22×Dic11C22×C414yes—
337C22×Dic11C2×D414yes—
338C22×Dic11#4114yes—
339C22×Dic11C2412yes—
340C22×Dic11C2412yes—
341C22×Dic11C2412yes—
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2412yes—
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C2×D44—24no—
348C2×D44—24no—
349C2×D44—42no—
350C2×D44—42no—
351C2×D44—416no—
352C2×D44C22×C414yes—
353C2×D44C22×C414yes—
354C2×D44C22×C414yes—
355C2×D44C22×C414yes—
356C2×C4×D11—232no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—22no—
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—22no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—24no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—24no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11—42no—
374C2×C4×D11—42no—
375C2×C4×D11—42no—
376C2×C4×D11—42no—
377C2×C4×D11C22×C414yes—
378C2×C4×D11C22×C414yes—
379C2×C4×D11C22×C414yes—
380C2×C4×D11C22×C414yes—
381C11×C4⋊C4—24no—
382C11×C4⋊C4—42no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—42no—
388C11×C22⋊C4—42no—
389C11×C22⋊C4C22×C414yes—
390C11×C22⋊C4C22×C414yes—
391C11×C22⋊C4C22×C414yes—
392C11×C22⋊C4C22×C414yes—
393C11×C22⋊C4C2×D414yes—
394C42×C11—24no—
395C42×C11—42no—
396C22⋊Dic11—24no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399C22⋊Dic11—22no—
400C22⋊Dic11—42no—
401C22⋊Dic11—42no—
402C22⋊Dic11C2×D414yes—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—24no—
406(C2×D11)⋊C4—24no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—24no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4—42no—
412(C2×D11)⋊C4—42no—
413(C2×D11)⋊C4—42no—
414(C2×D11)⋊C4—42no—
415(C2×D11)⋊C4C22×C414yes—
416(C2×D11)⋊C4C22×C414yes—
417(C2×D11)⋊C4C22×C414yes—
418(C2×D11)⋊C4C22×C414yes—
419C4⋊Dic11—24no—
420C4⋊Dic11—42no—
421Dic11⋊C4—24no—
422Dic11⋊C4—24no—
423Dic11⋊C4—24no—
424Dic11⋊C4—42no—
425Dic11⋊C4—42no—
426Dic11⋊C4C22×C414yes—
427Dic11⋊C4C22×C414yes—
428Dic11⋊C4C22×C414yes—
429Dic11⋊C4C22×C414yes—
430Dic11⋊C4C2×D418yescomplemented
431C4×Dic11—24no—
432C4×Dic11—24no—
433C4×Dic11—24no—
434C4×Dic11—24no—
435C4×Dic11—42no—
436C4×Dic11—42no—
437C4×Dic11—42no—
438C4×Dic11C2×D418yescomplemented
439C22×#121—111no—
440C2×#518—111no—
441C22×#117—111no—
442#2363—112no—
443#2363—112no—
444#2361—112no—
445#2361—112no—
446#2342—111no—
447#2342—111no—
448#2342—111no—
449#2342D1111yescharacteristic, complemented
450D4×C22⋊C4—111no—
451D4×C22⋊C4—111no—
452D4×C22⋊C4—111no—
453D4×C22⋊C4—111no—
454#2324—112no—
455#2324—112no—
456#2316—111no—
457#2309—111no—
458C4×#121—112no—
459C4×#121—112no—
460#2280—111no—
461#2274—111no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—21no—
465C23×C11—21no—
466C23×C11—21no—
467C23×C11—21no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—28no—
473C23×C11—44no—
474C23×C11—44no—
475C23×C11—84no—
476C23×C11—84no—
477C23×C11C23×C412yes—
478C23×C11C23×C412yes—
479C23×C11C23×C412yes—
480C23×C11C22×D412yes—
481C23×C11C2×#4112yes—
482C23×C11C2511yescharacteristic
483C22×D11—21no—
484C22×D11—21no—
485C22×D11—22no—
486C22×D11—28no—
487C22×D11—21no—
488C22×D11—21no—
489C22×D11—21no—
490C22×D11—21no—
491C22×D11—21no—
492C22×D11—21no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—22no—
498C22×D11—22no—
499C22×D11—28no—
500C22×D11—28no—
501C22×D11—44no—
502C22×D11—44no—
503C22×D11—44no—
504C22×D11—48no—
505C22×D11—48no—
506C22×D11—84no—
507C22×D11—84no—
508C22×D11C23×C412yes—
509C22×D11C23×C412yes—
510C22×D11C23×C412yes—
511C22×D11C23×C412yes—
512C22×D11H(5,𝔽2)14yes—
513C2×C4×C11—28no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—44no—
532C2×C4×C11—84no—
533C2×C4×C11C23×C412yes—
534C2×C4×C11C23×C412yes—
535C2×C4×C11C23×C412yes—
536C2×C4×C11C23×C412yes—
537C2×C4×C11C22×D414yes—
538C22⋊D11—28no—
539C22⋊D11—28no—
540C22⋊D11—28no—
541C22⋊D11—28no—
542C22⋊D11—28no—
543C22⋊D11—28no—
544C22⋊D11—44no—
545C22⋊D11—44no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—44no—
560C2×Dic11—84no—
561C2×Dic11C4×D4116yescomplemented
562C2×Dic11C23×C412yes—
563C2×Dic11C23×C412yes—
564C2×Dic11C23×C412yes—
565C2×Dic11C23×C412yes—
566C2×Dic11C22×D414yes—
567C2×Dic11C22×D412yes—
568C2×Dic11C22×D412yes—
569C2×Dic11C2×#4112yes—
570C2×Dic11C2×#4112yes—
571D44—28no—
572D44—28no—
573D44—44no—
574D44—44no—
575C4×D11—28no—
576C4×D11—28no—
577C4×D11—28no—
578C4×D11—28no—
579C4×D11—48no—
580C4×D11—48no—
581C4×D11—84no—
582C4×D11—84no—
583C23×D4—111no—
584C23×D4—111no—
585C23×D4—111no—
586C24×C4—111no—
587C2×#121—111no—
588C2×#121—111no—
589C2×#121—111no—
590C2×#121—111no—
591C2×#121—111no—
592C2×#121—111no—
593C2×#121—111no—
594C2×#121—111no—
595C2×#121—1116no—
596#518—228no—
597C2×C4×D4—112no—
598C2×C4×D4—112no—
599C2×C4×D4—112no—
600C2×C4×D4—112no—
601C2×C4×D4—112no—
602C2×C4×D4—112no—
603C2×C4×D4—112no—
604C2×C4×D4—112no—
605C2×#117—111no—
606C2×#117—112no—
607C2×#117—111no—
608C2×#117—111no—
609C2×#117—111no—
610C2×#117—111no—
611C2×#117—112no—
612C2×#117—228no—
613C2×#117C2×D1111yescharacteristic
614C22×C4⋊C4—111no—
615C22×C4⋊C4—112no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4C2×D1111yescharacteristic
623C22×C22⋊C4C2×D1111yescharacteristic
624C22×C42—112no—
625#390—112no—
626#390—112no—
627#390—112no—
628#390—112no—
629#390—112no—
630#390—112no—
631#390—112no—
632#390—112no—
633#389—112no—
634#389—112no—
635#389—112no—
636#389—112no—
637#388—112no—
638#388—112no—
639#388—112no—
640#388—112no—
641#388—112no—
642#388—112no—
643#388C2×D1112yescomplemented
644#388C2×D1112yescomplemented
645#386—112no—
646#386—112no—
647#386—112no—
648#386—112no—
649#386—112no—
650#386—112no—
651#386—112no—
652#386—112no—
653#385—112no—
654#385—112no—
655#385—112no—
656#385C2×D1112yescomplemented
657#381—111no—
658#381C2×D1111yescharacteristic
659#380—111no—
660#380—111no—
661#380—111no—
662#380—112no—
663#380—112no—
664#380C2×D1111yescharacteristic
665#379—111no—
666#379—111no—
667#379—111no—
668#379—111no—
669#379—111no—
670#379C2×D1111yescharacteristic
671C4×C4⋊C4—112no—
672C4×C4⋊C4—112no—
673C4×C4⋊C4—112no—
674C4×C4⋊C4—112no—
675C4×C22⋊C4—111no—
676C4×C22⋊C4—111no—
677C4×C22⋊C4—111no—
678C4×C22⋊C4—112no—
679C4×C22⋊C4—112no—
680C4×C22⋊C4—112no—
681C4×C22⋊C4—112no—
682C4×C22⋊C4—112no—
683C4×C22⋊C4C2×D1111yescharacteristic
684C4×C22⋊C4C2×D1112yescomplemented
685C22×C11—22no—
686C22×C11—22no—
687C22×C11—24no—
688C22×C11—24no—
689C22×C11—22no—
690C22×C11—22no—
691C22×C11—22no—
692C22×C11—22no—
693C22×C11—22no—
694C22×C11—22no—
695C22×C11—42no—
696C22×C11—42no—
697C22×C11—42no—
698C22×C11—42no—
699C22×C11—88no—
700C22×C11C2×C4×D414yes—
701C22×C11C24×C411yescharacteristic
702C22×C11C23×D411yescharacteristic
703C22×C11C22×#4111yescharacteristic
704C22×C11C2×H(5,𝔽2)12yes—
705C22×C11#58512yes—
706C2×D11—22no—
707C2×D11—22no—
708C2×D11—24no—
709C2×D11—24no—
710C2×D11—22no—
711C2×D11—22no—
712C2×D11—22no—
713C2×D11—22no—
714C2×D11—22no—
715C2×D11—22no—
716C2×D11—22no—
717C2×D11—22no—
718C2×D11—22no—
719C2×D11—416no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—42no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—88no—
727C2×D11#51814yescomplemented
728C4×C11—22no—
729C4×C11—22no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—24no—
733C4×C11—42no—
734C4×C11—42no—
735C4×C11—42no—
736Dic11—22no—
737Dic11—22no—
738Dic11—24no—
739Dic11—42no—
740Dic11—42no—
741Dic11—42no—
742Dic11C2×C4×D414yes—
743Dic11C2×C4×D414yes—
744C25—111no—
745C25—111no—
746C25C22×D1111yescharacteristic
747C22×D4—118no—
748C22×D4—111no—
749C22×D4—111no—
750C22×D4—111no—
751C22×D4—111no—
752C22×D4—111no—
753C22×D4—111no—
754C22×D4—118no—
755C22×D4—111no—
756C22×D4—111no—
757C22×D4—118no—
758C22×D4—111no—
759C22×D4—111no—
760C22×D4—111no—
761C22×D4—111no—
762C22×D4—224no—
763C22×D4—224no—
764C22×D4—444no—
765C22×D4—444no—
766C23×C4—111no—
767C23×C4—111no—
768C23×C4—118no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—112no—
774C23×C4—112no—
775C23×C4—112no—
776C23×C4—112no—
777C23×C4—112no—
778C23×C4—224no—
779C23×C4—224no—
780C23×C4C22×D1111yescharacteristic
781C23×C4C22×D1112yes—
782C23×C4C22×D1111yescharacteristic
783#121—118no—
784#121—118no—
785#121—118no—
786#121—118no—
787#121—118no—
788#121—118no—
789#121—118no—
790#121—118no—
791C4×D4—228no—
792C4×D4—228no—
793C4×D4—228no—
794C4×D4—228no—
795C4×D4—444no—
796C4×D4—444no—
797C4×D4—444no—
798C4×D4—444no—
799#117—24no—
800#117—118no—
801#117—228no—
802#117—228no—
803#117—224no—
804#117—224no—
805#117—224no—
806#117—224no—
807C2×C4⋊C4—118no—
808C2×C4⋊C4—112no—
809C2×C4⋊C4—111no—
810C2×C4⋊C4—111no—
811C2×C4⋊C4—111no—
812C2×C4⋊C4—111no—
813C2×C4⋊C4—112no—
814C2×C4⋊C4—112no—
815C2×C4⋊C4—112no—
816C2×C4⋊C4—112no—
817C2×C4⋊C4—112no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—228no—
821C2×C4⋊C4C22×D1112yes—
822C2×C4⋊C4C22×D1112yes—
823C2×C22⋊C4—24no—
824C2×C22⋊C4—111no—
825C2×C22⋊C4—118no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—111no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—111no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—112no—
842C2×C22⋊C4—112no—
843C2×C22⋊C4—112no—
844C2×C22⋊C4—112no—
845C2×C22⋊C4—112no—
846C2×C22⋊C4—112no—
847C2×C22⋊C4—112no—
848C2×C22⋊C4—224no—
849C2×C22⋊C4—224no—
850C2×C22⋊C4—224no—
851C2×C22⋊C4—224no—
852C2×C22⋊C4—224no—
853C2×C22⋊C4C4×D1118yescomplemented
854C2×C22⋊C4C22×D1111yescharacteristic
855C2×C22⋊C4C22×D1111yescharacteristic
856C2×C22⋊C4C22×D1112yes—
857C2×C22⋊C4C22×D1111yescharacteristic
858C2×C22⋊C4C22×D1112yes—
859C2×C22⋊C4C22×D1112yes—
860C2×C22⋊C4C22×D1111yescharacteristic
861C2×C22⋊C4C22×D1111yescharacteristic
862C2×C22⋊C4C22×D1111yescharacteristic
863C2×C22⋊C4C22×D1111yescharacteristic
864C2×C22⋊C4C22×D1111yescharacteristic
865C2×C42—112no—
866C2×C42—112no—
867C2×C42—112no—
868C2×C42—112no—
869C2×C42—112no—
870C2×C42—112no—
871C2×C42—112no—
872C2×C42—112no—
873C2×C42—228no—
874C2×C42C22×D1112yes—
875C2×C42C22×D1112yes—
876#95—112no—
877#95—112no—
878#95—112no—
879#95—112no—
880#95—112no—
881#95—112no—
882#95—112no—
883#95—112no—
884#95C22×D1112yes—
885#95C22×D1112yes—
886#95C22×D1112yes—
887#95C22×D1112yes—
888C2×C11—24no—
889C2×C11—42no—
890C2×C11—42no—
891C2×C11C22×C4×D411yescharacteristic
892C2×C11C2×#51811yescharacteristic
893C2×C11#342811yescharacteristic
894C2×C11#348812yes—
895C2×C11#349412yes—
896D11—24no—
897D11—42no—
898D11—42no—
899D11—42no—
900C24—22no—
901C24—22no—
902C24—42no—
903C24—42no—
904C24—111no—
905C24—111no—
906C24—111no—
907C24—111no—
908C24—114no—
909C24—114no—
910C24—224no—
911C24—222no—
912C24—222no—
913C24—222no—
914C24—222no—
915C24—442no—
916C24—442no—
917C24—442no—
918C24C2×C4×D1114yes—
919C24C23×D1111yescharacteristic
920C24C23×D1111yescharacteristic
921C24C23×D1111yescharacteristic
922C2×D4—114no—
923C2×D4—114no—
924C2×D4—114no—
925C2×D4—114no—
926C2×D4—114no—
927C2×D4—114no—
928C2×D4—114no—
929C2×D4—114no—
930C2×D4—114no—
931C2×D4—114no—
932C2×D4—114no—
933C2×D4—114no—
934C2×D4—224no—
935C2×D4—224no—
936C2×D4—222no—
937C2×D4—222no—
938C2×D4—222no—
939C2×D4—222no—
940C2×D4—2232no—
941C2×D4—222no—
942C2×D4—222no—
943C2×D4—222no—
944C2×D4—222no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—442no—
948C2×D4—442no—
949C2×D4—4416no—
950C2×D4—442no—
951C2×D4—442no—
952C2×D4—4416no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—24no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—114no—
960C22×C4—114no—
961C22×C4—114no—
962C22×C4—111no—
963C22×C4—111no—
964C22×C4—111no—
965C22×C4—111no—
966C22×C4—112no—
967C22×C4—114no—
968C22×C4—114no—
969C22×C4—114no—
970C22×C4—114no—
971C22×C4—114no—
972C22×C4—112no—
973C22×C4—112no—
974C22×C4—112no—
975C22×C4—222no—
976C22×C4—222no—
977C22×C4—222no—
978C22×C4—222no—
979C22×C4—2232no—
980C22×C4—222no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—222no—
984C22×C4—224no—
985C22×C4—224no—
986C22×C4—224no—
987C22×C4—224no—
988C22×C4—224no—
989C22×C4—224no—
990C22×C4—224no—
991C22×C4—442no—
992C22×C4—442no—
993C22×C4—442no—
994C22×C4—442no—
995C22×C4—442no—
996C22×C4—442no—
997C22×C4—442no—
998C22×C4—442no—
999C22×C4—442no—
1000C22×C4C2×C4×D1114yes—
1001C22×C4C2×C4×D1114yes—
1002C22×C4C23×D1112yes—
1003C22×C4C23×D1112yes—
1004C22×C4C23×D1112yes—
1005C22×C4C23×D1111yescharacteristic
1006C22×C4C23×D1111yescharacteristic
1007C22×C4C23×D1111yescharacteristic
1008C22×C4C23×D1111yescharacteristic
1009C22×C4C23×D1112yes—
1010C4⋊C4—24no—
1011C4⋊C4—42no—
1012C4⋊C4—114no—
1013C4⋊C4—114no—
1014C4⋊C4—114no—
1015C4⋊C4—114no—
1016C4⋊C4—118no—
1017C4⋊C4—224no—
1018C4⋊C4—224no—
1019C4⋊C4—224no—
1020C4⋊C4—224no—
1021C4⋊C4—442no—
1022C4⋊C4—442no—
1023C4⋊C4—442no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—24no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—114no—
1031C22⋊C4—114no—
1032C22⋊C4—114no—
1033C22⋊C4—114no—
1034C22⋊C4—114no—
1035C22⋊C4—224no—
1036C22⋊C4—224no—
1037C22⋊C4—224no—
1038C22⋊C4—224no—
1039C22⋊C4—224no—
1040C22⋊C4—222no—
1041C22⋊C4—222no—
1042C22⋊C4—222no—
1043C22⋊C4—224no—
1044C22⋊C4—224no—
1045C22⋊C4—442no—
1046C22⋊C4—442no—
1047C22⋊C4—442no—
1048C22⋊C4—442no—
1049C22⋊C4—442no—
1050C22⋊C4—442no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C22⋊C4C2×C4×D1114yes—
1054C22⋊C4C2×C4×D1114yes—
1055C22⋊C4C2×C4×D1114yes—
1056C22⋊C4C2×C4×D1114yes—
1057C22⋊C4D4×D1114yes—
1058C42—24no—
1059C42—42no—
1060C42—118no—
1061C42—224no—
1062C42—224no—
1063C42—224no—
1064C42—224no—
1065C42—442no—
1066C42—442no—
1067C42—442no—
1068C11#3420411yescharacteristic, complemented, Sylow
1069C23—22no—
1070C23—22no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—28no—
1080C23—44no—
1081C23—44no—
1082C23—84no—
1083C23—84no—
1084C23—112no—
1085C23—114no—
1086C23—112no—
1087C23—112no—
1088C23—112no—
1089C23—228no—
1090C23—221no—
1091C23—221no—
1092C23—222no—
1093C23—228no—
1094C23—221no—
1095C23—221no—
1096C23—221no—
1097C23—221no—
1098C23—221no—
1099C23—221no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—228no—
1107C23—444no—
1108C23—444no—
1109C23—444no—
1110C23—448no—
1111C23—448no—
1112C23—884no—
1113C23—884no—
1114C23C22×C4×D1112yes—
1115C23C22×C4×D1112yes—
1116C23C22×C4×D1112yes—
1117C23C2×D4×D1112yes—
1118C23#41×D1112yes—
1119C23C24×D1111yescharacteristic
1120D4—228no—
1121D4—228no—
1122D4—228no—
1123D4—228no—
1124D4—228no—
1125D4—228no—
1126D4—228no—
1127D4—228no—
1128D4—444no—
1129D4—444no—
1130D4—444no—
1131D4—444no—
1132C2×C4—28no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—44no—
1151C2×C4—84no—
1152C2×C4—1116no—
1153C2×C4—112no—
1154C2×C4—112no—
1155C2×C4—112no—
1156C2×C4—112no—
1157C2×C4—112no—
1158C2×C4—112no—
1159C2×C4—112no—
1160C2×C4—112no—
1161C2×C4—114no—
1162C2×C4—228no—
1163C2×C4—228no—
1164C2×C4—228no—
1165C2×C4—228no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—448no—
1180C2×C4—448no—
1181C2×C4—444no—
1182C2×C4—884no—
1183C2×C4—884no—
1184C2×C4—884no—
1185C2×C4C22×C4×D1112yes—
1186C2×C4C22×C4×D1112yes—
1187C2×C4C22×C4×D1112yes—
1188C2×C4C22×C4×D1112yes—
1189C2×C4C2×D4×D1114yes—
1190C22—24no—
1191C22—22no—
1192C22—22no—
1193C22—24no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—88no—
1205C22—114no—
1206C22—224no—
1207C22—222no—
1208C22—222no—
1209C22—224no—
1210C22—222no—
1211C22—222no—
1212C22—222no—
1213C22—222no—
1214C22—222no—
1215C22—222no—
1216C22—222no—
1217C22—222no—
1218C22—222no—
1219C22—4416no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—888no—
1227C22C4×D4×D1114yes—
1228C22C23×C4×D1111yescharacteristic
1229C22C22×D4×D1111yescharacteristic
1230C22C2×#41×D1111yescharacteristic
1231C22#1062345312yes—
1232C22D11×H(5,𝔽2)12yes—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—114no—
1242C4—114no—
1243C4—224no—
1244C4—222no—
1245C4—222no—
1246C4—442no—
1247C4—442no—
1248C4—442no—
1249C2—24no—
1250C2—42no—
1251C2—42no—
1252C2—224no—
1253C2—442no—
1254C2—442no—
1255C2—442no—
1256C2C2×C4×D4×D1111yescharacteristic
1257C2D11×#51811yescharacteristic
1258C2#1308181711yescharacteristic
1259C2#1308227912yes—
1260C2#1308234212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2342C2
socle, cosocleC23×C11C25
prime radicalC22×#66937C2
hypercenter#2342D11
hypocenterC11#34204
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C2×#10623017C2semidirect
3. C2×D11×#117C2semidirect
4. #13071655C2semidirect
5. #13071649C2semidirect
6. #13071635C2semidirect
7. #13071629C2semidirect
8. #13071466C2semidirect
9. #13071465C2semidirect
10. #13071458C2semidirect
11. C22⋊C4×D44C2semidirect
12. #13071436C2semidirect
13. C22⋊C4×C22⋊D11C2semidirect
14. #13071432C2semidirect
15. #13071308C2semidirect
16. #13071304C2semidirect
17. #13071233C2semidirect
18. #13071197C2semidirect
19. #13071128C2semidirect
20. C4×#66937C2semidirect
21. #13070996C2semidirect
22. #13070971C2semidirect
23. C11×#2342C2semidirect
32. C2×C4×C22⋊D11C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
39. C2×#66946C22semidirect
40. C2×#66945C22semidirect
41. C2×C4⋊C4×D11C22semidirect
42. C2×#66937C4semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
63. C2×C4×D44C22semidirect
64. C2×#66925C22semidirect
65. C2×C42×D11C22semidirect
66. C11×#388C22semidirect
67. C11×#388C22semidirect
68. C11×#385C22semidirect
73. C4×C11×C22⋊C4C22semidirect
75. #10622826C22semidirect
79. #10622603C22semidirect
80. #10622602C22semidirect
81. #10622601C22semidirect
82. #10622585C22semidirect
83. #10622585C22semidirect
84. #10622571C22semidirect
85. #10622570C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
97. #10622564C22semidirect
98. #10622564C22semidirect
99. #10622563C22semidirect
104. C22⋊C4×Dic11C22semidirect
105. #10622553C22semidirect
106. #10622552C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. #10622283C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622280C22semidirect
114. #10622280C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
135. C22×C22⋊D11C2×C4semidirect
136. C22×C22⋊D11C2×C4semidirect
149. C22×D44C2×C4semidirect
156. C22×C4×D11C2×C4semidirect
169. C2×C11×C22⋊C4C2×C4semidirect
194. C2×(C2×D11)⋊C4C2×C4semidirect
214. C2×Dic11⋊C4C2×C4semidirect
236. #66937C2×C4semidirect
237. #66937C2×C4semidirect
238. #66937C2×C4semidirect
239. #66937C2×C4semidirect
240. #66937C2×C4semidirect
241. #66937C2×C4semidirect
242. #66937C2×C4semidirect
243. #66937C2×C4semidirect
254. #66930D4semidirect
430. Dic11⋊C4C2×D4semidirect
438. C4×Dic11C2×D4semidirect
449. #2342D11semidirect
561. C2×Dic11C4×D4semidirect
643. #388C2×D11semidirect
644. #388C2×D11semidirect
656. #385C2×D11semidirect
684. C4×C22⋊C4C2×D11semidirect
727. C2×D11#518semidirect
853. C2×C22⋊C4C4×D11semidirect
1068. C11#34204semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106230172
C2×D11×#1172
#130716552
#130716492
#130716352
#130716292
#130714662
#130714652
#130714582
C22⋊C4×D442
#130714362
C22⋊C4×C22⋊D112
#130714322
#130713082
#130713042
#130712332
#130711972
#130711282
C4×#669372
#130709962
#130709712
C11×#23422
#3420411