Finite Group Databasebeta

← C2×#13082588 #15661877

Subgroups — C2×#13082588 #15661877

Order 2816.

7142 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082588C2132yesmaximal, direct product factor
2C2×#10623216C211yesmaximal, characteristic, complemented
3C2×#10623221C211yesmaximal, characteristic, complemented
4C2×#10623042C211yesmaximal, characteristic, complemented
5C2×#10623226C211yesmaximal, characteristic, complemented
6C2×#10623045C211yesmaximal, characteristic, complemented
7C2×#10623225C211yesmaximal, characteristic, complemented
8C2×#10623044C212yesmaximal, complemented
9C2×#10623044C211yesmaximal, characteristic, complemented
10C2×#10623224C212yesmaximal, complemented
11C2×#10623224C212yesmaximal, complemented
12C2×#10623038C211yesmaximal, characteristic, complemented
13C2×#10623038C212yesmaximal, complemented
14C2×#10623227C212yesmaximal, complemented
15C2×#10623223C212yesmaximal, complemented
16C2×#10623046C212yesmaximal, complemented
17C2×#10623219C211yesmaximal, characteristic, complemented
18C2×#10623222C211yesmaximal, characteristic, complemented
19C2×#10623222C211yesmaximal, characteristic, complemented
20C2×#10623010C211yesmaximal, characteristic, complemented
21C2×D11×#125C211yesmaximal, characteristic, complemented
22C2×#10623035C212yesmaximal, complemented
23C2×C4×#4339C211yesmaximal, characteristic, complemented
24C22×C11×#125C211yesmaximal, characteristic, complemented
25C22×#4339C2211yescharacteristic
26C22×#4339C2212yes—
27C2×C11×#125C2212yes—
28C2×C11×#125C2211yescharacteristic
29C2×C11×#125C2211yescharacteristic
30C2×C11×#125C2211yescharacteristic
31C2×C11×#125C2211yescharacteristic
32C2×C11×#125C2212yes—
33C2×C11×#125C22116yescomplemented
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊C4C2212yes—
36C22×C11×C4⋊C4C2211yescharacteristic
37C22×C11×C4⋊C4C2212yes—
38C22×C42×C11C2211yescharacteristic
39C2×#66983C2211yescharacteristic
40C2×#66983C2212yes—
41C2×#66982C2212yes—
42C2×#66982C2212yes—
43C2×#66982C2212yes—
44C2×C4×C22⋊D11C2211yescharacteristic
45C2×C4×C22⋊D11C2212yes—
46C2×C4×C22⋊D11C2212yes—
47C2×C4×C22⋊D11C2211yescharacteristic
48C2×C4×C22⋊D11C2212yes—
49C2×C4×C22⋊D11C2211yescharacteristic
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×#66979C2211yescharacteristic
52C2×#66979C2212yes—
53C2×#66977C2211yescharacteristic
54C2×#66977C2212yes—
55#10623227C22132yescomplemented
56#10623226C22116yescomplemented
57#10623225C22116yescomplemented
58#10623224C22132yescomplemented
59#10623224C22132yescomplemented
60#10623223C22132yescomplemented
61#10623222C22116yescomplemented
62#10623222C22116yescomplemented
63#10623221C22116yescomplemented
64#10623219C22116yescomplemented
65D11×#125C22116yescomplemented
66#10623216C22116yescomplemented
67#10623046C22132yescomplemented
68#10623045C22116yescomplemented
69#10623044C22116yescomplemented
70#10623044C22132yescomplemented
71C2×#66951C2212yes—
72C2×#66951C2212yes—
73C2×#66951C2212yes—
74C2×#66951C2212yes—
75C2×#66951C2212yes—
76C2×#66951C2212yes—
77#10623042C22116yescomplemented
78C2×#66950C2211yescharacteristic
79C2×#66950C2212yes—
80C2×#66950C2211yescharacteristic
81C2×#66949C2212yes—
82C2×#66949C2212yes—
83C2×#66949C2212yes—
84C2×#66949C2212yes—
85C2×#66949C2212yes—
86C2×#66949C2212yes—
87#10623038C22116yescomplemented
88#10623038C22132yescomplemented
89C2×#66948C2211yescharacteristic
90C2×#66948C2211yescharacteristic
91C2×#66948C2212yes—
92C2×#66947C2212yes—
93C2×#66947C2212yes—
94C2×#66947C2212yes—
95C2×#66947C2212yes—
96C2×#66947C2212yes—
97C2×#66947C2212yes—
98#10623035C22132yescomplemented
99C2×#66946C2212yes—
100C2×#66946C2212yes—
101C2×#66946C2211yescharacteristic
102C2×#66946C2211yescharacteristic
103C2×#66946C2212yes—
104C2×#66945C2212yes—
105C2×#66945C2212yes—
106C2×#66945C2211yescharacteristic
107C2×#66945C2211yescharacteristic
108C2×#66945C2212yes—
109C2×C4⋊C4×D11C2212yes—
110C2×C4⋊C4×D11C2212yes—
111C2×C4⋊C4×D11C2211yescharacteristic
112C2×C4⋊C4×D11C2211yescharacteristic
113C2×C4⋊C4×D11C2212yes—
114C2×#66943C2211yescharacteristic
115C2×#66943C2211yescharacteristic
116C2×#66943C2212yes—
117C2×#66942C2212yes—
118C2×#66942C2212yes—
119C2×#66942C2212yes—
120C2×#66942C2212yes—
121C2×#66942C2212yes—
122C2×#66942C2212yes—
123C2×#66941C2211yescharacteristic
124C2×#66941C2211yescharacteristic
125C2×#66941C2212yes—
126C2×#66940C2212yes—
127C2×#66940C2212yes—
128C2×#66940C2211yescharacteristic
129C2×#66940C2211yescharacteristic
130C2×#66940C2212yes—
131#10623010C22116yescomplemented
132C2×#66929C2212yes—
133C2×#66928C2211yescharacteristic
134C4×#4339C22116yescomplemented
135C2×C4×D44C2211yescharacteristic
136C2×C4×D44C2211yescharacteristic
137C2×C4×D44C2211yescharacteristic
138C2×#66925C2212yes—
139C2×#66925C2211yescharacteristic
140C2×#66925C2211yescharacteristic
141C2×C42×D11C2211yescharacteristic
142C2×C42×D11C2211yescharacteristic
143C2×#66923C2211yescharacteristic
144C2×C4×Dic22C2211yescharacteristic
145C2×C4×Dic22C2211yescharacteristic
146C2×C4×Dic22C2211yescharacteristic
147C23×C4×C11C2311yescharacteristic
148C23×C4×C11C2311yescharacteristic
149C23×C4×C11C2312yes—
150C23×C4×C11C2312yes—
151C23×C4×C11C2311yescharacteristic
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2312yes—
154C22×C22⋊D11C2311yescharacteristic
155C2×#4339—28no—
156C2×#4339—216no—
157C2×#4339C2318yes—
158C2×#4339C23116yes—
159C22×D44C2311yescharacteristic
160C22×D44C2311yescharacteristic
161C22×D44C2312yes—
162C22×D44C2312yes—
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2311yescharacteristic
167C22×C4×D11C2312yes—
168C22×C4×D11C2312yes—
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2311yescharacteristic
171C22×C4×D11C2312yes—
172C22×C4×D11C2312yes—
173C22×C4×D11C2312yes—
174C22×Dic22C2311yescharacteristic
175C22×Dic22C2311yescharacteristic
176C22×Dic22C2312yes—
177C22×Dic22C2312yes—
178C11×#125C2318yes—
179C11×#125C2318yes—
180C11×#125C2318yes—
181C11×#125C2318yes—
182C11×#125C23116yes—
183C11×#125C23116yes—
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2311yescharacteristic
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2312yes—
189C2×C11×C4⋊C4C2312yes—
190C2×C11×C4⋊C4C2311yescharacteristic
191C2×C11×C4⋊C4C2312yes—
192C2×C11×C4⋊C4C2312yes—
193C2×C11×C4⋊C4C2312yes—
194C2×C11×C4⋊C4C2312yes—
195C2×C11×C4⋊C4C2311yescharacteristic
196C2×C11×C4⋊C4C2312yes—
197C2×C11×C4⋊C4C2312yes—
198C2×C11×C4⋊C4C23116yes—
199C2×C11×C4⋊C4C2318yes—
200C2×C11×C4⋊C4C23116yes—
201C2×C11×C4⋊C4C2318yes—
202C2×C42×C11C2311yescharacteristic
203C2×C42×C11C2311yescharacteristic
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2318yes—
207C2×C22⋊Dic11C2312yes—
208C2×C22⋊Dic11C2311yescharacteristic
209C2×C22⋊Dic11C2311yescharacteristic
210#66983C2318yes—
211#66983C23116yes—
212#66982C23116yes—
213#66982C23116yes—
214#66982C23116yes—
215C4×C22⋊D11C2318yes—
216C4×C22⋊D11C2318yes—
217C4×C22⋊D11C2318yes—
218C4×C22⋊D11C2318yes—
219C4×C22⋊D11C23116yes—
220C4×C22⋊D11C23116yes—
221C4×C22⋊D11C23116yes—
222C2×(C2×D11)⋊C4C2311yescharacteristic
223C2×(C2×D11)⋊C4C2311yescharacteristic
224C2×(C2×D11)⋊C4C2311yescharacteristic
225C2×(C2×D11)⋊C4C2311yescharacteristic
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×(C2×D11)⋊C4C2312yes—
229C2×(C2×D11)⋊C4C2312yes—
230C2×(C2×D11)⋊C4C2312yes—
231C2×(C2×D11)⋊C4C2312yes—
232C2×(C2×D11)⋊C4C2312yes—
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2312yes—
235C2×(C2×D11)⋊C4C2312yes—
236C2×(C2×D11)⋊C4C2312yes—
237C2×(C2×D11)⋊C4C2312yes—
238#66979C2318yes—
239#66979C23116yes—
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2311yescharacteristic
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2312yes—
245C2×C4⋊Dic11C2312yes—
246C2×C4⋊Dic11C2312yes—
247C2×C4⋊Dic11C2312yes—
248#66977C2318yes—
249#66977C23116yes—
250C2×Dic11⋊C4C2311yescharacteristic
251C2×Dic11⋊C4C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2312yes—
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C2312yes—
261C2×Dic11⋊C4C2312yes—
262C2×Dic11⋊C4C2312yes—
263C2×Dic11⋊C4C2312yes—
264C2×Dic11⋊C4C2312yes—
265C2×Dic11⋊C4C2312yes—
266C2×C4×Dic11C2311yescharacteristic
267C2×C4×Dic11C2311yescharacteristic
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2312yes—
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2312yes—
274C2×C4×Dic11C2312yes—
275C2×C4×Dic11C2312yes—
276C2×C4×Dic11C2312yes—
277#66951C23116yes—
278#66951C23116yes—
279#66951C23116yes—
280#66951C23116yes—
281#66951C23116yes—
282#66951C23116yes—
283#66950C2318yes—
284#66950C23116yes—
285#66950C2318yes—
286#66949C23116yes—
287#66949C23116yes—
288#66949C23116yes—
289#66949C23116yes—
290#66949C23116yes—
291#66949C23116yes—
292#66948C2318yes—
293#66948C23116yes—
294#66948C2318yes—
295#66947C23116yes—
296#66947C23116yes—
297#66947C23116yes—
298#66947C23116yes—
299#66947C23116yes—
300#66947C23116yes—
301#66946C23116yes—
302#66946C23116yes—
303#66946C2318yes—
304#66946C23116yes—
305#66946C2318yes—
306#66945C23116yes—
307#66945C23116yes—
308#66945C2318yes—
309#66945C23116yes—
310#66945C2318yes—
311C4⋊C4×D11C23116yes—
312C4⋊C4×D11C23116yes—
313C4⋊C4×D11C23116yes—
314C4⋊C4×D11C2318yes—
315C4⋊C4×D11C2318yes—
316#66943C2318yes—
317#66943C23116yes—
318#66943C2318yes—
319#66942C23116yes—
320#66942C23116yes—
321#66942C23116yes—
322#66942C23116yes—
323#66942C23116yes—
324#66942C23116yes—
325#66941C2318yes—
326#66941C23116yes—
327#66941C2318yes—
328#66940C23116yes—
329#66940C23116yes—
330#66940C2318yes—
331#66940C2318yes—
332#66940C23116yes—
333#66929C23116yes—
334#66928C2318yes—
335C4×D44C2318yes—
336C4×D44C2318yes—
337C4×D44C2318yes—
338#66925C2318yes—
339#66925C2318yes—
340#66925C23116yes—
341C42×D11C2318yes—
342C42×D11C2318yes—
343#66923C2318yes—
344C4×Dic22C2318yes—
345C4×Dic22C2318yes—
346C4×Dic22C2318yes—
347C2×#3515—111nomaximal, Sylow
348C24×C11C2411yescharacteristic
349C23×D11C2411yescharacteristic
350C23×D11C2412yes—
351C23×D11C2411yescharacteristic
352C22×C4×C11—24no—
353C22×C4×C11—28no—
354C22×C4×C11—24no—
355C22×C4×C11—44no—
356C22×C4×C11—42no—
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2412yes—
361C22×C4×C11C2412yes—
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2412yes—
366C22×C4×C11C2414yes—
367C22×C4×C11C2414yes—
368C22×C4×C11C2418yes—
369C22×C4×C11C2418yes—
370C22×C4×C11C2414yes—
371C22×C4×C11C2411yescharacteristic
372C2×C22⋊D11—24no—
373C2×C22⋊D11—28no—
374C2×C22⋊D11#4118yes—
375C2×C22⋊D11C2414yes—
376C2×C22⋊D11C2418yes—
377C2×C22⋊D11C2414yes—
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2412yes—
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2412yes—
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2412yes—
386C22×Dic11C2411yescharacteristic
387#4339—232no—
388#4339—264no—
389C2×D44—24no—
390C2×D44—28no—
391C2×D44—24no—
392C2×D44—44no—
393C2×D44C2414yes—
394C2×D44C2414yes—
395C2×D44C2418yes—
396C2×D44C2418yes—
397C2×C4×D11—24no—
398C2×C4×D11—28no—
399C2×C4×D11—24no—
400C2×C4×D11—28no—
401C2×C4×D11—24no—
402C2×C4×D11—24no—
403C2×C4×D11—44no—
404C2×C4×D11—42no—
405C2×C4×D11—44no—
406C2×C4×D11—42no—
407C2×C4×D11—44no—
408C2×C4×D11C2414yes—
409C2×C4×D11C2414yes—
410C2×C4×D11C2414yes—
411C2×C4×D11C2414yes—
412C2×C4×D11C2418yes—
413C2×C4×D11C2418yes—
414C2×C4×D11C2414yes—
415C2×C4×D11C2414yes—
416C2×C4×D11C2418yes—
417C2×C4×D11C2418yes—
418C2×C4×D11C2418yes—
419C2×Dic22—24no—
420C2×Dic22—28no—
421C2×Dic22—24no—
422C2×Dic22—44no—
423C2×Dic22C2414yes—
424C2×Dic22C2414yes—
425C2×Dic22C2418yes—
426C2×Dic22C2418yes—
427C11×C4⋊C4C2414yes—
428C11×C4⋊C4C2418yes—
429C11×C4⋊C4C2414yes—
430C11×C4⋊C4C2418yes—
431C11×C4⋊C4C2418yes—
432C11×C4⋊C4C2418yes—
433C11×C4⋊C4C2414yes—
434C11×C4⋊C4C2418yes—
435C11×C4⋊C4C2418yes—
436C11×C4⋊C4C2418yes—
437C11×C4⋊C4C2418yes—
438C11×C4⋊C4C2414yes—
439C11×C4⋊C4C2418yes—
440C11×C4⋊C4C2418yes—
441C42×C11C2414yes—
442C42×C11C2414yes—
443C42×C11C2414yes—
444C42×C11C2414yes—
445C22⋊Dic11C2418yes—
446C22⋊Dic11C2414yes—
447C22⋊Dic11C2414yes—
448(C2×D11)⋊C4C2414yes—
449(C2×D11)⋊C4C2414yes—
450(C2×D11)⋊C4C2414yes—
451(C2×D11)⋊C4C2414yes—
452(C2×D11)⋊C4C2418yes—
453(C2×D11)⋊C4C2418yes—
454(C2×D11)⋊C4C2418yes—
455(C2×D11)⋊C4C2418yes—
456(C2×D11)⋊C4C2418yes—
457(C2×D11)⋊C4C2418yes—
458(C2×D11)⋊C4C2418yes—
459(C2×D11)⋊C4C2418yes—
460(C2×D11)⋊C4C2418yes—
461(C2×D11)⋊C4C2418yes—
462(C2×D11)⋊C4C2418yes—
463(C2×D11)⋊C4C2418yes—
464C4⋊Dic11C2414yes—
465C4⋊Dic11C2414yes—
466C4⋊Dic11C2414yes—
467C4⋊Dic11C2414yes—
468C4⋊Dic11C2418yes—
469C4⋊Dic11C2418yes—
470C4⋊Dic11C2418yes—
471C4⋊Dic11C2418yes—
472Dic11⋊C4C2414yes—
473Dic11⋊C4C2414yes—
474Dic11⋊C4C2414yes—
475Dic11⋊C4C2414yes—
476Dic11⋊C4C2418yes—
477Dic11⋊C4C2418yes—
478Dic11⋊C4C2418yes—
479Dic11⋊C4C2418yes—
480Dic11⋊C4C2418yes—
481Dic11⋊C4C2418yes—
482Dic11⋊C4C2418yes—
483Dic11⋊C4C2418yes—
484Dic11⋊C4C2418yes—
485Dic11⋊C4C2418yes—
486Dic11⋊C4C2418yes—
487Dic11⋊C4C2418yes—
488C4×Dic11C2414yes—
489C4×Dic11C2414yes—
490C4×Dic11C2414yes—
491C4×Dic11C2414yes—
492C4×Dic11C2418yes—
493C4×Dic11C2414yes—
494C4×Dic11C2414yes—
495C4×Dic11C2418yes—
496C4×Dic11C2418yes—
497C4×Dic11C2418yes—
498C4×Dic11C2418yes—
499#3515—1132no—
500C2×#557—111no—
501C2×#554—111no—
502C2×#554—111no—
503C2×#553—111no—
504C2×#553—111no—
505C2×#552—112no—
506C2×#552—112no—
507C2×#552—111no—
508C2×#552—112no—
509C2×#552—111no—
510C2×#547—111no—
511C2×#547—112no—
512C2×#541—112no—
513C2×#539—112no—
514C2×#539—112no—
515C2×#533—111no—
516C2×#529—111no—
517C2×#529—111no—
518C2×#529—111no—
519C22×#125—111no—
520C22×#125D1111yescharacteristic, complemented
521C2×#520—112no—
522C2×C4×#41—111no—
523C23×C11—22no—
524C23×C11—22no—
525C23×C11C2×#4114yes—
526C23×C11C2512yes—
527C23×C11C2511yescharacteristic
528C22×D11—22no—
529C22×D11—22no—
530C22×D11—22no—
531C22×D11—24no—
532C22×D11—22no—
533C22×D11—24no—
534C22×D11—24no—
535C22×D11—22no—
536C22×D11C2×#4114yes—
537C22×D11C2512yes—
538C22×D11C2514yes—
539C22×D11C2512yes—
540C2×C4×C11—24no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—24no—
544C2×C4×C11—28no—
545C2×C4×C11—216no—
546C2×C4×C11—22no—
547C2×C4×C11—24no—
548C2×C4×C11—22no—
549C2×C4×C11—22no—
550C2×C4×C11—24no—
551C2×C4×C11—28no—
552C2×C4×C11—48no—
553C2×C4×C11—44no—
554C2×C4×C112−1+414yes—
555C2×C4×C11C2512yes—
556C2×C4×C11C2512yes—
557C2×C4×C11C2512yes—
558C2×C4×C11C2514yes—
559C2×C4×C11C2514yes—
560C2×C4×C11C2514yes—
561C2×C4×C11C2512yes—
562C2×C4×C11C2512yes—
563C2×C4×C11C2514yes—
564C2×C4×C11C2512yes—
565C22⋊D11—28no—
566C22⋊D11—216no—
567C22⋊D11C2×#41116yes—
568C2×Dic11—22no—
569C2×Dic11—24no—
570C2×Dic11—24no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—24no—
575C2×Dic11—22no—
576C2×Dic11C2×#4114yes—
577C2×Dic11C2512yes—
578C2×Dic11C2512yes—
579C2×Dic11C2514yes—
580C2×Dic11C2512yes—
581C2×Dic11C2514yes—
582C2×Dic11C2512yes—
583C2×Dic11C2512yes—
584C2×Dic11C2514yes—
585C2×Dic11C2512yes—
586D44—28no—
587D44—216no—
588D44—28no—
589D44—48no—
590C4×D11—28no—
591C4×D11—216no—
592C4×D11—28no—
593C4×D11—28no—
594C4×D11—28no—
595C4×D11—216no—
596C4×D11—44no—
597C4×D11—48no—
598C4×D11—48no—
599C4×D11—48no—
600C4×D11—44no—
601Dic22—28no—
602Dic22—28no—
603Dic22—216no—
604Dic22—48no—
605C22×#41—111no—
606C22×#41—112no—
607#557—1116no—
608#554—1116no—
609#554—1116no—
610#553—1116no—
611#553—1116no—
612#552—1132no—
613#552—1132no—
614#552—1116no—
615#552—1132no—
616#552—1116no—
617#547—1116no—
618#547—1132no—
619#541—1132no—
620#539—1132no—
621#539—1132no—
622#533—1116no—
623C2×C4⋊Q8—111no—
624C2×C4⋊Q8—111no—
625C2×C4⋊Q8—112no—
626#529—1116no—
627#529—1116no—
628#529—1116no—
629C2×#126—112no—
630C2×#126—112no—
631C2×#126—112no—
632C2×#126—112no—
633C2×#126—112no—
634C2×#126—112no—
635C2×#126—112no—
636C2×#125—1116no—
637C2×#125—112no—
638C2×#125—112no—
639C2×#125—112no—
640C2×#125—112no—
641C2×#125—112no—
642C2×#125—112no—
643C2×#125—111no—
644C2×#125—111no—
645C2×#125—112no—
646C2×#125—111no—
647C2×#125C2×D1111yescharacteristic
648C2×#125C2×D1111yescharacteristic
649C2×#125C2×D1112yes—
650C2×#125C2×D1112yes—
651C2×#125C2×D1111yescharacteristic
652C2×#125C2×D1111yescharacteristic
653C2×#125C2×D11116yescomplemented
654C2×#124—111no—
655C2×#123—112no—
656C2×#123—112no—
657C2×#123—112no—
658C2×#123—112no—
659C2×#123—112no—
660C2×#123—112no—
661C2×#123—112no—
662C2×#123—112no—
663C2×#123—112no—
664C2×C22⋊Q8—111no—
665C2×C22⋊Q8—112no—
666C2×C22⋊Q8—112no—
667C2×C22⋊Q8—112no—
668C2×C22⋊Q8—112no—
669C2×C22⋊Q8—112no—
670C2×C22⋊Q8—112no—
671C2×C22⋊Q8—112no—
672C2×C22⋊Q8—111no—
673C2×C22⋊Q8—111no—
674C2×C22⋊Q8—112no—
675C2×#121—111no—
676C2×#121—112no—
677C2×#121—111no—
678C2×#121—111no—
679C2×#121—112no—
680#520—1132no—
681C4×#41—1116no—
682C2×C4×Q8—112no—
683C2×C4×Q8—112no—
684C2×C4×Q8—111no—
685C2×C4×Q8—111no—
686C2×C4×Q8—112no—
687C2×C4×Q8—111no—
688C2×C4×Q8—111no—
689C2×C4×Q8—111no—
690C2×C4×D4—111no—
691C2×C4×D4—111no—
692C2×C4×D4—111no—
693C2×C4×D4—111no—
694C2×C4×D4—112no—
695C2×C4×D4—112no—
696C2×C4×D4—112no—
697C2×C4×D4—112no—
698C2×C4×D4—112no—
699C2×C4×D4—112no—
700C2×C4×D4—111no—
701C2×C4×D4—111no—
702C2×C4×D4—111no—
703C2×C4×D4—111no—
704C2×C4×D4—111no—
705C2×#117—111no—
706C2×#117—112no—
707C2×#117—112no—
708C2×#117—112no—
709C2×#117—112no—
710C2×#117—111no—
711C2×#117—111no—
712C2×#117—111no—
713C2×#117—111no—
714C2×#117—112no—
715C22×C4⋊C4—112no—
716C22×C4⋊C4—112no—
717C22×C4⋊C4—111no—
718C22×C4⋊C4—112no—
719C22×C4⋊C4—111no—
720C22×C4⋊C4C2×D1112yes—
721C22×C4⋊C4C2×D1111yescharacteristic
722C22×C4⋊C4C2×D1112yes—
723C22×C4⋊C4C2×D1111yescharacteristic
724C22×C42—111no—
725C22×C42—111no—
726C22×C42C2×D1111yescharacteristic
727C22×C11—22no—
728C22×C11—22no—
729C22×C11—28no—
730C22×C11C22×#4114yes—
731C22×C11C22×#4112yes—
732C22×C11C2×2−1+412yes—
733C22×C11#58512yes—
734C22×C11C2611yescharacteristic
735C2×D11—22no—
736C2×D11—22no—
737C2×D11—28no—
738C2×D11—22no—
739C2×D11—24no—
740C2×D11—22no—
741C2×D11—24no—
742C2×D11—24no—
743C2×D11—22no—
744C2×D11—44no—
745C2×D11—48no—
746C2×D11C22×#4114yes—
747C4×C11—24no—
748C4×C11—22no—
749C4×C11—22no—
750C4×C11—24no—
751C4×C11—22no—
752C4×C11—24no—
753C4×C11—22no—
754C4×C11—22no—
755C4×C11—24no—
756C4×C11C2×2−1+414yes—
757Dic11—22no—
758Dic11—24no—
759Dic11—24no—
760Dic11—22no—
761Dic11—22no—
762Dic11—22no—
763Dic11—24no—
764Dic11—22no—
765Dic11C22×#4114yes—
766C2×#41—118no—
767C2×#41—1116no—
768C2×#41—228no—
769C2×#41—2216no—
770C22×Q8—111no—
771C22×Q8—112no—
772C22×Q8—111no—
773C22×Q8—112no—
774C22×D4—111no—
775C22×D4—111no—
776C22×D4—112no—
777C22×D4—111no—
778C22×D4—112no—
779C22×D4—111no—
780C22×D4—112no—
781C23×C4—112no—
782C23×C4—111no—
783C23×C4—111no—
784C23×C4—112no—
785C23×C4—111no—
786C23×C4—111no—
787C23×C4—112no—
788C23×C4—111no—
789C23×C4—112no—
790C23×C4—112no—
791C23×C4—111no—
792C23×C4C22×D1112yes—
793C23×C4C22×D1111yescharacteristic
794C23×C4C22×D1111yescharacteristic
795C23×C4C22×D1112yes—
796C23×C4C22×D1111yescharacteristic
797C4⋊Q8—118no—
798C4⋊Q8—118no—
799C4⋊Q8—1116no—
800#126—1116no—
801#126—1116no—
802#126—1116no—
803#126—1116no—
804#126—1116no—
805#126—1116no—
806#126—1116no—
807#125—1116no—
808#125—1116no—
809#125—118no—
810#125—118no—
811#125—1116no—
812#125—1116no—
813#125—1116no—
814#125—1116no—
815#125—1116no—
816#125—118no—
817#125C22×D1118yes—
818#125C22×D1118yes—
819#125C22×D11116yes—
820#125C22×D11116yes—
821#125C22×D1118yes—
822#125C22×D1118yes—
823#124—118no—
824#123—1116no—
825#123—1116no—
826#123—1116no—
827#123—1116no—
828#123—1116no—
829#123—1116no—
830#123—1116no—
831#123—1116no—
832#123—1116no—
833C22⋊Q8—118no—
834C22⋊Q8—1116no—
835C22⋊Q8—118no—
836C22⋊Q8—118no—
837C22⋊Q8—1116no—
838C22⋊Q8—1116no—
839C22⋊Q8—1116no—
840C22⋊Q8—1116no—
841C22⋊Q8—1116no—
842C22⋊Q8—1116no—
843C22⋊Q8—1116no—
844#121—118no—
845#121—1116no—
846#121—118no—
847#121—118no—
848#121—1116no—
849C4×Q8—1116no—
850C4×Q8—1116no—
851C4×Q8—118no—
852C4×Q8—118no—
853C4×Q8—1116no—
854C4×Q8—118no—
855C4×Q8—118no—
856C4×Q8—118no—
857C4×D4—118no—
858C4×D4—118no—
859C4×D4—118no—
860C4×D4—118no—
861C4×D4—1116no—
862C4×D4—1116no—
863C4×D4—1116no—
864C4×D4—1116no—
865C4×D4—1116no—
866C4×D4—1116no—
867C4×D4—118no—
868C4×D4—118no—
869C4×D4—118no—
870C4×D4—118no—
871C4×D4—118no—
872#117—118no—
873#117—1116no—
874#117—1116no—
875#117—1116no—
876#117—1116no—
877#117—118no—
878#117—118no—
879#117—118no—
880#117—118no—
881#117—1116no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—112no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—111no—
886C2×C4⋊C4—112no—
887C2×C4⋊C4—112no—
888C2×C4⋊C4—112no—
889C2×C4⋊C4—112no—
890C2×C4⋊C4—112no—
891C2×C4⋊C4—112no—
892C2×C4⋊C4—112no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—112no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4—111no—
897C2×C4⋊C4—111no—
898C2×C4⋊C4—111no—
899C2×C4⋊C4—111no—
900C2×C4⋊C4—112no—
901C2×C4⋊C4—112no—
902C2×C4⋊C4—112no—
903C2×C4⋊C4—112no—
904C2×C4⋊C4—112no—
905C2×C4⋊C4—112no—
906C2×C4⋊C4—1116no—
907C2×C4⋊C4—1116no—
908C2×C4⋊C4—118no—
909C2×C4⋊C4—1116no—
910C2×C4⋊C4—118no—
911C2×C4⋊C4C22×D1112yes—
912C2×C4⋊C4C22×D1112yes—
913C2×C4⋊C4C22×D1111yescharacteristic
914C2×C4⋊C4C22×D1112yes—
915C2×C4⋊C4C22×D1111yescharacteristic
916C2×C4⋊C4C22×D1111yescharacteristic
917C2×C4⋊C4C22×D1111yescharacteristic
918C2×C4⋊C4C22×D1112yes—
919C2×C4⋊C4C22×D1112yes—
920C2×C4⋊C4C22×D1112yes—
921C2×C4⋊C4C22×D11116yes—
922C2×C4⋊C4C22×D1112yes—
923C2×C4⋊C4C22×D1112yes—
924C2×C4⋊C4C22×D1112yes—
925C2×C4⋊C4C22×D1112yes—
926C2×C4⋊C4C22×D1118yes—
927C2×C4⋊C4C22×D11116yes—
928C2×C4⋊C4C22×D1118yes—
929C2×C22⋊C4—111no—
930C2×C22⋊C4—112no—
931C2×C22⋊C4—111no—
932C2×C22⋊C4—111no—
933C2×C22⋊C4—112no—
934C2×C22⋊C4—112no—
935C2×C22⋊C4—112no—
936C2×C22⋊C4—111no—
937C2×C22⋊C4—111no—
938C2×C22⋊C4—111no—
939C2×C22⋊C4—112no—
940C2×C22⋊C4—112no—
941C2×C22⋊C4—112no—
942C2×C22⋊C4—112no—
943C2×C22⋊C4—112no—
944C2×C22⋊C4—112no—
945C2×C22⋊C4—112no—
946C2×C22⋊C4—112no—
947C2×C22⋊C4—112no—
948C2×C42—111no—
949C2×C42—111no—
950C2×C42—112no—
951C2×C42—112no—
952C2×C42—112no—
953C2×C42—112no—
954C2×C42—111no—
955C2×C42—112no—
956C2×C42—111no—
957C2×C42—111no—
958C2×C42—111no—
959C2×C42—118no—
960C2×C42—118no—
961C2×C42C22×D1111yescharacteristic
962C2×C42C22×D1111yescharacteristic
963C2×C42C22×D1111yescharacteristic
964C2×C42C22×D1118yes—
965C2×C42C22×D1111yescharacteristic
966C2×C11—24no—
967C2×C11#351514yescomplemented
968C2×C11C23×#4111yescharacteristic
969C2×C11C22×2−1+411yescharacteristic
970C2×C11C2×#58511yescharacteristic
971D11—24no—
972D11—42no—
973D11—44no—
974C24—111no—
975C24—111no—
976C24—112no—
977C24C23×D1111yescharacteristic
978#41—2232no—
979#41—2264no—
980C2×Q8—114no—
981C2×Q8—118no—
982C2×Q8—114no—
983C2×Q8—118no—
984C2×Q8—228no—
985C2×Q8—224no—
986C2×Q8—224no—
987C2×Q8—444no—
988C2×D4—118no—
989C2×D4—114no—
990C2×D4—114no—
991C2×D4—118no—
992C2×D4—114no—
993C2×D4—118no—
994C2×D4—114no—
995C2×D4—118no—
996C2×D4—228no—
997C2×D4—224no—
998C2×D4—224no—
999C2×D4—228no—
1000C2×D4—224no—
1001C2×D4—444no—
1002C22×C4—28no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—111no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—112no—
1011C22×C4—111no—
1012C22×C4—111no—
1013C22×C4—112no—
1014C22×C4—111no—
1015C22×C4—112no—
1016C22×C4—114no—
1017C22×C4—114no—
1018C22×C4—114no—
1019C22×C4—114no—
1020C22×C4—118no—
1021C22×C4—118no—
1022C22×C4—114no—
1023C22×C4—114no—
1024C22×C4—118no—
1025C22×C4—118no—
1026C22×C4—118no—
1027C22×C4—228no—
1028C22×C4—224no—
1029C22×C4—228no—
1030C22×C4—224no—
1031C22×C4—224no—
1032C22×C4—224no—
1033C22×C4—442no—
1034C22×C4—444no—
1035C22×C4—442no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4C23×D1114yes—
1039C22×C4C23×D1114yes—
1040C22×C4C23×D1118yes—
1041C22×C4C23×D1111yescharacteristic
1042C22×C4C23×D1111yescharacteristic
1043C22×C4C23×D1111yescharacteristic
1044C22×C4C23×D1112yes—
1045C22×C4C23×D1112yes—
1046C22×C4C23×D1112yes—
1047C22×C4C23×D1111yescharacteristic
1048C22×C4C23×D1111yescharacteristic
1049C22×C4C23×D1112yes—
1050C22×C4C23×D1114yes—
1051C22×C4C23×D1118yes—
1052C22×C4C23×D1111yescharacteristic
1053C4⋊C4—114no—
1054C4⋊C4—118no—
1055C4⋊C4—114no—
1056C4⋊C4—114no—
1057C4⋊C4—118no—
1058C4⋊C4—118no—
1059C4⋊C4—118no—
1060C4⋊C4—118no—
1061C4⋊C4—118no—
1062C4⋊C4—118no—
1063C4⋊C4—118no—
1064C4⋊C4—118no—
1065C4⋊C4—118no—
1066C4⋊C4—114no—
1067C4⋊C4—114no—
1068C4⋊C4—114no—
1069C4⋊C4—114no—
1070C4⋊C4—114no—
1071C4⋊C4—118no—
1072C4⋊C4—118no—
1073C4⋊C4—118no—
1074C4⋊C4—118no—
1075C4⋊C4—118no—
1076C4⋊C4—118no—
1077C4⋊C4C23×D1118yes—
1078C4⋊C4C23×D1118yes—
1079C4⋊C4C23×D1114yes—
1080C4⋊C4C23×D1118yes—
1081C4⋊C4C23×D1114yes—
1082C4⋊C4C23×D1114yes—
1083C4⋊C4C23×D1114yes—
1084C4⋊C4C23×D1118yes—
1085C4⋊C4C23×D1118yes—
1086C4⋊C4C23×D1118yes—
1087C4⋊C4C23×D1118yes—
1088C4⋊C4C23×D1118yes—
1089C4⋊C4C23×D1118yes—
1090C4⋊C4C23×D1118yes—
1091C22⋊C4—114no—
1092C22⋊C4—118no—
1093C22⋊C4—114no—
1094C22⋊C4—114no—
1095C22⋊C4—118no—
1096C22⋊C4—118no—
1097C22⋊C4—118no—
1098C22⋊C4—114no—
1099C22⋊C4—114no—
1100C22⋊C4—114no—
1101C22⋊C4—118no—
1102C22⋊C4—118no—
1103C22⋊C4—118no—
1104C22⋊C4—118no—
1105C22⋊C4—118no—
1106C22⋊C4—118no—
1107C22⋊C4—118no—
1108C22⋊C4—118no—
1109C22⋊C4—118no—
1110C42—114no—
1111C42—114no—
1112C42—114no—
1113C42—114no—
1114C42—114no—
1115C42—114no—
1116C42—118no—
1117C42—118no—
1118C42—118no—
1119C42—118no—
1120C42—118no—
1121C42C23×D1114yes—
1122C42C23×D1114yes—
1123C42C23×D1114yes—
1124C42C23×D1114yes—
1125C11C2×#351511yescharacteristic, complemented, Sylow
1126C23—22no—
1127C23—22no—
1128C23—114no—
1129C23—112no—
1130C23—112no—
1131C23—114no—
1132C23—222no—
1133C23—222no—
1134C23—222no—
1135C23—224no—
1136C23—222no—
1137C23—224no—
1138C23—224no—
1139C23—222no—
1140C23#41×D1114yes—
1141C23C24×D1112yes—
1142C23C24×D1111yescharacteristic
1143Q8—2216no—
1144Q8—228no—
1145Q8—228no—
1146Q8—448no—
1147D4—1116no—
1148D4—2216no—
1149D4—228no—
1150D4—228no—
1151D4—2216no—
1152D4—228no—
1153D4—448no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—28no—
1160C2×C4—216no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—28no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—114no—
1169C2×C4—112no—
1170C2×C4—112no—
1171C2×C4—112no—
1172C2×C4—114no—
1173C2×C4—112no—
1174C2×C4—112no—
1175C2×C4—112no—
1176C2×C4—114no—
1177C2×C4—114no—
1178C2×C4—228no—
1179C2×C4—2216no—
1180C2×C4—228no—
1181C2×C4—2216no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—224no—
1185C2×C4—224no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—224no—
1189C2×C4—222no—
1190C2×C4—228no—
1191C2×C4—228no—
1192C2×C4—444no—
1193C2×C4—448no—
1194C2×C4—444no—
1195C2×C4—448no—
1196C2×C4—448no—
1197C2×C4#6704014yes—
1198C2×C4C24×D1112yes—
1199C2×C4C24×D1112yes—
1200C2×C4C24×D1112yes—
1201C2×C4C24×D1114yes—
1202C2×C4C24×D1114yes—
1203C2×C4C24×D1114yes—
1204C2×C4C24×D1112yes—
1205C2×C4C24×D1112yes—
1206C2×C4C24×D1114yes—
1207C2×C4C24×D1112yes—
1208C22—22no—
1209C22—22no—
1210C22—28no—
1211C22—114no—
1212C22—222no—
1213C22—222no—
1214C22—228no—
1215C22—222no—
1216C22—224no—
1217C22—222no—
1218C22—224no—
1219C22—224no—
1220C22—222no—
1221C22—444no—
1222C22—448no—
1223C22C2×#6704012yes—
1224C22C2×#41×D1114yes—
1225C22C2×#41×D1112yes—
1226C22#1062345312yes—
1227C22C25×D1111yescharacteristic
1228C4—22no—
1229C4—24no—
1230C4—24no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—24no—
1236C4—24no—
1237C4—114no—
1238C4—222no—
1239C4—224no—
1240C4—222no—
1241C4—222no—
1242C4—224no—
1243C4—222no—
1244C4—224no—
1245C4—222no—
1246C4C2×#6704014yes—
1247C2—24no—
1248C2—224no—
1249C2—442no—
1250C2—444no—
1251C2#1308258814yesdirect product factor
1252C2C22×#41×D1111yescharacteristic
1253C2C22×#6704011yescharacteristic
1254C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#125C2
socleC23×C11C25
hypercenterC22×#125D11
hypocenterC11C2×#3515
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #13082588C2direct (N × H)
2. C2×#10623216C2semidirect
3. C2×#10623221C2semidirect
4. C2×#10623042C2semidirect
5. C2×#10623226C2semidirect
6. C2×#10623045C2semidirect
7. C2×#10623225C2semidirect
8. C2×#10623044C2semidirect
9. C2×#10623044C2semidirect
10. C2×#10623224C2semidirect
11. C2×#10623224C2semidirect
12. C2×#10623038C2semidirect
13. C2×#10623038C2semidirect
14. C2×#10623227C2semidirect
15. C2×#10623223C2semidirect
16. C2×#10623046C2semidirect
17. C2×#10623219C2semidirect
18. C2×#10623222C2semidirect
19. C2×#10623222C2semidirect
20. C2×#10623010C2semidirect
21. C2×D11×#125C2semidirect
22. C2×#10623035C2semidirect
23. C2×C4×#4339C2semidirect
24. C22×C11×#125C2semidirect
33. C2×C11×#125C22semidirect
55. #10623227C22semidirect
56. #10623226C22semidirect
57. #10623225C22semidirect
58. #10623224C22semidirect
59. #10623224C22semidirect
60. #10623223C22semidirect
61. #10623222C22semidirect
62. #10623222C22semidirect
63. #10623221C22semidirect
64. #10623219C22semidirect
65. D11×#125C22semidirect
66. #10623216C22semidirect
67. #10623046C22semidirect
68. #10623045C22semidirect
69. #10623044C22semidirect
70. #10623044C22semidirect
77. #10623042C22semidirect
87. #10623038C22semidirect
88. #10623038C22semidirect
98. #10623035C22semidirect
131. #10623010C22semidirect
134. C4×#4339C22semidirect
520. C22×#125D11semidirect
653. C2×#125C2×D11semidirect
967. C2×C11#3515semidirect
1125. C11C2×#3515semidirect
1251. C2#13082588direct (N × H)

Maximal subgroups

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

subgroupindex
#130825882
C2×#106232162
C2×#106232212
C2×#106230422
C2×#106232262
C2×#106230452
C2×#106232252
C2×#106230442
C2×#106232242
C2×#106230382
C2×#106232272
C2×#106232232
C2×#106230462
C2×#106232192
C2×#106232222
C2×#106230102
C2×D11×#1252
C2×#106230352
C2×C4×#43392
C22×C11×#1252
C2×#351511