Finite Group Databasebeta

← C2×#13079498 #15624459

Subgroups — C2×#13079498 #15624459

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2#13079498C2116yesmaximal, direct product factor
3C2×#10622657C211yesmaximal, characteristic, complemented
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622656C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622664C211yesmaximal, characteristic, complemented
10C2×#10622661C211yesmaximal, characteristic, complemented
11C2×#10622660C211yesmaximal, characteristic, complemented
12C2×#10622660C211yesmaximal, characteristic, complemented
13C2×#10622841C211yesmaximal, characteristic, complemented
14C2×#10622840C211yesmaximal, characteristic, complemented
15C2×#10622847C211yesmaximal, characteristic, complemented
16C2×C11×#536C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C11×#536—24no—
21C11×#536C2218yescomplemented
22C2×C11×C4⋊Q8—21no—
23C2×C11×#124—21no—
24C2×C11×#123—21no—
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31#10623364—24no—
32#10623364C2218yes—
33C2×#66999—21no—
34C22×#4326C2211yescharacteristic
35C22×#4326C2211yescharacteristic
36C22×#4325C2211yescharacteristic
37C22×#4325C2211yescharacteristic
38C2×#66992—21no—
39C2×#66992—21no—
40C2×#66991—21no—
41C2×#66983C2211yescharacteristic
42C2×#66983C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C2×#66977C2211yescharacteristic
45C2×#66977C2211yescharacteristic
46C22×#4318C2211yescharacteristic
47C23×C11⋊C8C2211yescharacteristic
48#10622847C2218yescomplemented
49#10622841C2218yescomplemented
50#10622840C2218yescomplemented
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58C2×C22⋊(C11⋊C8)C2211yescharacteristic
59#10622665C2218yescomplemented
60#10622664C2218yescomplemented
61#10622662C2218yescomplemented
62#10622661C2218yescomplemented
63#10622660C2218yescomplemented
64#10622660C2218yescomplemented
65#10622657C2218yescomplemented
66#10622656C2218yescomplemented
67#10622616C2218yescomplemented
68#10622609C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66874C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66873C2211yescharacteristic
73C2×#66872C2211yescharacteristic
74C2×#66872C2211yescharacteristic
75C2×#66871C2211yescharacteristic
76C2×#66871C2211yescharacteristic
77C2×C11×#41—42no—
78C2×C11×#41—42no—
79C2×C11×#41D414yes—
80C2×C11×#41C2314yes—
81C22×Q8×C11—21no—
82C22×Q8×C11—22no—
83C22×Q8×C11—42no—
84C22×Q8×C11—42no—
85C22×Q8×C11D411yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2314yes—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11D411yescharacteristic
91C22×D4×C11D411yescharacteristic
92C23×C4×C11—21no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C23×Dic11—21no—
100C2×#4339—22no—
101C2×#4339—42no—
102C2×#4339—42no—
103C2×#4339C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×Dic22C2311yescharacteristic
107C11×C4⋊Q8—28no—
108C11×#124—28no—
109C11×#123—28no—
110C11×#123—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8C2314yes—
116C11×C22⋊Q8C2314yes—
117C11×C22⋊Q8C2314yes—
118C11×C22⋊Q8C2314yes—
119C11×#117—22no—
120C11×#117C2314yes—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135#66999—28no—
136C2×#4326—42no—
137C2×#4326—42no—
138C2×#4326C2314yes—
139C2×#4326C2314yes—
140C2×#4325—42no—
141C2×#4325—42no—
142C2×#4325C2314yes—
143C2×#4325C2314yes—
144#66992—28no—
145#66992—28no—
146#66991—28no—
147#66983—22no—
148#66983—22no—
149#66983C2314yes—
150#66983C2314yes—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×C4⋊Dic11—21no—
154C2×C4⋊Dic11—22no—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×C4⋊Dic11C2314yes—
158#66977—22no—
159#66977—22no—
160#66977C2314yes—
161#66977C2314yes—
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×#4318—42no—
165C2×#4318C2314yes—
166C22×C11⋊C8—42no—
167C22×C11⋊C8C2311yescharacteristic
168C22×C11⋊C8C2311yescharacteristic
169C22×C11⋊C8C2311yescharacteristic
170C22×C11⋊C8C2311yescharacteristic
171C22×C11⋊C8C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176C22⋊(C11⋊C8)C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66872C2314yes—
185#66872C2314yes—
186#66871C2314yes—
187#66871C2314yes—
188C2×#3201—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C24×C11C2×D411yescharacteristic
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C11×#41—48no—
194C11×#41—44no—
195C11×#41—44no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—24no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—42no—
204C2×Q8×C11—44no—
205C2×Q8×C11—44no—
206C2×Q8×C11—44no—
207C2×Q8×C11—48no—
208C2×Q8×C11C2×D414yes—
209C2×Q8×C11C2412yes—
210C2×Q8×C11C2412yes—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11C2×D414yes—
215C2×D4×C11C2×D414yes—
216C2×D4×C11C2×D414yes—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—24no—
228C22×C4×C11—44no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2411yescharacteristic
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—82no—
244C2×C22⋊D11—82no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—24no—
249C22×Dic11—82no—
250#4339—44no—
251#4339—44no—
252#4339—48no—
253C2×D44—21no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—44no—
259C2×Dic22—21no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22C2412yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C42×C11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279#4326—44no—
280#4326—44no—
281#4325—44no—
282#4325—44no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285C4⋊Dic11—21no—
286C4⋊Dic11—21no—
287C4⋊Dic11—24no—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2412yes—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292#4318—44no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—44no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301C2×C11⋊C8C2412yes—
302C2×#537—111no—
303C2×#536D1111yescharacteristic, complemented
304#3201—1116no—
305C2×#484—111no—
306C2×#485—111no—
307C2×#482—111no—
308C2×#483—111no—
309C2×#470—111no—
310C2×#468—111no—
311C2×#467—111no—
312C2×#465—111no—
313C2×#452—111no—
314C2×#452—111no—
315C2×#451—111no—
316C2×#448—111no—
317C2×#408—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C22×D412yes—
328C23×C11C22×D412yes—
329C23×C11C22×D412yes—
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—44no—
340Q8×C11—48no—
341Q8×C11—42no—
342Q8×C11—42no—
343D4×C11—44no—
344D4×C11—44no—
345D4×C11—44no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—48no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—48no—
375C22⋊D11—84no—
376C22⋊D11—84no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—84no—
384D44—22no—
385D44—22no—
386D44—42no—
387C4×D11—48no—
388Dic22—22no—
389Dic22—22no—
390Dic22—42no—
391C11⋊C8—22no—
392C11⋊C8—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41C2×D1111yescharacteristic
397C23×Q8C2×D1111yescharacteristic
398C22×Q16—111no—
399C22×Q16—111no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×M16—111no—
403C23×C8—111no—
404#537—118no—
405#537—224no—
406#536—24no—
407#536C2×D1118yescomplemented
408C2×C4⋊Q8—21no—
409C2×#124—21no—
410C2×#123—21no—
411C2×#123—21no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×C22⋊Q8C2×D1111yescharacteristic
416C2×C22⋊Q8C2×D1111yescharacteristic
417C2×C22⋊Q8C2×D1111yescharacteristic
418C2×C22⋊Q8C2×D1111yescharacteristic
419C2×#121—111no—
420C2×#121—111no—
421C2×#121—221no—
422C2×#121—221no—
423C2×#121—221no—
424C2×#117C2×D1111yescharacteristic
425C22×C4⋊C4—111no—
426#485—118no—
427#484—118no—
428#483—118no—
429#482—118no—
430#470—118no—
431#468—118no—
432#467—118no—
433#465—118no—
434#452—118no—
435#452—118no—
436#451—118no—
437#448—118no—
438C2×#107—111no—
439C2×#107—111no—
440C2×#106—111no—
441C2×#106—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#103—111no—
446C2×#103—111no—
447C2×#103—111no—
448C2×#102—111no—
449C2×#102—111no—
450#408—118no—
451C2×C22⋊C8—111no—
452C2×C22⋊C8—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—44no—
465C22×C11—44no—
466C22×C11—44no—
467C22×C11#53412yes—
468C22×C11#57712yes—
469C22×C11#57812yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11#53412yes—
483C4×C11C2×H(5,𝔽2)11yescharacteristic
484C4×C11C2×H(5,𝔽2)11yescharacteristic
485Dic11—42no—
486Dic11—42no—
487Dic11—42no—
488C2×#41—42no—
489C2×#41—42no—
490C2×#41—114no—
491C2×#41—222no—
492C2×#41—442no—
493C2×#41—442no—
494C2×#41C22⋊D1114yes—
495C2×#41C22×D1114yes—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—42no—
499C22×Q8—42no—
500C22×Q8—111no—
501C22×Q8C22⋊D1111yescharacteristic
502C22×Q8C22×D1111yescharacteristic
503C22×Q8C22×D1111yescharacteristic
504C22×Q8C22×D1114yes—
505C22×D4—111no—
506C22×D4—221no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4C22⋊D1111yescharacteristic
510C22×D4C22⋊D1111yescharacteristic
511C22×D4C22⋊D1111yescharacteristic
512C23×C4—21no—
513C23×C4—221no—
514C23×C4—221no—
515C23×C4C22×D1111yescharacteristic
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C2×Q16—114no—
519C2×Q16—114no—
520C2×Q16—442no—
521C2×Q16—442no—
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—442no—
525C2×SD16—442no—
526C2×M16—114no—
527C2×M16—442no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—114no—
533C22×C8—442no—
534C4⋊Q8—28no—
535#124—28no—
536#123—28no—
537#123—28no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—114no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547C22⋊Q8C22×D1114yes—
548C22⋊Q8C22×D1114yes—
549C22⋊Q8C22×D1114yes—
550C22⋊Q8C22×D1114yes—
551#121—114no—
552#121—114no—
553#121—228no—
554#121—228no—
555#121—228no—
556#121—222no—
557#121—222no—
558#117—22no—
559#117C22×D1114yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C42—21no—
583#107—114no—
584#107—114no—
585#106—114no—
586#106—114no—
587#103—114no—
588#103—114no—
589#103—114no—
590#103—114no—
591#103—114no—
592#103—114no—
593#102—114no—
594#102—114no—
595C22⋊C8—114no—
596C22⋊C8—114no—
597C22⋊C8—114no—
598C22⋊C8—114no—
599C2×C11—42no—
600C2×C11—42no—
601C2×C11—42no—
602C2×C11#320114yescomplemented
603C2×C11C2×#53411yescharacteristic
604C2×C11C2×#57711yescharacteristic
605C2×C11C2×#57811yescharacteristic
606D11—82no—
607C24—221no—
608C24C2×C22⋊D1111yescharacteristic
609C24C2×C22⋊D1111yescharacteristic
610C24C2×C22⋊D1111yescharacteristic
611#41—44no—
612#41—44no—
613#41—48no—
614#41—444no—
615#41—444no—
616#41—448no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—24no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—42no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—48no—
629C2×Q8—112no—
630C2×Q8—221no—
631C2×Q8—222no—
632C2×Q8—222no—
633C2×Q8C2×C22⋊D1114yes—
634C2×Q8C23×D1112yes—
635C2×Q8C23×D1112yes—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—112no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—222no—
644C2×D4—222no—
645C2×D4—221no—
646C2×D4—444no—
647C2×D4—882no—
648C2×D4—882no—
649C2×D4C2×C22⋊D1114yes—
650C2×D4C2×C22⋊D1114yes—
651C2×D4C2×C22⋊D1114yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—44no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—224no—
668C22×C4—224no—
669C22×C4—444no—
670C22×C4—882no—
671C22×C4C2×C22⋊D1112yes—
672C22×C4C2×C22⋊D1112yes—
673C22×C4C2×C22⋊D1112yes—
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681Q16—444no—
682Q16—444no—
683SD16—444no—
684SD16—444no—
685M16—444no—
686C2×C8—112no—
687C2×C8—112no—
688C2×C8—112no—
689C2×C8—112no—
690C2×C8—222no—
691C2×C8—222no—
692C2×C8—222no—
693C2×C8—222no—
694C2×C8—444no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—224no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—224no—
707C4⋊C4—224no—
708C4⋊C4C23×D1112yes—
709C4⋊C4C23×D1112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C42—24no—
720C11C2×#320111yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—222no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23C22×C22⋊D1112yes—
735C23C22×C22⋊D1112yes—
736C23C22×C22⋊D1112yes—
737C23C22×C22⋊D1111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—222no—
747Q8—222no—
748Q8—442no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—222no—
753D4—222no—
754D4—448no—
755D4—442no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—448no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—884no—
787C2×C4#6703712yes—
788C2×C4#6703712yes—
789C2×C4C22×C22⋊D1112yes—
790C2×C4C22×C22⋊D1112yes—
791C2×C4C22×C22⋊D1112yes—
792C2×C4C22×C22⋊D1111yescharacteristic
793C2×C4C24×D1111yescharacteristic
794C8—222no—
795C8—222no—
796C8—222no—
797C8—222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—884no—
814C22#1062333512yes—
815C22#1062336812yes—
816C22#1062336912yes—
817C22C23×C22⋊D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4#1062333512yes—
829C4C2×#6703711yescharacteristic
830C4C2×#6703711yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—882no—
835C2#1307949814yesdirect product factor
836C2C2×#1062333511yescharacteristic
837C2C2×#1062336811yescharacteristic
838C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#536D11
hypocenterC11C2×#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #13079498C2direct (N × H)
3. C2×#10622657C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622656C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622664C2semidirect
10. C2×#10622661C2semidirect
11. C2×#10622660C2semidirect
12. C2×#10622660C2semidirect
13. C2×#10622841C2semidirect
14. C2×#10622840C2semidirect
15. C2×#10622847C2semidirect
16. C2×C11×#536C2semidirect
21. C11×#536C22semidirect
48. #10622847C22semidirect
49. #10622841C22semidirect
50. #10622840C22semidirect
59. #10622665C22semidirect
60. #10622664C22semidirect
61. #10622662C22semidirect
62. #10622661C22semidirect
63. #10622660C22semidirect
64. #10622660C22semidirect
65. #10622657C22semidirect
66. #10622656C22semidirect
67. #10622616C22semidirect
68. #10622609C22semidirect
303. C2×#536D11semidirect
407. #536C2×D11semidirect
602. C2×C11#3201semidirect
720. C11C2×#3201semidirect
835. C2#13079498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
#130794982
C2×#106226572
C2×#106226092
C2×#106226162
C2×#106226562
C2×#106226652
C2×#106226622
C2×#106226642
C2×#106226612
C2×#106226602
C2×#106228412
C2×#106228402
C2×#106228472
C2×C11×#5362
C2×#320111