Finite Group Databasebeta

← C2×#13079491 #15624452

Subgroups — C2×#13079491 #15624452

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×#10623139C211yesmaximal, characteristic
2C2×#10623159C211yesmaximal, characteristic, complemented
3#13079491C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622480C211yesmaximal, characteristic, complemented
6C2×#10622397C211yesmaximal, characteristic, complemented
7C2×#10622475C211yesmaximal, characteristic, complemented
8C2×#10622665C211yesmaximal, characteristic, complemented
9C2×#10622655C211yesmaximal, characteristic, complemented
10C2×#10622729C211yesmaximal, characteristic, complemented
11C2×#10622396C211yesmaximal, characteristic, complemented
12C2×#10622786C211yesmaximal, characteristic, complemented
13C2×#10622421C211yesmaximal, characteristic, complemented
14C2×#10622783C211yesmaximal, characteristic, complemented
15C2×#10622723C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66992—21no—
27C2×#66991—21no—
28C2×#66991C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×Dic44C2211yescharacteristic
34#10623159—24no—
35#10623159C2218yescomplemented
36#10623139—24no—
37#10623139C2218yes—
38C2×#66950C2211yescharacteristic
39C2×#66950C2211yescharacteristic
40C2×#66947—21no—
41C2×#66945C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66941—21no—
44C2×#66938—21no—
45C2×#66937—21no—
46C2×#66936—21no—
47C2×#66931—21no—
48C11×#465C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622786C2218yescomplemented
55#10622783C2218yescomplemented
56#10622729C2218yescomplemented
57#10622723C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65#10622665C2218yescomplemented
66#10622655C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622480C2218yescomplemented
72#10622475C2218yescomplemented
73#10622422C2218yescomplemented
74#10622421C2218yescomplemented
75#10622397C2218yescomplemented
76#10622396C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11D411yescharacteristic
84C22×C22⋊D11D411yescharacteristic
85C23×Dic11—21no—
86C2×Q8×D11—22no—
87C2×Q8×D11—42no—
88C2×Q8×D11—42no—
89C2×Q8×D11C2314yes—
90C2×#4341—22no—
91C2×#4341—42no—
92C2×#4341—42no—
93C2×#4341C2314yes—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339D414yes—
97C2×#4339C2314yes—
98C22×D44D411yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×Dic22—21no—
104C22×Dic22D411yescharacteristic
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2311yescharacteristic
107C2×C11×SD16—42no—
108C2×C11×SD16C2314yes—
109C22×C8×C11—42no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2314yes—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8C2314yes—
115C11×#121—22no—
116C11×#121C2314yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125#66999—22no—
126#66999C2314yes—
127C2×#4326—42no—
128C2×#4326C2314yes—
129#66992—28no—
130#66991—28no—
131#66991—22no—
132#66991C2314yes—
133C2×#4324—42no—
134C2×#4324C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977—22no—
145#66977C2314yes—
146#66977C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×#4318—42no—
153C2×#4318C2314yes—
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C2×Dic44—42no—
157C2×Dic44C2314yes—
158#66950—22no—
159#66950—22no—
160#66950C2314yes—
161#66950C2314yes—
162#66947—28no—
163#66945—22no—
164#66945C2314yes—
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2314yes—
167#66941—28no—
168#66938—28no—
169#66937—28no—
170#66936—28no—
171#66931—28no—
172C11×#106C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175#66899C2314yes—
176#66896C2314yes—
177(C2×D11)⋊C8C2314yes—
178(C2×D11)⋊C8C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66882C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66874C2314yes—
185#66874C2314yes—
186#66872C2314yes—
187#66871C2314yes—
188C2×#3201—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11C2×D411yescharacteristic
192C23×D11C2×D411yescharacteristic
193C2×Q8×C11—21no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×D4×C11—24no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—82no—
202C2×D4×C11C2412yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—42no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—82no—
218C2×C22⋊D11C2×D414yes—
219C2×C22⋊D11C2×D414yes—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—44no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228Q8×D11—44no—
229Q8×D11—44no—
230Q8×D11—48no—
231#4341—44no—
232#4341—44no—
233#4341—48no—
234#4339—48no—
235#4339—44no—
236#4339—44no—
237C2×D44—42no—
238C2×D44C2×D414yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—44no—
246C2×C4×D11—82no—
247C2×C4×D11C2×D412yes—
248C2×C4×D11C2×D412yes—
249C2×C4×D11C2412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—24no—
252C2×Dic22—21no—
253C2×Dic22—21no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22—42no—
259C2×Dic22—44no—
260C2×Dic22C2×D414yes—
261C2×Dic22C2412yes—
262C2×Dic22C2412yes—
263C11×SD16—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—44no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279#4326—44no—
280#4324—44no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285C4⋊Dic11—24no—
286C4⋊Dic11—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295C4×Dic11—24no—
296#4318—44no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301Dic44—44no—
302C2×#537—111no—
303C2×#536—111no—
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×#465D1111yescharacteristic, complemented
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—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11C22×D412yes—
326C23×C11C22×D411yescharacteristic
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11C22×D412yes—
334C22×D11C22×D412yes—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—42no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—42no—
341D4×C11—84no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—44no—
358C22⋊D11—44no—
359C22⋊D11—48no—
360C22⋊D11—84no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—48no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374D44—44no—
375C4×D11—24no—
376C4×D11—24no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—48no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—22no—
386Dic22—22no—
387Dic22—44no—
388Dic22—48no—
389Dic22—42no—
390Dic22—42no—
391C8×C11—22no—
392C8×C11—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41—111no—
397C23×Q8—111no—
398C22×Q16—111no—
399C22×Q16—111no—
400C22×SD16—111no—
401C22×SD16C2×D1111yescharacteristic
402C22×M16—111no—
403C23×C8C2×D1111yescharacteristic
404#537—118no—
405#537—224no—
406#536—118no—
407#536—224no—
408C2×C4⋊Q8—221no—
409C2×#124—221no—
410C2×#123—221no—
411C2×#123—221no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—221no—
418C2×C22⋊Q8C2×D1111yescharacteristic
419C2×#121—111no—
420C2×#121—221no—
421C2×#121—221no—
422C2×#121—221no—
423C2×#121C2×D1111yescharacteristic
424C2×#117—111no—
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#465C2×D1118yescomplemented
434#452—118no—
435#452—118no—
436#451—118no—
437#448—118no—
438C2×#107—111no—
439C2×#107—111no—
440C2×#106—111no—
441C2×#106C2×D1111yescharacteristic
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#103—111no—
446C2×#103—111no—
447C2×#103C2×D1111yescharacteristic
448C2×#102—111no—
449C2×#102C2×D1111yescharacteristic
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—44no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—84no—
463C22×C11#53412yes—
464C22×C11#57712yes—
465C22×C11#57812yes—
466C22×C11C23×D411yescharacteristic
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—44no—
474C2×D11—44no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#53412yes—
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487Dic11—42no—
488C2×#41—114no—
489C2×#41—114no—
490C2×#41—114no—
491C2×#41—222no—
492C2×#41—442no—
493C2×#41—442no—
494C2×#41—442no—
495C2×#41—442no—
496C22×Q8—111no—
497C22×Q8—114no—
498C22×Q8—111no—
499C22×Q8—111no—
500C22×Q8—221no—
501C22×Q8—222no—
502C22×Q8—442no—
503C22×Q8—442no—
504C22×Q8C22×D1111yescharacteristic
505C22×D4—21no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4C22×D1111yescharacteristic
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4—221no—
517C23×C4C22×D1111yescharacteristic
518C2×Q16—114no—
519C2×Q16—114no—
520C2×Q16—442no—
521C2×Q16—442no—
522C2×SD16—42no—
523C2×SD16—114no—
524C2×SD16—442no—
525C2×SD16C22×D1114yes—
526C2×M16—114no—
527C2×M16—442no—
528C22×C8—42no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1114yes—
534C4⋊Q8—228no—
535#124—228no—
536#123—228no—
537#123—228no—
538C22⋊Q8—22no—
539C22⋊Q8—114no—
540C22⋊Q8—114no—
541C22⋊Q8—114no—
542C22⋊Q8—114no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547C22⋊Q8—222no—
548C22⋊Q8—222no—
549C22⋊Q8—222no—
550C22⋊Q8C22×D1114yes—
551#121—22no—
552#121—114no—
553#121—228no—
554#121—222no—
555#121—228no—
556#121—228no—
557#121C22×D1114yes—
558#117—114no—
559#117—222no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—221no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
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—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C42—221no—
583#107—114no—
584#107—114no—
585#106—114no—
586#106C22×D1114yes—
587#103—114no—
588#103—114no—
589#103—114no—
590#103—114no—
591#103—114no—
592#103C22×D1114yes—
593#102—114no—
594#102C22×D1114yes—
595C22⋊C8—114no—
596C22⋊C8—114no—
597C22⋊C8—114no—
598C22⋊C8—114no—
599C2×C11—42no—
600C2×C11—82no—
601C2×C11#320114yescomplemented
602C2×C11C2×#53411yescharacteristic
603C2×C11C2×#57711yescharacteristic
604C2×C11C2×#57811yescharacteristic
605D11—42no—
606D11—42no—
607C24—21no—
608C24—111no—
609C24—111no—
610C24D4×D1111yescharacteristic
611#41—448no—
612#41—444no—
613#41—444no—
614#41—444no—
615#41—444no—
616#41—448no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—114no—
621C2×Q8—112no—
622C2×Q8—112no—
623C2×Q8—224no—
624C2×Q8—221no—
625C2×Q8—221no—
626C2×Q8—222no—
627C2×Q8—222no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×Q8—442no—
631C2×Q8—444no—
632C2×Q8—444no—
633C2×Q8—444no—
634C2×Q8—448no—
635C2×Q8C23×D1112yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—82no—
641C2×D4—114no—
642C2×D4—114no—
643C2×D4—114no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—444no—
650C2×D4—882no—
651C2×D4C23×D1112yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4—882no—
677C22×C4D4×D1112yes—
678C22×C4D4×D1111yescharacteristic
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681Q16—444no—
682Q16—444no—
683SD16—44no—
684SD16—444no—
685M16—444no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—44no—
689C2×C8—112no—
690C2×C8—112no—
691C2×C8—222no—
692C2×C8—222no—
693C2×C8C23×D1112yes—
694C2×C8C23×D1112yes—
695C4⋊C4—24no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—112no—
699C4⋊C4—112no—
700C4⋊C4—224no—
701C4⋊C4—224no—
702C4⋊C4—224no—
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—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C42—224no—
720C11C2×#320111yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—112no—
729C23—112no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23C2×D4×D1112yes—
737C23C2×D4×D1111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741Q8—222no—
742Q8—222no—
743Q8—222no—
744Q8—222no—
745Q8—444no—
746Q8—448no—
747Q8—442no—
748Q8—442no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—84no—
753D4—444no—
754D4—444no—
755D4—444no—
756D4—448no—
757D4—884no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—112no—
769C2×C4—112no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—224no—
773C2×C4—224no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—448no—
783C2×C4—448no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—884no—
789C2×C4C2×D4×D1112yes—
790C2×C4C2×D4×D1111yescharacteristic
791C2×C4#6703712yes—
792C2×C4#6704212yes—
793C2×C4C24×D1111yescharacteristic
794C8—22no—
795C8—22no—
796C8—222no—
797C8—222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—84no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—222no—
811C22—222no—
812C22—444no—
813C22—444no—
814C22#1062313612yes—
815C22#1062329312yes—
816C22#1062330212yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4#1062313612yes—
829C4C2×#6703711yescharacteristic
830C4C2×#6704211yescharacteristic
831C2—42no—
832C2—82no—
833C2—442no—
834C2—442no—
835C2#1307949114yesdirect product factor
836C2C2×#1062313611yescharacteristic
837C2C2×#1062329311yescharacteristic
838C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×#10623139C2
hypercenterC2×#465D11
hypocenterC11C2×#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#10623159C2semidirect
3. #13079491C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622475C2semidirect
8. C2×#10622665C2semidirect
9. C2×#10622655C2semidirect
10. C2×#10622729C2semidirect
11. C2×#10622396C2semidirect
12. C2×#10622786C2semidirect
13. C2×#10622421C2semidirect
14. C2×#10622783C2semidirect
15. C2×#10622723C2semidirect
16. C2×C11×#465C2semidirect
35. #10623159C22semidirect
48. C11×#465C22semidirect
54. #10622786C22semidirect
55. #10622783C22semidirect
56. #10622729C22semidirect
57. #10622723C22semidirect
65. #10622665C22semidirect
66. #10622655C22semidirect
71. #10622480C22semidirect
72. #10622475C22semidirect
73. #10622422C22semidirect
74. #10622421C22semidirect
75. #10622397C22semidirect
76. #10622396C22semidirect
312. C2×#465D11semidirect
433. #465C2×D11semidirect
601. C2×C11#3201semidirect
720. C11C2×#3201semidirect
835. C2#13079491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231392
C2×#106231592
#130794912
C2×#106224222
C2×#106224802
C2×#106223972
C2×#106224752
C2×#106226652
C2×#106226552
C2×#106227292
C2×#106223962
C2×#106227862
C2×#106224212
C2×#106227832
C2×#106227232
C2×C11×#4652
C2×#320111