Finite Group Databasebeta

← C2×#13078144 #15620686

Subgroups — C2×#13078144 #15620686

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic
2C22×Q16×D11C211yesmaximal, characteristic, complemented
3C2×#10623206C211yesmaximal, characteristic
4C2×#10623103C211yesmaximal, characteristic, complemented
5#13078144C2116yesmaximal, direct product factor
6C2×#10622380C211yesmaximal, characteristic, complemented
7C2×#10622779C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622462C211yesmaximal, characteristic, complemented
10C2×#10622644C211yesmaximal, characteristic, complemented
11C2×#10622406C211yesmaximal, characteristic, complemented
12C2×#10622795C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×Q16×D11—28no—
32C2×Q16×D11C2218yescomplemented
33C2×#66968—28no—
34C2×#66968C2218yes—
35C22×Dic44C2211yescharacteristic
36C22×Dic44C2211yescharacteristic
37C22×#4313C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623206—24no—
40#10623206C2218yes—
41#10623103—24no—
42#10623103C2218yescomplemented
43C2×#66945—21no—
44C2×#66945C2211yescharacteristic
45C2×#66940—21no—
46C2×#66940C2211yescharacteristic
47C2×#66936—21no—
48C2×#66936—21no—
49C2×#66931—21no—
50C2×#66931—21no—
51C2×#66925—21no—
52C2×#66925C2211yescharacteristic
53C2×#66922C2211yescharacteristic
54C2×C4×Dic22—21no—
55C2×C4×Dic22C2211yescharacteristic
56C11×#464C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic
58C2×C11×#103C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62#10622795C2218yescomplemented
63#10622779C2218yescomplemented
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×Dic11⋊C8C2211yescharacteristic
68#10622667C2218yescomplemented
69#10622644C2218yescomplemented
70C2×#66874C2211yescharacteristic
71C2×#66874C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73#10622462C2218yescomplemented
74#10622452C2218yescomplemented
75#10622415C2218yescomplemented
76#10622406C2218yescomplemented
77#10622385C2218yes—
78#10622380C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×Q8×D11—22no—
85C2×Q8×D11—22no—
86C2×Q8×D11—24no—
87C2×Q8×D11—24no—
88C2×Q8×D11—24no—
89C2×Q8×D11D418yes—
90C2×Q8×D11C2314yes—
91C2×Q8×D11C2314yes—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—24no—
95C2×#4341C2314yes—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22—21no—
101C22×Dic22C2311yescharacteristic
102C22×Dic22C2311yescharacteristic
103C22×Dic22C2311yescharacteristic
104C2×C11×Q16—24no—
105C2×C11×Q16C2314yes—
106C2×C11×SD16—24no—
107C2×C11×SD16C2314yes—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×#124—22no—
111C11×#124C2314yes—
112C4×Q8×C11—22no—
113C4×Q8×C11C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122Q8×Dic11—22no—
123Q8×Dic11C2314yes—
124#66997—22no—
125#66997C2314yes—
126C2×#4326—24no—
127C2×#4326—24no—
128C2×#4326—24no—
129C2×#4326C2314yes—
130C2×#4326C2314yes—
131C2×#4326C2314yes—
132#66989—22no—
133#66989C2314yes—
134C2×#4324—24no—
135C2×#4324C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4D411yescharacteristic
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156Q16×D11—232no—
157#66968—232no—
158C2×Dic44—24no—
159C2×Dic44—24no—
160C2×Dic44C2314yes—
161C2×Dic44C2314yes—
162C2×#4313—24no—
163C2×#4313C2314yes—
164C2×C8×D11—24no—
165C2×C8×D11C2314yes—
166#66945—22no—
167#66945—28no—
168#66945C2314yes—
169#66940—28no—
170#66940—22no—
171#66940C2314yes—
172#66936—28no—
173#66936—28no—
174#66931—28no—
175#66931—28no—
176#66925—28no—
177#66925D414yes—
178#66925C2314yes—
179#66922—22no—
180#66922C2314yes—
181C4×Dic22—22no—
182C4×Dic22—28no—
183C4×Dic22C2314yes—
184C11×C4⋊C8C2314yes—
185C11×#103C2314yes—
186C11×#102C2314yes—
187#66899C2314yes—
188#66896C2314yes—
189#66880C2314yes—
190#66880C2314yes—
191Dic11⋊C8C2314yes—
192Dic11⋊C8C2314yes—
193#66874C2314yes—
194#66874C2314yes—
195C4⋊(C11⋊C8)C2314yes—
196C2×#3044—111nomaximal, Sylow
197C24×C11—21no—
198C23×D11C2×D411yescharacteristic
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11C2×D414yes—
205C2×Q8×C11C2412yes—
206C2×Q8×C11C2412yes—
207C2×D4×C11—22no—
208C2×D4×C11—21no—
209C2×D4×C11—22no—
210C2×D4×C11C2412yes—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—44no—
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228Q8×D11—216no—
229Q8×D11—28no—
230Q8×D11—28no—
231Q8×D11—28no—
232Q8×D11—48no—
233Q8×D11C2×D4116yes—
234#4341—28no—
235#4341—28no—
236#4341—48no—
237C2×C4×D11—28no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—44no—
241C2×C4×D11C2×D414yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11#4114yes—
244C2×C4×D11C2412yes—
245C2×Dic22—28no—
246C2×Dic22—24no—
247C2×Dic22—24no—
248C2×Dic22—21no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—21no—
252C2×Dic22—21no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22—44no—
257C2×Dic22C2×D414yes—
258C2×Dic22C2412yes—
259C2×Dic22C2412yes—
260C2×Dic22C2412yes—
261C11×Q16—28no—
262C11×SD16—28no—
263C2×C8×C11—22no—
264C2×C8×C11—22no—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C2412yes—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C42×C11—24no—
273C42×C11C2×D412yes—
274C42×C11C2412yes—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277#4326—28no—
278#4326—28no—
279#4326—28no—
280#4324—28no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4C2×D414yes—
283(C2×D11)⋊C4C2×D414yes—
284C4⋊Dic11—24no—
285C4⋊Dic11—21no—
286C4⋊Dic11—24no—
287C4⋊Dic11—24no—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4C2×D414yes—
294Dic11⋊C4C2×D414yes—
295C4×Dic11—24no—
296C4×Dic11—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C4×Dic11C2×D412yes—
300C4×Dic11C2412yes—
301C2×C11⋊C8—22no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8C2412yes—
304C2×C11⋊C8C2412yes—
305Dic44—28no—
306Dic44—28no—
307#4313—28no—
308C8×D11—28no—
309C22×#137—111no—
310C23×Q16—111no—
311C2×#536—111no—
312C2×#519—111no—
313#3044—1116no—
314C2×#464—111no—
315C2×#464—111no—
316C2×#464—111no—
317C2×#464D1111yescharacteristic, complemented
318C2×#462—111no—
319C2×#462—111no—
320C2×#462—111no—
321C2×#462—111no—
322C2×#424—111no—
323C2×#419—111no—
324C2×#416—111no—
325C23×C11—22no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11C22×D411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11#12114yes—
333C22×D11C22×D412yes—
334Q8×C11—24no—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339Q8×C11C22×D414yes—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—42no—
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×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D412yes—
355C2×C4×C11C2×#4112yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—48no—
358C2×Dic11—24no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—48no—
369C2×Dic11#12114yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373C4×D11—216no—
374C4×D11—48no—
375C4×D11#12118yes—
376C4×D11C22×D414yes—
377C4×D11C2×#4114yes—
378Dic22—24no—
379Dic22—22no—
380Dic22—216no—
381Dic22—22no—
382Dic22—22no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386Dic22—42no—
387Dic22—48no—
388Dic22C22×D414yes—
389C8×C11—22no—
390C8×C11—22no—
391C11⋊C8—22no—
392C11⋊C8—22no—
393C22×#41—111no—
394C23×Q8—111no—
395C23×Q8—111no—
396C2×#137—118no—
397C2×#137—228no—
398C22×Q16—111no—
399C22×Q16—111no—
400C22×Q16—111no—
401C22×Q16—118no—
402C22×Q16—111no—
403C22×Q16—111no—
404C22×Q16—228no—
405C22×Q16C2×D1111yescharacteristic
406C22×SD16—111no—
407C22×SD16C2×D1111yescharacteristic
408C22×M16—111no—
409C23×C8—111no—
410#536—118no—
411#536—224no—
412C2×C4⋊Q8—111no—
413C2×C4⋊Q8—111no—
414C2×#124—111no—
415C2×#124C2×D1111yescharacteristic
416C2×#123—221no—
417C2×#123—221no—
418C2×C22⋊Q8—221no—
419C2×C22⋊Q8—221no—
420#519—118no—
421#519—224no—
422C2×C4×Q8—111no—
423C2×C4×Q8—111no—
424C2×C4×Q8—111no—
425C2×C4×Q8—221no—
426C2×C4×Q8—221no—
427C2×C4×Q8C2×D1111yescharacteristic
428C2×#117—111no—
429C2×#117—111no—
430C2×#117—221no—
431C2×#117—221no—
432#464—118no—
433#464—118no—
434#464—118no—
435#464C2×D1118yescomplemented
436#462—118no—
437#462—118no—
438#462—118no—
439#462—118no—
440#424—118no—
441C2×C4⋊C8—111no—
442C2×C4⋊C8—111no—
443C2×C4⋊C8—111no—
444C2×C4⋊C8C2×D1111yescharacteristic
445#419—118no—
446#416—118no—
447C2×#103—111no—
448C2×#103—111no—
449C2×#103—111no—
450C2×#103—111no—
451C2×#103—111no—
452C2×#103C2×D1111yescharacteristic
453C2×#102—111no—
454C2×#102C2×D1111yescharacteristic
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—84no—
459C22×C11C2×#12112yes—
460C22×C11#57812yes—
461C22×C11#57812yes—
462C22×C11C23×D411yescharacteristic
463C2×D11—28no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11C2×#12114yes—
467C4×C11—24no—
468C4×C11—22no—
469C4×C11—22no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11C2×#12112yes—
473C4×C11C23×D411yescharacteristic
474C4×C11C22×#4111yescharacteristic
475Dic11—24no—
476Dic11—22no—
477Dic11—22no—
478Dic11—42no—
479Dic11—42no—
480Dic11—42no—
481Dic11C2×#12114yes—
482C2×#41—114no—
483C2×#41—222no—
484C2×#41—224no—
485C2×#41—224no—
486C22×Q8—118no—
487C22×Q8—114no—
488C22×Q8—114no—
489C22×Q8—111no—
490C22×Q8—111no—
491C22×Q8—111no—
492C22×Q8—221no—
493C22×Q8—221no—
494C22×Q8—222no—
495C22×Q8—224no—
496C22×Q8—222no—
497C22×Q8—224no—
498C22×Q8—224no—
499C22×Q8C22×D1111yescharacteristic
500C22×Q8C22×D1111yescharacteristic
501C22×D4—221no—
502C22×D4C22×D1111yescharacteristic
503C23×C4—111no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507#137—2232no—
508C2×Q16—24no—
509C2×Q16—114no—
510C2×Q16—114no—
511C2×Q16—114no—
512C2×Q16—114no—
513C2×Q16—114no—
514C2×Q16—224no—
515C2×Q16—224no—
516C2×Q16—2232no—
517C2×Q16—224no—
518C2×Q16—224no—
519C2×Q16—224no—
520C2×Q16C22×D1114yes—
521C2×SD16—24no—
522C2×SD16—114no—
523C2×SD16—224no—
524C2×SD16C22×D1114yes—
525C2×M16—114no—
526C2×M16—224no—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8—114no—
530C22×C8—224no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C4⋊Q8—114no—
534C4⋊Q8—114no—
535C4⋊Q8—222no—
536C4⋊Q8—222no—
537#124—22no—
538#124—114no—
539#124—222no—
540#124C22×D1114yes—
541#123—228no—
542#123—228no—
543C22⋊Q8—228no—
544C22⋊Q8—228no—
545C4×Q8—22no—
546C4×Q8—114no—
547C4×Q8—114no—
548C4×Q8—114no—
549C4×Q8—228no—
550C4×Q8—222no—
551C4×Q8—222no—
552C4×Q8—228no—
553C4×Q8—222no—
554C4×Q8C22×D1114yes—
555#117—114no—
556#117—114no—
557#117—114no—
558#117—228no—
559#117—228no—
560#117—222no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
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⋊C4—221no—
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C42—21no—
581C2×C42—111no—
582C2×C42—221no—
583C2×C42—221no—
584C2×C42—221no—
585C2×C42—221no—
586C2×C42C22×D1111yescharacteristic
587C4⋊C8—114no—
588C4⋊C8—114no—
589C4⋊C8—114no—
590C4⋊C8C22×D1114yes—
591#103—114no—
592#103—114no—
593#103—114no—
594#103—114no—
595#103—114no—
596#103C22×D1114yes—
597#102—114no—
598#102C22×D1114yes—
599C2×C11—82no—
600C2×C11#304414yescomplemented
601C2×C11C22×#12111yescharacteristic
602C2×C11C2×#57811yescharacteristic
603C2×C11C2×#57811yescharacteristic
604D11—24no—
605C24—21no—
606C24—111no—
607#41—228no—
608#41—228no—
609#41—448no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—1116no—
616C2×Q8—114no—
617C2×Q8—112no—
618C2×Q8—112no—
619C2×Q8—112no—
620C2×Q8—224no—
621C2×Q8—228no—
622C2×Q8—224no—
623C2×Q8—2216no—
624C2×Q8—228no—
625C2×Q8—228no—
626C2×Q8—228no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×Q8—221no—
630C2×Q8—222no—
631C2×Q8—222no—
632C2×Q8—222no—
633C2×Q8—222no—
634C2×Q8—222no—
635C2×Q8—444no—
636C2×Q8—448no—
637C2×Q8D4×D1114yes—
638C2×Q8C23×D1112yes—
639C2×Q8C23×D1112yes—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—224no—
644C2×D4—444no—
645C2×D4C23×D1112yes—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—111no—
650C22×C4—112no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—224no—
657C22×C4—228no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—444no—
665C22×C4—444no—
666C22×C4D4×D1111yescharacteristic
667C22×C4D4×D1111yescharacteristic
668C22×C4C23×D1111yescharacteristic
669Q16—28no—
670Q16—228no—
671Q16—228no—
672Q16—228no—
673Q16—228no—
674Q16—228no—
675SD16—28no—
676SD16—228no—
677M16—228no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—228no—
683C2×C8—222no—
684C2×C8—222no—
685C2×C8C23×D1112yes—
686C2×C8C23×D1112yes—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—114no—
690C4⋊C4—114no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—224no—
696C4⋊C4—221no—
697C4⋊C4—224no—
698C4⋊C4—224no—
699C4⋊C4—224no—
700C4⋊C4C23×D1112yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—114no—
704C22⋊C4—114no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C42—24no—
709C42—112no—
710C42—112no—
711C42—224no—
712C42—224no—
713C42—224no—
714C42—224no—
715C42D4×D1112yes—
716C42C23×D1112yes—
717C11C2×#304411yescharacteristic, complemented, Sylow
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—114no—
723C23—112no—
724C23—222no—
725C23—222no—
726C23C2×D4×D1111yescharacteristic
727Q8—24no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—42no—
732Q8—114no—
733Q8—2216no—
734Q8—224no—
735Q8—222no—
736Q8—222no—
737Q8—222no—
738Q8—222no—
739Q8—222no—
740Q8—448no—
741Q8—442no—
742Q8—442no—
743Q8C2×D4×D1114yes—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—448no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—114no—
757C2×C4—112no—
758C2×C4—118no—
759C2×C4—114no—
760C2×C4—114no—
761C2×C4—112no—
762C2×C4—112no—
763C2×C4—2216no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—448no—
772C2×C4—448no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4C2×D4×D1112yes—
777C2×C4C2×D4×D1112yes—
778C2×C4C2×D4×D1111yescharacteristic
779C2×C4C2×D4×D1112yes—
780C2×C4#41×D1112yes—
781C2×C4C24×D1111yescharacteristic
782C8—22no—
783C8—22no—
784C8—222no—
785C8—222no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—84no—
790C22—114no—
791C22—228no—
792C22—222no—
793C22—222no—
794C22D11×#12112yes—
795C22#1062330212yes—
796C22#1062331012yes—
797C22C22×D4×D1111yescharacteristic
798C4—24no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—114no—
804C4—224no—
805C4—222no—
806C4—222no—
807C4—442no—
808C4—442no—
809C4—442no—
810C4D11×#12112yes—
811C4C22×D4×D1111yescharacteristic
812C4C2×#41×D1111yescharacteristic
813C2—82no—
814C2—224no—
815C2#1307814414yesdirect product factor
816C2C2×D11×#12111yescharacteristic
817C2C2×#1062330211yescharacteristic
818C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#464D11
hypocenterC11C2×#3044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C22×Q16×D11C2semidirect
4. C2×#10623103C2semidirect
5. #13078144C2direct (N × H)
6. C2×#10622380C2semidirect
7. C2×#10622779C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622462C2semidirect
10. C2×#10622644C2semidirect
11. C2×#10622406C2semidirect
12. C2×#10622795C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622415C2semidirect
16. C2×C11×#464C2semidirect
32. C2×Q16×D11C22semidirect
42. #10623103C22semidirect
56. C11×#464C22semidirect
62. #10622795C22semidirect
63. #10622779C22semidirect
68. #10622667C22semidirect
69. #10622644C22semidirect
73. #10622462C22semidirect
74. #10622452C22semidirect
75. #10622415C22semidirect
76. #10622406C22semidirect
78. #10622380C22semidirect
317. C2×#464D11semidirect
435. #464C2×D11semidirect
600. C2×C11#3044semidirect
717. C11C2×#3044semidirect
815. C2#13078144direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C22×Q16×D112
C2×#106232062
C2×#106231032
#130781442
C2×#106223802
C2×#106227792
C2×#106226672
C2×#106224622
C2×#106226442
C2×#106224062
C2×#106227952
C2×#106224522
C2×#106224152
C2×#106223852
C2×C11×#4642
C2×#304411