Finite Group Databasebeta

← C2×#13079485 #15624445

Subgroups — C2×#13079485 #15624445

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623159C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic
3#13079485C2116yesmaximal, direct product factor
4C2×#10622336C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622787C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622783C211yesmaximal, characteristic, complemented
14C2×#10622831C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic, complemented
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#67006—21no—
24C2×#67006—21no—
25C2×#66999C2211yescharacteristic, complemented
26#10623336—24no—
27#10623336C2218yes—
28C2×#66993—21no—
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66989—21no—
34C22×#4324C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4313C2211yescharacteristic, complemented
39C22×C8×D11C2211yescharacteristic, complemented
40#10623159—24no—
41#10623159C2218yescomplemented
42C2×#66950C2211yescharacteristic, complemented
43C2×#66947—21no—
44C2×#66945C2211yescharacteristic, complemented
45C2×#66941—21no—
46C2×#66938—21no—
47C2×#66936—21no—
48C11×#450C2218yescomplemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54#10622831C2218yescomplemented
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622787C2218yescomplemented
59#10622784C2218yescomplemented
60#10622783C2218yescomplemented
61#10622783C2218yescomplemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622397C2218yescomplemented
72#10622393C2218yescomplemented
73#10622392C2218yescomplemented
74#10622391C2218yescomplemented
75#10622340C2218yescomplemented
76#10622336C2218yescomplemented
77C25×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C22×C22⋊D11D411yescharacteristic
93C2×Q8×D11—22no—
94C2×Q8×D11—42no—
95C2×Q8×D11—42no—
96C2×Q8×D11C2314yescomplemented
97C2×#4339—42no—
98C2×#4339—42no—
99C2×#4339D414yes—
100C2×#4339C2314yes—
101C22×D44D411yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C22×Dic22D411yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×SD16—42no—
109C2×C11×SD16—42no—
110C2×C11×SD16C2314yes—
111C2×C11×SD16C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8C2314yes—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119#67006—28no—
120#67006—28no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127#66999—22no—
128#66999C2314yescomplemented
129#66993—28no—
130#66991—22no—
131#66991—22no—
132#66991—22no—
133#66991—22no—
134#66991C2314yes—
135#66991C2314yes—
136#66991C2314yes—
137#66991C2314yes—
138#66989—28no—
139C2×#4324—42no—
140C2×#4324—42no—
141C2×#4324C2314yes—
142C2×#4324C2314yes—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146#66979—22no—
147#66979C2314yes—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152#66977—22no—
153#66977C2314yes—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×C4×Dic11—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yescomplemented
162C2×C8×D11—42no—
163C2×C8×D11C2314yescomplemented
164#66950—22no—
165#66950C2314yescomplemented
166#66947—28no—
167#66945—22no—
168#66945C2314yescomplemented
169#66941—28no—
170#66938—28no—
171#66936—28no—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×C22⋊C8C2314yes—
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180(C2×D11)⋊C8C2314yescomplemented
181(C2×D11)⋊C8C2314yescomplemented
182#66882C2314yescomplemented
183#66881C2314yescomplemented
184#66880C2314yescomplemented
185#66880C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3200—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—24no—
192C24×C11—44no—
193C24×C11—82no—
194C24×C11—82no—
195C24×C11C2×D411yescharacteristic
196C23×D11C2×D411yescharacteristic
197C23×D11C2×D411yescharacteristic
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—44no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—48no—
213C2×D4×C11C2412yes—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—42no—
229C2×C22⋊D11—82no—
230C2×C22⋊D11—82no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11—82no—
233C2×C22⋊D11C2×D414yes—
234C2×C22⋊D11C2×D414yes—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241Q8×D11—44no—
242Q8×D11—44no—
243Q8×D11—48no—
244#4339—48no—
245#4339—44no—
246#4339—44no—
247C2×D44—42no—
248C2×D44C2×D414yes—
249C2×C4×D11—24no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—24no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—42no—
264C2×Dic22—44no—
265C2×Dic22C2×D414yes—
266C2×Dic22C2412yes—
267C11×SD16—44no—
268C11×SD16—44no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—24no—
282C22⋊Dic11—24no—
283#4324—44no—
284#4324—44no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—24no—
289C4⋊Dic11—21no—
290C4⋊Dic11—21no—
291C4⋊Dic11—21no—
292C4⋊Dic11C2412yes—
293C4⋊Dic11C2412yes—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303#4313—44no—
304C8×D11—44no—
305C2×#536—111no—
306C2×#535—111no—
307#3200—1116no—
308C2×#485—111no—
309C2×#485—111no—
310C2×#482—111no—
311C2×#482—111no—
312C2×#468—111no—
313C2×#468—111no—
314C2×#465—111no—
315C2×#465—111no—
316C2×#448—111no—
317C2×#448—111no—
318C2×#450—111no—
319C2×#450D1111yescharacteristic, complemented
320C2×#408—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—48no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—84no—
334C23×C11—84no—
335C23×C11—816no—
336C23×C11C22×D412yes—
337C23×C11C22×D411yescharacteristic
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11C22×D412yes—
345C22×D11C22×D412yes—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—48no—
354D4×C11—42no—
355D4×C11—42no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11H(5,𝔽2)12yes—
368C2×C4×C11C2511yescharacteristic
369C22⋊D11—44no—
370C22⋊D11—44no—
371C22⋊D11—84no—
372C22⋊D11—84no—
373C22⋊D11—84no—
374C22⋊D11—84no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11C22×D412yes—
386C2×Dic11C22×D412yes—
387D44—44no—
388C4×D11—24no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—48no—
395Dic22—22no—
396Dic22—22no—
397Dic22—44no—
398Dic22—48no—
399Dic22—42no—
400C8×C11—22no—
401C8×C11—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C22×#41—111no—
405C23×Q8—111no—
406C23×D4C2×D1111yescharacteristic
407C22×SD16—111no—
408C22×SD16—111no—
409C22×SD16C2×D1111yescharacteristic
410C22×SD16C2×D1111yescharacteristic
411C22×M16—111no—
412C23×C8—111no—
413#536—118no—
414#536—224no—
415#535—118no—
416#535—224no—
417C2×C4⋊Q8—221no—
418C2×#127—221no—
419C2×#124—221no—
420C2×#124—221no—
421C2×#123—221no—
422C2×#123—221no—
423C2×C22⋊Q8—111no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—111no—
426C2×C22⋊Q8C2×D1111yescharacteristic
427C2×#121—111no—
428C2×#121—111no—
429C2×#121—111no—
430C2×#121—111no—
431C2×#120—221no—
432C2×#120—221no—
433C2×#117—111no—
434C2×#117—111no—
435#485—118no—
436#485—118no—
437#482—118no—
438#482—118no—
439#468—118no—
440#468—118no—
441#465—118no—
442#465—118no—
443#450—118no—
444#450C2×D1118yescomplemented
445#448—118no—
446#448—118no—
447C2×#107—111no—
448C2×#107—111no—
449C2×#106—111no—
450C2×#106—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#103—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102C2×D1111yescharacteristic
458C2×#102C2×D1111yescharacteristic
459#408—118no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8—111no—
463C2×C22⋊C8C2×D1111yescharacteristic
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—44no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—816no—
475C22×C11—84no—
476C22×C11—84no—
477C22×C11#53412yes—
478C22×C11#57712yes—
479C22×C11#57712yes—
480C22×C11C23×D411yescharacteristic
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—22no—
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—44no—
488C2×D11—44no—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11#53412yes—
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494C4×C11C2×H(5,𝔽2)11yescharacteristic
495Dic11—22no—
496Dic11—22no—
497Dic11—42no—
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501C25—21no—
502C2×#41—114no—
503C2×#41—114no—
504C2×#41—442no—
505C2×#41—442no—
506C22×Q8—111no—
507C22×Q8—114no—
508C22×Q8—111no—
509C22×Q8—221no—
510C22×Q8—222no—
511C22×Q8—442no—
512C22×Q8—442no—
513C22×Q8C22×D1111yescharacteristic
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—42no—
517C22×D4—42no—
518C22×D4—111no—
519C22×D4—111no—
520C22×D4—111no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4C22×D1111yescharacteristic
526C22×D4C22×D1111yescharacteristic
527C22×D4C22×D1114yes—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—221no—
531C23×C4C22×D1111yescharacteristic
532C2×SD16—42no—
533C2×SD16—42no—
534C2×SD16—114no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16—442no—
538C2×SD16C22×D1114yes—
539C2×SD16C22×D1114yes—
540C2×M16—114no—
541C2×M16—442no—
542C22×C8—111no—
543C22×C8—111no—
544C22×C8—114no—
545C22×C8—442no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548C4⋊Q8—228no—
549#127—228no—
550#124—228no—
551#124—228no—
552#123—228no—
553#123—228no—
554C22⋊Q8—22no—
555C22⋊Q8—114no—
556C22⋊Q8—114no—
557C22⋊Q8—114no—
558C22⋊Q8—222no—
559C22⋊Q8—222no—
560C22⋊Q8—222no—
561C22⋊Q8C22×D1114yes—
562#121—114no—
563#121—114no—
564#121—114no—
565#121—114no—
566#121—222no—
567#121—222no—
568#121—222no—
569#121—222no—
570#120—228no—
571#120—228no—
572#117—114no—
573#117—114no—
574#117—222no—
575#117—222no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—221no—
595C2×C42—221no—
596#107—114no—
597#107—114no—
598#106—114no—
599#106—114no—
600#103—114no—
601#103—114no—
602#103—114no—
603#103—114no—
604#102—114no—
605#102—114no—
606#102C22×D1114yes—
607#102C22×D1114yes—
608C22⋊C8—114no—
609C22⋊C8—114no—
610C22⋊C8—114no—
611C22⋊C8C22×D1114yes—
612C2×C11—42no—
613C2×C11—82no—
614C2×C11—82no—
615C2×C11#320014yescomplemented
616C2×C11C2×#53411yescharacteristic
617C2×C11C2×#57711yescharacteristic
618C2×C11C2×#57711yescharacteristic
619D11—42no—
620D11—42no—
621C24—21no—
622C24—21no—
623C24—24no—
624C24—44no—
625C24—82no—
626C24—82no—
627C24—111no—
628C24—111no—
629C24D4×D1111yescharacteristic
630#41—448no—
631#41—444no—
632#41—444no—
633C2×Q8—21no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—114no—
637C2×Q8—112no—
638C2×Q8—224no—
639C2×Q8—221no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—442no—
643C2×Q8—444no—
644C2×Q8—444no—
645C2×Q8—444no—
646C2×Q8—448no—
647C2×Q8C23×D1112yes—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C2×D4—114no—
660C2×D4—114no—
661C2×D4—114no—
662C2×D4—224no—
663C2×D4—224no—
664C2×D4—224no—
665C2×D4—224no—
666C2×D4—442no—
667C2×D4—442no—
668C2×D4—442no—
669C2×D4—882no—
670C2×D4—882no—
671C2×D4—882no—
672C2×D4—882no—
673C2×D4C23×D1112yes—
674C2×D4C23×D1112yes—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—111no—
680C22×C4—111no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—224no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—444no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699SD16—44no—
700SD16—44no—
701SD16—444no—
702SD16—444no—
703M16—444no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—112no—
707C2×C8—112no—
708C2×C8—222no—
709C2×C8—222no—
710C2×C8—444no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—112no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—221no—
723C4⋊C4—224no—
724C4⋊C4C23×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C42—224no—
736C42—224no—
737C11C2×#320011yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—84no—
751C23—84no—
752C23—816no—
753C23—112no—
754C23—112no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23C2×D4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—222no—
767Q8—222no—
768Q8—444no—
769Q8—448no—
770Q8—442no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—48no—
776D4—42no—
777D4—42no—
778D4—444no—
779D4—444no—
780D4—444no—
781D4—884no—
782D4—884no—
783D4—884no—
784D4—884no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—224no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—448no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4C2×D4×D1112yes—
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4#6703712yes—
815C2×C4#6703712yes—
816C2×C4C24×D1111yescharacteristic
817C8—22no—
818C8—22no—
819C8—222no—
820C8—222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—816no—
832C22—84no—
833C22—84no—
834C22—222no—
835C22—222no—
836C22—222no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—444no—
841C22—444no—
842C22#1062312012yes—
843C22#1062329312yes—
844C22#1062330612yes—
845C22C22×D4×D1111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—222no—
850C4—222no—
851C4—442no—
852C4—442no—
853C4—442no—
854C4—442no—
855C4#1062312012yes—
856C4C2×#6703711yescharacteristic
857C4C2×#6703711yescharacteristic
858C2—42no—
859C2—82no—
860C2—82no—
861C2—442no—
862C2—442no—
863C2#1307948514yesdirect product factor
864C2C2×#1062312011yescharacteristic
865C2C2×#1062329311yescharacteristic
866C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
hypercenterC2×#450D11
hypocenterC11C2×#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10623159C2semidirect
3. #13079485C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622783C2semidirect
14. C2×#10622831C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#450C2semidirect
18. C22×Q8×D11C22semidirect
25. C2×#66999C22semidirect
38. C22×#4313C22semidirect
39. C22×C8×D11C22semidirect
41. #10623159C22semidirect
42. C2×#66950C22semidirect
44. C2×#66945C22semidirect
48. C11×#450C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
54. #10622831C22semidirect
58. #10622787C22semidirect
59. #10622784C22semidirect
60. #10622783C22semidirect
61. #10622783C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622397C22semidirect
72. #10622393C22semidirect
73. #10622392C22semidirect
74. #10622391C22semidirect
75. #10622340C22semidirect
76. #10622336C22semidirect
96. C2×Q8×D11C23semidirect
128. #66999C23semidirect
161. C2×#4313C23semidirect
163. C2×C8×D11C23semidirect
165. #66950C23semidirect
168. #66945C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. #66882C23semidirect
183. #66881C23semidirect
184. #66880C23semidirect
185. #66880C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
319. C2×#450D11semidirect
444. #450C2×D11semidirect
615. C2×C11#3200semidirect
737. C11C2×#3200semidirect
863. C2#13079485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231592
C2×#106233362
#130794852
C2×#106223362
C2×#106226582
C2×#106223922
C2×#106223972
C2×#106223932
C2×#106227872
C2×#106223912
C2×#106227842
C2×#106227832
C2×#106228312
C2×#106223402
C2×C11×#4502
C2×#320011