Finite Group Databasebeta

← #14660495

Subgroups — #14660495

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C22×#66869C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4C22×#66889C211yesmaximal, characteristic, complemented
5#13068309C211yesmaximal, characteristic, complemented
6C4×C11⋊#95C211yesmaximal, characteristic, complemented
7C22×C11×#104C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12#10623363—22no—
13#10623363—22no—
14#10623363—22no—
15#10623363—22no—
16C2×#67000C411yescharacteristic, complemented
17C2×#66997C411yescharacteristic, complemented
18C2×#66993C411yescharacteristic, complemented
19C2×#66992—22no—
20C2×#66989C411yescharacteristic, complemented
21C2×C4×C22⋊D11—22no—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C11×#104—22no—
26C2×C11×#104—22no—
27C2×C11×#104—22no—
28C2×#66901—22no—
29C2×#66901—22no—
30C2×#66901—22no—
31C2×C11⋊#95—22no—
32C2×#66889—22no—
33C2×#66889—22no—
34C2×#66889—22no—
35C2×#66869—22no—
36C2×#66869—22no—
37C2×#66869—22no—
38#10622188—22no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41D412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11C2×C411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2×C411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C22×C22⋊D11—22no—
59C23×Dic11—21no—
60C23×Dic11D412yes—
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339D412yes—
72C2×#4339D412yes—
73C22×D44C2×C411yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2×C411yescharacteristic
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16D412yescomplemented
82C22×C8×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11D412yescomplemented
89C2×C22⋊Dic11—22no—
90#67000—22no—
91#67000—22no—
92#66997—22no—
93#66997—22no—
94#66993—22no—
95#66993—22no—
96#66992—28no—
97#66992—28no—
98#66989—22no—
99#66989—22no—
100C4×C22⋊D11—28no—
101C4×C22⋊D11—28no—
102C2×(C2×D11)⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11D412yes—
116C2×C4×Dic11D412yescomplemented
117C2×#4318—21no—
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—21no—
121C2×#4318—21no—
122C2×#4318D412yescomplemented
123C22×C11⋊C8—21no—
124C11×#104—28no—
125#66901—28no—
126C11⋊#95—28no—
127#66889—28no—
128#66869—28no—
129#11011—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C23×D11—21no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22⋊C412yes—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C22⋊C412yes—
167C22×C4×C11—24no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—42no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11#4111yescharacteristic
193C2×C22⋊D11—28no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—22no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—41no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C2×C22⋊D11—41no—
202C22×Dic11—24no—
203C22×Dic11—24no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—42no—
209C22×Dic11—42no—
210C22×Dic11—41no—
211C22×Dic11—41no—
212C22×Dic11C22⋊C412yes—
213C22×Dic11C22⋊C412yes—
214#4339—22no—
215#4339—22no—
216#4339—22no—
217#4339—22no—
218#4339—22no—
219#4339—22no—
220#4339—22no—
221#4339—22no—
222#4339—41no—
223#4339—41no—
224#4339—41no—
225#4339—41no—
226#4339—41no—
227#4339—41no—
228#4339—41no—
229#4339—41no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44C22⋊C412yes—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—41no—
239C2×C4×D11—41no—
240C2×C4×D11—41no—
241C2×C4×D11—41no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22—21no—
245C2×Dic22—21no—
246C2×Dic22—21no—
247C2×Dic22C22⋊C412yes—
248C11×M16—22no—
249C11×M16—22no—
250C11×M16—41no—
251C11×M16—41no—
252C2×C8×C11—22no—
253C2×C8×C11—41no—
254C2×C8×C11—41no—
255C42×C11—22no—
256C42×C11—22no—
257C42×C11—41no—
258C42×C11—41no—
259C22⋊Dic11—28no—
260(C2×D11)⋊C4—28no—
261Dic11⋊C4—28no—
262C4×Dic11—21no—
263C4×Dic11—21no—
264C4×Dic11—21no—
265C4×Dic11—21no—
266C4×Dic11—22no—
267C4×Dic11—22no—
268C4×Dic11—22no—
269C4×Dic11—22no—
270C4×Dic11—41no—
271C4×Dic11—41no—
272#4318—22no—
273#4318—22no—
274#4318—41no—
275#4318—41no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—41no—
278C2×C11⋊C8—41no—
279C2×#532—111no—
280C22×#104—111no—
281C22×#104—111no—
282C22×#104—111no—
283C22×#104D1111yescharacteristic, complemented
284#1728—111no—
285C4×#95—111no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11C2×C22⋊C411yescharacteristic
294C23×C11#12011yescharacteristic
295C23×C11#12011yescharacteristic
296C23×C11#12111yescharacteristic
297C23×C11#12111yescharacteristic
298C23×C11#12411yescharacteristic
299C23×C11#12711yescharacteristic
300C22×D11—22no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—42no—
304C22×D11—42no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—41no—
308Q8×C11—41no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—41no—
316D4×C11—41no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—42no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12111yescharacteristic
347C2×C4×C11#12111yescharacteristic
348C2×C4×C11#12111yescharacteristic
349C2×C4×C11#12111yescharacteristic
350C2×C4×C11#12111yescharacteristic
351C2×C4×C11#12311yescharacteristic
352C2×C4×C11#12311yescharacteristic
353C2×C4×C11#12311yescharacteristic
354C2×C4×C11#12311yescharacteristic
355C2×C4×C11#12411yescharacteristic
356C2×C4×C11#12711yescharacteristic
357C22⋊D11—416no—
358C22⋊D11—42no—
359C22⋊D11—42no—
360C22⋊D11—42no—
361C22⋊D11—42no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—42no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—42no—
377C2×Dic11#10414yescomplemented
378D44—22no—
379D44—22no—
380D44—41no—
381D44—41no—
382C4×D11—42no—
383C4×D11—42no—
384C4×D11—42no—
385C4×D11—42no—
386Dic22—22no—
387Dic22—22no—
388Dic22—41no—
389Dic22—41no—
390C8×C11—42no—
391C11⋊C8—42no—
392C22×#41—111no—
393C22×#41C2×D1111yescharacteristic
394C22×M16—111no—
395C22×M16C2×D1111yescharacteristic
396#532—222no—
397#532—222no—
398#532—222no—
399#532—222no—
400C2×C4⋊Q8—111no—
401C2×#127—111no—
402C2×#124—111no—
403C2×#124—111no—
404C2×#121—222no—
405C2×C4×D4—222no—
406C22×C42—111no—
407C22×C42—111no—
408C22×C42C2×D1111yescharacteristic
409C2×#104—22no—
410C2×#104—22no—
411C2×#104—22no—
412C2×#104—222no—
413C2×#104—222no—
414C2×#104—222no—
415C2×#104—222no—
416C2×#104—222no—
417C2×#104—222no—
418C2×#104—222no—
419C2×#104—222no—
420C2×#104—222no—
421C2×#95—222no—
422#336—222no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—21no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—42no—
432C22×C11—44no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—82no—
436C22×C11#37911yescharacteristic
437C22×C11#39011yescharacteristic
438C22×C11#39011yescharacteristic
439C22×C11#39211yescharacteristic
440C22×C11#39211yescharacteristic
441C22×C11#39411yescharacteristic
442C22×C11#39411yescharacteristic
443C22×C11C2×#10412yes—
444C22×C11#42112yes—
445C2×D11—42no—
446C2×D11—44no—
447C2×D11—81no—
448C2×D11—81no—
449C2×D11—82no—
450C4×C11—44no—
451C4×C11—42no—
452C4×C11#38611yescharacteristic
453C4×C11#38611yescharacteristic
454C4×C11#38611yescharacteristic
455C4×C11#38611yescharacteristic
456C4×C11#39211yescharacteristic
457C4×C11#39211yescharacteristic
458C4×C11#39411yescharacteristic
459C4×C11#39411yescharacteristic
460Dic11—24no—
461Dic11—44no—
462Dic11—42no—
463Dic11—42no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—112no—
475C2×#41—112no—
476C2×#41—221no—
477C2×#41—221no—
478C2×#41—221no—
479C2×#41—221no—
480C2×#41—221no—
481C2×#41—221no—
482C2×#41—221no—
483C2×#41—221no—
484C2×#41—221no—
485C2×#41—221no—
486C2×#41D4412yes—
487C2×#41C22⋊D1112yes—
488C22×Q8—111no—
489C22×Q8C4×D1111yescharacteristic
490C22×D4—21no—
491C22×D4—111no—
492C22×D4—222no—
493C22×D4—221no—
494C22×D4C4×D1111yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—112no—
498C23×C4—221no—
499C23×C4—221no—
500C23×C4C22×D1111yescharacteristic
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—112no—
507C2×M16—221no—
508C2×M16—221no—
509C2×M16—221no—
510C2×M16—221no—
511C2×M16—221no—
512C2×M16C22⋊D1112yescomplemented
513C22×C8—21no—
514C22×C8—221no—
515C4⋊Q8—222no—
516C4⋊Q8—222no—
517#127—222no—
518#127—222no—
519#124—222no—
520#124—222no—
521#124—222no—
522#124—222no—
523#121—228no—
524#121—228no—
525C4×D4—228no—
526C4×D4—228no—
527C2×C4⋊C4—222no—
528C2×C22⋊C4—222no—
529C2×C22⋊C4—222no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—21no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—112no—
538C2×C42—112no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—221no—
542C2×C42—221no—
543C2×C42—221no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42—221no—
547C2×C42—221no—
548C2×C42C22⋊D1112yescomplemented
549#104—28no—
550#104—228no—
551#104—228no—
552#104—228no—
553#95—228no—
554C2×C11—21no—
555C2×C11—21no—
556C2×C11—21no—
557C2×C11—21no—
558C2×C11—82no—
559C2×C11#143811yescharacteristic
560C2×C11#178912yes—
561C2×C11#196211yescharacteristic
562C2×C11#196311yescharacteristic
563C2×C11#198012yes—
564D11—82no—
565C24—21no—
566C24—221no—
567C24D4×D1111yescharacteristic
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—222no—
585#41—222no—
586#41—222no—
587#41—222no—
588#41—222no—
589#41—222no—
590#41—222no—
591#41—222no—
592#41—441no—
593#41—441no—
594#41—441no—
595#41—441no—
596#41—441no—
597#41—441no—
598#41—441no—
599#41—441no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—112no—
606C2×Q8—221no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—221no—
610C2×Q8—221no—
611C2×Q8(C2×D11)⋊C412yes—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—112no—
624C2×D4—228no—
625C2×D4—222no—
626C2×D4—222no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—444no—
633C2×D4—444no—
634C2×D4—441no—
635C2×D4—441no—
636C2×D4—441no—
637C2×D4—441no—
638C2×D4(C2×D11)⋊C412yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—42no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—221no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—441no—
664C22×C4—441no—
665C22×C4—441no—
666C22×C4—441no—
667C22×C4—441no—
668C22×C4—441no—
669C22×C4C2×C4×D1111yescharacteristic
670C22×C4C2×D4411yescharacteristic
671C22×C4#433911yescharacteristic
672C22×C4#433911yescharacteristic
673C22×C4D4×D1111yescharacteristic
674C22×C4D4×D1111yescharacteristic
675C22×C4D4×D1111yescharacteristic
676C22×C4D4×D1111yescharacteristic
677C22×C4D4×D1111yescharacteristic
678C22×C4#434111yescharacteristic
679C22×C4#434111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683M16—22no—
684M16—22no—
685M16—41no—
686M16—41no—
687M16—222no—
688M16—222no—
689M16—441no—
690M16—441no—
691C2×C8—22no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—222no—
695C2×C8—441no—
696C2×C8—441no—
697C4⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C42—22no—
701C42—22no—
702C42—41no—
703C42—41no—
704C42—221no—
705C42—221no—
706C42—222no—
707C42—221no—
708C42—221no—
709C42—222no—
710C42—222no—
711C42—222no—
712C42—441no—
713C42—441no—
714C11#1101111yescharacteristic, complemented, Sylow
715C23—22no—
716C23—22no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—222no—
723C23—441no—
724C23—441no—
725C23—442no—
726C23—442no—
727C23C22⋊C4×D1111yescharacteristic
728C23#6693511yescharacteristic
729C23#6693711yescharacteristic
730C23#6693811yescharacteristic
731C23#6699011yescharacteristic
732C23#6699211yescharacteristic
733C23#6699311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—41no—
737Q8—41no—
738Q8—222no—
739Q8—222no—
740Q8—441no—
741Q8—441no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—41no—
749D4—41no—
750D4—222no—
751D4—222no—
752D4—4416no—
753D4—442no—
754D4—442no—
755D4—442no—
756D4—442no—
757D4—441no—
758D4—441no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—114no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—224no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—442no—
783C2×C4—444no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—442no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4C22⋊C4×D1111yescharacteristic
792C2×C4(C22⋊D11)⋊C411yescharacteristic
793C2×C4(C22⋊D11)⋊C411yescharacteristic
794C2×C4#6693511yescharacteristic
795C2×C4#6693511yescharacteristic
796C2×C4#6693611yescharacteristic
797C2×C4#6693611yescharacteristic
798C2×C4#6693711yescharacteristic
799C2×C4#6693711yescharacteristic
800C2×C4#6693711yescharacteristic
801C2×C4#6693811yescharacteristic
802C2×C4#6693911yescharacteristic
803C2×C4C2×(C2×D11)⋊C411yescharacteristic
804C2×C4C4×C22⋊D1111yescharacteristic
805C2×C4C4×C22⋊D1111yescharacteristic
806C2×C4#6698211yescharacteristic
807C2×C4#6698311yescharacteristic
808C2×C4#6698311yescharacteristic
809C2×C4#6699011yescharacteristic
810C2×C4#6699011yescharacteristic
811C2×C4#6699011yescharacteristic
812C2×C4#6699111yescharacteristic
813C2×C4#6699111yescharacteristic
814C2×C4#6699211yescharacteristic
815C2×C4#6699211yescharacteristic
816C2×C4#6699211yescharacteristic
817C2×C4#6699311yescharacteristic
818C2×C4#6700611yescharacteristic
819C8—42no—
820C8—442no—
821C22—22no—
822C22—22no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—44no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—82no—
834C22—444no—
835C22—442no—
836C22—881no—
837C22—881no—
838C22—882no—
839C22D11×#10412yes—
840C22#1062243412yes—
841C22#1062256811yescharacteristic
842C22#1062257011yescharacteristic
843C22#1062257011yescharacteristic
844C22#1062257211yescharacteristic
845C22#1062257311yescharacteristic
846C22#1062257411yescharacteristic
847C22#1062283611yescharacteristic
848C4—44no—
849C4—42no—
850C4—224no—
851C4—444no—
852C4—442no—
853C4—442no—
854C4#1062256911yescharacteristic
855C4#1062256911yescharacteristic
856C4#1062257111yescharacteristic
857C4#1062257211yescharacteristic
858C4#1062257311yescharacteristic
859C4#1062257411yescharacteristic
860C4#1062282611yescharacteristic
861C4#1062283611yescharacteristic
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—82no—
867C2—882no—
868C2#1306685511yescharacteristic
869C2#1306855812yes—
870C2#1306944211yescharacteristic
871C2#1306944611yescharacteristic
872C2#1306953312yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#104C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623363C2
cosocleC23×C4×C11C23
hypercenterC22×#104D11
hypocenterC11#11011
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#66869C2semidirect
3. C22×#66901C2semidirect
4. C22×#66889C2semidirect
5. #13068309C2semidirect
6. C4×C11⋊#95C2semidirect
7. C22×C11×#104C2semidirect
16. C2×#67000C4semidirect
17. C2×#66997C4semidirect
18. C2×#66993C4semidirect
20. C2×#66989C4semidirect
81. C2×C11×M16D4semidirect
88. C2×C42×C11D4semidirect
116. C2×C4×Dic11D4semidirect
122. C2×#4318D4semidirect
283. C22×#104D11semidirect
377. C2×Dic11#104semidirect
512. C2×M16C22⋊D11semidirect
548. C2×C42C22⋊D11semidirect
714. C11#11011semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C22×#668692
C22×#669012
C22×#668892
#130683092
C4×C11⋊#952
C22×C11×#1042
#1101111