Finite Group Databasebeta

← #14780603

Subgroups — #14780603

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622579C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069624C212yesmaximal, complemented
7#13069619C212yesmaximal, complemented
8#13069617C212yesmaximal, complemented
9#13069612C212yesmaximal, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C2×C11×#537C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C11×#537—24no—
16C11×#537—24no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121—22no—
21C2×C11×#121C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23#10623364—24no—
24#10623364—24no—
25C2×#67003—24no—
26C2×#67003—24no—
27C2×#67003—24no—
28C2×#66999—21no—
29C22×#4326C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C2×#66992—22no—
32C2×#66991—21no—
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C2×#66983C2212yes—
36C22×C4⋊Dic11C2211yescharacteristic
37C2×#66977C2212yes—
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40#10622847—24no—
41#10622845—24no—
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44C2×C22⋊(C11⋊C8)C2212yes—
45C2×C22⋊(C11⋊C8)C2212yes—
46C2×#66874C2212yes—
47#10622579—24no—
48C2×#66873C2212yes—
49#10622167C2212yes—
50#10622167C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41D414yescomplemented
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11D411yescharacteristic
68C22×D4×C11D412yes—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×C22⋊D11—22no—
76C23×Dic11—21no—
77C2×#4339—22no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—22no—
82C2×#4339D414yescomplemented
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×Dic22C2311yescharacteristic
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8—24no—
89C11×#121—216no—
90C11×#121—28no—
91C11×#121—24no—
92C11×#121—24no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D414yescomplemented
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C22⋊Dic11—22no—
101#67003—232no—
102#66999—28no—
103C2×#4326—22no—
104C2×#4326—22no—
105C2×#4326—22no—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—22no—
109#66992—216no—
110#66991—28no—
111C2×#4324—22no—
112C2×#4324—22no—
113C2×#4324—22no—
114C2×#4323—22no—
115C2×#4323—22no—
116C2×#4323—22no—
117#66983—24no—
118#66983—24no—
119C2×(C2×D11)⋊C4—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11D414yescomplemented
123C2×C4⋊Dic11C2312yes—
124#66977—24no—
125#66977—24no—
126C2×Dic11⋊C4—22no—
127C2×#4318—22no—
128C2×#4318—22no—
129C2×#4318—22no—
130C22×C11⋊C8—22no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8D414yescomplemented
133C22×C11⋊C8C2312yes—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136#66899—24no—
137#66896—24no—
138C22⋊(C11⋊C8)—24no—
139C22⋊(C11⋊C8)—24no—
140#66874—24no—
141#66873—24no—
142#23390—111nomaximal, Sylow
143C24×C11—21no—
144C24×C11C2×D412yes—
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C11×#41—28no—
148C11×#41—28no—
149C11×#41—44no—
150C11×#41—44no—
151C11×#41—44no—
152C11×#41—44no—
153C11×#41—44no—
154C11×#41—44no—
155C2×Q8×C11—22no—
156C2×Q8×C11—22no—
157C2×Q8×C11—22no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C2×D412yes—
164C2×D4×C11—24no—
165C2×D4×C11—24no—
166C2×D4×C11—24no—
167C2×D4×C11—24no—
168C2×D4×C11—28no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11—82no—
180C2×D4×C11—82no—
181C2×D4×C11C2×D412yes—
182C22×C4×C11—22no—
183C22×C4×C11—21no—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11#4112yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—82no—
210C2×C22⋊D11—82no—
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—22no—
214C22×Dic11—81no—
215C22×Dic11—81no—
216#4339—28no—
217#4339—28no—
218#4339—44no—
219#4339—44no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44C2×D412yes—
226C2×C4×D11—24no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22C2×D412yes—
235C11×C4⋊C4—28no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4C2×D414yes—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—28no—
241C22⋊Dic11—28no—
242#4326—28no—
243#4325—28no—
244#4324—28no—
245#4323—28no—
246(C2×D11)⋊C4—28no—
247C4⋊Dic11—24no—
248C4⋊Dic11—22no—
249C4⋊Dic11C2×D414yes—
250Dic11⋊C4—28no—
251#4318—44no—
252C2×C11⋊C8—28no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8C2×D412yes—
261C2×C11⋊C8C2×D412yes—
262C22×#135—111no—
263C2×#537—111no—
264C2×#537D1111yescharacteristic, complemented
265C2×#417—111no—
266C2×#417—111no—
267C2×#408—111no—
268#2001—112no—
269#2000—112no—
270#2000—112no—
271#1999—112no—
272C2×#340—111no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11#12012yes—
292C23×C11#12012yes—
293C23×C11#12112yes—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—41no—
305Q8×C11—41no—
306Q8×C11—44no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—48no—
310D4×C11—48no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—44no—
314D4×C11—88no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—48no—
329C2×C4×C11—84no—
330C2×C4×C11#12014yes—
331C2×C4×C11#12012yes—
332C2×C4×C11#12012yes—
333C2×C4×C11#12114yes—
334C2×C4×C11#12114yes—
335C2×C4×C11#12112yes—
336C2×C4×C11#12714yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C22⋊D11—48no—
344C22⋊D11—88no—
345C2×Dic11—22no—
346C2×Dic11—24no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—84no—
352D44—22no—
353D44—22no—
354D44—41no—
355D44—41no—
356C4×D11—48no—
357Dic22—22no—
358Dic22—22no—
359Dic22—41no—
360Dic22—41no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C11⋊C8—42no—
364C22×#41—111no—
365C22×#41C2×D1111yescharacteristic
366C22×#41C2×D1111yescharacteristic
367C2×#135—224no—
368C2×#135—224no—
369C2×#135—224no—
370C22×Q16—111no—
371C22×SD16—111no—
372C22×SD16—111no—
373C22×D8—111no—
374C22×M16—111no—
375C23×C8—111no—
376#537—24no—
377#537—24no—
378#537—224no—
379#537—224no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8—112no—
382C2×C22⋊Q8—221no—
383C2×C22⋊Q8C2×D1112yes—
384C2×#121—21no—
385C2×#121—22no—
386C2×#121—112no—
387C2×#121—221no—
388C2×#121—222no—
389C2×#121C2×D1112yes—
390C22×C4⋊C4—111no—
391C22×C4⋊C4C2×D1111yescharacteristic
392#417—224no—
393#417—224no—
394C2×#103—112no—
395C2×#103—112no—
396C2×#102—112no—
397C2×#102—112no—
398#408—224no—
399C2×C22⋊C8—112no—
400C2×C22⋊C8—112no—
401#340—112no—
402#340—112no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11#39214yes—
424C22×C11C2×#12011yescharacteristic
425C22×C11C2×#12011yescharacteristic
426C22×C11C2×#12111yescharacteristic
427C22×C11#57611yescharacteristic
428C22×C11#57711yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57811yescharacteristic
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—81no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—44no—
441C4×C11#39214yes—
442C4×C11C2×#12011yescharacteristic
443C4×C11C2×#12111yescharacteristic
444C4×C11C2×#12111yescharacteristic
445C4×C11C2×#12711yescharacteristic
446Dic11—42no—
447Dic11—44no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—114no—
460C2×#41—222no—
461C2×#41—222no—
462C2×#41—222no—
463C2×#41—222no—
464C2×#41—222no—
465C2×#41C22⋊D1114yescomplemented
466C22×Q8—111no—
467C22×Q8C22⋊D1111yescharacteristic
468C22×Q8C22×D1111yescharacteristic
469C22×D4—21no—
470C22×D4—22no—
471C22×D4—111no—
472C22×D4—221no—
473C22×D4—222no—
474C22×D4C22⋊D1112yes—
475C22×D4C22⋊D1111yescharacteristic
476C22×D4C22×D1111yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—221no—
480C23×C4—221no—
481C23×C4C22×D1112yes—
482C23×C4C22×D1111yescharacteristic
483#135—2232no—
484C2×Q16—222no—
485C2×Q16—222no—
486C2×Q16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×SD16—222no—
490C2×SD16—222no—
491C2×SD16—222no—
492C2×SD16—222no—
493C2×D8—222no—
494C2×D8—222no—
495C2×D8—222no—
496C2×M16—222no—
497C2×M16—222no—
498C2×M16—222no—
499C22×C8—114no—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8—112no—
503C22×C8—222no—
504C22×C8—222no—
505C22⋊Q8—28no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—224no—
509C22⋊Q8—224no—
510C22⋊Q8—228no—
511#121—216no—
512#121—28no—
513#121—24no—
514#121—24no—
515#121—224no—
516#121—224no—
517#121—228no—
518#121—2216no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—222no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—222no—
527C2×C4⋊C4C22⋊D1114yescomplemented
528C2×C4⋊C4C22×D1112yes—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—222no—
532C2×C22⋊C4—222no—
533#103—224no—
534#103—224no—
535#102—224no—
536#102—224no—
537C22⋊C8—224no—
538C22⋊C8—224no—
539C2×C11—24no—
540C2×C11—82no—
541C2×C11—82no—
542C2×C11C2×#39211yescharacteristic
543C2×C11#301211yescharacteristic
544C2×C11#301211yescharacteristic
545C2×C11#301311yescharacteristic
546C2×C11#301311yescharacteristic
547C2×C11#306011yescharacteristic
548C2×C11#306111yescharacteristic
549D11—82no—
550C24—21no—
551C24—221no—
552C24C2×C22⋊D1112yes—
553C24C2×C22⋊D1111yescharacteristic
554#41—28no—
555#41—28no—
556#41—44no—
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561#41—44no—
562#41—228no—
563#41—228no—
564#41—444no—
565#41—444no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—112no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8C2×C22⋊D1112yes—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—28no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—82no—
597C2×D4—82no—
598C2×D4—112no—
599C2×D4—224no—
600C2×D4—228no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—221no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—442no—
607C2×D4—442no—
608C2×D4—882no—
609C2×D4—882no—
610C2×D4C2×C22⋊D1112yes—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—224no—
628C22×C4—224no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—881no—
632C22×C4—881no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1112yes—
635C22×C4D4×D1112yes—
636C22×C4#434112yes—
637C22×C4C2×C22⋊D1112yes—
638C22×C4C2×C22⋊D1111yescharacteristic
639C22×C4C2×C22⋊D1112yes—
640C22×C4C2×C22⋊D1112yes—
641C22×C4C23×D1111yescharacteristic
642Q16—228no—
643SD16—228no—
644SD16—228no—
645D8—228no—
646M16—444no—
647C2×C8—112no—
648C2×C8—112no—
649C2×C8—228no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—222no—
655C2×C8—222no—
656C2×C8—222no—
657C4⋊C4—28no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—114no—
661C4⋊C4—228no—
662C4⋊C4—224no—
663C4⋊C4—222no—
664C4⋊C4C2×C22⋊D1114yes—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—228no—
668C22⋊C4—228no—
669C11#2339011yescharacteristic, complemented, Sylow
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—222no—
689C23—441no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23#6699012yes—
696C23#6699212yes—
697C23#6700612yes—
698C23C22×C22⋊D1111yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—41no—
702Q8—41no—
703Q8—44no—
704Q8—222no—
705Q8—222no—
706Q8—441no—
707Q8—441no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—48no—
712D4—41no—
713D4—41no—
714D4—44no—
715D4—88no—
716D4—222no—
717D4—222no—
718D4—448no—
719D4—441no—
720D4—441no—
721D4—888no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—48no—
736C2×C4—84no—
737C2×C4—224no—
738C2×C4—222no—
739C2×C4—441no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—441no—
743C2×C4—448no—
744C2×C4—884no—
745C2×C4#6699014yes—
746C2×C4#6699012yes—
747C2×C4#6699114yes—
748C2×C4#6699214yes—
749C2×C4#6699212yes—
750C2×C4#6699314yes—
751C2×C4#6700612yes—
752C2×C4C2×D4×D1111yescharacteristic
753C2×C4C2×D4×D1111yescharacteristic
754C2×C4C2×D4×D1111yescharacteristic
755C2×C4C2×#434111yescharacteristic
756C2×C4C22×C22⋊D1111yescharacteristic
757C2×C4C22×C22⋊D1111yescharacteristic
758C8—222no—
759C8—222no—
760C8—442no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—881no—
785C22—881no—
786C22—881no—
787C22—881no—
788C22#1062283614yes—
789C22C2×#6699011yescharacteristic
790C22C2×#6699211yescharacteristic
791C22#1062336611yescharacteristic
792C22#1062336711yescharacteristic
793C22#1062336811yescharacteristic
794C22#1062336911yescharacteristic
795C22C2×#6700611yescharacteristic
796C4—44no—
797C4—42no—
798C4—42no—
799C4—444no—
800C4—442no—
801C4#1062283614yes—
802C4C2×#6699011yescharacteristic
803C4C2×#6699111yescharacteristic
804C4C2×#6699211yescharacteristic
805C4C2×#6699311yescharacteristic
806C2—24no—
807C2—82no—
808C2—82no—
809C2—882no—
810C2C2×#1062283611yescharacteristic
811C2#1307791711yescharacteristic
812C2#1307792011yescharacteristic
813C2#1307792811yescharacteristic
814C2#1307793111yescharacteristic
815C2#1307827511yescharacteristic
816C2#1307828311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11#23390
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C2×#10623364C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622579C2semidirect
5. C2×#10622847C2semidirect
6. #13069624C2semidirect
7. #13069619C2semidirect
8. #13069617C2semidirect
9. #13069612C2semidirect
10. C2×#10622167C2semidirect
11. C2×C11×#537C2semidirect
62. C2×C11×#41D4semidirect
82. C2×#4339D4semidirect
96. C2×C11×C4⋊C4D4semidirect
122. C2×C4⋊Dic11D4semidirect
132. C22×C11⋊C8D4semidirect
264. C2×#537D11semidirect
465. C2×#41C22⋊D11semidirect
527. C2×C4⋊C4C22⋊D11semidirect
669. C11#23390semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106233642
C2×#106228452
C2×#106225792
C2×#106228472
#130696242
#130696192
#130696172
#130696122
C2×#106221672
C2×C11×#5372
#2339011