Finite Group Databasebeta

← #14786671

Subgroups — #14786671

Order 2816.

1264 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078536C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3#13073102C211yesmaximal, characteristic, complemented
4#13069842C212yesmaximal, complemented
5#13069830C212yesmaximal, complemented
6#13069085C211yesmaximal, characteristic, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068849C212yesmaximal, complemented
9#13068575C212yesmaximal, complemented
10#13068560C211yesmaximal, characteristic, complemented
11C11×#3489C211yesmaximal, characteristic
12C2×C11×2−1+4C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14D4×Q8×C11—21no—
15C11×#548—21no—
16C11×#547—21no—
17C11×#547—22no—
18C11×#546—21no—
19C11×#546—22no—
20C11×#537—21no—
21C11×#537C2211yescharacteristic
22C11×#536—21no—
23C11×#536C2211yescharacteristic
24C11×#525—21no—
25C11×#525C2211yescharacteristic
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C11×#520C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C2×#66901C2212yes—
32C2×#66901C2212yes—
33C2×#66901C2212yescomplemented
34#10622845—21no—
35#10622845—21no—
36#10622845C2212yes—
37#10622845C2212yes—
38#10622845C2212yescomplemented
39#10622843C2212yescomplemented
40C2×#66900C2212yescomplemented
41C2×#66899—21no—
42C2×#66896—21no—
43C4×C22⋊Dic11C2211yescharacteristic
44#10622820C2211yescharacteristic
45#10622657—21no—
46#10622656—21no—
47#10622647—21no—
48#10622646—21no—
49#10622608C2212yescomplemented
50#10622599—22no—
51#10622590C2212yescomplemented
52#10622556—22no—
53#10622170C2212yescomplemented
54#10622168C2212yescomplemented
55C11×2−1+4—24no—
56C11×2−1+4—42no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—22no—
61C2×C11×#41—21no—
62C2×C11×#41—24no—
63C2×C11×#41—42no—
64C2×C11×#41D411yescharacteristic
65C2×C11×#41D411yescharacteristic
66C2×C11×#41C2311yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11—21no—
70C22×Q8×C11—21no—
71C22×Q8×C11D411yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11D411yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—21no—
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8—21no—
80C11×#124—22no—
81C11×#124—21no—
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—21no—
86C11×#123—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8D411yescharacteristic
99C11×C22⋊Q8D411yescharacteristic
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—22no—
106C11×#121D411yescharacteristic
107C11×#121D411yescharacteristic
108C11×#120—22no—
109C11×#120—21no—
110C4×Q8×C11—21no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11—21no—
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C11×#117—21no—
118C11×#117C2311yescharacteristic
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D412yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4D412yes—
125C2×C22⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×#4318—21no—
134C2×#4318—42no—
135C2×#4318C2312yes—
136C2×#4318C2312yes—
137C22×C11⋊C8—21no—
138#66901—24no—
139#66901—42no—
140#66901—42no—
141#66900—42no—
142#66899—22no—
143#66899—22no—
144#66899—22no—
145#66896—22no—
146#66896—22no—
147#66896—22no—
148C11⋊#95—24no—
149C11⋊#95—24no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—21no—
152C22⋊(C11⋊C8)—21no—
153#66872—22no—
154#66871—22no—
155#24029—111nomaximal, Sylow
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—44no—
166C11×#41—41no—
167C11×#41—41no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—48no—
171C11×#41—42no—
172C11×#41—42no—
173C11×#41#4114yes—
174C2×Q8×C11—22no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—22no—
179C2×Q8×C11—22no—
180C2×Q8×C11—22no—
181C2×Q8×C11—41no—
182C2×Q8×C11—44no—
183C2×Q8×C11—42no—
184C2×Q8×C11—42no—
185C2×Q8×C11C2×D411yescharacteristic
186C2×Q8×C11C2×D411yescharacteristic
187C2×Q8×C11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—41no—
200C2×D4×C11—44no—
201C2×D4×C11C2×D411yescharacteristic
202C2×D4×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—44no—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2411yescharacteristic
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—44no—
227C22×Dic11—41no—
228C22×Dic11—41no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4C2×D411yescharacteristic
240C11×C4⋊C4C2×D411yescharacteristic
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C42×C11—22no—
254C42×C11—21no—
255C22⋊Dic11—42no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258C4⋊Dic11—41no—
259C4⋊Dic11—41no—
260C4×Dic11—22no—
261C4×Dic11—22no—
262#4318—22no—
263#4318—22no—
264#4318—22no—
265#4318—22no—
266#4318—42no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—42no—
270#3489D1111yescharacteristic
271#3092—111no—
272C2×#417—111no—
273#2503—111no—
274#2040—112no—
275#2038—112no—
276#1901—111no—
277#1871—111no—
278#1860—112no—
279#1793—112no—
280#1789—111no—
281C23×C11—21no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—41no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—81no—
290C23×C11#12011yescharacteristic
291C23×C11#12011yescharacteristic
292C23×C11C22×D411yescharacteristic
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11—21no—
296Q8×C11—22no—
297Q8×C11—42no—
298Q8×C11—44no—
299Q8×C11—41no—
300Q8×C11—41no—
301Q8×C11—42no—
302Q8×C11#12312yes—
303D4×C11—24no—
304D4×C11—21no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—22no—
308D4×C11—42no—
309D4×C11—42no—
310D4×C11—42no—
311D4×C11—44no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—81no—
316D4×C11—82no—
317D4×C11#12312yes—
318C2×C4×C11—21no—
319C2×C4×C11—22no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—24no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—82no—
344C2×C4×C11#12011yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4112yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—44no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—82no—
356C2×Dic11—82no—
357C11⋊C8—42no—
358C11⋊C8—42no—
359C2×2−1+4C2×D1111yescharacteristic
360C22×#41C2×D1111yescharacteristic
361C22×M16—111no—
362D4×Q8—21no—
363#548—21no—
364#547—21no—
365#547—22no—
366#546—21no—
367#546—22no—
368#537—21no—
369#537C2×D1111yescharacteristic
370#536—21no—
371#536C2×D1111yescharacteristic
372#525—21no—
373#525C2×D1111yescharacteristic
374C2×C22⋊Q8—21no—
375C2×C22⋊Q8C2×D1111yescharacteristic
376#520C2×D1111yescharacteristic
377C22×C4⋊C4—111no—
378#484—221no—
379#483—221no—
380#481—221no—
381#480—221no—
382#428—112no—
383C2×#104—112no—
384C2×#104—112no—
385C2×#104—112no—
386#417—112no—
387#417—112no—
388#417—112no—
389#417—221no—
390#417—221no—
391C2×#103—221no—
392C2×#102—221no—
393C2×#101—112no—
394#407—111no—
395#400—222no—
396#391—112no—
397#382—112no—
398#381—222no—
399C4×C22⋊C4—111no—
400#343—112no—
401#339—112no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—22no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—44no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—84no—
420C22×C11#45412yes—
421C22×C11C2×#12011yescharacteristic
422C22×C11#54612yes—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—42no—
431C4×C11—41no—
432C4×C11C2×#12311yescharacteristic
433C4×C11#53411yescharacteristic
434C4×C11#54612yes—
435Dic11—82no—
436Dic11—82no—
4372−1+4—24no—
4382−1+4—42no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—22no—
443C2×#41—21no—
444C2×#41—24no—
445C2×#41—42no—
446C2×#41C22⋊D1111yescharacteristic
447C2×#41C22⋊D1111yescharacteristic
448C2×#41C22×D1111yescharacteristic
449C2×#41C22×D1111yescharacteristic
450C2×#41C22×D1111yescharacteristic
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8C22⋊D1111yescharacteristic
454C22×Q8C22×D1111yescharacteristic
455C22×D4—21no—
456C22×D4C22⋊D1111yescharacteristic
457C23×C4—21no—
458C23×C4—221no—
459C23×C4C22×D1111yescharacteristic
460C2×M16—112no—
461C2×M16—112no—
462C2×M16—221no—
463C2×M16—442no—
464C22×C8—221no—
465C4⋊Q8—22no—
466C4⋊Q8—21no—
467#124—22no—
468#124—21no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—21no—
473#123—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8C22⋊D1111yescharacteristic
486C22⋊Q8C22⋊D1111yescharacteristic
487#121—22no—
488#121—22no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121C22⋊D1111yescharacteristic
494#121C22⋊D1111yescharacteristic
495#120—22no—
496#120—21no—
497C4×Q8—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504#117—21no—
505#117C22×D1111yescharacteristic
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22⋊D1112yes—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—22no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4C22⋊D1112yes—
519C2×C42—112no—
520#107—222no—
521#106—222no—
522#104—224no—
523#104—442no—
524#104—442no—
525#103—222no—
526#103—222no—
527#103—222no—
528#102—222no—
529#102—222no—
530#102—222no—
531#101—442no—
532C22⋊C8—221no—
533C22⋊C8—221no—
534#95—221no—
535#95—224no—
536#95—224no—
537C2×C11—22no—
538C2×C11—22no—
539C2×C11—41no—
540C2×C11—42no—
541C2×C11—81no—
542C2×C11—81no—
543C2×C11#240511yescharacteristic
544C2×C11C2×#45411yescharacteristic
545C2×C11#302211yescharacteristic
546C24—21no—
547C24C2×C22⋊D1111yescharacteristic
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—44no—
556#41—41no—
557#41—41no—
558#41—44no—
559#41—44no—
560#41—48no—
561#41—42no—
562#41—42no—
563#41#434114yes—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—41no—
572C2×Q8—44no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8C2×C22⋊D1111yescharacteristic
576C2×Q8C2×C22⋊D1111yescharacteristic
577C2×Q8C2×C22⋊D1111yescharacteristic
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—44no—
591C2×D4C2×C22⋊D1111yescharacteristic
592C2×D4C2×C22⋊D1111yescharacteristic
593C2×D4C2×C22⋊D1111yescharacteristic
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—44no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—444no—
609C22×C4—441no—
610C22×C4—441no—
611C22×C4C2×C22⋊D1112yes—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C2×C22⋊D1112yes—
618C22×C4C23×D1111yescharacteristic
619M16—222no—
620M16—222no—
621M16—222no—
622M16—222no—
623M16—442no—
624C2×C8—222no—
625C2×C8—222no—
626C2×C8—442no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—222no—
638C4⋊C4—222no—
639C4⋊C4—441no—
640C4⋊C4—441no—
641C4⋊C4C2×C22⋊D1111yescharacteristic
642C4⋊C4C2×C22⋊D1111yescharacteristic
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—442no—
656C42—22no—
657C42—21no—
658C42—222no—
659C42—222no—
660C11#2402911yescharacteristic, complemented, Sylow
661C23—22no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—81no—
670C23#6700611yescharacteristic
671C23#6700611yescharacteristic
672C23C22×C22⋊D1111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—22no—
677Q8—42no—
678Q8—44no—
679Q8—41no—
680Q8—41no—
681Q8—42no—
682Q8#6698812yes—
683D4—24no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—81no—
696D4—82no—
697D4#6698812yes—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—82no—
724C2×C4—442no—
725C2×C4—444no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—882no—
730C2×C4—882no—
731C2×C4#6700611yescharacteristic
732C2×C4#6700611yescharacteristic
733C2×C4C2×#434112yes—
734C2×C4#6703712yes—
735C2×C4C22×C22⋊D1111yescharacteristic
736C2×C4C22×C22⋊D1111yescharacteristic
737C8—442no—
738C8—442no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—21no—
746C22—21no—
747C22—44no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—84no—
757C22#1062285812yes—
758C22#1062333712yes—
759C22C2×#6700611yescharacteristic
760C4—21no—
761C4—21no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—882no—
770C4—882no—
771C4C2×#6698811yescharacteristic
772C4#1062333511yescharacteristic
773C4#1062333712yes—
774C2—22no—
775C2—22no—
776C2—41no—
777C2—42no—
778C2—81no—
779C2—81no—
780C2#1307193911yescharacteristic
781C2C2×#1062285811yescharacteristic
782C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3489C2
socleC22×C11C2×#120
hypercenter#3489D11
hypocenterC11#24029
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13078536C2semidirect
2. C2×#10622845C2semidirect
3. #13073102C2semidirect
4. #13069842C2semidirect
5. #13069830C2semidirect
6. #13069085C2semidirect
7. #13068919C2semidirect
8. #13068849C2semidirect
9. #13068575C2semidirect
10. #13068560C2semidirect
33. C2×#66901C22semidirect
38. #10622845C22semidirect
39. #10622843C22semidirect
40. C2×#66900C22semidirect
49. #10622608C22semidirect
51. #10622590C22semidirect
53. #10622170C22semidirect
54. #10622168C22semidirect
660. C11#24029semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106228452
#130731022
#130698422
#130698302
#130690852
#130689192
#130688492
#130685752
#130685602
C11×#34892
#2402911