Finite Group Databasebeta

← #14800865

Subgroups — #14800865

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622655C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13072045C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069802C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13069486C211yesmaximal, characteristic, complemented
11#13069316C211yesmaximal, characteristic, complemented
12#13069050C211yesmaximal, characteristic, complemented
13#13069037C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2407C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#394—21no—
28C11×#392—21no—
29C11×#391C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#386—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34#10622852—24no—
35#10622846—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622835—21no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622655—24no—
47#10622624—24no—
48#10622585—21no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622565—21no—
54#10622558—21no—
55#10622542C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11D411yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×Dic22C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—41no—
80C11×#121—22no—
81C11×#121—41no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—41no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—41no—
106#66979—22no—
107#66979—41no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113#66977—22no—
114#66977—41no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318—41no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—22no—
124C22×C11⋊C8—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#66899—22no—
133#66899—22no—
134#66899—22no—
135#66896—22no—
136#66896—22no—
137#66896D414yescomplemented
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)D414yescomplemented
144#66874—22no—
145#66874—41no—
146#66872—41no—
147#66871—22no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25129—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C11×#41—28no—
155C11×#41—44no—
156C11×#41—44no—
157C11×#41—44no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11#4112yes—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—42no—
177C2×D4×C11—81no—
178C2×D4×C11C2×D412yes—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—42no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4—81no—
225C42×C11—21no—
226C42×C11—21no—
227C22⋊Dic11—42no—
228C22⋊Dic11—42no—
229C22⋊Dic11—42no—
230C22⋊Dic11—42no—
231#4326—44no—
232#4324—44no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11C2×D412yes—
239Dic11⋊C4—42no—
240Dic11⋊C4—42no—
241Dic11⋊C4—42no—
242C4×Dic11—42no—
243#4318—44no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—44no—
254C2×C11⋊C8C2×D412yes—
255C2×C11⋊C8C2×D412yes—
256C2×C11⋊C8C2×D412yes—
257C2×#468—111no—
258C2×#452—111no—
259C2×#435—111no—
260C2×#416—111no—
261#2415—111no—
262#2407D1111yescharacteristic
263#2068—111no—
264#2055—111no—
265#2034—111no—
266#2001—111no—
267#1971—111no—
268#1936—111no—
269#1894—111no—
270#1892—111no—
271#1854—111no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—22no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11#12112yes—
293C23×C11C22×D411yescharacteristic
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—41no—
297Q8×C11—41no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—44no—
301D4×C11—48no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—84no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—48no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11#12112yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×Dic11—22no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353Dic22—41no—
354Dic22—41no—
355Dic22—41no—
356Dic22—41no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C11⋊C8—41no—
361C22×#41C2×D1111yescharacteristic
362C22×Q16—111no—
363C22×SD16—111no—
364C22×M16—111no—
365C23×C8—111no—
366C2×C22⋊Q8—111no—
367C2×C22⋊Q8—111no—
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121C2×D1111yescharacteristic
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117—111no—
372#468—224no—
373#452—224no—
374#435—224no—
375C2×#107—111no—
376C2×#106—111no—
377C2×C4⋊C8—111no—
378#416—224no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×#97—111no—
390#397—221no—
391#394—21no—
392#394—221no—
393#392—21no—
394#391—111no—
395#391C2×D1111yescharacteristic
396#390C2×D1111yescharacteristic
397#389—111no—
398#389—221no—
399#388—221no—
400#386—21no—
401#385—21no—
402#380—111no—
403#380C2×D1111yescharacteristic
404#340—111no—
405#340—111no—
406#340—111no—
407#340—111no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—42no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—42no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11C2×#12111yescharacteristic
430C22×C11D4211yescharacteristic
431C22×C11#54611yescharacteristic
432C22×C11#57511yescharacteristic
433C22×C11#57511yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—42no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11#52511yescharacteristic
444C4×C11#53811yescharacteristic
445C4×C11D4211yescharacteristic
446C4×C11#54611yescharacteristic
447Dic11—42no—
448Dic11—81no—
449Dic11—81no—
450Dic11—81no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—41no—
456C2×#41—41no—
457C22×Q8—111no—
458C22×Q8C22×D1111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C22⋊D1111yescharacteristic
462C22×D4C22×D1111yescharacteristic
463C23×C4—21no—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C2×Q16—222no—
467C2×Q16—222no—
468C2×Q16—441no—
469C2×SD16—222no—
470C2×SD16—222no—
471C2×SD16—441no—
472C2×M16—222no—
473C2×M16—222no—
474C2×M16—441no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—222no—
480C22×C8—222no—
481C22×C8—441no—
482C22⋊Q8—22no—
483C22⋊Q8—41no—
484C22⋊Q8—222no—
485C22⋊Q8—222no—
486C22⋊Q8—222no—
487C22⋊Q8—441no—
488#121—22no—
489#121—41no—
490C4×D4—22no—
491C4×D4—22no—
492#117—222no—
493#117—441no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4C22⋊D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4C22⋊D1111yescharacteristic
514C2×C22⋊C4C22⋊D1111yescharacteristic
515C2×C42—221no—
516C2×C42C22×D1111yescharacteristic
517#107—222no—
518#106—441no—
519C4⋊C8—222no—
520#103—222no—
521#103—222no—
522#103—222no—
523#103—222no—
524#103—441no—
525#102—114no—
526#102—222no—
527#102—222no—
528C22⋊C8—114no—
529C22⋊C8—222no—
530#97—222no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—221no—
535#95—221no—
536#95—221no—
537#95—221no—
538C2×C11—42no—
539C2×C11—81no—
540C2×C11—82no—
541C2×C11#242411yescharacteristic
542C2×C11#305411yescharacteristic
543C2×C11#306311yescharacteristic
544C2×C11#326711yescharacteristic
545C2×C11#326911yescharacteristic
546C2×C11#331311yescharacteristic
547C2×C11#331711yescharacteristic
548C24—21no—
549C24C2×C22⋊D1111yescharacteristic
550C24C2×C22⋊D1111yescharacteristic
551#41—28no—
552#41—44no—
553#41—44no—
554#41—44no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—221no—
561C2×Q8—221no—
562C2×Q8—221no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8#434112yes—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4D4×D1112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4D4×D1112yes—
603C22×C4#434112yes—
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C2×C22⋊D1111yescharacteristic
606C22×C4C2×C22⋊D1111yescharacteristic
607C22×C4C2×C22⋊D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609Q16—444no—
610SD16—444no—
611M16—444no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—444no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—42no—
631C4⋊C4—112no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—442no—
638C4⋊C4—442no—
639C4⋊C4—442no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C42—21no—
652C42—21no—
653C42—442no—
654C11#2512911yescharacteristic, complemented, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#6699212yes—
676C23C22×C22⋊D1111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—441no—
682Q8—441no—
683Q8—441no—
684Q8—441no—
685D4—22no—
686D4—22no—
687D4—44no—
688D4—48no—
689D4—41no—
690D4—41no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—48no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—222no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4#6699212yes—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4C2×D4×D1111yescharacteristic
736C2×C4C2×#434111yescharacteristic
737C2×C4C2×#434111yescharacteristic
738C2×C4#6703711yescharacteristic
739C2×C4#6703711yescharacteristic
740C8—222no—
741C8—222no—
742C8—222no—
743C8—441no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22D4×C22⋊D1111yescharacteristic
766C22C2×#6699211yescharacteristic
767C22#1062333711yescharacteristic
768C22#1062335311yescharacteristic
769C22#1062335311yescharacteristic
770C22#1062336711yescharacteristic
771C22#1062336911yescharacteristic
772C4—22no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—442no—
780C4—881no—
781C4—881no—
782C4—881no—
783C4#1062311711yescharacteristic
784C4#1062312111yescharacteristic
785C4#1062312211yescharacteristic
786C4#1062312411yescharacteristic
787C2—42no—
788C2—81no—
789C2—82no—
790C2#1307215611yescharacteristic
791C2#1307822211yescharacteristic
792C2#1307830911yescharacteristic
793C2#1308013711yescharacteristic
794C2#1308016711yescharacteristic
795C2#1308068211yescharacteristic
796C2#1308074211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2407C2
socleC23×C11C22×D4
hypercenter#2407D11
hypocenterC11#25129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#10622655C2semidirect
2. C2×#10622852C2semidirect
3. C2×#10622624C2semidirect
4. C2×#10622846C2semidirect
5. #13072045C2semidirect
6. #13070011C2semidirect
7. #13069933C2semidirect
8. #13069802C2semidirect
9. #13069624C2semidirect
10. #13069486C2semidirect
11. #13069316C2semidirect
12. #13069050C2semidirect
13. #13069037C2semidirect
14. #13068813C2semidirect
137. #66896D4semidirect
143. C22⋊(C11⋊C8)D4semidirect
654. C11#25129semidirect

Maximal subgroups

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

subgroupindex
C2×#106226552
C2×#106228522
C2×#106226242
C2×#106228462
#130720452
#130700112
#130699332
#130698022
#130696242
#130694862
#130693162
#130690502
#130690372
#130688132
C11×#24072
#2512911