Finite Group Databasebeta

← #14800867

Subgroups — #14800867

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×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622660C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5#13071961C211yesmaximal, characteristic
6#13070008C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13069486C211yesmaximal, characteristic, complemented
11#13069312C211yesmaximal, characteristic, complemented
12#13069047C211yesmaximal, characteristic, complemented
13#13069040C211yesmaximal, characteristic, complemented
14#13068815C211yesmaximal, characteristic, complemented
15C11×#2415C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#397—21no—
28C11×#394—21no—
29C11×#391C2211yescharacteristic
30C11×#389—21no—
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C11×#380C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622836—21no—
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622662—24no—
41#10622660—24no—
42#10622624—24no—
43#10622615—24no—
44#10622602—21no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622572—21no—
54#10622569—21no—
55#10622552C2211yescharacteristic
56#10622542C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—41no—
74C2×#4339—41no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×Dic22C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—41no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C11×#117—22no—
85C11×#117—41no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×#4326—22no—
104C2×#4326—22no—
105C2×#4326—41no—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—41no—
109#66983—22no—
110#66983—41no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116#66977—22no—
117#66977—41no—
118C2×Dic11⋊C4—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—
132C11×#95—21no—
133#66899—22no—
134#66899—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139C22⋊(C11⋊C8)D414yescomplemented
140#66874—22no—
141#66874—22no—
142#66874—22no—
143#66873—22no—
144#66873—22no—
145#66873D414yescomplemented
146#66872—41no—
147#66871—22no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25129—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—42no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—81no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193#4339—28no—
194#4339—44no—
195#4339—44no—
196#4339—44no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44C2×D412yes—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22#4112yes—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4C2×D412yes—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—81no—
233#4326—44no—
234#4325—44no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—81no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242Dic11⋊C4—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#2415D1111yescharacteristic, complemented
262#2407—111no—
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—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11#12112yes—
286C23×C11C22×D411yescharacteristic
287C22×D11—22no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294Q8×C11—41no—
295Q8×C11—41no—
296Q8×C11—41no—
297Q8×C11—41no—
298D4×C11—44no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
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#12112yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C22⋊D11—48no—
338C22⋊D11—84no—
339C2×Dic11—22no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348D44—22no—
349D44—22no—
350D44—41no—
351D44—41no—
352C4×D11—48no—
353Dic22—22no—
354Dic22—22no—
355Dic22—41no—
356Dic22—41no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C11⋊C8—41no—
361C22×#41—111no—
362C22×Q16—111no—
363C22×SD16—111no—
364C22×M16—111no—
365C23×C8—111no—
366C2×C22⋊Q8—111no—
367C2×C22⋊Q8C2×D1111yescharacteristic
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121—111no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117C2×D1111yescharacteristic
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—21no—
391#394—21no—
392#394—221no—
393#392—221no—
394#391—111no—
395#391C2×D1111yescharacteristic
396#390—111no—
397#389—21no—
398#389C2×D1111yescharacteristic
399#388—21no—
400#386—221no—
401#385—221no—
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—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11C2×#12111yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11#54611yescharacteristic
425C22×C11#57511yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57711yescharacteristic
428C22×C11#57811yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—42no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11—81no—
444C4×C11#52511yescharacteristic
445C4×C11#53811yescharacteristic
446C4×C11D4211yescharacteristic
447C4×C11#54611yescharacteristic
448Dic11—42no—
449Dic11—81no—
450Dic11—81no—
451C2×#41—222no—
452C2×#41—222no—
453C2×#41—222no—
454C2×#41—222no—
455C2×#41—441no—
456C2×#41—441no—
457C22×Q8—111no—
458C22×Q8C22×D1111yescharacteristic
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22⋊D1111yescharacteristic
463C23×C4—221no—
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—22no—
484C22⋊Q8—22no—
485C22⋊Q8—41no—
486C22⋊Q8—222no—
487C22⋊Q8—441no—
488#121—222no—
489#121—441no—
490C4×D4—22no—
491C4×D4—22no—
492#117—22no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4C22⋊D1111yescharacteristic
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—221no—
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—21no—
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—21no—
535#95—221no—
536#95—221no—
537#95—221no—
538C2×C11—42no—
539C2×C11—81no—
540C2×C11#242411yescharacteristic
541C2×C11#305411yescharacteristic
542C2×C11#306311yescharacteristic
543C2×C11#326711yescharacteristic
544C2×C11#326911yescharacteristic
545C2×C11#331311yescharacteristic
546C2×C11#331711yescharacteristic
547D11—82no—
548C24—221no—
549C24C2×C22⋊D1111yescharacteristic
550C24C2×C22⋊D1111yescharacteristic
551#41—228no—
552#41—444no—
553#41—444no—
554#41—444no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—112no—
562C2×Q8—221no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×D4—22no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—112no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—442no—
577C2×D4—442no—
578C2×D4—442no—
579C2×D4—442no—
580C2×D4—442no—
581C2×D4—881no—
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—21no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—442no—
600C22×C4—442no—
601C22×C4—442no—
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—21no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—442no—
639C4⋊C4D4×D1112yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—442no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4—881no—
650C22⋊C4—881no—
651C42—21no—
652C42—21no—
653C42—42no—
654C11#2512911yescharacteristic, complemented, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—222no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23#6699212yes—
676C23C22×C22⋊D1111yescharacteristic
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—222no—
682Q8—222no—
683Q8—441no—
684Q8—441no—
685D4—44no—
686D4—222no—
687D4—222no—
688D4—448no—
689D4—441no—
690D4—441no—
691D4—884no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
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—41no—
722C2×C4—41no—
723C2×C4—222no—
724C2×C4—448no—
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×C4#6703711yescharacteristic
738C2×C4#41×D1111yescharacteristic
739C2×C4#6704211yescharacteristic
740C8—222no—
741C8—222no—
742C8—222no—
743C8—441no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22D4×C22⋊D1111yescharacteristic
766C22C2×#6699211yescharacteristic
767C22#1062335311yescharacteristic
768C22#1062335311yescharacteristic
769C22#1062336011yescharacteristic
770C22#1062336811yescharacteristic
771C22#1062336911yescharacteristic
772C4—22no—
773C4—41no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—442no—
781C4—881no—
782C4—881no—
783C4#1062313711yescharacteristic
784C4#1062314011yescharacteristic
785C4#1062314111yescharacteristic
786C4#1062314811yescharacteristic
787C2—42no—
788C2—81no—
789C2—882no—
790C2#1307215811yescharacteristic
791C2#1307822211yescharacteristic
792C2#1307830311yescharacteristic
793C2#1308014211yescharacteristic
794C2#1308017211yescharacteristic
795C2#1308067611yescharacteristic
796C2#1308073611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2415C2
socleC23×C11C22×D4
prime radical#13071961C2
hypercenter#2415D11
hypocenterC11#25129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622660C2semidirect
3. C2×#10622624C2semidirect
4. C2×#10622615C2semidirect
6. #13070008C2semidirect
7. #13069931C2semidirect
8. #13069805C2semidirect
9. #13069624C2semidirect
10. #13069486C2semidirect
11. #13069312C2semidirect
12. #13069047C2semidirect
13. #13069040C2semidirect
14. #13068815C2semidirect
15. C11×#2415C2semidirect
139. C22⋊(C11⋊C8)D4semidirect
145. #66873D4semidirect
261. #2415D11semidirect
654. C11#25129semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106226602
C2×#106226242
C2×#106226152
#130719612
#130700082
#130699312
#130698052
#130696242
#130694862
#130693122
#130690472
#130690402
#130688152
C11×#24152
#2512911