Finite Group Databasebeta

← #14801548

Subgroups — #14801548

Order 2816.

1106 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×#10622667C211yesmaximal, characteristic, complemented
2C2×#10622660C211yesmaximal, characteristic, complemented
3C2×#10622650C211yesmaximal, characteristic
4C2×#10622643C211yesmaximal, characteristic, complemented
5#13071456C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069802C211yesmaximal, characteristic, complemented
9#13069693C211yesmaximal, characteristic, complemented
10#13069491C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic, complemented
13#13068971C211yesmaximal, characteristic, complemented
14#13068883C211yesmaximal, characteristic, complemented
15C11×#2426C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#396—21no—
28C11×#394—21no—
29C11×#390—21no—
30C11×#390C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C4×C11×C22⋊C4C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622667—24no—
42#10622660—24no—
43#10622650—24no—
44#10622643—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51#10622570—21no—
52#10622570—21no—
53#10622552C2211yescharacteristic
54#10622552C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622280—21no—
58#10622279—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—41no—
73C2×#4339—41no—
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×Dic22C2311yescharacteristic
77C11×#124—22no—
78C11×#124—41no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—41no—
81C11×#121—22no—
82C11×#121—41no—
83C4×Q8×C11—22no—
84C4×Q8×C11—41no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×#4326—22no—
103C2×#4326—22no—
104C2×#4326D414yescomplemented
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—41no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×#4323—41no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C4×Dic22—22no—
129C4×Dic22—22no—
130C4×Dic22—41no—
131C4×Dic22—41no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135#66899—22no—
136#66899—22no—
137#66896—22no—
138#66896—41no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874D414yes—
144#66873—22no—
145#66873—22no—
146#66872—22no—
147#66872—41no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25175—111nomaximal, Sylow
151C24×C11—21no—
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×C11C2×D412yes—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—81no—
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×C11—21no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—24no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190#4339—44no—
191#4339—44no—
192#4339—44no—
193#4339—44no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44#4112yes—
200C2×C4×D11—24no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22C2×D412yes—
207C2×Dic22C2×D412yes—
208C2×Dic22#4112yes—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4C2×D412yes—
216C11×C22⋊C4—41no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—81no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—42no—
229C22⋊Dic11—81no—
230#4326—28no—
231#4325—44no—
232#4324—44no—
233#4323—44no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—81no—
237(C2×D11)⋊C4—81no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
244C4×Dic11—42no—
245C4×Dic11—42no—
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—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D412yes—
258C2×#464—111no—
259C2×#452—111no—
260C2×#449—111no—
261C2×#441—111no—
262#2426D1111yescharacteristic, complemented
263#2341—111no—
264#2065—111no—
265#2035—111no—
266#2034—111no—
267#2012—111no—
268#1972—111no—
269#1924—111no—
270#1880—111no—
271#1880—111no—
272#1865—111no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11C22×D411yescharacteristic
288C22×D11—22no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—41no—
298Q8×C11—41no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—84no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
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—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
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—41no—
331C2×C4×C11—41no—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C22⋊D11—48no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
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—22no—
356Dic22#12114yes—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C22×#41—111no—
362C22×Q16—111no—
363C22×SD16—111no—
364C22×SD16—111no—
365C22×D8—111no—
366C2×#124C2×D1111yescharacteristic
367C2×C22⋊Q8C2×D1111yescharacteristic
368C2×#121C2×D1111yescharacteristic
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×Q8C2×D1111yescharacteristic
372#464—224no—
373#452—224no—
374#449—224no—
375#441—224no—
376C2×#106—111no—
377C2×#106—111no—
378C2×C4⋊C8—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×#97—111no—
390#396—21no—
391#394—21no—
392#390—21no—
393#390—111no—
394#390—111no—
395#390—221no—
396#390—221no—
397#390C2×D1111yescharacteristic
398#389C2×D1111yescharacteristic
399#388—21no—
400#380—111no—
401#380—221no—
402C4×C22⋊C4—221no—
403C4×C22⋊C4C2×D1111yescharacteristic
404#340—111no—
405#340—111no—
406#336—111no—
407#336—111no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11#52511yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11D4211yescharacteristic
425C22×C11#57511yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57711yescharacteristic
428C22×C11#57711yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—41no—
437C4×C11—42no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—41no—
442C4×C11—42no—
443C4×C11—81no—
444C4×C11C2×#12111yescharacteristic
445C4×C11#53811yescharacteristic
446C4×C11#54611yescharacteristic
447C4×C11#54611yescharacteristic
448Dic11—24no—
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—21no—
460C22×D4—111no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C23×C4—221no—
464C23×C4C22×D1111yescharacteristic
465C2×Q16—114no—
466C2×Q16—222no—
467C2×Q16—222no—
468C2×SD16—222no—
469C2×SD16—222no—
470C2×SD16—222no—
471C2×SD16—222no—
472C2×SD16—222no—
473C2×SD16—441no—
474C2×D8—222no—
475C2×D8—222no—
476C2×D8—441no—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—111no—
481#124—22no—
482#124—41no—
483C22⋊Q8—22no—
484C22⋊Q8—41no—
485#121—22no—
486#121—41no—
487C4×Q8—22no—
488C4×Q8—41no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×Q8—441no—
492C4×Q8—441no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
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×C42—221no—
517C2×C42—221no—
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520#106—222no—
521#106—441no—
522C4⋊C8—222no—
523#103—114no—
524#103—222no—
525#103—222no—
526#103—222no—
527#102—222no—
528#102—222no—
529#102—222no—
530#102—441no—
531C22⋊C8—222no—
532C22⋊C8—222no—
533#97—222no—
534#95—21no—
535#95—221no—
536#95C22⋊D1111yescharacteristic
537#95C22⋊D1111yescharacteristic
538C2×C11—81no—
539C2×C11—161no—
540C2×C11#242411yescharacteristic
541C2×C11#311111yescharacteristic
542C2×C11#312511yescharacteristic
543C2×C11#327111yescharacteristic
544C2×C11#327111yescharacteristic
545C2×C11#327111yescharacteristic
546C2×C11#327511yescharacteristic
547D11—82no—
548C24—21no—
549C24—221no—
550C24C2×C22⋊D1111yescharacteristic
551#41—444no—
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—112no—
561C2×Q8—112no—
562C2×Q8—112no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8D4×D1112yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—81no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—442no—
584C2×D4—442no—
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—224no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C23×D1111yescharacteristic
606Q16—228no—
607SD16—444no—
608SD16—444no—
609D8—444no—
610C2×C8—112no—
611C2×C8—112no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—81no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4—221no—
632C4⋊C4—442no—
633C4⋊C4—442no—
634C4⋊C4D4×D1112yes—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—442no—
644C22⋊C4—442no—
645C22⋊C4—881no—
646C22⋊C4—881no—
647C22⋊C4—881no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—42no—
653C42—442no—
654C42—442no—
655C11#2517511yescharacteristic, complemented, Sylow
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—222no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23C22×C22⋊D1111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—114no—
683Q8—222no—
684Q8—222no—
685Q8—222no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—84no—
691D4—222no—
692D4—222no—
693D4—448no—
694D4—441no—
695D4—441no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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—41no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—448no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4C2×D4×D1111yescharacteristic
736C2×C4#6703711yescharacteristic
737C2×C4#6703711yescharacteristic
738C2×C4#41×D1111yescharacteristic
739C2×C4#41×D1111yescharacteristic
740C8—222no—
741C8—222no—
742C8—441no—
743C8—441no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22D4×C22⋊D1111yescharacteristic
766C22D4×C22⋊D1111yescharacteristic
767C22#1062335311yescharacteristic
768C22#1062335311yescharacteristic
769C22#1062335911yescharacteristic
770C22#1062336711yescharacteristic
771C22#1062336811yescharacteristic
772C4—41no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—81no—
780C4—224no—
781C4—881no—
782C4—881no—
783C4D11×#12111yescharacteristic
784C4#1062314111yescharacteristic
785C4#1062314311yescharacteristic
786C4#1062314411yescharacteristic
787C2—81no—
788C2—161no—
789C2—882no—
790C2#1307214911yescharacteristic
791C2#1307871911yescharacteristic
792C2#1307888711yescharacteristic
793C2#1308019711yescharacteristic
794C2#1308020211yescharacteristic
795C2#1308020211yescharacteristic
796C2#1308024311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2426C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
hypercenter#2426D11
hypocenterC11#25175
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#10622667C2semidirect
2. C2×#10622660C2semidirect
4. C2×#10622643C2semidirect
5. #13071456C2semidirect
6. #13069987C2semidirect
7. #13069809C2semidirect
8. #13069802C2semidirect
9. #13069693C2semidirect
10. #13069491C2semidirect
11. #13069231C2semidirect
12. #13068974C2semidirect
13. #13068971C2semidirect
14. #13068883C2semidirect
15. C11×#2426C2semidirect
104. C2×#4326D4semidirect
262. #2426D11semidirect
655. C11#25175semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×#106226602
C2×#106226502
C2×#106226432
#130714562
#130699872
#130698092
#130698022
#130696932
#130694912
#130692312
#130689742
#130689712
#130688832
C11×#24262
#2517511