Finite Group Databasebeta

← #14960881

Subgroups — #14960881

Order 2816.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076893C212yesmaximal, complemented
2#13075662C211yesmaximal, characteristic, complemented
3#13075657C211yesmaximal, characteristic, complemented
4#13075653C212yesmaximal, complemented
5#13075179C212yesmaximal, complemented
6#13075011C212yesmaximal, complemented
7#13075007C212yesmaximal, complemented
8#13074996C212yesmaximal, complemented
9#13074945C212yesmaximal, complemented
10#13074842C211yesmaximal, characteristic, complemented
11#13074824C211yesmaximal, characteristic, complemented
12#13074421C211yesmaximal, characteristic, complemented
13#13074350C211yesmaximal, characteristic, complemented
14#13072856C212yesmaximal, complemented
15#13072736C212yesmaximal, complemented
16#13072152C212yesmaximal, complemented
17#13072078C212yesmaximal, complemented
18#13071274C212yesmaximal, complemented
19C2×C11×#379C211yesmaximal, characteristic, complemented
20C26×C11C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C2×#67006C2212yes—
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#67006C2212yes—
29C2×#67006C2212yes—
30C2×#67006C2212yes—
31C2×#67006C2212yes—
32C2×#66983C2211yescharacteristic, complemented
33C2×C4×C22⋊D11C2212yescomplemented
34C2×#66977C2211yescharacteristic, complemented
35C2×#66938C2212yescomplemented
36C2×#66937C2212yescomplemented
37C2×#66936C2212yescomplemented
38C2×#66932C2212yescomplemented
39C11×#379C2212yes—
40C11×#379C2212yes—
41C11×#379C2211yescharacteristic
42C11×#379C2211yescharacteristic
43C11×#379C2211yescharacteristic
44C11×#379C2211yescharacteristic
45#10622860C2212yes—
46#10622860C2212yes—
47#10622860C2212yes—
48#10622860C2212yes—
49#10622860C2212yes—
50#10622860C2212yes—
51#10622860C2212yes—
52#10622826C2212yescomplemented
53#10622826C2212yescomplemented
54#10622825C2211yescharacteristic, complemented
55#10622825C2211yescharacteristic, complemented
56#10622823C2212yescomplemented
57#10622823C2212yescomplemented
58C4×C22⋊Dic11C2212yescomplemented
59#10622574C2212yescomplemented
60#10622574C2212yescomplemented
61#10622574C2212yescomplemented
62#10622574C2212yescomplemented
63#10622573C2211yescharacteristic, complemented
64#10622573C2212yescomplemented
65#10622573C2211yescharacteristic, complemented
66#10622572C2212yescomplemented
67#10622572C2212yescomplemented
68#10622572C2212yescomplemented
69#10622572C2212yescomplemented
70#10622570C2212yescomplemented
71#10622570C2212yescomplemented
72#10622570C2212yescomplemented
73#10622570C2212yescomplemented
74#10622569C2212yescomplemented
75#10622569C2212yescomplemented
76#10622569C2212yescomplemented
77#10622569C2212yescomplemented
78#10622566C2212yescomplemented
79#10622566C2211yescharacteristic, complemented
80#10622566C2211yescharacteristic, complemented
81#10622565C2212yescomplemented
82#10622565C2212yescomplemented
83#10622565C2212yescomplemented
84#10622565C2212yescomplemented
85#10622564C2212yescomplemented
86#10622564C2212yescomplemented
87#10622564C2212yescomplemented
88#10622564C2212yescomplemented
89#10622562C2212yescomplemented
90#10622562C2211yescharacteristic, complemented
91#10622562C2211yescharacteristic, complemented
92#10622561C2212yescomplemented
93#10622561C2212yescomplemented
94#10622561C2212yescomplemented
95#10622561C2212yescomplemented
96#10622560C2211yescharacteristic, complemented
97#10622560C2212yescomplemented
98#10622560C2211yescharacteristic, complemented
99#10622558C2212yescomplemented
100#10622558C2212yescomplemented
101#10622558C2212yescomplemented
102#10622558C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622557C2212yescomplemented
106#10622557C2212yescomplemented
107C25×C11—24no—
108C25×C11—44no—
109C25×C11—44no—
110C25×C11—42no—
111C25×C11—42no—
112C25×C11C2312yes—
113C25×C11C2312yes—
114C25×C11C2311yescharacteristic
115C25×C11C2311yescharacteristic
116C25×C11C2311yescharacteristic
117C23×C4×C11C2311yescharacteristic
118C23×C4×C11C2312yes—
119C23×C4×C11C2311yescharacteristic
120C22×C22⋊D11C2312yes—
121C22×C22⋊D11C2312yes—
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C2312yes—
127C22×D44C2311yescharacteristic, complemented
128C22×C4×D11C2312yescomplemented
129C22×Dic22C2311yescharacteristic, complemented
130C2×C11×C22⋊C4—44no—
131C2×C11×C22⋊C4—44no—
132C2×C11×C22⋊C4—42no—
133C2×C11×C22⋊C4—42no—
134C2×C11×C22⋊C4C2312yes—
135C2×C11×C22⋊C4C2312yes—
136C2×C11×C22⋊C4C2312yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4C2312yes—
149#67006—28no—
150#67006—44no—
151#67006—44no—
152#67006—44no—
153#67006—44no—
154#67006—44no—
155#67006—44no—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177#66983—42no—
178C4×C22⋊D11—44no—
179C2×(C2×D11)⋊C4C2312yescomplemented
180C2×(C2×D11)⋊C4C2312yescomplemented
181C2×(C2×D11)⋊C4C2312yescomplemented
182C2×(C2×D11)⋊C4C2312yescomplemented
183C2×(C2×D11)⋊C4C2312yescomplemented
184C2×(C2×D11)⋊C4C2312yescomplemented
185C2×C4⋊Dic11C2312yescomplemented
186C2×C4⋊Dic11C2312yescomplemented
187C2×C4⋊Dic11C2311yescharacteristic, complemented
188C2×C4⋊Dic11C2311yescharacteristic, complemented
189#66977—42no—
190C2×Dic11⋊C4C2312yescomplemented
191C2×Dic11⋊C4C2312yescomplemented
192C2×Dic11⋊C4C2312yescomplemented
193C2×Dic11⋊C4C2312yescomplemented
194C2×Dic11⋊C4C2312yescomplemented
195C2×Dic11⋊C4C2312yescomplemented
196C2×C4×Dic11C2312yescomplemented
197C2×C4×Dic11C2312yescomplemented
198C2×C4×Dic11C2312yescomplemented
199#66938—44no—
200#66937—44no—
201#66936—44no—
202#66932—44no—
203C11⋊#95C2312yescomplemented
204C11⋊#95C2311yescharacteristic, complemented
205C11⋊#95C2312yescomplemented
206C11⋊#95C2312yescomplemented
207C11⋊#95C2312yescomplemented
208C11⋊#95C2312yescomplemented
209C11⋊#95C2312yescomplemented
210C11⋊#95C2311yescharacteristic, complemented
211C11⋊#95C2311yescharacteristic, complemented
212C11⋊#95C2312yescomplemented
213C11⋊#95C2312yescomplemented
214C11⋊#95C2312yescomplemented
215C11⋊#95C2312yescomplemented
216C11⋊#95C2311yescharacteristic, complemented
217#36725—111nomaximal, Sylow
218C24×C11—24no—
219C24×C11—24no—
220C24×C11—24no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—24no—
224C24×C11—22no—
225C24×C11—22no—
226C24×C11—24no—
227C24×C11—24no—
228C24×C11—24no—
229C24×C11—24no—
230C24×C11—24no—
231C24×C11—24no—
232C24×C11—42no—
233C24×C11—42no—
234C24×C11—42no—
235C24×C11—42no—
236C24×C11—42no—
237C24×C11—42no—
238C24×C11—42no—
239C24×C11—42no—
240C24×C11—42no—
241C24×C11—41no—
242C24×C11—41no—
243C24×C11—42no—
244C24×C11—41no—
245C24×C11—41no—
246C24×C11—432no—
247C24×C11—416no—
248C24×C11—416no—
249C24×C11—432no—
250C24×C11—416no—
251C24×C11#4114yes—
252C24×C11C2411yescharacteristic
253C24×C11C2411yescharacteristic
254C24×C11C2412yes—
255C24×C11C2412yes—
256C24×C11C2411yescharacteristic
257C23×D11C2412yes—
258C22×C4×C11—22no—
259C22×C4×C11—24no—
260C22×C4×C11—22no—
261C22×C4×C11—42no—
262C22×C4×C11—42no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C2×C22⋊D11—24no—
272C2×C22⋊D11—24no—
273C2×C22⋊D11—24no—
274C2×C22⋊D11—24no—
275C2×C22⋊D11—24no—
276C2×C22⋊D11—24no—
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—42no—
281C2×C22⋊D11—42no—
282C2×C22⋊D11—42no—
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C2×D44—42no—
300C2×D44—41no—
301C2×C4×D11—42no—
302C2×C4×D11—42no—
303C2×C4×D11—42no—
304C2×Dic22—42no—
305C2×Dic22—41no—
306C11×C22⋊C4—24no—
307C11×C22⋊C4—24no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—42no—
311C11×C22⋊C4—42no—
312C11×C22⋊C4—41no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4—41no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—42no—
317C11×C22⋊C4—41no—
318C11×C22⋊C4—42no—
319C11×C22⋊C4—41no—
320C11×C22⋊C4—41no—
321C22⋊Dic11—24no—
322C22⋊Dic11—24no—
323C22⋊Dic11—24no—
324C22⋊Dic11—24no—
325C22⋊Dic11—24no—
326C22⋊Dic11—24no—
327C22⋊Dic11—24no—
328C22⋊Dic11—24no—
329C22⋊Dic11—24no—
330C22⋊Dic11—42no—
331C22⋊Dic11—42no—
332C22⋊Dic11—42no—
333C22⋊Dic11—42no—
334C22⋊Dic11—42no—
335C22⋊Dic11—42no—
336C22⋊Dic11—42no—
337C22⋊Dic11—42no—
338C22⋊Dic11—42no—
339C22⋊Dic11—42no—
340C22⋊Dic11—42no—
341C22⋊Dic11—42no—
342(C2×D11)⋊C4—42no—
343(C2×D11)⋊C4—42no—
344(C2×D11)⋊C4—42no—
345(C2×D11)⋊C4—42no—
346(C2×D11)⋊C4—42no—
347(C2×D11)⋊C4—42no—
348C4⋊Dic11—42no—
349C4⋊Dic11—42no—
350C4⋊Dic11—41no—
351C4⋊Dic11—41no—
352Dic11⋊C4—42no—
353Dic11⋊C4—42no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356Dic11⋊C4—42no—
357Dic11⋊C4—42no—
358C4×Dic11—42no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361#2846—112no—
362#2736—111no—
363#2735—112no—
364#2735—111no—
365#2697—112no—
366#2685—112no—
367#2685—112no—
368#2684—112no—
369#2678—112no—
370#2670—111no—
371#2668—111no—
372#2626—111no—
373#2617—111no—
374#2480—112no—
375#2472—112no—
376#2424—112no—
377#2418—112no—
378#2321—112no—
379C2×#379D1111yescharacteristic, complemented
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—216no—
383C23×C11—28no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—21no—
399C23×C11—21no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—48no—
405C23×C11—48no—
406C23×C11—48no—
407C23×C11—48no—
408C23×C11—48no—
409C23×C11—48no—
410C23×C11—48no—
411C23×C11—48no—
412C23×C11—48no—
413C23×C11—44no—
414C23×C11—48no—
415C23×C11—44no—
416C23×C11—48no—
417C23×C11—44no—
418C23×C11—48no—
419C23×C11—44no—
420C23×C11—48no—
421C23×C11—44no—
422C23×C11—44no—
423C23×C11—48no—
424C23×C11—48no—
425C23×C11—48no—
426C23×C11—48no—
427C23×C11—4128no—
428C23×C11—44no—
429C23×C11—48no—
430C23×C11—44no—
431C23×C11—48no—
432C23×C11C2×#4112yes—
433C23×C11C2×#4112yes—
434C23×C11C2×#4112yes—
435C23×C11H(5,𝔽2)14yes—
436C23×C11H(5,𝔽2)14yes—
437C23×C11H(5,𝔽2)12yes—
438C23×C11H(5,𝔽2)12yes—
439C23×C11C2511yescharacteristic
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—82no—
462C2×C4×C11—84no—
463C2×C4×C11—82no—
464C22⋊D11—48no—
465C22⋊D11—84no—
466C22⋊D11—84no—
467C22⋊D11—84no—
468C22⋊D11—84no—
469C22⋊D11—84no—
470C22⋊D11—84no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492D44—82no—
493C4×D11—84no—
494Dic22—82no—
495C26C2×D1111yescharacteristic
496C2×#126—112no—
497C2×#124—112no—
498C2×#123—112no—
499C2×C22⋊Q8—111no—
500C2×#121—111no—
501C2×#121—112no—
502C2×#120—112no—
503C2×#120—112no—
504C2×#120—112no—
505C2×#120—112no—
506C2×#120—112no—
507C2×#120—112no—
508C2×#120—112no—
509C2×C4×D4—112no—
510C22×C22⋊C4C2×D1111yescharacteristic
511C22×C22⋊C4C2×D1111yescharacteristic
512C22×C22⋊C4C2×D1112yes—
513C22×C22⋊C4C2×D1112yes—
514#399—111no—
515#399—111no—
516#399—112no—
517#397—111no—
518#397—111no—
519#397—112no—
520#397—112no—
521#397—112no—
522#397—112no—
523#397—112no—
524#396—112no—
525#396—112no—
526#396—112no—
527#396—112no—
528#394—112no—
529#394—112no—
530#394—112no—
531#394—112no—
532#394—112no—
533#394—112no—
534#394—112no—
535#394—112no—
536#393—111no—
537#393—111no—
538#393—112no—
539#392—111no—
540#392—111no—
541#392—112no—
542#390—112no—
543#390—112no—
544#390—112no—
545#390—112no—
546#388—112no—
547#388—112no—
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388—112no—
556#388—112no—
557#388—112no—
558#386—112no—
559#386—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386—112no—
564#385—112no—
565#385—112no—
566#380—111no—
567#380—111no—
568#379—112no—
569#379—112no—
570#379—112no—
571#379—112no—
572#379—112no—
573#379—112no—
574#379—112no—
575#379C2×D1111yescharacteristic
576#379C2×D1111yescharacteristic
577#379C2×D1112yes—
578#379C2×D1112yes—
579#379C2×D1111yescharacteristic
580#379C2×D1111yescharacteristic
581C4×C22⋊C4—112no—
582C22×C11—24no—
583C22×C11—22no—
584C22×C11—24no—
585C22×C11—22no—
586C22×C11—22no—
587C22×C11—22no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—432no—
597C22×C11—416no—
598C22×C11—416no—
599C22×C11—416no—
600C22×C11—432no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—41no—
606C22×C11—42no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—41no—
613C22×C11—42no—
614C22×C11—41no—
615C22×C11#53814yes—
616C22×C11C22×#4111yescharacteristic
617C22×C11C2×H(5,𝔽2)11yescharacteristic
618C22×C11C2×H(5,𝔽2)11yescharacteristic
619C22×C11C2×H(5,𝔽2)12yes—
620C22×C11C2×H(5,𝔽2)12yes—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C4×C11—42no—
629C4×C11—41no—
630C4×C11—41no—
631C4×C11—41no—
632C4×C11—42no—
633C4×C11—41no—
634Dic11—42no—
635Dic11—42no—
636Dic11—42no—
637Dic11—42no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641C25—24no—
642C25—44no—
643C25—44no—
644C25—42no—
645C25—42no—
646C25C22×D1112yes—
647C25C22×D1111yescharacteristic
648C25C22×D1111yescharacteristic
649C25C22×D1112yes—
650C25C22×D1111yescharacteristic
651C22×Q8—111no—
652C22×D4—112no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—112no—
656C22×D4—112no—
657C22×D4—112no—
658C22×D4—112no—
659C22×D4—111no—
660C23×C4—112no—
661C23×C4C22×D1112yes—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664#126—444no—
665#124—444no—
666#123—444no—
667C22⋊Q8—442no—
668#121—444no—
669#121—442no—
670#120—228no—
671#120—444no—
672#120—444no—
673#120—444no—
674#120—444no—
675#120—444no—
676#120—444no—
677C4×D4—444no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—111no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4—112no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—42no—
691C2×C22⋊C4—42no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—112no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—112no—
701C2×C22⋊C4—112no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—112no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—112no—
706C2×C22⋊C4—112no—
707C2×C22⋊C4—112no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4—112no—
710C2×C22⋊C4—112no—
711C2×C22⋊C4—112no—
712C2×C22⋊C4—112no—
713C2×C22⋊C4—112no—
714C2×C22⋊C4—112no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4C22×D1112yes—
720C2×C22⋊C4C22×D1112yes—
721C2×C22⋊C4C22×D1112yes—
722C2×C22⋊C4C22×D1112yes—
723C2×C22⋊C4C22×D1111yescharacteristic
724C2×C22⋊C4C22×D1112yes—
725C2×C22⋊C4C22×D1112yes—
726C2×C22⋊C4C22×D1112yes—
727C2×C22⋊C4C22×D1111yescharacteristic
728C2×C22⋊C4C22×D1112yes—
729C2×C22⋊C4C22×D1112yes—
730C2×C22⋊C4C22×D1111yescharacteristic
731C2×C22⋊C4C22×D1111yescharacteristic
732C2×C22⋊C4C22×D1111yescharacteristic
733C2×C22⋊C4C22×D1111yescharacteristic
734C2×C42—112no—
735C2×C42—112no—
736C2×C42—112no—
737#95—112no—
738#95—112no—
739#95—111no—
740#95—111no—
741#95—111no—
742#95—111no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95—112no—
749#95—112no—
750#95—112no—
751C2×C11—24no—
752C2×C11—42no—
753C2×C11—42no—
754C2×C11—44no—
755C2×C11—44no—
756C2×C11C2×#53811yescharacteristic
757C2×C11#349012yes—
758C2×C11#353211yescharacteristic
759C2×C11#353212yes—
760C2×C11#353211yescharacteristic
761D11—82no—
762C24—24no—
763C24—24no—
764C24—24no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—24no—
770C24—24no—
771C24—24no—
772C24—24no—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—42no—
780C24—41no—
781C24—41no—
782C24—42no—
783C24—42no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—41no—
788C24—41no—
789C24—42no—
790C24—432no—
791C24—416no—
792C24—432no—
793C24—416no—
794C24—416no—
795C24—112no—
796C24#433914yes—
797C24C23×D1111yescharacteristic
798C24C23×D1111yescharacteristic
799C24C23×D1112yes—
800C24C23×D1112yes—
801C24C23×D1111yescharacteristic
802C2×Q8—441no—
803C2×Q8—442no—
804C2×D4—224no—
805C2×D4—224no—
806C2×D4—224no—
807C2×D4—224no—
808C2×D4—224no—
809C2×D4—224no—
810C2×D4—224no—
811C2×D4—224no—
812C2×D4—224no—
813C2×D4—442no—
814C2×D4—441no—
815C2×D4—442no—
816C2×D4—442no—
817C2×D4—442no—
818C2×D4—442no—
819C2×D4—442no—
820C2×D4—442no—
821C2×D4—442no—
822C2×D4—442no—
823C2×D4—442no—
824C2×D4—442no—
825C2×D4—442no—
826C2×D4—442no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—442no—
842C22×C4—442no—
843C22×C4—442no—
844C22×C4C23×D1112yes—
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1112yes—
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1111yescharacteristic
850C4⋊C4—442no—
851C4⋊C4—442no—
852C4⋊C4—441no—
853C4⋊C4—442no—
854C4⋊C4—441no—
855C4⋊C4—442no—
856C4⋊C4—442no—
857C4⋊C4—442no—
858C4⋊C4—442no—
859C4⋊C4—442no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—42no—
865C22⋊C4—42no—
866C22⋊C4—41no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—41no—
871C22⋊C4—41no—
872C22⋊C4—41no—
873C22⋊C4—41no—
874C22⋊C4—41no—
875C22⋊C4—224no—
876C22⋊C4—224no—
877C22⋊C4—224no—
878C22⋊C4—224no—
879C22⋊C4—224no—
880C22⋊C4—224no—
881C22⋊C4—224no—
882C22⋊C4—224no—
883C22⋊C4—224no—
884C22⋊C4—442no—
885C22⋊C4—442no—
886C22⋊C4—442no—
887C22⋊C4—442no—
888C22⋊C4—442no—
889C22⋊C4—442no—
890C22⋊C4—442no—
891C22⋊C4—442no—
892C22⋊C4—442no—
893C22⋊C4—442no—
894C22⋊C4—442no—
895C22⋊C4—442no—
896C22⋊C4—442no—
897C22⋊C4—442no—
898C22⋊C4—442no—
899C22⋊C4—442no—
900C22⋊C4—442no—
901C22⋊C4—442no—
902C42—442no—
903C42—442no—
904C42—442no—
905C11#3672511yescharacteristic, complemented, Sylow
906C23—22no—
907C23—22no—
908C23—216no—
909C23—28no—
910C23—22no—
911C23—22no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—48no—
931C23—48no—
932C23—48no—
933C23—48no—
934C23—48no—
935C23—48no—
936C23—44no—
937C23—44no—
938C23—48no—
939C23—48no—
940C23—48no—
941C23—48no—
942C23—48no—
943C23—44no—
944C23—44no—
945C23—48no—
946C23—44no—
947C23—44no—
948C23—48no—
949C23—48no—
950C23—48no—
951C23—48no—
952C23—48no—
953C23—4128no—
954C23—48no—
955C23—44no—
956C23—44no—
957C23—48no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23C2×#433912yes—
966C23C2×#433912yes—
967C23C2×#433912yes—
968C23#6703714yes—
969C23#6703714yes—
970C23#6703712yes—
971C23#6703712yes—
972C23C24×D1111yescharacteristic
973Q8—882no—
974D4—448no—
975D4—882no—
976D4—884no—
977D4—884no—
978D4—884no—
979D4—884no—
980D4—884no—
981D4—884no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—84no—
997C2×C4—82no—
998C2×C4—82no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—884no—
1021C22—24no—
1022C22—22no—
1023C22—22no—
1024C22—24no—
1025C22—22no—
1026C22—22no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—432no—
1036C22—416no—
1037C22—432no—
1038C22—416no—
1039C22—416no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22#1062302514yes—
1062C22C22×#433911yescharacteristic
1063C22C2×#6703711yescharacteristic
1064C22C2×#6703711yescharacteristic
1065C22C2×#6703712yes—
1066C22C2×#6703712yes—
1067C4—42no—
1068C4—41no—
1069C4—41no—
1070C4—42no—
1071C4—41no—
1072C4—41no—
1073C4—442no—
1074C4—442no—
1075C4—442no—
1076C4—442no—
1077C4—442no—
1078C4—442no—
1079C4—442no—
1080C2—24no—
1081C2—42no—
1082C2—42no—
1083C2—44no—
1084C2—44no—
1085C2—882no—
1086C2C2×#1062302511yescharacteristic
1087C2#1308230512yes—
1088C2#1308277112yes—
1089C2#1308277111yescharacteristic
1090C2#1308277111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#379C2
hypercenterC2×#379D11
hypocenterC11#36725
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. #13076893C2semidirect
2. #13075662C2semidirect
3. #13075657C2semidirect
4. #13075653C2semidirect
5. #13075179C2semidirect
6. #13075011C2semidirect
7. #13075007C2semidirect
8. #13074996C2semidirect
9. #13074945C2semidirect
10. #13074842C2semidirect
11. #13074824C2semidirect
12. #13074421C2semidirect
13. #13074350C2semidirect
14. #13072856C2semidirect
15. #13072736C2semidirect
16. #13072152C2semidirect
17. #13072078C2semidirect
18. #13071274C2semidirect
19. C2×C11×#379C2semidirect
32. C2×#66983C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×#66977C22semidirect
35. C2×#66938C22semidirect
36. C2×#66937C22semidirect
37. C2×#66936C22semidirect
38. C2×#66932C22semidirect
52. #10622826C22semidirect
53. #10622826C22semidirect
54. #10622825C22semidirect
55. #10622825C22semidirect
56. #10622823C22semidirect
57. #10622823C22semidirect
58. C4×C22⋊Dic11C22semidirect
59. #10622574C22semidirect
60. #10622574C22semidirect
61. #10622574C22semidirect
62. #10622574C22semidirect
63. #10622573C22semidirect
64. #10622573C22semidirect
65. #10622573C22semidirect
66. #10622572C22semidirect
67. #10622572C22semidirect
68. #10622572C22semidirect
69. #10622572C22semidirect
70. #10622570C22semidirect
71. #10622570C22semidirect
72. #10622570C22semidirect
73. #10622570C22semidirect
74. #10622569C22semidirect
75. #10622569C22semidirect
76. #10622569C22semidirect
77. #10622569C22semidirect
78. #10622566C22semidirect
79. #10622566C22semidirect
80. #10622566C22semidirect
81. #10622565C22semidirect
82. #10622565C22semidirect
83. #10622565C22semidirect
84. #10622565C22semidirect
85. #10622564C22semidirect
86. #10622564C22semidirect
87. #10622564C22semidirect
88. #10622564C22semidirect
89. #10622562C22semidirect
90. #10622562C22semidirect
91. #10622562C22semidirect
92. #10622561C22semidirect
93. #10622561C22semidirect
94. #10622561C22semidirect
95. #10622561C22semidirect
96. #10622560C22semidirect
97. #10622560C22semidirect
98. #10622560C22semidirect
99. #10622558C22semidirect
100. #10622558C22semidirect
101. #10622558C22semidirect
102. #10622558C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
105. #10622557C22semidirect
106. #10622557C22semidirect
127. C22×D44C23semidirect
128. C22×C4×D11C23semidirect
129. C22×Dic22C23semidirect
179. C2×(C2×D11)⋊C4C23semidirect
180. C2×(C2×D11)⋊C4C23semidirect
181. C2×(C2×D11)⋊C4C23semidirect
182. C2×(C2×D11)⋊C4C23semidirect
183. C2×(C2×D11)⋊C4C23semidirect
184. C2×(C2×D11)⋊C4C23semidirect
185. C2×C4⋊Dic11C23semidirect
186. C2×C4⋊Dic11C23semidirect
187. C2×C4⋊Dic11C23semidirect
188. C2×C4⋊Dic11C23semidirect
190. C2×Dic11⋊C4C23semidirect
191. C2×Dic11⋊C4C23semidirect
192. C2×Dic11⋊C4C23semidirect
193. C2×Dic11⋊C4C23semidirect
194. C2×Dic11⋊C4C23semidirect
195. C2×Dic11⋊C4C23semidirect
196. C2×C4×Dic11C23semidirect
197. C2×C4×Dic11C23semidirect
198. C2×C4×Dic11C23semidirect
203. C11⋊#95C23semidirect
204. C11⋊#95C23semidirect
205. C11⋊#95C23semidirect
206. C11⋊#95C23semidirect
207. C11⋊#95C23semidirect
208. C11⋊#95C23semidirect
209. C11⋊#95C23semidirect
210. C11⋊#95C23semidirect
211. C11⋊#95C23semidirect
212. C11⋊#95C23semidirect
213. C11⋊#95C23semidirect
214. C11⋊#95C23semidirect
215. C11⋊#95C23semidirect
216. C11⋊#95C23semidirect
379. C2×#379D11semidirect
905. C11#36725semidirect

Maximal subgroups

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

subgroupindex
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#130756532
#130751792
#130750112
#130750072
#130749962
#130749452
#130748422
#130748242
#130744212
#130743502
#130728562
#130727362
#130721522
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#130712742
C2×C11×#3792
#3672511