Finite Group Databasebeta

← #14926159

Subgroups — #14926159

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073464C212yesmaximal, complemented
2#13073384C212yesmaximal, complemented
3#13073209C211yesmaximal, characteristic, complemented
4#13073144C211yesmaximal, characteristic, complemented
5#13073045C211yesmaximal, characteristic, complemented
6#13072968C211yesmaximal, characteristic, complemented
7#13072795C212yesmaximal, complemented
8#13072731C212yesmaximal, complemented
9#13072490C211yesmaximal, characteristic, complemented
10#13072375C211yesmaximal, characteristic, complemented
11#13072206C211yesmaximal, characteristic
12#13071878C212yesmaximal, complemented
13#13071855C212yesmaximal, complemented
14#13071180C211yesmaximal, characteristic, complemented
15#13071171C211yesmaximal, characteristic, complemented
16#13071133C212yesmaximal, complemented
17#121×Dic11C211yesmaximal, characteristic, complemented
18#13071126C212yesmaximal, complemented
19#13071122C211yesmaximal, characteristic, complemented
20#13071074C211yesmaximal, characteristic, complemented
21C4×D4×Dic11C211yesmaximal, characteristic, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C11×#2420C211yesmaximal, characteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×#66992C2212yes—
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2212yes—
31C2×#66983C2211yescharacteristic
32C2×#66982C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2212yes—
35C2×#66946C2211yescharacteristic
36C2×#66945C2212yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×#66930C2211yescharacteristic
41C2×#66930C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C11×#397C2212yes—
44C11×#394C2212yes—
45C11×#390C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#386C2212yes—
48C11×#382C2211yescharacteristic
49C11×#381C2212yes—
50C11×#380C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52#10622836C2212yes—
53#10622834C2211yescharacteristic
54#10622833C2212yes—
55#10622826C2212yes—
56#10622825C2211yescharacteristic
57C4×C22⋊Dic11C2211yescharacteristic
58C4×C22⋊Dic11C2212yes—
59#10622603C2212yes—
60#10622601C2211yescharacteristic
61#10622601C2211yescharacteristic
62#10622598C2211yescharacteristic
63#10622598C2211yescharacteristic
64#10622596C2212yes—
65#10622593C2212yes—
66#10622589C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70#10622586C2211yescharacteristic
71#10622586C2211yescharacteristic
72#10622586C2211yescharacteristic
73#10622572C2212yes—
74#10622572C2212yes—
75#10622572C2212yes—
76#10622572C2212yes—
77#10622571C2212yes—
78#10622571C2212yes—
79#10622570C2212yes—
80#10622570C2212yes—
81#10622570C2212yes—
82#10622564C2212yes—
83#10622562C2212yes—
84#10622561C2212yes—
85#10622561C2212yes—
86#10622559C2212yes—
87#10622557C2212yes—
88#10622555C2212yes—
89C22⋊C4×Dic11C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2211yescharacteristic
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2211yescharacteristic
94#10622552C2211yescharacteristic
95#10622552C2211yescharacteristic
96C4×C4⋊Dic11C2211yescharacteristic
97C4×Dic11⋊C4C2211yescharacteristic
98C4×Dic11⋊C4C2211yescharacteristic
99C42×Dic11C2211yescharacteristic
100C42×Dic11C2211yescharacteristic
101#10622288C2212yes—
102#10622288C2212yes—
103#10622287C2212yes—
104#10622283C2212yes—
105#10622283C2212yes—
106#10622282C2212yes—
107#10622282C2212yes—
108#10622282C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111#10622272C2212yes—
112#10622265C2212yes—
113#10622265C2212yes—
114#10622265C2212yes—
115#10622265C2212yes—
116#10622262C2211yescharacteristic
117#10622262C2212yes—
118#10622262C2211yescharacteristic
119#10622262C2212yes—
120#10622261C2211yescharacteristic
121#10622261C2211yescharacteristic
122#10622260C2212yes—
123C22×D4×C11C2312yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11C2312yes—
136C11×#121—24no—
137C4×D4×C11—24no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2311yescharacteristic
158#66993—24no—
159#66992—28no—
160D4×Dic11—24no—
161D4×Dic11—24no—
162D4×Dic11—44no—
163#66983—24no—
164#66982—28no—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2311yescharacteristic
191C2×C4×Dic11—24no—
192C2×C4×Dic11—44no—
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211#66946—24no—
212#66945—44no—
213(C22⋊D11)⋊C4—44no—
214(C22⋊D11)⋊C4—44no—
215(C22⋊D11)⋊C4—44no—
216#66930—24no—
217#66930—24no—
218#66923—24no—
219C11×#95C2312yes—
220C11×#95C2311yescharacteristic
221C11×#95C2311yescharacteristic
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11⋊#95C2311yescharacteristic
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241#34970—111nomaximal, Sylow
242C24×C11C2411yescharacteristic
243C24×C11C2412yes—
244C23×D11C2412yes—
245C2×D4×C11—24no—
246C2×D4×C11—24no—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—42no—
250C2×D4×C11#4114yes—
251C22×C4×C11—24no—
252C22×C4×C11—22no—
253C22×C4×C11—24no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—42no—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—24no—
267C2×C22⋊D11—24no—
268C2×C22⋊D11—24no—
269C2×C22⋊D11—24no—
270C2×C22⋊D11—24no—
271C2×C22⋊D11—24no—
272C2×C22⋊D11—42no—
273C2×C22⋊D11—42no—
274C2×C22⋊D11—42no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—24no—
279C22×Dic11—24no—
280C22×Dic11—24no—
281C22×Dic11—22no—
282C22×Dic11—24no—
283C22×Dic11—24no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—42no—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2412yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C2×D44—22no—
299C2×D44—22no—
300C2×D44—22no—
301C2×C4×D11—24no—
302C2×C4×D11—24no—
303C2×C4×D11—24no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—42no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4—42no—
315C42×C11—22no—
316C42×C11—22no—
317C22⋊Dic11—22no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—42no—
322C22⋊Dic11—42no—
323C22⋊Dic11#4114yes—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—42no—
330(C2×D11)⋊C4—42no—
331(C2×D11)⋊C4—42no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334C4⋊Dic11—22no—
335C4⋊Dic11—22no—
336C4⋊Dic11—42no—
337C4⋊Dic11—42no—
338C4⋊Dic11#4114yes—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343Dic11⋊C4—22no—
344Dic11⋊C4—24no—
345Dic11⋊C4—24no—
346Dic11⋊C4—42no—
347Dic11⋊C4—42no—
348Dic11⋊C4—42no—
349Dic11⋊C4#4114yes—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11—24no—
358C4×Dic11—22no—
359C4×Dic11—24no—
360C4×Dic11—22no—
361C4×Dic11—22no—
362C4×Dic11—22no—
363C4×Dic11—22no—
364C4×Dic11—22no—
365C4×Dic11—42no—
366C4×Dic11—42no—
367C4×Dic11#4114yes—
368#2531—112no—
369#2526—112no—
370#2513—111no—
371#2507—111no—
372#2497—111no—
373#2490—111no—
374#2476—112no—
375#2471—112no—
376#2454—111no—
377#2445—111no—
378#2428—111no—
379#2420D1111yescharacteristic, complemented
380#2395—112no—
381#2392—112no—
382C4×#127—111no—
383C4×#125—111no—
384C4×#123—112no—
385C4×#121—112no—
386C4×#121—111no—
387C4×#121—111no—
388#2293—111no—
389C42×D4—111no—
390C4×#117—111no—
391C23×C11—21no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—21no—
396C23×C11—22no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11—21no—
400C23×C11—22no—
401C23×C11—21no—
402C23×C11—22no—
403C23×C11C2×#4114yes—
404C23×C11C2×#4112yes—
405C23×C11C2511yescharacteristic
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413D4×C11—28no—
414D4×C11—48no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—48no—
439C2×C4×C11—44no—
440C2×C4×C11C2×#4112yes—
441C2×C4×C11C2×#4112yes—
442C2×C4×C11C2×#4112yes—
443C2×C4×C11C2×#4112yes—
444C22⋊D11—48no—
445C22⋊D11—48no—
446C22⋊D11—48no—
447C2×Dic11—28no—
448C2×Dic11—21no—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—21no—
462C2×Dic11—21no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—21no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—21no—
470C2×Dic11—22no—
471C2×Dic11—21no—
472C2×Dic11—48no—
473C2×Dic11—44no—
474C2×Dic11—48no—
475C2×Dic11C2×#4112yes—
476C2×Dic11C2×#4112yes—
477C2×Dic11C2×#4112yes—
478C2×Dic11C2×#4112yes—
479C2×Dic11C2×#4114yes—
480C2×Dic11C2×#4112yes—
481C2×Dic11C2×#4112yes—
482C2×Dic11H(5,𝔽2)12yes—
483C2×Dic11H(5,𝔽2)12yes—
484D44—44no—
485C4×D11—48no—
486C2×#127—111no—
487C2×#125—111no—
488C2×#123—112no—
489C2×#121—112no—
490C2×#121—111no—
491C2×#121C2×D1111yescharacteristic
492C2×C4×D4—111no—
493C2×C4×D4—111no—
494C2×C4×D4—112no—
495C2×C4×D4—111no—
496C2×C4×D4—112no—
497C2×C4×D4—112no—
498C2×C4×D4—112no—
499C2×C4×D4C2×D1111yescharacteristic
500C2×#117—112no—
501C2×#117—111no—
502C2×#117—111no—
503C22×C42—111no—
504C22×C42—112no—
505#400—112no—
506#399—112no—
507#398—112no—
508#398—112no—
509#397—112no—
510#397—112no—
511#397—112no—
512#397C2×D1112yes—
513#396—112no—
514#396—112no—
515#394—112no—
516#394—112no—
517#394—112no—
518#394—112no—
519#394C2×D1112yes—
520#392—112no—
521#390—111no—
522#390—111no—
523#390—111no—
524#390—112no—
525#390—112no—
526#390—112no—
527#390—111no—
528#390—111no—
529#390C2×D1111yescharacteristic
530#389—111no—
531#389—111no—
532#389—111no—
533#389—111no—
534#389—111no—
535#389—112no—
536#389C2×D1111yescharacteristic
537#388—112no—
538#388—112no—
539#388—112no—
540#388—112no—
541#388—112no—
542#388—112no—
543#388—112no—
544#388—112no—
545#387—112no—
546#387—112no—
547#387—112no—
548#387—112no—
549#386—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386C2×D1112yes—
554#385—112no—
555#384—111no—
556#382C2×D1111yescharacteristic
557#381C2×D1112yes—
558#380—111no—
559#380—112no—
560#380C2×D1111yescharacteristic
561C4×C4⋊C4—111no—
562C4×C4⋊C4—111no—
563C4×C4⋊C4—111no—
564C4×C4⋊C4—111no—
565C4×C4⋊C4—111no—
566C4×C4⋊C4—111no—
567C4×C4⋊C4—112no—
568C4×C4⋊C4—112no—
569C4×C4⋊C4—111no—
570C4×C4⋊C4—111no—
571C4×C22⋊C4—111no—
572C4×C22⋊C4—112no—
573C4×C22⋊C4—111no—
574C4×C22⋊C4—112no—
575C4×C22⋊C4—112no—
576C4×C22⋊C4—112no—
577C4×C22⋊C4—111no—
578C4×C22⋊C4—112no—
579C4×C22⋊C4—112no—
580C4×C22⋊C4C2×D1111yescharacteristic
581#376—111no—
582#376—111no—
583C43—111no—
584C43—111no—
585C22×C11—24no—
586C22×C11—22no—
587C22×C11—24no—
588C22×C11—22no—
589C22×C11—24no—
590C22×C11—22no—
591C22×C11—41no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—41no—
595C22×C11—41no—
596C22×C11—42no—
597C22×C11—41no—
598C22×C11—42no—
599C22×C11C22×#4111yescharacteristic
600C22×C11C22×#4111yescharacteristic
601C22×C11C22×#4111yescharacteristic
602C22×C11C22×#4111yescharacteristic
603C22×C11C22×#4111yescharacteristic
604C22×C11C2×H(5,𝔽2)11yescharacteristic
605C22×C11C2×H(5,𝔽2)11yescharacteristic
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C4×C11—22no—
614C4×C11—41no—
615C4×C11—42no—
616C4×C11—41no—
617C4×C11—41no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—41no—
621C4×C11#52914yes—
622Dic11—22no—
623Dic11—22no—
624Dic11—22no—
625Dic11—24no—
626Dic11—22no—
627Dic11—22no—
628Dic11—41no—
629Dic11—42no—
630Dic11—41no—
631Dic11—42no—
632Dic11#54014yes—
633C22×D4—112no—
634C22×D4—112no—
635C22×D4—112no—
636C22×D4—111no—
637C22×D4C22×D1112yes—
638C22×D4C22×D1111yescharacteristic
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—112no—
642C23×C4—112no—
643C23×C4—112no—
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1112yes—
646#127—224no—
647#125—224no—
648#123—228no—
649#121—24no—
650#121—228no—
651#121—224no—
652C4×D4—24no—
653C4×D4—224no—
654C4×D4—224no—
655C4×D4—224no—
656C4×D4—444no—
657C4×D4—444no—
658C4×D4—444no—
659C4×D4—444no—
660#117—224no—
661#117—224no—
662#117—444no—
663C2×C4⋊C4—111no—
664C2×C4⋊C4—111no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—112no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C4⋊C4C22×D1111yescharacteristic
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C4⋊C4C22×D1112yes—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—111no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—112no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
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⋊C4C22×D1111yescharacteristic
701C2×C22⋊C4C22×D1111yescharacteristic
702C2×C22⋊C4C22×D1112yes—
703C2×C22⋊C4C22×D1112yes—
704C2×C22⋊C4C22×D1112yes—
705C2×C22⋊C4C22×D1112yes—
706C2×C22⋊C4C22×D1112yes—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—112no—
710C2×C42—111no—
711C2×C42—111no—
712C2×C42—111no—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—111no—
716C2×C42—111no—
717C2×C42—112no—
718C2×C42—111no—
719C2×C42—111no—
720C2×C42—111no—
721C2×C42—111no—
722C2×C42—111no—
723C2×C42—112no—
724C2×C42—112no—
725C2×C42—224no—
726C2×C42—444no—
727C2×C42C22×D1111yescharacteristic
728C2×C42C22×D1111yescharacteristic
729#95—111no—
730#95—111no—
731#95—111no—
732#95—111no—
733#95—111no—
734#95—111no—
735#95—112no—
736#95—112no—
737#95—112no—
738#95—112no—
739#95—112no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95C22×D1111yescharacteristic
746#95C22×D1111yescharacteristic
747#95C22×D1112yes—
748#95C22×D1112yes—
749#95C22×D1112yes—
750#95C22×D1112yes—
751C2×C11—44no—
752C2×C11—42no—
753C2×C11C2×#52911yescharacteristic
754C2×C11#344411yescharacteristic
755C2×C11C2×#54011yescharacteristic
756C2×C11#348111yescharacteristic
757C2×C11#348111yescharacteristic
758C2×C11#348111yescharacteristic
759C2×C11#348311yescharacteristic
760D11—82no—
761C24—112no—
762C24C23×D1112yes—
763C24C23×D1111yescharacteristic
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—42no—
769C2×D4—224no—
770C2×D4—224no—
771C2×D4—224no—
772C2×D4—224no—
773C2×D4—224no—
774C2×D4—224no—
775C2×D4—222no—
776C2×D4—222no—
777C2×D4—222no—
778C2×D4—442no—
779C2×D4—442no—
780C2×D4—442no—
781C2×D4#434114yes—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—42no—
788C22×C4—111no—
789C22×C4—111no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—111no—
794C22×C4—112no—
795C22×C4—111no—
796C22×C4—111no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—224no—
800C22×C4—224no—
801C22×C4—224no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—224no—
806C22×C4—224no—
807C22×C4—224no—
808C22×C4—222no—
809C22×C4—224no—
810C22×C4—222no—
811C22×C4—224no—
812C22×C4—222no—
813C22×C4—442no—
814C22×C4C23×D1111yescharacteristic
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1111yescharacteristic
818C22×C4C23×D1112yes—
819C22×C4C23×D1111yescharacteristic
820C22×C4C23×D1111yescharacteristic
821C22×C4C23×D1111yescharacteristic
822C22×C4C23×D1111yescharacteristic
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—42no—
827C4⋊C4—114no—
828C4⋊C4—114no—
829C4⋊C4—222no—
830C4⋊C4—222no—
831C4⋊C4—222no—
832C4⋊C4—224no—
833C4⋊C4—224no—
834C4⋊C4—224no—
835C4⋊C4—224no—
836C4⋊C4—222no—
837C4⋊C4—222no—
838C4⋊C4—442no—
839C4⋊C4—442no—
840C4⋊C4—442no—
841C4⋊C4—442no—
842C4⋊C4—442no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—42no—
850C22⋊C4—114no—
851C22⋊C4—224no—
852C22⋊C4—224no—
853C22⋊C4—224no—
854C22⋊C4—224no—
855C22⋊C4—222no—
856C22⋊C4—224no—
857C22⋊C4—224no—
858C22⋊C4—224no—
859C22⋊C4—224no—
860C22⋊C4—442no—
861C22⋊C4—442no—
862C22⋊C4—442no—
863C22⋊C4—442no—
864C22⋊C4—442no—
865C22⋊C4—442no—
866C22⋊C4—442no—
867C42—22no—
868C42—22no—
869C42—114no—
870C42—222no—
871C42—222no—
872C42—222no—
873C42—224no—
874C42—222no—
875C42—222no—
876C42—222no—
877C42—222no—
878C42—224no—
879C42—222no—
880C42—222no—
881C42—222no—
882C42—222no—
883C42—222no—
884C42—222no—
885C42—442no—
886C42—442no—
887C11#3497011yescharacteristic, complemented, Sylow
888C23—21no—
889C23—21no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—21no—
894C23—21no—
895C23—22no—
896C23—21no—
897C23—22no—
898C23—22no—
899C23—21no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23C2×#434114yes—
908C23#41×D1112yes—
909C23C24×D1111yescharacteristic
910D4—28no—
911D4—48no—
912D4—448no—
913D4—448no—
914D4—448no—
915D4—444no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—48no—
940C2×C4—44no—
941C2×C4—112no—
942C2×C4—112no—
943C2×C4—112no—
944C2×C4—112no—
945C2×C4—112no—
946C2×C4—112no—
947C2×C4—112no—
948C2×C4—112no—
949C2×C4—114no—
950C2×C4—228no—
951C2×C4—221no—
952C2×C4—221no—
953C2×C4—221no—
954C2×C4—221no—
955C2×C4—221no—
956C2×C4—221no—
957C2×C4—221no—
958C2×C4—222no—
959C2×C4—221no—
960C2×C4—222no—
961C2×C4—221no—
962C2×C4—221no—
963C2×C4—221no—
964C2×C4—221no—
965C2×C4—221no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—221no—
971C2×C4—222no—
972C2×C4—221no—
973C2×C4—222no—
974C2×C4—221no—
975C2×C4—448no—
976C2×C4—444no—
977C2×C4—448no—
978C2×C4—448no—
979C2×C4C2×#434112yes—
980C2×C4#41×D1112yes—
981C2×C4#41×D1112yes—
982C2×C4#41×D1112yes—
983C22—24no—
984C22—22no—
985C22—24no—
986C22—22no—
987C22—24no—
988C22—22no—
989C22—41no—
990C22—42no—
991C22—41no—
992C22—42no—
993C22—42no—
994C22—41no—
995C22—41no—
996C22—42no—
997C22—442no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—442no—
1003C22—442no—
1004C22C22×#434111yescharacteristic
1005C22C2×#41×D1111yescharacteristic
1006C22C2×#41×D1111yescharacteristic
1007C22C2×#41×D1111yescharacteristic
1008C22C2×#41×D1111yescharacteristic
1009C22D11×H(5,𝔽2)11yescharacteristic
1010C22D11×H(5,𝔽2)11yescharacteristic
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—42no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—114no—
1020C4—222no—
1021C4—222no—
1022C4—222no—
1023C4—222no—
1024C4—222no—
1025C4—224no—
1026C4—441no—
1027C4—442no—
1028C4—441no—
1029C4—442no—
1030C4#1062318014yes—
1031C2—44no—
1032C2—42no—
1033C2—882no—
1034C2C2×#1062318011yescharacteristic
1035C2#1308191011yescharacteristic
1036C2D11×#54011yescharacteristic
1037C2#1308222111yescharacteristic
1038C2#1308222111yescharacteristic
1039C2#1308222311yescharacteristic
1040C2#1308224111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2420C2
prime radical#13072206C2
hypercenter#2420D11
hypocenterC11#34970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2420

Complements

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

NH ≅ G/Ntype
1. #13073464C2semidirect
2. #13073384C2semidirect
3. #13073209C2semidirect
4. #13073144C2semidirect
5. #13073045C2semidirect
6. #13072968C2semidirect
7. #13072795C2semidirect
8. #13072731C2semidirect
9. #13072490C2semidirect
10. #13072375C2semidirect
12. #13071878C2semidirect
13. #13071855C2semidirect
14. #13071180C2semidirect
15. #13071171C2semidirect
16. #13071133C2semidirect
17. #121×Dic11C2semidirect
18. #13071126C2semidirect
19. #13071122C2semidirect
20. #13071074C2semidirect
21. C4×D4×Dic11C2semidirect
22. C4×#66930C2semidirect
23. C11×#2420C2semidirect
379. #2420D11semidirect
887. C11#34970semidirect

Maximal subgroups

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

subgroupindex
#130734642
#130733842
#130732092
#130731442
#130730452
#130729682
#130727952
#130727312
#130724902
#130723752
#130722062
#130718782
#130718552
#130711802
#130711712
#130711332
#121×Dic112
#130711262
#130711222
#130710742
C4×D4×Dic112
C4×#669302
C11×#24202
#3497011