Finite Group Databasebeta

← #14770261

Subgroups — #14770261

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082176C211yesmaximal, characteristic
2#13077348C211yesmaximal, characteristic, complemented
3#13071053C211yesmaximal, characteristic, complemented
4#13069595C211yesmaximal, characteristic, complemented
5#13069558C211yesmaximal, characteristic, complemented
6#13069056C211yesmaximal, characteristic, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068915C211yesmaximal, characteristic, complemented
9#13068714C211yesmaximal, characteristic, complemented
10#13068713C211yesmaximal, characteristic, complemented
11#13068634C211yesmaximal, characteristic, complemented
12#13068428C211yesmaximal, characteristic, complemented
13#13068326C211yesmaximal, characteristic, complemented
14D11×#339C211yesmaximal, characteristic, complemented
15C11×#1897C211yesmaximal, characteristic, complemented
16C11×#525C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18#10623359C2211yescharacteristic
19#41×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×M16×D11C2211yescharacteristic
24#10623189—21no—
25#10623181—21no—
26#10623173C411yescharacteristic, complemented
27#10623172C411yescharacteristic, complemented
28#10623170C411yescharacteristic, complemented
29#10623166C411yescharacteristic, complemented
30#10623149C411yescharacteristic, complemented
31#10623147C411yescharacteristic, complemented
32#10623145C411yescharacteristic, complemented
33#10623142C411yescharacteristic, complemented
34#10623122—21no—
35#10623118—21no—
36#10623088—21no—
37#10623069—21no—
38#10623069—21no—
39C4×#4341—21no—
40D11×#117C2211yescharacteristic
41#10623048C2211yescharacteristic
42C2×C42×D11C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C11×#407C2211yescharacteristic
46C2×#66901C2211yescharacteristic
47C2×#66901C2211yescharacteristic
48C4×C22⋊Dic11C2211yescharacteristic
49#10622739C2211yescharacteristic
50#10622731C2211yescharacteristic
51M16×Dic11C2211yescharacteristic
52#10622602—21no—
53#10622591—21no—
54#10622569—21no—
55#10622557—21no—
56C4×(C2×D11)⋊C4C2211yescharacteristic
57#10622545C2211yescharacteristic
58C4×Dic11⋊C4C2211yescharacteristic
59#10622343—21no—
60#10622342—21no—
61#10622341—21no—
62(C22⋊D11)⋊C8—21no—
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65#10622193C2211yescharacteristic
66#10622193C2211yescharacteristic
67#10622193C2211yescharacteristic
68#10622193C2211yescharacteristic
69#10622170C2211yescharacteristic
70#10622170C2211yescharacteristic
71#10622161C2211yescharacteristic
72#10622161C2211yescharacteristic
73#10622161C2211yescharacteristic
74#10622161C2211yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C2×#4341—21no—
79C22×C4×D11—21no—
80C22×C4×D11C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C11×#123—21no—
84C11×C22⋊Q8C2×C411yescharacteristic, complemented
85C11×C22⋊Q8C2×C411yescharacteristic, complemented
86C11×#121C2×C411yescharacteristic, complemented
87C11×#121C2×C411yescharacteristic, complemented
88C11×#120—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C11×#117—22no—
92C11×#117—41no—
93C11×#117C2311yescharacteristic
94C2×C11×C4⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11D411yescharacteristic
101#66999C2×C411yescharacteristic
102#66999C2×C411yescharacteristic
103Q8×Dic11C2×C411yescharacteristic, complemented
104Q8×Dic11C2×C411yescharacteristic, complemented
105#66992—21no—
106#66992—21no—
107#66991—21no—
108#66991C2×C411yescharacteristic
109#66991C2×C411yescharacteristic
110#66990—21no—
111#66989—21no—
112#66988—21no—
113#66988—21no—
114#66988—21no—
115D4×Dic11—21no—
116D4×Dic11—21no—
117D4×Dic11—21no—
118D4×Dic11C2×C411yescharacteristic, complemented
119D4×Dic11C2×C411yescharacteristic, complemented
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11C2×C411yescharacteristic
123C4×C22⋊D11C2×C411yescharacteristic
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11D411yescharacteristic
127C4×C22⋊D11D411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4D411yescharacteristic
132#66979—21no—
133#66979—21no—
134#66979—21no—
135#66979C2×C411yescharacteristic, complemented
136#66979C2×C411yescharacteristic, complemented
137#66979C2311yescharacteristic
138#66979C2311yescharacteristic
139C2×C4⋊Dic11C2×C411yescharacteristic, complemented
140C2×C4⋊Dic11C2×C411yescharacteristic, complemented
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4D411yescharacteristic
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149C2×#4318—21no—
150C2×#4318—22no—
151C2×#4318—41no—
152C2×#4318C2311yescharacteristic
153C2×#4318C2311yescharacteristic
154C22×C11⋊C8—21no—
155M16×D11—22no—
156M16×D11—41no—
157C2×#4313—21no—
158C2×C8×D11—21no—
159#66951—21no—
160#66951—21no—
161#66950—21no—
162#66945—21no—
163#66945C2×C411yescharacteristic
164#66945C2×C411yescharacteristic
165C4⋊C4×D11C2×C411yescharacteristic
166C4⋊C4×D11C2×C411yescharacteristic
167#66943—21no—
168#66943C2×C411yescharacteristic, complemented
169#66943C2×C411yescharacteristic, complemented
170#66942—21no—
171#66942—21no—
172#66941C2×C411yescharacteristic, complemented
173#66941C2×C411yescharacteristic, complemented
174#66940—21no—
175#66939—21no—
176#66939—21no—
177#66938—21no—
178#66938—21no—
179#66936—21no—
180#66936—21no—
181(C22⋊D11)⋊C4—21no—
182(C22⋊D11)⋊C4—21no—
183C22⋊C4×D11—21no—
184#66932—21no—
185#66932—21no—
186#66932—21no—
187#66932—21no—
188#66931—21no—
189#66931—21no—
190#66931—21no—
191#66931—21no—
192#66930—21no—
193#66930—21no—
194#66930—21no—
195#66925—21no—
196C42×D11—21no—
197C42×D11—22no—
198C42×D11—41no—
199C4×Dic22—21no—
200C4×Dic22—21no—
201C11×#104—22no—
202C11×#104—41no—
203C11×C22⋊C8—21no—
204C11×C22⋊C8—21no—
205#66901—22no—
206#66901—41no—
207C11⋊#95—21no—
208C11⋊#95—21no—
209C11⋊#95—21no—
210C11⋊#95—21no—
211C11⋊#95—21no—
212(C2×D11)⋊C8—21no—
213(C2×D11)⋊C8—21no—
214#66879—21no—
215Dic11⋊C8—21no—
216Dic11⋊C8—21no—
217C8×Dic11—21no—
218#22506—111nomaximal, Sylow
219C24×C11C2×D411yescharacteristic
220C23×D11C2×D411yescharacteristic
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C2×Q8×C11C22×C411yescharacteristic
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11C22×C411yescharacteristic
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11C22×C411yescharacteristic
238C22×C4×C11C22×C411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—21no—
244C2×C22⋊D11—21no—
245C2×C22⋊D11—42no—
246C2×C22⋊D11C22⋊C411yescharacteristic
247C2×C22⋊D11C22⋊C411yescharacteristic
248C2×C22⋊D11C22⋊C411yescharacteristic
249C2×C22⋊D11C22⋊C411yescharacteristic
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258C22×Dic11C2×D411yescharacteristic
259#4341—44no—
260C2×C4×D11—21no—
261C2×C4×D11—21no—
262C2×C4×D11—21no—
263C2×C4×D11—21no—
264C2×C4×D11—21no—
265C2×C4×D11—21no—
266C2×C4×D11—42no—
267C2×C4×D11—42no—
268C2×C4×D11—42no—
269C2×C4×D11C22×C411yescharacteristic
270C2×C4×D11C22×C411yescharacteristic
271C2×C4×D11C2×D411yescharacteristic
272C2×C4×D11C2×D411yescharacteristic
273C2×Dic22—21no—
274C2×Dic22—21no—
275C11×M16—21no—
276C11×M16—21no—
277C11×M16—21no—
278C11×M16—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—42no—
284C11×C4⋊C4C22×C411yescharacteristic
285C11×C4⋊C4C22×C411yescharacteristic
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—42no—
292C42×C11—21no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11#4112yescomplemented
297C22⋊Dic11—21no—
298C22⋊Dic11—21no—
299C22⋊Dic11—21no—
300C22⋊Dic11—21no—
301C22⋊Dic11—21no—
302C22⋊Dic11—21no—
303C22⋊Dic11—21no—
304C22⋊Dic11—21no—
305C22⋊Dic11—42no—
306C22⋊Dic11C22⋊C411yescharacteristic
307C22⋊Dic11C22⋊C411yescharacteristic
308C22⋊Dic11C22⋊C411yescharacteristic
309C22⋊Dic11C22⋊C411yescharacteristic
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—21no—
314(C2×D11)⋊C4—42no—
315(C2×D11)⋊C4C22⋊C411yescharacteristic
316(C2×D11)⋊C4C22⋊C411yescharacteristic
317(C2×D11)⋊C4C22⋊C411yescharacteristic
318(C2×D11)⋊C4C22⋊C411yescharacteristic
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11C22×C411yescharacteristic
326C4⋊Dic11C22×C411yescharacteristic
327C4⋊Dic11C22×C411yescharacteristic
328C4⋊Dic11C22×C411yescharacteristic
329Dic11⋊C4—21no—
330Dic11⋊C4—21no—
331Dic11⋊C4—21no—
332Dic11⋊C4—21no—
333Dic11⋊C4—21no—
334Dic11⋊C4—21no—
335Dic11⋊C4—21no—
336Dic11⋊C4—21no—
337Dic11⋊C4—42no—
338Dic11⋊C4C22⋊C411yescharacteristic
339Dic11⋊C4C22⋊C411yescharacteristic
340Dic11⋊C4C22⋊C411yescharacteristic
341Dic11⋊C4C22⋊C411yescharacteristic
342C4×Dic11—21no—
343C4×Dic11—21no—
344C4×Dic11—21no—
345C4×Dic11—21no—
346C4×Dic11—21no—
347C4×Dic11—21no—
348C4×Dic11—21no—
349C4×Dic11—21no—
350C4×Dic11—21no—
351C4×Dic11—21no—
352C4×Dic11—21no—
353C4×Dic11—21no—
354C4×Dic11—42no—
355C4×Dic11C22×C411yescharacteristic
356C4×Dic11C22×C411yescharacteristic
357C4×Dic11C2×D411yescharacteristic
358C4×Dic11C2×D411yescharacteristic
359#4318—21no—
360#4318—21no—
361#4318—21no—
362#4318—42no—
363#4318#4112yescomplemented
364C2×C11⋊C8—21no—
365C2×C11⋊C8—21no—
366C2×C11⋊C8—42no—
367#4313—42no—
368C8×D11—42no—
369#3475—111no—
370D4×M16—111no—
371#2290—111no—
372#1995—111no—
373#1986—111no—
374#1897D1111yescharacteristic, complemented
375#1896—111no—
376#1871—111no—
377#1871—111no—
378#1826—111no—
379#1826—111no—
380#1806—111no—
381#1759—111no—
382#1733—111no—
383C2×#339—111no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11C2×C22⋊C411yescharacteristic
390C23×C11C2×C22⋊C411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—22no—
395C22×D11—41no—
396C22×D11C2×C22⋊C411yescharacteristic
397C22×D11C2×C22⋊C411yescharacteristic
398Q8×C11—21no—
399Q8×C11—21no—
400D4×C11—21no—
401D4×C11—21no—
402D4×C11—42no—
403D4×C11—41no—
404D4×C11—41no—
405D4×C11—81no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—22no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11C2×C22⋊C411yescharacteristic
428C2×C4×C11C2×C22⋊C411yescharacteristic
429C2×C4×C11C23×C411yescharacteristic
430C2×C4×C11C22×D411yescharacteristic
431C2×C4×C11C2×#4111yescharacteristic
432C2×C4×C11C2×#4111yescharacteristic
433C2×C4×C11H(5,𝔽2)11yescharacteristic
434C2×C4×C112−1+411yescharacteristic
435C22⋊D11—22no—
436C22⋊D11—22no—
437C22⋊D11—41no—
438C22⋊D11—41no—
439C22⋊D11—42no—
440C22⋊D11—81no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—22no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—42no—
451C2×Dic11—41no—
452C2×Dic11—42no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—81no—
458C2×Dic11—81no—
459C2×Dic11C2×C22⋊C411yescharacteristic
460C2×Dic11C2×C22⋊C411yescharacteristic
461C2×Dic11C2×C22⋊C411yescharacteristic
462C2×Dic11C2×C22⋊C411yescharacteristic
463C2×Dic11C2×C22⋊C411yescharacteristic
464C2×Dic11C2×C22⋊C411yescharacteristic
465C4×D11—21no—
466C4×D11—21no—
467C4×D11—21no—
468C4×D11—21no—
469C4×D11—21no—
470C4×D11—21no—
471C4×D11—21no—
472C4×D11—21no—
473C4×D11—48no—
474C4×D11—42no—
475C4×D11—81no—
476Dic22—42no—
477Dic22—81no—
478C8×C11—41no—
479C8×C11—41no—
480C11⋊C8—22no—
481C11⋊C8—41no—
482C22×M16—111no—
483C22×M16—111no—
484#556—111no—
485#555—111no—
486#554—111no—
487#553—111no—
488#553—111no—
489#552—111no—
490#552—111no—
491#552—221no—
492#551—221no—
493#551—221no—
494#547—111no—
495#546—221no—
496#533—111no—
497#529—221no—
498#529—221no—
499#529—221no—
500#525—111no—
501#525C2×D1111yescharacteristic
502C4×#41—111no—
503C4×#41—221no—
504C2×C4×D4—111no—
505C2×#117—111no—
506C2×#117—111no—
507C2×#117C2×D1111yescharacteristic
508C22×C42—111no—
509#436—221no—
510#435—221no—
511#435—221no—
512C8×D4—221no—
513#423—111no—
514C2×#104—111no—
515C2×#104—111no—
516C2×#104C2×D1111yescharacteristic
517C2×#104C2×D1111yescharacteristic
518#407—111no—
519#407C2×D1111yescharacteristic
520C4×M16—111no—
521#388—221no—
522#387—221no—
523#386—221no—
524#385—221no—
525C4×C4⋊C4—111no—
526C4×C22⋊C4—111no—
527C4×C22⋊C4—111no—
528#376—111no—
529#339—111no—
530#339—111no—
531#339—111no—
532#339—111no—
533#339—111no—
534#339—111no—
535#339—111no—
536#339—111no—
537#339—111no—
538#339—111no—
539#339C2×D1111yescharacteristic
540#339C2×D1111yescharacteristic
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—21no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—41no—
550C22×C11—41no—
551C22×C11—41no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11C22×C22⋊C411yescharacteristic
555C22×C11#54611yescharacteristic
556C22×C11#54711yescharacteristic
557C2×D11—21no—
558C2×D11—21no—
559C2×D11—21no—
560C2×D11—21no—
561C2×D11—21no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11#42112yes—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—42no—
568C4×C11—41no—
569C4×C11—41no—
570C4×C11—41no—
571C4×C11—81no—
572C4×C11C4×#4111yescharacteristic
573C4×C11#52011yescharacteristic
574C4×C11#54611yescharacteristic
575C4×C11#54711yescharacteristic
576Dic11—21no—
577Dic11—21no—
578Dic11—21no—
579Dic11—21no—
580Dic11—21no—
581Dic11—21no—
582Dic11—42no—
583Dic11—41no—
584Dic11—41no—
585Dic11—41no—
586Dic11—41no—
587Dic11—81no—
588C2×#41—221no—
589C2×#41C22×D1111yescharacteristic
590C22×D4—111no—
591C23×C4—111no—
592C23×C4—221no—
593C23×C4C22×D1111yescharacteristic
594C2×M16—111no—
595C2×M16—111no—
596C2×M16—221no—
597C2×M16—221no—
598C2×M16—222no—
599C2×M16—222no—
600C2×M16—441no—
601C2×M16—441no—
602C2×M16C22×D1111yescharacteristic
603C2×M16C22×D1111yescharacteristic
604C22×C8—221no—
605C22×C8—221no—
606C4⋊Q8—111no—
607C4⋊Q8—111no—
608#126—221no—
609#126—221no—
610#126—221no—
611#126—221no—
612#126—221no—
613#126—221no—
614#125—111no—
615#125—111no—
616#125—221no—
617#125—221no—
618#125—221no—
619#124—221no—
620#124—221no—
621#124—221no—
622#123—21no—
623#123—221no—
624#123—221no—
625#123—221no—
626#123—221no—
627#123—221no—
628#123—221no—
629#123—221no—
630C22⋊Q8—111no—
631C22⋊Q8—111no—
632C22⋊Q8—221no—
633C22⋊Q8—221no—
634C22⋊Q8—221no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8C4×D1111yescharacteristic, complemented
638C22⋊Q8C4×D1111yescharacteristic, complemented
639#121—111no—
640#121—111no—
641#121—221no—
642#121—221no—
643#121—221no—
644#121C4×D1111yescharacteristic, complemented
645#121C4×D1111yescharacteristic, complemented
646#120—21no—
647#120—221no—
648C4×Q8—111no—
649C4×Q8—111no—
650C4×Q8—221no—
651C4×Q8—221no—
652C4×Q8—221no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—111no—
656C4×D4—111no—
657C4×D4—111no—
658C4×D4—111no—
659C4×D4—111no—
660C4×D4—111no—
661C4×D4—111no—
662C4×D4—111no—
663C4×D4—111no—
664C4×D4—111no—
665C4×D4—221no—
666C4×D4—221no—
667C4×D4—221no—
668C4×D4—221no—
669C4×D4—221no—
670C4×D4—221no—
671C4×D4—221no—
672#117—22no—
673#117—41no—
674#117—111no—
675#117—111no—
676#117—111no—
677#117—111no—
678#117—111no—
679#117—111no—
680#117—221no—
681#117—221no—
682#117—221no—
683#117—221no—
684#117—221no—
685#117—221no—
686#117—221no—
687#117—221no—
688#117C22×D1111yescharacteristic
689C2×C4⋊C4—21no—
690C2×C4⋊C4—111no—
691C2×C4⋊C4—111no—
692C2×C4⋊C4—111no—
693C2×C4⋊C4—111no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4—221no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—111no—
698C2×C22⋊C4—111no—
699C2×C22⋊C4—221no—
700C2×C22⋊C4—221no—
701C2×C22⋊C4—221no—
702C2×C22⋊C4—221no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—221no—
707C2×C42—221no—
708C2×C42—221no—
709C2×C42—222no—
710C2×C42—221no—
711C2×C42—441no—
712C2×C42C22×D1111yescharacteristic
713C2×C42C22×D1111yescharacteristic
714C4⋊C8—221no—
715C4⋊C8—221no—
716#104—22no—
717#104—41no—
718#104—222no—
719#104—441no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722C22⋊C8—221no—
723C22⋊C8—221no—
724#97—221no—
725C4×C8—221no—
726#95—221no—
727#95—221no—
728#95—221no—
729#95—221no—
730#95—221no—
731C2×C11—21no—
732C2×C11—21no—
733C2×C11—41no—
734C2×C11—41no—
735C2×C11—81no—
736C2×C11#233911yescharacteristic
737C2×C11C2×#42111yescharacteristic
738C2×C11#290111yescharacteristic
739D11—22no—
740D11—41no—
741C24—111no—
742C24D4×D1111yescharacteristic
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—444no—
748C2×Q8—221no—
749C2×Q8—221no—
750C2×Q8C2×C4×D1111yescharacteristic
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—111no—
755C2×D4—111no—
756C2×D4—111no—
757C2×D4—111no—
758C2×D4—221no—
759C2×D4—221no—
760C2×D4—442no—
761C2×D4C2×C4×D1111yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—442no—
789C22×C4—442no—
790C22×C4—442no—
791C22×C4C2×C4×D1111yescharacteristic
792C22×C4C2×C4×D1111yescharacteristic
793C22×C4D4×D1111yescharacteristic
794C22×C4D4×D1111yescharacteristic
795C22×C4D4×D1111yescharacteristic
796C22×C4C23×D1111yescharacteristic
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—112no—
802M16—221no—
803M16—221no—
804M16—221no—
805M16—442no—
806M16—442no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—221no—
810C2×C8—221no—
811C2×C8—442no—
812C2×C8—442no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4—111no—
817C4⋊C4—111no—
818C4⋊C4—111no—
819C4⋊C4—111no—
820C4⋊C4—111no—
821C4⋊C4—111no—
822C4⋊C4—111no—
823C4⋊C4—111no—
824C4⋊C4—221no—
825C4⋊C4—221no—
826C4⋊C4—221no—
827C4⋊C4—221no—
828C4⋊C4—221no—
829C4⋊C4—221no—
830C4⋊C4—221no—
831C4⋊C4—221no—
832C4⋊C4—221no—
833C4⋊C4—221no—
834C4⋊C4—221no—
835C4⋊C4—221no—
836C4⋊C4—221no—
837C4⋊C4—221no—
838C4⋊C4—442no—
839C4⋊C4C2×C4×D1111yescharacteristic
840C4⋊C4C2×C4×D1111yescharacteristic
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—42no—
847C22⋊C4—111no—
848C22⋊C4—111no—
849C22⋊C4—111no—
850C22⋊C4—111no—
851C22⋊C4—111no—
852C22⋊C4—111no—
853C22⋊C4—111no—
854C22⋊C4—111no—
855C22⋊C4—221no—
856C22⋊C4—221no—
857C22⋊C4—221no—
858C22⋊C4—221no—
859C22⋊C4—221no—
860C22⋊C4—221no—
861C22⋊C4—221no—
862C22⋊C4—221no—
863C22⋊C4—221no—
864C22⋊C4—221no—
865C22⋊C4—221no—
866C22⋊C4—221no—
867C22⋊C4—442no—
868C22⋊C4—442no—
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—111no—
874C42—111no—
875C42—111no—
876C42—111no—
877C42—221no—
878C42—221no—
879C42—221no—
880C42—221no—
881C42—221no—
882C42—221no—
883C42—221no—
884C42—221no—
885C42—221no—
886C42—221no—
887C42—221no—
888C42—221no—
889C42—442no—
890C42#434112yescomplemented
891C11#2250611yescharacteristic, complemented, Sylow
892C23—21no—
893C23—21no—
894C23—21no—
895C23—41no—
896C23—41no—
897C23—111no—
898C23—111no—
899C23—222no—
900C23—221no—
901C23—221no—
902C23—441no—
903C23C22⋊C4×D1111yescharacteristic
904C23C22⋊C4×D1111yescharacteristic
905C23C2×D4×D1111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—442no—
909Q8—881no—
910D4—21no—
911D4—21no—
912D4—42no—
913D4—41no—
914D4—41no—
915D4—81no—
916D4—222no—
917D4—222no—
918D4—441no—
919D4—441no—
920D4—442no—
921D4—881no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—111no—
944C2×C4—111no—
945C2×C4—111no—
946C2×C4—111no—
947C2×C4—111no—
948C2×C4—111no—
949C2×C4—221no—
950C2×C4—221no—
951C2×C4—221no—
952C2×C4—221no—
953C2×C4—221no—
954C2×C4—221no—
955C2×C4—221no—
956C2×C4—221no—
957C2×C4—221no—
958C2×C4—221no—
959C2×C4—222no—
960C2×C4—221no—
961C2×C4—221no—
962C2×C4—221no—
963C2×C4—221no—
964C2×C4—442no—
965C2×C4—448no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—442no—
969C2×C4—441no—
970C2×C4—442no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—881no—
976C2×C4—881no—
977C2×C4—881no—
978C2×C4C22⋊C4×D1111yescharacteristic
979C2×C4C22⋊C4×D1111yescharacteristic
980C2×C4C22×C4×D1111yescharacteristic
981C2×C4C2×D4×D1111yescharacteristic
982C2×C4C2×#434111yescharacteristic
983C2×C4#6703711yescharacteristic
984C2×C4#41×D1111yescharacteristic
985C2×C4#6704311yescharacteristic
986C8—41no—
987C8—41no—
988C8—222no—
989C8—441no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—81no—
1002C22—81no—
1003C22—112no—
1004C22—221no—
1005C22—221no—
1006C22—221no—
1007C22—221no—
1008C22—221no—
1009C22—442no—
1010C22—442no—
1011C22C2×C22⋊C4×D1111yescharacteristic
1012C22#1062312211yescharacteristic
1013C22#1062318611yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—42no—
1017C4—41no—
1018C4—41no—
1019C4—41no—
1020C4—81no—
1021C4—221no—
1022C4—221no—
1023C4—221no—
1024C4—221no—
1025C4—221no—
1026C4—221no—
1027C4—442no—
1028C4—441no—
1029C4—441no—
1030C4—441no—
1031C4—441no—
1032C4—881no—
1033C4C4×#434111yescharacteristic
1034C4#1062307711yescharacteristic
1035C4#1062314111yescharacteristic
1036C4#1062314211yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—41no—
1040C2—41no—
1041C2—81no—
1042C2—222no—
1043C2—441no—
1044C2#1307144211yescharacteristic
1045C2D11×#42111yescharacteristic
1046C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1897C2
socleC22×C11C22×C22⋊C4
prime radical#13082176C2
cosocleC22×C4×C11C24
hypercenter#1897D11
hypocenterC11#22506
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #13077348C2semidirect
3. #13071053C2semidirect
4. #13069595C2semidirect
5. #13069558C2semidirect
6. #13069056C2semidirect
7. #13068919C2semidirect
8. #13068915C2semidirect
9. #13068714C2semidirect
10. #13068713C2semidirect
11. #13068634C2semidirect
12. #13068428C2semidirect
13. #13068326C2semidirect
14. D11×#339C2semidirect
15. C11×#1897C2semidirect
26. #10623173C4semidirect
27. #10623172C4semidirect
28. #10623170C4semidirect
29. #10623166C4semidirect
30. #10623149C4semidirect
31. #10623147C4semidirect
32. #10623145C4semidirect
33. #10623142C4semidirect
84. C11×C22⋊Q8C2×C4semidirect
85. C11×C22⋊Q8C2×C4semidirect
86. C11×#121C2×C4semidirect
87. C11×#121C2×C4semidirect
103. Q8×Dic11C2×C4semidirect
104. Q8×Dic11C2×C4semidirect
118. D4×Dic11C2×C4semidirect
119. D4×Dic11C2×C4semidirect
135. #66979C2×C4semidirect
136. #66979C2×C4semidirect
139. C2×C4⋊Dic11C2×C4semidirect
140. C2×C4⋊Dic11C2×C4semidirect
168. #66943C2×C4semidirect
169. #66943C2×C4semidirect
172. #66941C2×C4semidirect
173. #66941C2×C4semidirect
296. C42×C11#41semidirect
363. #4318#41semidirect
374. #1897D11semidirect
637. C22⋊Q8C4×D11semidirect
638. C22⋊Q8C4×D11semidirect
644. #121C4×D11semidirect
645. #121C4×D11semidirect
890. C42#4341semidirect
891. C11#22506semidirect

Maximal subgroups

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

subgroupindex
#130821762
#130773482
#130710532
#130695952
#130695582
#130690562
#130689192
#130689152
#130687142
#130687132
#130686342
#130684282
#130683262
D11×#3392
C11×#18972
#2250611