Finite Group Databasebeta

← #14770268

Subgroups — #14770268

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#13082174C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3#13069597C211yesmaximal, characteristic, complemented
4#13069559C211yesmaximal, characteristic, complemented
5#13069064C211yesmaximal, characteristic, complemented
6#13069059C211yesmaximal, characteristic, complemented
7#13068916C211yesmaximal, characteristic, complemented
8#13068916C211yesmaximal, characteristic, complemented
9#13068716C211yesmaximal, characteristic, complemented
10#13068716C211yesmaximal, characteristic, complemented
11#13068637C211yesmaximal, characteristic, complemented
12#13068427C211yesmaximal, characteristic, complemented
13#13068326C211yesmaximal, characteristic, complemented
14C2×#10622161C211yesmaximal, characteristic, complemented
15C11×#2290C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19#10623337—21no—
20#10623322C2211yescharacteristic
21#10623322C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10623096C411yescharacteristic, complemented
27#10623096C411yescharacteristic, complemented
28#10623094C411yescharacteristic, complemented
29#10623088—21no—
30#10623086C411yescharacteristic, complemented
31#10623074C411yescharacteristic, complemented
32#10623073C411yescharacteristic, complemented
33#10623072C411yescharacteristic, complemented
34#10623072C411yescharacteristic, complemented
35#10623069—21no—
36#10623069—21no—
37C4×#4341—21no—
38#10623044—21no—
39#10623026—21no—
40#10623026—21no—
41C4×#4339C2211yescharacteristic
42#10623001C2211yescharacteristic
43C11×#388—21no—
44C11×#387—21no—
45C11×#386—21no—
46C11×#385—21no—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#376C2211yescharacteristic
51#10622820C2211yescharacteristic
52#10622820C2211yescharacteristic
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57C2×#66869C2211yescharacteristic
58C2×#66869C2211yescharacteristic
59C2×#66869C2211yescharacteristic
60C2×#66869C2211yescharacteristic
61#10622537C2211yescharacteristic
62C4×#4318C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67#10622161C2211yescharacteristic
68#10622161C2211yescharacteristic
69#10622161C2211yescharacteristic
70#10622161C2211yescharacteristic
71#10622161C2211yescharacteristic
72#10622161C2211yescharacteristic
73#10622161C2211yescharacteristic
74#10622161C2211yescharacteristic
75C22×D4×C11D411yescharacteristic
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C2×#4341—21no—
80C2×#4339C2311yescharacteristic
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2×C411yescharacteristic
83C4×D4×C11C2×C411yescharacteristic
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D411yescharacteristic
89C11×#117—22no—
90C11×#117—41no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11—22no—
100C2×C42×C11—21no—
101C2×C42×C11—41no—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107#67006—21no—
108#67006—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111#66992—21no—
112#66992—21no—
113#66991—21no—
114#66989—21no—
115#66988—21no—
116#66988—21no—
117D4×Dic11—21no—
118#66983C2×C411yescharacteristic
119#66983C2×C411yescharacteristic
120#66983C2×C411yescharacteristic, complemented
121#66983C2×C411yescharacteristic, complemented
122#66982—21no—
123#66982—21no—
124C4×C22⋊D11—21no—
125C4×C22⋊D11—21no—
126C4×C22⋊D11—21no—
127C4×C22⋊D11—21no—
128C4×C22⋊D11—21no—
129C4×C22⋊D11—21no—
130#66979—21no—
131#66979—21no—
132#66979—21no—
133#66979—21no—
134#66979C2×C411yescharacteristic
135#66979C2×C411yescharacteristic
136#66979C2×C411yescharacteristic, complemented
137#66979C2×C411yescharacteristic, complemented
138#66979C2311yescharacteristic
139#66979C2311yescharacteristic
140#66979C2311yescharacteristic
141C2×C4⋊Dic11C2×C411yescharacteristic
142C2×C4⋊Dic11C2×C411yescharacteristic
143C2×C4⋊Dic11C2×C411yescharacteristic, complemented
144C2×C4⋊Dic11C2×C411yescharacteristic, complemented
145#66977—21no—
146#66977—21no—
147#66977C2×C411yescharacteristic
148#66977C2×C411yescharacteristic
149#66977C2×C411yescharacteristic, complemented
150#66977C2×C411yescharacteristic, complemented
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×#4318—21no—
154C2×#4318—21no—
155C2×#4318—22no—
156C2×#4318—22no—
157C2×#4318—41no—
158C2×#4318—41no—
159C2×#4318C2311yescharacteristic
160C2×#4318C2311yescharacteristic
161C2×#4318C2311yescharacteristic
162C2×#4318C2311yescharacteristic
163C22×C11⋊C8—21no—
164C22×C11⋊C8—21no—
165#66951—21no—
166#66951—21no—
167#66950—21no—
168#66945—21no—
169#66943—21no—
170#66942—21no—
171#66942—21no—
172#66940—21no—
173#66939—21no—
174#66939—21no—
175#66938—21no—
176#66938—21no—
177#66936—21no—
178#66936—21no—
179(C22⋊D11)⋊C4—21no—
180(C22⋊D11)⋊C4—21no—
181#66932—21no—
182#66932—21no—
183#66932—21no—
184#66932—21no—
185#66931—21no—
186#66931—21no—
187#66930—21no—
188#66930—21no—
189C4×D44C2×C411yescharacteristic, complemented
190C4×D44C2×C411yescharacteristic, complemented
191#66925—21no—
192C42×D11—21no—
193#66923C2×C411yescharacteristic, complemented
194#66923C2×C411yescharacteristic, complemented
195#66922C2×C411yescharacteristic, complemented
196#66922C2×C411yescharacteristic, complemented
197C4×Dic22—21no—
198C4×Dic22—21no—
199C4×Dic22C2×C411yescharacteristic, complemented
200C4×Dic22C2×C411yescharacteristic, complemented
201C11×#95—21no—
202C11×#95—21no—
203C11×#95—21no—
204C11×#95—21no—
205C11×#95—21no—
206C22⋊(C11⋊C8)—21no—
207C22⋊(C11⋊C8)—21no—
208C22⋊(C11⋊C8)—21no—
209C22⋊(C11⋊C8)—21no—
210#66869—22no—
211#66869—22no—
212#66869—41no—
213#66869—41no—
214C4⋊(C11⋊C8)—21no—
215C4⋊(C11⋊C8)—21no—
216#66867—21no—
217C4×C11⋊C8—21no—
218#22506—111nomaximal, Sylow
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C2×D4×C11—42no—
222C2×D4×C11C22⋊C411yescharacteristic
223C2×D4×C11C22⋊C411yescharacteristic
224C2×D4×C11C22⋊C411yescharacteristic
225C2×D4×C11C22⋊C411yescharacteristic
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
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×C11—21no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11C22×C411yescharacteristic
242C22×C4×C11C22×C411yescharacteristic
243C22×C4×C11C22×C411yescharacteristic
244C22×C4×C11C22×C411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—21no—
255C2×C22⋊D11—21no—
256C2×C22⋊D11—21no—
257C2×C22⋊D11—21no—
258C2×C22⋊D11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263#4341—44no—
264#4339—21no—
265#4339—21no—
266#4339—21no—
267#4339—21no—
268C2×D44C22×C411yescharacteristic
269C2×C4×D11—21no—
270C2×C4×D11—21no—
271C2×C4×D11—21no—
272C2×Dic22—21no—
273C2×Dic22—21no—
274C2×Dic22C22×C411yescharacteristic
275C11×C4⋊C4—42no—
276C11×C4⋊C4—42no—
277C11×C4⋊C4C22⋊C411yescharacteristic
278C11×C4⋊C4C22⋊C411yescharacteristic
279C11×C4⋊C4C22⋊C411yescharacteristic
280C11×C4⋊C4C22⋊C411yescharacteristic
281C11×C22⋊C4—42no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4C22⋊C411yescharacteristic
285C11×C22⋊C4C22⋊C411yescharacteristic
286C11×C22⋊C4C22⋊C411yescharacteristic
287C11×C22⋊C4C22⋊C411yescharacteristic
288C11×C22⋊C4C22⋊C411yescharacteristic
289C11×C22⋊C4C22⋊C411yescharacteristic
290C11×C22⋊C4C22⋊C411yescharacteristic
291C11×C22⋊C4C22⋊C411yescharacteristic
292C42×C11—21no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—42no—
300C42×C11C22×C411yescharacteristic
301C42×C11C22×C411yescharacteristic
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304C42×C11#4112yescomplemented
305C22⋊Dic11—21no—
306C22⋊Dic11—21no—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309C22⋊Dic11—21no—
310C22⋊Dic11—21no—
311C22⋊Dic11—21no—
312C22⋊Dic11—21no—
313C22⋊Dic11—21no—
314C22⋊Dic11—21no—
315C22⋊Dic11—21no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—21no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4—21no—
320(C2×D11)⋊C4—21no—
321(C2×D11)⋊C4—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11—21no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11C22×C411yescharacteristic
329C4⋊Dic11C22×C411yescharacteristic
330C4⋊Dic11C22×C411yescharacteristic
331C4⋊Dic11C22×C411yescharacteristic
332C4⋊Dic11C22×C411yescharacteristic
333C4⋊Dic11C22×C411yescharacteristic
334Dic11⋊C4—21no—
335Dic11⋊C4—21no—
336Dic11⋊C4—21no—
337Dic11⋊C4—21no—
338Dic11⋊C4—21no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341Dic11⋊C4—21no—
342Dic11⋊C4—21no—
343Dic11⋊C4—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—
353#4318—21no—
354#4318—21no—
355#4318—21no—
356#4318—21no—
357#4318—21no—
358#4318—21no—
359#4318—21no—
360#4318—42no—
361#4318—42no—
362#4318#4112yescomplemented
363C2×C11⋊C8—21no—
364C2×C11⋊C8—21no—
365C2×C11⋊C8—21no—
366C2×C11⋊C8—21no—
367C2×C11⋊C8—42no—
368C2×C11⋊C8—42no—
369#3475—111no—
370D4×M16—111no—
371#2290D1111yescharacteristic, complemented
372#1995—111no—
373#1986—111no—
374#1897—111no—
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—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11C2×C22⋊C411yescharacteristic
393C23×C11C2×C22⋊C411yescharacteristic
394C23×C11C2×C22⋊C411yescharacteristic
395C23×C11C2×C22⋊C411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C22×D11—21no—
398D4×C11—22no—
399D4×C11—22no—
400D4×C11—41no—
401D4×C11—41no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
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—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—48no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11C2×C22⋊C411yescharacteristic
438C2×C4×C11C2×C22⋊C411yescharacteristic
439C2×C4×C11C2×C22⋊C411yescharacteristic
440C2×C4×C11C2×C22⋊C411yescharacteristic
441C2×C4×C11C2×C22⋊C411yescharacteristic
442C2×C4×C11C2×C22⋊C411yescharacteristic
443C2×C4×C11C2×C22⋊C411yescharacteristic
444C2×C4×C11C2×C22⋊C411yescharacteristic
445C2×C4×C11C23×C411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C2×#4111yescharacteristic
448C2×C4×C11C2×#4111yescharacteristic
449C2×C4×C11H(5,𝔽2)11yescharacteristic
450C2×C4×C112−1+411yescharacteristic
451C22⋊D11—42no—
452C22⋊D11—41no—
453C22⋊D11—41no—
454C22⋊D11—42no—
455C22⋊D11—81no—
456C22⋊D11—81no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—21no—
462C2×Dic11—21no—
463C2×Dic11—21no—
464C2×Dic11—42no—
465C2×Dic11—42no—
466C2×Dic11—81no—
467C2×Dic11—81no—
468D44—21no—
469D44—21no—
470C4×D11—42no—
471C4×D11—41no—
472C4×D11—41no—
473C4×D11—81no—
474Dic22—21no—
475Dic22—21no—
476Dic22—42no—
477Dic22—81no—
478C11⋊C8—22no—
479C11⋊C8—41no—
480C11⋊C8—41no—
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#525—111no—
502C4×#41—111no—
503C4×#41—221no—
504C2×C4×D4C2×D1111yescharacteristic
505C2×#117—111no—
506C2×#117—111no—
507C2×#117C2×D1111yescharacteristic
508C22×C42C2×D1111yescharacteristic
509#436—221no—
510#435—221no—
511#435—221no—
512C8×D4—221no—
513#423—111no—
514C2×#104—111no—
515C2×#104—111no—
516C2×#104—111no—
517C2×#104—111no—
518#407—111no—
519#407—111no—
520C4×M16—111no—
521#388—21no—
522#387—21no—
523#386—21no—
524#385—21no—
525C4×C4⋊C4C2×D1111yescharacteristic
526C4×C22⋊C4C2×D1111yescharacteristic
527C4×C22⋊C4C2×D1111yescharacteristic
528#376C2×D1111yescharacteristic
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#339—111no—
540#339—111no—
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—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—81no—
557C22×C11—81no—
558C22×C11#42112yes—
559C22×C11C22×C22⋊C411yescharacteristic
560C22×C11#54611yescharacteristic
561C22×C11#54711yescharacteristic
562C2×D11—41no—
563C2×D11—41no—
564C2×D11—41no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—21no—
572C4×C11—21no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—81no—
576C4×C11—81no—
577C4×C11C4×#4111yescharacteristic
578C4×C11#52011yescharacteristic
579C4×C11#54611yescharacteristic
580C4×C11#54711yescharacteristic
581Dic11—41no—
582Dic11—41no—
583Dic11—41no—
584Dic11—41no—
585Dic11—41no—
586Dic11—41no—
587Dic11—41no—
588C2×#41—111no—
589C2×#41—221no—
590C22×D4C22⋊D1111yescharacteristic
591C23×C4—21no—
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C2×M16—111no—
595C2×M16—111no—
596C2×M16—111no—
597C2×M16—111no—
598C2×M16—221no—
599C2×M16—221no—
600C2×M16—222no—
601C2×M16—222no—
602C2×M16—441no—
603C2×M16—441no—
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—221no—
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—111no—
633C22⋊Q8—111no—
634C22⋊Q8—221no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8—221no—
638C22⋊Q8—221no—
639#121—111no—
640#121—111no—
641#121—111no—
642#121—111no—
643#121—221no—
644#121—221no—
645#121—221no—
646#120—221no—
647#120—221no—
648C4×Q8—111no—
649C4×Q8—111no—
650C4×Q8—221no—
651C4×Q8—221no—
652C4×Q8—221no—
653C4×D4—111no—
654C4×D4—111no—
655C4×D4—221no—
656C4×D4—221no—
657C4×D4—221no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4—221no—
661C4×D4—221no—
662C4×D4—221no—
663C4×D4—221no—
664C4×D4C4×D1111yescharacteristic
665C4×D4C4×D1111yescharacteristic
666C4×D4C4×D1111yescharacteristic
667C4×D4C4×D1111yescharacteristic
668C4×D4D4411yescharacteristic
669C4×D4D4411yescharacteristic
670C4×D4D4411yescharacteristic
671C4×D4D4411yescharacteristic
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—111no—
681#117—221no—
682#117—221no—
683#117—221no—
684#117—221no—
685#117—221no—
686#117—221no—
687#117—221no—
688#117—221no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—111no—
692C2×C4⋊C4—111no—
693C2×C4⋊C4—111no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4C22⋊D1111yescharacteristic
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—221no—
700C2×C22⋊C4—221no—
701C2×C22⋊C4C22⋊D1111yescharacteristic
702C2×C22⋊C4C22⋊D1111yescharacteristic
703C2×C42—22no—
704C2×C42—21no—
705C2×C42—41no—
706C2×C42—221no—
707C2×C42—221no—
708C2×C42—221no—
709C2×C42C22×D1111yescharacteristic
710C2×C42C22×D1111yescharacteristic
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1111yescharacteristic
713C2×C42C22×D1111yescharacteristic
714C4⋊C8—221no—
715C4⋊C8—221no—
716#104—222no—
717#104—222no—
718#104—441no—
719#104—441no—
720C22⋊C8—221no—
721C22⋊C8—221no—
722C22⋊C8—221no—
723C22⋊C8—221no—
724#97—221no—
725C4×C8—221no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731C2×C11—21no—
732C2×C11—21no—
733C2×C11—22no—
734C2×C11—41no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11#233911yescharacteristic
738C2×C11C2×#42111yescharacteristic
739C2×C11#290111yescharacteristic
740D11—81no—
741C24C2×C22⋊D1111yescharacteristic
742C24C2×C22⋊D1111yescharacteristic
743#41—221no—
744#41—221no—
745#41—221no—
746#41—221no—
747#41—444no—
748C2×Q8—111no—
749C2×Q8—221no—
750C2×Q8—221no—
751C2×D4—42no—
752C2×D4—111no—
753C2×D4—221no—
754C2×D4—221no—
755C2×D4—221no—
756C2×D4—221no—
757C2×D4—221no—
758C2×D4(C2×D11)⋊C411yescharacteristic
759C2×D4(C2×D11)⋊C411yescharacteristic
760C2×D4(C2×D11)⋊C411yescharacteristic
761C2×D4(C2×D11)⋊C411yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4C2×C4×D1111yescharacteristic
785C22×C4C2×C4×D1111yescharacteristic
786C22×C4C2×C4×D1111yescharacteristic
787C22×C4C2×C4×D1111yescharacteristic
788C22×C4C2×D4411yescharacteristic
789C22×C4C2×D4411yescharacteristic
790C22×C4C2×D4411yescharacteristic
791C22×C4C2×D4411yescharacteristic
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C23×D1111yescharacteristic
797M16—112no—
798M16—221no—
799M16—221no—
800M16—221no—
801M16—221no—
802M16—221no—
803M16—221no—
804M16—221no—
805M16—442no—
806M16—442no—
807C2×C8—221no—
808C2×C8—221no—
809C2×C8—221no—
810C2×C8—221no—
811C2×C8—442no—
812C2×C8—442no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—111no—
816C4⋊C4—111no—
817C4⋊C4—111no—
818C4⋊C4—111no—
819C4⋊C4—111no—
820C4⋊C4—111no—
821C4⋊C4—221no—
822C4⋊C4—221no—
823C4⋊C4—221no—
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(C2×D11)⋊C411yescharacteristic
838C4⋊C4(C2×D11)⋊C411yescharacteristic
839C4⋊C4(C2×D11)⋊C411yescharacteristic
840C4⋊C4(C2×D11)⋊C411yescharacteristic
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—221no—
845C22⋊C4—221no—
846C22⋊C4—221no—
847C22⋊C4—221no—
848C22⋊C4—221no—
849C22⋊C4—221no—
850C22⋊C4—221no—
851C22⋊C4—221no—
852C22⋊C4—221no—
853C22⋊C4—221no—
854C22⋊C4—221no—
855C22⋊C4—221no—
856C22⋊C4—221no—
857C22⋊C4—221no—
858C22⋊C4—221no—
859C22⋊C4—221no—
860C22⋊C4—221no—
861C22⋊C4(C2×D11)⋊C411yescharacteristic
862C22⋊C4(C2×D11)⋊C411yescharacteristic
863C22⋊C4(C2×D11)⋊C411yescharacteristic
864C22⋊C4(C2×D11)⋊C411yescharacteristic
865C22⋊C4(C2×D11)⋊C411yescharacteristic
866C22⋊C4(C2×D11)⋊C411yescharacteristic
867C22⋊C4(C2×D11)⋊C411yescharacteristic
868C22⋊C4(C2×D11)⋊C411yescharacteristic
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—42no—
877C42—221no—
878C42—221no—
879C42—221no—
880C42—221no—
881C42—221no—
882C42—221no—
883C42—221no—
884C42—221no—
885C42—221no—
886C42C2×C4×D1111yescharacteristic
887C42C2×C4×D1111yescharacteristic
888C42C2×D4411yescharacteristic
889C42C2×D4411yescharacteristic
890C42#434112yescomplemented
891C11#2250611yescharacteristic, complemented, Sylow
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—221no—
901C23C2×(C2×D11)⋊C411yescharacteristic
902C23C2×(C2×D11)⋊C411yescharacteristic
903C23C2×(C2×D11)⋊C411yescharacteristic
904C23C2×(C2×D11)⋊C411yescharacteristic
905C23C22×C22⋊D1111yescharacteristic
906Q8—221no—
907Q8—221no—
908Q8—442no—
909Q8—881no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—221no—
915D4—221no—
916D4—442no—
917D4—441no—
918D4—441no—
919D4—442no—
920D4—881no—
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—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—48no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—221no—
958C2×C4—221no—
959C2×C4—221no—
960C2×C4—221no—
961C2×C4—221no—
962C2×C4—221no—
963C2×C4—221no—
964C2×C4—442no—
965C2×C4—442no—
966C2×C4—442no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—881no—
970C2×C4—881no—
971C2×C4—881no—
972C2×C4C2×(C2×D11)⋊C411yescharacteristic
973C2×C4C2×(C2×D11)⋊C411yescharacteristic
974C2×C4C2×(C2×D11)⋊C411yescharacteristic
975C2×C4C2×(C2×D11)⋊C411yescharacteristic
976C2×C4C2×(C2×D11)⋊C411yescharacteristic
977C2×C4C2×(C2×D11)⋊C411yescharacteristic
978C2×C4C2×(C2×D11)⋊C411yescharacteristic
979C2×C4C2×(C2×D11)⋊C411yescharacteristic
980C2×C4C22×C4×D1111yescharacteristic
981C2×C4C22×D4411yescharacteristic
982C2×C4C2×#434111yescharacteristic
983C2×C4#6703711yescharacteristic
984C2×C4#41×D1111yescharacteristic
985C2×C4#6704311yescharacteristic
986C8—222no—
987C8—441no—
988C8—441no—
989C8—441no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—441no—
1008C22—441no—
1009C22—441no—
1010C22#1062261812yes—
1011C22C22×(C2×D11)⋊C411yescharacteristic
1012C22#1062333711yescharacteristic
1013C22#1062335511yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—441no—
1027C4—441no—
1028C4—441no—
1029C4—441no—
1030C4—441no—
1031C4—441no—
1032C4—441no—
1033C4C4×#434111yescharacteristic
1034C4#1062307711yescharacteristic
1035C4#1062308511yescharacteristic
1036C4#1062308611yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—881no—
1044C2#1307144111yescharacteristic
1045C2C2×#1062261811yescharacteristic
1046C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2290C2
socleC22×C11C22×C22⋊C4
prime radical#13082174C2
cosocleC22×C4×C11C24
hypercenter#2290D11
hypocenterC11#22506
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. #13069597C2semidirect
4. #13069559C2semidirect
5. #13069064C2semidirect
6. #13069059C2semidirect
7. #13068916C2semidirect
8. #13068916C2semidirect
9. #13068716C2semidirect
10. #13068716C2semidirect
11. #13068637C2semidirect
12. #13068427C2semidirect
13. #13068326C2semidirect
14. C2×#10622161C2semidirect
15. C11×#2290C2semidirect
26. #10623096C4semidirect
27. #10623096C4semidirect
28. #10623094C4semidirect
30. #10623086C4semidirect
31. #10623074C4semidirect
32. #10623073C4semidirect
33. #10623072C4semidirect
34. #10623072C4semidirect
120. #66983C2×C4semidirect
121. #66983C2×C4semidirect
136. #66979C2×C4semidirect
137. #66979C2×C4semidirect
143. C2×C4⋊Dic11C2×C4semidirect
144. C2×C4⋊Dic11C2×C4semidirect
149. #66977C2×C4semidirect
150. #66977C2×C4semidirect
189. C4×D44C2×C4semidirect
190. C4×D44C2×C4semidirect
193. #66923C2×C4semidirect
194. #66923C2×C4semidirect
195. #66922C2×C4semidirect
196. #66922C2×C4semidirect
199. C4×Dic22C2×C4semidirect
200. C4×Dic22C2×C4semidirect
304. C42×C11#41semidirect
362. #4318#41semidirect
371. #2290D11semidirect
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
#130821742
D4×#43182
#130695972
#130695592
#130690642
#130690592
#130689162
#130687162
#130686372
#130684272
#130683262
C2×#106221612
C11×#22902
#2250611