Finite Group Databasebeta

← #15630859

Subgroups — #15630859

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4341C211yesmaximal, characteristic, complemented
2D11×#547C211yesmaximal, characteristic, complemented
3#13080946C211yesmaximal, characteristic, complemented
4#13080942C211yesmaximal, characteristic, complemented
5#13080923C211yesmaximal, characteristic, complemented
6#13080918C211yesmaximal, characteristic, complemented
7#13080613C212yesmaximal, complemented
8#13080605C212yesmaximal, complemented
9#13080581C212yesmaximal, complemented
10#13080573C212yesmaximal, complemented
11#13080482C211yesmaximal, characteristic, complemented
12#13080475C211yesmaximal, characteristic, complemented
13#13080429C211yesmaximal, characteristic, complemented
14#13079006C211yesmaximal, characteristic, complemented
15#13078535C212yesmaximal, complemented
16#13078424C211yesmaximal, characteristic, complemented
17#13078232C212yesmaximal, complemented
18#13078075C211yesmaximal, characteristic, complemented
19#13077863C212yesmaximal, complemented
20C4×#66964C211yesmaximal, characteristic, complemented
21D4×#4313C211yesmaximal, characteristic, complemented
22C2×#10622384C212yesmaximal, complemented
23C11×#3294C211yesmaximal, characteristic, complemented
24C2×#41×D11—21no—
25C22×#4341C2212yes—
26C11×#547C2211yescharacteristic
27D42×C11C2211yescharacteristic, complemented
28#10623355—21no—
29#10623337C2212yescomplemented
30D4×C22⋊D11—21no—
31C2×D4×Dic11—21no—
32C2×#66964C2211yescharacteristic
33C2×#66964C2212yescomplemented
34C22×#4313C2212yescomplemented
35#10623257C2211yescharacteristic, complemented
36D11×C4⋊Q8C2211yescharacteristic, complemented
37#10623249C2211yescharacteristic, complemented
38#10623247C2211yescharacteristic
39#10623186—22no—
40D11×#123—22no—
41#10623162—21no—
42D11×C22⋊Q8—21no—
43#10623142—21no—
44#10623142C2212yescomplemented
45#10623137C2212yes—
46D11×#121C2212yescomplemented
47#10623129C2212yescomplemented
48#10623127—21no—
49#10623122—22no—
50#10623117—22no—
51#10623086C2211yescharacteristic
52#10623086C2211yescharacteristic, complemented
53#10623082C2211yescharacteristic, complemented
54C4×D4×D11C2211yescharacteristic
55C4×D4×D11C2211yescharacteristic, complemented
56D4×Dic22C2211yescharacteristic, complemented
57C4×#4341C2211yescharacteristic
58#10623038C2212yescomplemented
59C2×C4⋊C4×D11C2212yescomplemented
60C11×#486C2211yescharacteristic, complemented
61C11×#480C2212yescomplemented
62C11×#474C2211yescharacteristic, complemented
63C11×#466C2212yescomplemented
64C11×#459C2211yescharacteristic, complemented
65C11×#447C2212yescomplemented
66C4×C11×D8C2211yescharacteristic, complemented
67C8×D4×C11C2211yescharacteristic, complemented
68C2×C11×#102C2212yescomplemented
69#10622830C2212yescomplemented
70C2×#66896C2212yescomplemented
71#10622772C2212yescomplemented
72#10622771C2212yescomplemented
73#10622771C2212yescomplemented
74#10622766C2212yescomplemented
75#10622765C2211yescharacteristic, complemented
76#10622727C2212yescomplemented
77#10622724C2212yescomplemented
78C2×#66880C2212yescomplemented
79#10622707C2211yescharacteristic, complemented
80#10622706C2211yescharacteristic, complemented
81#10622685C2211yescharacteristic, complemented
82#10622683C2211yescharacteristic, complemented
83#10622654C2212yescomplemented
84#10622653C2212yescomplemented
85#10622651C2212yescomplemented
86#10622646C2212yescomplemented
87#10622632C2211yescharacteristic, complemented
88C4×#4324C2211yescharacteristic, complemented
89C4×#4323C2211yescharacteristic, complemented
90D4×C11⋊C8C2211yescharacteristic, complemented
91#10622620C2211yescharacteristic, complemented
92#10622584C2212yescomplemented
93C2×#66874C2212yescomplemented
94#10622502C2211yescharacteristic, complemented
95#10622499C2212yescomplemented
96#10622497C2212yescomplemented
97#10622497C2212yescomplemented
98#10622494C2211yescharacteristic, complemented
99#10622494C2212yescomplemented
100#10622488C2212yescomplemented
101#10622464C2211yescharacteristic, complemented
102#10622454C2211yescharacteristic, complemented
103#10622451C2211yescharacteristic, complemented
104#10622450C2211yescharacteristic, complemented
105#10622400C2212yescomplemented
106#10622398C2211yescharacteristic, complemented
107#10622395C2212yescomplemented
108#10622394C2212yescomplemented
109#10622394C2212yescomplemented
110#10622393C2212yescomplemented
111#10622390C2212yescomplemented
112#10622390C2212yescomplemented
113#10622384C2212yes—
114#10622384C2211yescharacteristic
115#10622384C2212yescomplemented
116#10622384C2212yescomplemented
117#10622384C2212yescomplemented
118#10622384C2212yescomplemented
119#10622384C2212yescomplemented
120#10622384C2212yescomplemented
121#10622384C2212yescomplemented
122#10622383C2211yescharacteristic, complemented
123#10622378C2212yescomplemented
124#10622378C2212yescomplemented
125#10622374C2212yescomplemented
126#10622370C2211yescharacteristic, complemented
127#10622351C2212yescomplemented
128#10622343C2212yescomplemented
129#10622339C2212yescomplemented
130#10622334C2212yescomplemented
131C4×#4314C2211yescharacteristic, complemented
132#10622301C2211yescharacteristic, complemented
133C4×#4313C2211yescharacteristic, complemented
134#10622294C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C22×D4×C11—21no—
137C22×D4×C11C2312yes—
138C22×C22⋊D11—22no—
139C23×Dic11—22no—
140#41×D11—48no—
141C2×#4343—21no—
142C2×Q8×D11—21no—
143C2×#4341—28no—
144C2×#4341—21no—
145C2×#4341—22no—
146C2×#4341—22no—
147C2×#4341—22no—
148C2×#4341—44no—
149C2×#4341C2312yes—
150C2×#4341C2312yes—
151C2×#4341C2312yes—
152C2×#4341C2311yescharacteristic
153C2×D4×D11—22no—
154C2×D4×D11D411yescharacteristic
155C2×D4×D11C2311yescharacteristic
156C2×#4339—22no—
157C2×#4339—21no—
158C22×C4×D11—22no—
159C22×C4×D11—21no—
160C22×C4×D11C2312yes—
161C22×Dic22C2312yes—
162C2×C11×D8C2311yescharacteristic
163C2×C11×D8C2312yes—
164C22×C8×C11C2312yes—
165C11×C4⋊Q8C2311yescharacteristic
166C11×#127C2311yescharacteristic
167C11×#123—22no—
168C11×C22⋊Q8—21no—
169C11×#121—21no—
170C11×#121C2312yes—
171C11×#121C2312yes—
172C11×#120—22no—
173C4×D4×C11C2311yescharacteristic
174C4×D4×C11C2311yescharacteristic
175C4×D4×C11C2311yescharacteristic
176C2×C11×C4⋊C4C2312yes—
177#67006—22no—
178C2×C22⋊Dic11—22no—
179#66999—21no—
180#66997—21no—
181#66993—21no—
182#66992—22no—
183#66992—22no—
184#66992—22no—
185#66992—22no—
186#66991—21no—
187#66991—21no—
188#66991C2312yes—
189#66991C2312yes—
190#66990—22no—
191#66989C2312yes—
192#66988—22no—
193#66988—22no—
194D4×Dic11—21no—
195D4×Dic11—22no—
196D4×Dic11—22no—
197D4×Dic11—21no—
198D4×Dic11—21no—
199D4×Dic11—21no—
200D4×Dic11D411yescharacteristic
201D4×Dic11C2311yescharacteristic
202D4×Dic11C2311yescharacteristic
203C2×#4324C2311yescharacteristic
204C2×#4324C2312yes—
205C2×#4323C2311yescharacteristic
206C2×#4323C2312yes—
207#66983—21no—
208#66983C2312yes—
209#66982—22no—
210C4×C22⋊D11—21no—
211C4×C22⋊D11—21no—
212C4×C22⋊D11C2312yes—
213C2×C4⋊Dic11—21no—
214C2×C4⋊Dic11C2312yes—
215#66977—21no—
216#66977C2312yes—
217C2×Dic11⋊C4—22no—
218C2×C4×Dic11—21no—
219C22×C11⋊C8C2312yes—
220#66964—24no—
221#66964—44no—
222C2×#4314C2311yescharacteristic
223C2×#4314C2312yes—
224C2×#4313—44no—
225C2×#4313C2312yes—
226C2×#4313C2311yescharacteristic
227C2×#4313C2311yescharacteristic
228C2×#4313C2312yes—
229C2×#4313C2312yes—
230#66950—21no—
231#66950C2312yes—
232#66949—22no—
233#66948C2312yes—
234#66947—22no—
235#66947—22no—
236#66946D411yescharacteristic
237#66946C2311yescharacteristic
238#66945C2311yescharacteristic
239C4⋊C4×D11—21no—
240C4⋊C4×D11—22no—
241C4⋊C4×D11—22no—
242C4⋊C4×D11D411yescharacteristic
243C4⋊C4×D11C2312yes—
244C4⋊C4×D11C2312yes—
245C4⋊C4×D11C2311yescharacteristic
246C4⋊C4×D11C2312yes—
247#66941—21no—
248#66941—21no—
249#66941C2312yes—
250#66940C2311yescharacteristic
251#66939—22no—
252#66939—22no—
253#66938—22no—
254#66937—22no—
255#66936—22no—
256#66936—22no—
257#66936—22no—
258(C22⋊D11)⋊C4—21no—
259(C22⋊D11)⋊C4—22no—
260(C22⋊D11)⋊C4—21no—
261(C22⋊D11)⋊C4D412yes—
262C22⋊C4×D11—21no—
263C22⋊C4×D11—22no—
264C22⋊C4×D11D412yes—
265#66931—22no—
266#66931—22no—
267#66931—22no—
268#66930—21no—
269C4×D44C2311yescharacteristic
270C4×D44C2311yescharacteristic
271C42×D11C2311yescharacteristic
272#66922C2311yescharacteristic
273#66922C2311yescharacteristic
274C4×Dic22C2311yescharacteristic
275C11×#107C2312yes—
276C11×#107C2311yescharacteristic
277C11×C4⋊C8C2311yescharacteristic
278C11×#102C2311yescharacteristic
279C11×#102C2312yes—
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×#102C2311yescharacteristic
283C11×#102C2312yes—
284C11×C22⋊C8C2312yes—
285C4×C8×C11C2311yescharacteristic
286#66896C2311yescharacteristic
287#66896C2311yescharacteristic
288#66896C2312yes—
289#66896C2312yes—
290#66896C2312yes—
291#66896C2312yes—
292C22⋊(C11⋊C8)C2312yes—
293#66885C2311yescharacteristic
294(C2×D11)⋊C8C2312yes—
295(C2×D11)⋊C8C2312yes—
296#66881C2312yes—
297#66881C2311yescharacteristic
298#66880C2312yes—
299#66880C2312yes—
300#66880C2312yes—
301#66880C2312yes—
302#66880C2311yescharacteristic
303#66879C2311yescharacteristic
304#66879C2311yescharacteristic
305Dic11⋊C8C2312yes—
306#66874C2312yes—
307#66874C2312yes—
308#66874C2312yes—
309#66874C2312yes—
310#66874C2311yescharacteristic
311#66873C2311yescharacteristic
312#66872C2311yescharacteristic
313#66872C2312yes—
314#66871C2312yes—
315#66871C2311yescharacteristic
316C4⋊(C11⋊C8)C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61161—111nomaximal, Sylow
319C24×C11—22no—
320C23×D11—21no—
321C23×D11C2×D412yes—
322C11×#41—44no—
323C2×Q8×C11—21no—
324C2×D4×C11—24no—
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—22no—
329C2×D4×C11—21no—
330C2×D4×C11—42no—
331C2×D4×C11—44no—
332C2×D4×C11C2×D411yescharacteristic
333C2×D4×C11C2412yes—
334C2×D4×C11C2411yescharacteristic
335C2×D4×C11C2411yescharacteristic
336C22×C4×C11—22no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11C2412yes—
340C2×C22⋊D11—21no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—21no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—48no—
349C2×C22⋊D11C2×D412yes—
350C22×Dic11—21no—
351C22×Dic11—21no—
352C22×Dic11—22no—
353C22×Dic11—22no—
354C22×Dic11—22no—
355C22×Dic11—21no—
356C22×Dic11—22no—
357C22×Dic11—22no—
358C22×Dic11—48no—
359C22×Dic11C2×D412yes—
360#4343—44no—
361Q8×D11—44no—
362#4341—24no—
363#4341—22no—
364#4341—24no—
365#4341—24no—
366#4341—24no—
367#4341—42no—
368#4341—42no—
369#4341—48no—
370#4341—48no—
371#4341—48no—
372#4341—44no—
373#4341#4114yescomplemented
374D4×D11—22no—
375D4×D11—22no—
376D4×D11—24no—
377D4×D11—48no—
378#4339—44no—
379#4339—48no—
380C2×D44—22no—
381C2×D44C2×D411yescharacteristic
382C2×D44C2411yescharacteristic
383C2×C4×D11—24no—
384C2×C4×D11—24no—
385C2×C4×D11—21no—
386C2×C4×D11—21no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—21no—
391C2×C4×D11—48no—
392C2×C4×D11—44no—
393C2×C4×D11C2×D411yescharacteristic
394C2×C4×D11C2×D412yes—
395C2×C4×D11C2×D412yes—
396C2×C4×D11C2×D411yescharacteristic
397C2×C4×D11C2412yes—
398C2×C4×D11C2411yescharacteristic
399C2×Dic22—24no—
400C2×Dic22—22no—
401C2×Dic22—21no—
402C2×Dic22—22no—
403C2×Dic22—42no—
404C2×Dic22C2412yes—
405C2×Dic22C2411yescharacteristic
406C11×D8—22no—
407C11×D8—42no—
408C2×C8×C11—42no—
409C2×C8×C11C2412yes—
410C2×C8×C11C2411yescharacteristic
411C2×C8×C11C2411yescharacteristic
412C11×C4⋊C4—21no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4C2×D411yescharacteristic
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C22⋊C4—21no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4C2×D412yes—
423C42×C11C2411yescharacteristic
424C22⋊Dic11—21no—
425C22⋊Dic11—22no—
426C22⋊Dic11—22no—
427C22⋊Dic11—21no—
428C22⋊Dic11—22no—
429C22⋊Dic11—22no—
430C22⋊Dic11—22no—
431C22⋊Dic11C2×D412yes—
432#4324—22no—
433#4324—42no—
434#4323—22no—
435#4323—42no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—21no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—21no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4C2×D412yes—
443(C2×D11)⋊C4C2×D412yes—
444C4⋊Dic11—22no—
445C4⋊Dic11—21no—
446C4⋊Dic11—21no—
447C4⋊Dic11—21no—
448C4⋊Dic11—22no—
449C4⋊Dic11C2×D411yescharacteristic
450C4⋊Dic11C2412yes—
451C4⋊Dic11C2411yescharacteristic
452C4⋊Dic11C2411yescharacteristic
453Dic11⋊C4—21no—
454Dic11⋊C4—22no—
455Dic11⋊C4—21no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—21no—
460Dic11⋊C4—22no—
461Dic11⋊C4C2×D412yes—
462C4×Dic11—21no—
463C4×Dic11—21no—
464C4×Dic11—21no—
465C4×Dic11C2×D411yescharacteristic
466C4×Dic11C2×D411yescharacteristic
467C4×Dic11C2411yescharacteristic
468C2×C11⋊C8—42no—
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2412yes—
472#4314—22no—
473#4314—42no—
474#4313—22no—
475#4313—22no—
476#4313—24no—
477#4313—42no—
478#4313—42no—
479D4×#41—111no—
480C2×#547—111no—
481#3332—111no—
482#3332—111no—
483#3330—111no—
484#3330—111no—
485#3308—112no—
486#3308—112no—
487#3306—112no—
488#3306—112no—
489#3298—111no—
490#3298—111no—
491#3294—111no—
492#3294D1111yescharacteristic, complemented
493#3141—111no—
494#3092—112no—
495#3079—111no—
496#3055—112no—
497#3036—111no—
498#3006—112no—
499C4×AGL(1,ℤ/8)—111no—
500D4×M16—111no—
501C2×#417—112no—
502C23×C11—21no—
503C23×C11—21no—
504C23×C11—22no—
505C23×C11—44no—
506C23×C11—44no—
507C23×C11—82no—
508C23×C11C22×D412yes—
509C22×D11—24no—
510C22×D11—24no—
511C22×D11—21no—
512C22×D11—42no—
513C22×D11—42no—
514C22×D11—42no—
515C22×D11—42no—
516C22×D11C22×D412yes—
517C22×D11C22×D411yescharacteristic
518Q8×C11—42no—
519D4×C11—21no—
520D4×C11—22no—
521D4×C11—21no—
522D4×C11—22no—
523D4×C11—21no—
524D4×C11—44no—
525D4×C11—44no—
526D4×C11—44no—
527D4×C11—42no—
528D4×C11—81no—
529D4×C11AGL(1,ℤ/8)14yescomplemented
530D4×C11C2×#4112yescomplemented
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—44no—
537C2×C4×C11—42no—
538C2×C4×C11—42no—
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C22×D412yes—
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C2511yescharacteristic
543C22⋊D11—24no—
544C22⋊D11—24no—
545C22⋊D11—44no—
546C22⋊D11—44no—
547C22⋊D11—44no—
548C22⋊D11—44no—
549C22⋊D11—44no—
550C22⋊D11—42no—
551C22⋊D11—82no—
552C2×Dic11—21no—
553C2×Dic11—24no—
554C2×Dic11—24no—
555C2×Dic11—21no—
556C2×Dic11—22no—
557C2×Dic11—21no—
558C2×Dic11—22no—
559C2×Dic11—44no—
560C2×Dic11—44no—
561C2×Dic11—44no—
562C2×Dic11—42no—
563C2×Dic11—44no—
564C2×Dic11—44no—
565C2×Dic11—81no—
566C2×Dic11C22×D411yescharacteristic
567C2×Dic11C22×D411yescharacteristic
568C2×Dic11C22×D412yes—
569C2×Dic11C22×D411yescharacteristic
570D44—22no—
571D44—21no—
572D44—21no—
573D44—44no—
574C4×D11—24no—
575C4×D11—22no—
576C4×D11—22no—
577C4×D11—22no—
578C4×D11—24no—
579C4×D11—41no—
580C4×D11—42no—
581C4×D11—42no—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—44no—
585C4×D11—42no—
586C4×D11C2×#4112yes—
587C4×D11H(5,𝔽2)12yes—
588Dic22—21no—
589Dic22—22no—
590Dic22—22no—
591Dic22—44no—
592Dic22—44no—
593Dic22—42no—
594Dic22C2×#4112yescomplemented
595C8×C11—21no—
596C8×C11—21no—
597C8×C11—22no—
598C11⋊C8—21no—
599C11⋊C8—21no—
600C11⋊C8—22no—
601C22×#41—112no—
602C22×#41—221no—
603C2×AGL(1,ℤ/8)—111no—
604C2×AGL(1,ℤ/8)—112no—
605C22×M16—112no—
606#550—111no—
607D4×Q8—111no—
608#548—112no—
609#547—111no—
610#547—112no—
611#547—111no—
612#547—111no—
613#547—112no—
614#547—111no—
615#547—221no—
616#547—221no—
617#547—222no—
618#547—221no—
619#547C2×D1111yescharacteristic
620#546—112no—
621#546—222no—
622D42—221no—
623D42C2×D1111yescharacteristic, complemented
624#532—111no—
625#532—221no—
626C2×C4⋊Q8—111no—
627#525—112no—
628#525—222no—
629C2×#123—222no—
630C2×C22⋊Q8—221no—
631C2×#121—112no—
632C4×#41—111no—
633C2×C4×D4—111no—
634C2×C4×D4—111no—
635C2×C4×D4—221no—
636C22×C4⋊C4—112no—
637#489—112no—
638#489—112no—
639#487—111no—
640#487—111no—
641#486—111no—
642#486C2×D1111yescharacteristic, complemented
643#484—112no—
644#484—112no—
645#483—112no—
646#483—112no—
647#481—112no—
648#481—112no—
649#480—112no—
650#480C2×D1112yescomplemented
651#477—112no—
652#476—112no—
653#475—111no—
654#475—111no—
655#474—111no—
656#474C2×D1111yescharacteristic, complemented
657#469—112no—
658#469—112no—
659#468—112no—
660#468—112no—
661#466—112no—
662#466C2×D1112yescomplemented
663#465—112no—
664#465—112no—
665#463—112no—
666#463—112no—
667#461—111no—
668#461—111no—
669#459—111no—
670#459C2×D1111yescharacteristic, complemented
671#449—112no—
672#449—112no—
673#449—112no—
674#449—112no—
675#448—112no—
676#448—112no—
677#447—112no—
678#447C2×D1112yescomplemented
679#442—111no—
680#442—111no—
681#440—111no—
682#440—111no—
683C4×SD16—111no—
684C4×SD16—111no—
685C4×D8—111no—
686C4×D8C2×D1111yescharacteristic, complemented
687#436—111no—
688#436—111no—
689#435—112no—
690#435—112no—
691C8×D4—111no—
692C8×D4C2×D1111yescharacteristic, complemented
693#428—112no—
694#428—111no—
695#423—111no—
696#418—111no—
697#417—112no—
698#417—112no—
699#417—112no—
700#417—112no—
701#417—112no—
702#417—112no—
703#417—112no—
704#417—112no—
705#417—111no—
706C2×#103—112no—
707C2×#103—112no—
708C2×#102—112no—
709C2×#102C2×D1112yescomplemented
710#407—112no—
711C4×M16—111no—
712C22×C11—22no—
713C22×C11—22no—
714C22×C11—22no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11—42no—
718C22×C11—41no—
719C22×C11—42no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11—42no—
723C22×C11—88no—
724C22×C11C2×AGL(1,ℤ/8)14yes—
725C22×C11C23×D411yescharacteristic
726C2×D11—21no—
727C2×D11—21no—
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—48no—
732C2×D11—41no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—84no—
736C2×D11#54612yes—
737C4×C11—21no—
738C4×C11—22no—
739C4×C11—41no—
740C4×C11—41no—
741C4×C11—42no—
742C4×C11C2×AGL(1,ℤ/8)12yes—
743C4×C11C22×#4111yescharacteristic
744C4×C11C2×H(5,𝔽2)11yescharacteristic
745Dic11—21no—
746Dic11—22no—
747Dic11—22no—
748Dic11—21no—
749Dic11—41no—
750Dic11—42no—
751Dic11—42no—
752Dic11—41no—
753Dic11#54612yes—
754C2×#41—21no—
755C2×#41—111no—
756C2×#41—112no—
757C2×#41—112no—
758C2×#41—112no—
759C2×#41—222no—
760C2×#41—221no—
761C2×#41—222no—
762C2×#41—222no—
763C2×#41—222no—
764C2×#41—221no—
765C2×#41—221no—
766C2×#41—228no—
767C2×#41—444no—
768C2×#41—448no—
769C22×Q8—112no—
770C22×Q8—221no—
771C22×D4—21no—
772C22×D4—111no—
773C22×D4—111no—
774C22×D4—222no—
775C22×D4—222no—
776C22×D4C22×D1112yes—
777C23×C4—112no—
778C23×C4—221no—
779C23×C4—222no—
780C23×C4—222no—
781AGL(1,ℤ/8)—224no—
782AGL(1,ℤ/8)—444no—
783C2×SD16—111no—
784C2×SD16—112no—
785C2×SD16—111no—
786C2×SD16—112no—
787C2×D8—111no—
788C2×D8—112no—
789C2×D8C22×D1111yescharacteristic
790C2×D8C22×D1112yes—
791C2×M16—111no—
792C2×M16—112no—
793C2×M16—111no—
794C2×M16—112no—
795C2×M16—112no—
796C2×M16—444no—
797C22×C8—112no—
798C22×C8C22×D1112yes—
799C4⋊Q8—112no—
800C4⋊Q8—111no—
801C4⋊Q8—111no—
802C4⋊Q8—221no—
803C4⋊Q8—221no—
804C4⋊Q8—221no—
805C4⋊Q8C22×D1111yescharacteristic
806#127—221no—
807#127C22×D1111yescharacteristic
808#124—112no—
809#124—222no—
810#123—22no—
811#123—222no—
812#123—222no—
813#123—222no—
814#123—222no—
815#123—222no—
816#123—222no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123—222no—
821C22⋊Q8—21no—
822C22⋊Q8—112no—
823C22⋊Q8—112no—
824C22⋊Q8—222no—
825C22⋊Q8—222no—
826C22⋊Q8—222no—
827C22⋊Q8—221no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8—222no—
831#121—21no—
832#121—112no—
833#121—112no—
834#121—112no—
835#121—112no—
836#121—222no—
837#121—222no—
838#121—222no—
839#121—221no—
840#121—222no—
841#121—221no—
842#121—221no—
843#121—222no—
844#121C22×D1112yes—
845#121C22×D1112yes—
846#120—22no—
847#120—222no—
848#120—222no—
849C4×Q8—111no—
850C4×Q8—111no—
851C4×D4—111no—
852C4×D4—112no—
853C4×D4—111no—
854C4×D4—112no—
855C4×D4—111no—
856C4×D4—111no—
857C4×D4—111no—
858C4×D4—111no—
859C4×D4—111no—
860C4×D4—221no—
861C4×D4—221no—
862C4×D4—221no—
863C4×D4—221no—
864C4×D4—221no—
865C4×D4—222no—
866C4×D4—222no—
867C4×D4—221no—
868C4×D4—221no—
869C4×D4—222no—
870C4×D4—221no—
871C4×D4C22×D1111yescharacteristic
872C4×D4C22×D1111yescharacteristic
873C4×D4C22×D1111yescharacteristic
874#117—111no—
875#117—221no—
876C2×C4⋊C4—111no—
877C2×C4⋊C4—112no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—112no—
880C2×C4⋊C4—112no—
881C2×C4⋊C4—112no—
882C2×C4⋊C4—222no—
883C2×C4⋊C4—222no—
884C2×C4⋊C4—221no—
885C2×C4⋊C4—221no—
886C2×C4⋊C4—222no—
887C2×C4⋊C4C22×D1112yes—
888C2×C22⋊C4—112no—
889C2×C22⋊C4—221no—
890C2×C22⋊C4—222no—
891C2×C22⋊C4—222no—
892C2×C42—111no—
893C2×C42—221no—
894#107—111no—
895#107—112no—
896#107C22×D1111yescharacteristic
897#107C22×D1112yes—
898#106—111no—
899#106—112no—
900#106—111no—
901#106—112no—
902C4⋊C8—112no—
903C4⋊C8—111no—
904C4⋊C8C22×D1111yescharacteristic
905#103—111no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—112no—
910#103—111no—
911#103—112no—
912#103—112no—
913#103—112no—
914#103—112no—
915#102—111no—
916#102—112no—
917#102—112no—
918#102—112no—
919#102—112no—
920#102—111no—
921#102—111no—
922#102—111no—
923#102C22×D1111yescharacteristic
924#102C22×D1112yes—
925#102C22×D1112yes—
926#102C22×D1112yes—
927#102C22×D1112yes—
928#102C22×D1111yescharacteristic
929C22⋊C8—112no—
930C22⋊C8—112no—
931C22⋊C8—112no—
932C22⋊C8C22×D1112yes—
933#97—111no—
934#97—111no—
935C4×C8—111no—
936C4×C8C22×D1111yescharacteristic
937C2×C11—24no—
938C2×C11—42no—
939C2×C11—81no—
940C2×C11—82no—
941C2×C11C2×#54611yescharacteristic
942C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
943C2×C11#358611yescharacteristic
944D11—22no—
945D11—42no—
946D11—81no—
947C24—22no—
948C24—112no—
949C24—221no—
950#41—44no—
951#41—114no—
952#41—222no—
953#41—224no—
954#41—224no—
955#41—224no—
956#41—224no—
957#41—448no—
958#41—444no—
959#41—448no—
960#41—442no—
961#41—442no—
962#41—448no—
963#41—448no—
964#41—444no—
965#41—444no—
966C2×Q8—21no—
967C2×Q8—111no—
968C2×Q8—112no—
969C2×Q8—222no—
970C2×Q8—224no—
971C2×Q8—222no—
972C2×Q8—221no—
973C2×Q8—442no—
974C2×Q8—444no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—21no—
979C2×D4—22no—
980C2×D4—21no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—112no—
984C2×D4—111no—
985C2×D4—111no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—221no—
990C2×D4—221no—
991C2×D4—224no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—222no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—448no—
999C2×D4—448no—
1000C2×D4D4×D1111yescharacteristic
1001C2×D4C23×D1112yes—
1002C2×D4C23×D1111yescharacteristic
1003C2×D4C23×D1111yescharacteristic
1004C22×C4—22no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—111no—
1008C22×C4—112no—
1009C22×C4—111no—
1010C22×C4—112no—
1011C22×C4—112no—
1012C22×C4—112no—
1013C22×C4—111no—
1014C22×C4—224no—
1015C22×C4—224no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—221no—
1022C22×C4—222no—
1023C22×C4—221no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—221no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—221no—
1030C22×C4—444no—
1031C22×C4—448no—
1032C22×C4—448no—
1033C22×C4C23×D1112yes—
1034SD16—222no—
1035SD16—222no—
1036SD16—442no—
1037SD16—442no—
1038D8—22no—
1039D8—42no—
1040D8—222no—
1041D8—442no—
1042M16—222no—
1043M16—224no—
1044M16—222no—
1045M16—442no—
1046M16—442no—
1047C2×C8—42no—
1048C2×C8—111no—
1049C2×C8—111no—
1050C2×C8—112no—
1051C2×C8—442no—
1052C2×C8C23×D1111yescharacteristic
1053C2×C8C23×D1111yescharacteristic
1054C2×C8C23×D1112yes—
1055C4⋊C4—22no—
1056C4⋊C4—21no—
1057C4⋊C4—111no—
1058C4⋊C4—112no—
1059C4⋊C4—111no—
1060C4⋊C4—112no—
1061C4⋊C4—111no—
1062C4⋊C4—221no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4—222no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—221no—
1069C4⋊C4—222no—
1070C4⋊C4—221no—
1071C4⋊C4—221no—
1072C4⋊C4—221no—
1073C4⋊C4—222no—
1074C4⋊C4—221no—
1075C4⋊C4D4×D1111yescharacteristic
1076C4⋊C4C23×D1111yescharacteristic
1077C4⋊C4C23×D1111yescharacteristic
1078C4⋊C4C23×D1112yes—
1079C22⋊C4—21no—
1080C22⋊C4—22no—
1081C22⋊C4—21no—
1082C22⋊C4—22no—
1083C22⋊C4—112no—
1084C22⋊C4—112no—
1085C22⋊C4—112no—
1086C22⋊C4—221no—
1087C22⋊C4—222no—
1088C22⋊C4—221no—
1089C22⋊C4—222no—
1090C22⋊C4—221no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—221no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—221no—
1098C22⋊C4—222no—
1099C22⋊C4D4×D1112yes—
1100C42—111no—
1101C42—111no—
1102C42—111no—
1103C42—221no—
1104C42—221no—
1105C42—221no—
1106C42C23×D1111yescharacteristic
1107C11#6116111yescharacteristic, complemented, Sylow
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—44no—
1112C23—44no—
1113C23—82no—
1114C23—111no—
1115C23—112no—
1116C23—224no—
1117C23—224no—
1118C23—221no—
1119C23—442no—
1120C23—442no—
1121C23—442no—
1122C23—442no—
1123C23C2×D4×D1112yes—
1124Q8—42no—
1125Q8—112no—
1126Q8—221no—
1127Q8—222no—
1128Q8—222no—
1129Q8—444no—
1130Q8—444no—
1131Q8—442no—
1132D4—21no—
1133D4—22no—
1134D4—21no—
1135D4—21no—
1136D4—22no—
1137D4—44no—
1138D4—44no—
1139D4—44no—
1140D4—42no—
1141D4—81no—
1142D4—224no—
1143D4—224no—
1144D4—222no—
1145D4—221no—
1146D4—221no—
1147D4—444no—
1148D4—442no—
1149D4—444no—
1150D4—444no—
1151D4—444no—
1152D4—444no—
1153D4—444no—
1154D4—882no—
1155D4#6696414yescomplemented
1156D4#41×D1112yescomplemented
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—44no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—111no—
1166C2×C4—112no—
1167C2×C4—112no—
1168C2×C4—111no—
1169C2×C4—111no—
1170C2×C4—112no—
1171C2×C4—224no—
1172C2×C4—224no—
1173C2×C4—224no—
1174C2×C4—224no—
1175C2×C4—221no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—221no—
1180C2×C4—222no—
1181C2×C4—221no—
1182C2×C4—222no—
1183C2×C4—441no—
1184C2×C4—442no—
1185C2×C4—442no—
1186C2×C4—444no—
1187C2×C4—444no—
1188C2×C4—444no—
1189C2×C4—444no—
1190C2×C4—444no—
1191C2×C4—444no—
1192C2×C4—444no—
1193C2×C4—442no—
1194C2×C4—444no—
1195C2×C4—442no—
1196C2×C4—881no—
1197C2×C4C2×D4×D1111yescharacteristic
1198C2×C4C2×D4×D1112yes—
1199C2×C4C2×D4×D1111yescharacteristic
1200C2×C4C24×D1111yescharacteristic
1201C8—21no—
1202C8—21no—
1203C8—22no—
1204C8—221no—
1205C8—221no—
1206C8—222no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—42no—
1213C22—41no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—88no—
1219C22—112no—
1220C22—221no—
1221C22—221no—
1222C22—222no—
1223C22—222no—
1224C22—222no—
1225C22—448no—
1226C22—441no—
1227C22—441no—
1228C22—441no—
1229C22—884no—
1230C22C2×#6696414yes—
1231C22C22×D4×D1111yescharacteristic
1232C4—21no—
1233C4—22no—
1234C4—41no—
1235C4—42no—
1236C4—41no—
1237C4—112no—
1238C4—221no—
1239C4—222no—
1240C4—222no—
1241C4—221no—
1242C4—441no—
1243C4—442no—
1244C4—441no—
1245C4—442no—
1246C4C2×#6696412yes—
1247C4C2×#41×D1111yescharacteristic
1248C4D11×H(5,𝔽2)11yescharacteristic
1249C2—24no—
1250C2—42no—
1251C2—82no—
1252C2—81no—
1253C2—222no—
1254C2—442no—
1255C2—881no—
1256C2D11×#54611yescharacteristic
1257C2C22×#6696411yescharacteristic
1258C2#1308339811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3294C2
socleC22×C11C23×D4
hypercenter#3294D11
hypocenterC11#61161
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. D4×#4341C2semidirect
2. D11×#547C2semidirect
3. #13080946C2semidirect
4. #13080942C2semidirect
5. #13080923C2semidirect
6. #13080918C2semidirect
7. #13080613C2semidirect
8. #13080605C2semidirect
9. #13080581C2semidirect
10. #13080573C2semidirect
11. #13080482C2semidirect
12. #13080475C2semidirect
13. #13080429C2semidirect
14. #13079006C2semidirect
15. #13078535C2semidirect
16. #13078424C2semidirect
17. #13078232C2semidirect
18. #13078075C2semidirect
19. #13077863C2semidirect
20. C4×#66964C2semidirect
21. D4×#4313C2semidirect
22. C2×#10622384C2semidirect
23. C11×#3294C2semidirect
27. D42×C11C22semidirect
29. #10623337C22semidirect
33. C2×#66964C22semidirect
34. C22×#4313C22semidirect
35. #10623257C22semidirect
36. D11×C4⋊Q8C22semidirect
37. #10623249C22semidirect
44. #10623142C22semidirect
46. D11×#121C22semidirect
47. #10623129C22semidirect
52. #10623086C22semidirect
53. #10623082C22semidirect
55. C4×D4×D11C22semidirect
56. D4×Dic22C22semidirect
58. #10623038C22semidirect
59. C2×C4⋊C4×D11C22semidirect
60. C11×#486C22semidirect
61. C11×#480C22semidirect
62. C11×#474C22semidirect
63. C11×#466C22semidirect
64. C11×#459C22semidirect
65. C11×#447C22semidirect
66. C4×C11×D8C22semidirect
67. C8×D4×C11C22semidirect
68. C2×C11×#102C22semidirect
69. #10622830C22semidirect
70. C2×#66896C22semidirect
71. #10622772C22semidirect
72. #10622771C22semidirect
73. #10622771C22semidirect
74. #10622766C22semidirect
75. #10622765C22semidirect
76. #10622727C22semidirect
77. #10622724C22semidirect
78. C2×#66880C22semidirect
79. #10622707C22semidirect
80. #10622706C22semidirect
81. #10622685C22semidirect
82. #10622683C22semidirect
83. #10622654C22semidirect
84. #10622653C22semidirect
85. #10622651C22semidirect
86. #10622646C22semidirect
87. #10622632C22semidirect
88. C4×#4324C22semidirect
89. C4×#4323C22semidirect
90. D4×C11⋊C8C22semidirect
91. #10622620C22semidirect
92. #10622584C22semidirect
93. C2×#66874C22semidirect
94. #10622502C22semidirect
95. #10622499C22semidirect
96. #10622497C22semidirect
97. #10622497C22semidirect
98. #10622494C22semidirect
99. #10622494C22semidirect
100. #10622488C22semidirect
101. #10622464C22semidirect
102. #10622454C22semidirect
103. #10622451C22semidirect
104. #10622450C22semidirect
105. #10622400C22semidirect
106. #10622398C22semidirect
107. #10622395C22semidirect
108. #10622394C22semidirect
109. #10622394C22semidirect
110. #10622393C22semidirect
111. #10622390C22semidirect
112. #10622390C22semidirect
115. #10622384C22semidirect
116. #10622384C22semidirect
117. #10622384C22semidirect
118. #10622384C22semidirect
119. #10622384C22semidirect
120. #10622384C22semidirect
121. #10622384C22semidirect
122. #10622383C22semidirect
123. #10622378C22semidirect
124. #10622378C22semidirect
125. #10622374C22semidirect
126. #10622370C22semidirect
127. #10622351C22semidirect
128. #10622343C22semidirect
129. #10622339C22semidirect
130. #10622334C22semidirect
131. C4×#4314C22semidirect
132. #10622301C22semidirect
133. C4×#4313C22semidirect
134. #10622294C22semidirect
373. #4341#41semidirect
492. #3294D11semidirect
529. D4×C11AGL(1,ℤ/8)semidirect
530. D4×C11C2×#41semidirect
594. Dic22C2×#41semidirect
623. D42C2×D11semidirect
642. #486C2×D11semidirect
650. #480C2×D11semidirect
656. #474C2×D11semidirect
662. #466C2×D11semidirect
670. #459C2×D11semidirect
678. #447C2×D11semidirect
686. C4×D8C2×D11semidirect
692. C8×D4C2×D11semidirect
709. C2×#102C2×D11semidirect
1107. C11#61161semidirect
1155. D4#66964semidirect
1156. D4#41×D11semidirect

Maximal subgroups

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

subgroupindex
D4×#43412
D11×#5472
#130809462
#130809422
#130809232
#130809182
#130806132
#130806052
#130805812
#130805732
#130804822
#130804752
#130804292
#130790062
#130785352
#130784242
#130782322
#130780752
#130778632
C4×#669642
D4×#43132
C2×#106223842
C11×#32942
#6116111