Finite Group Databasebeta

← #15631206

Subgroups — #15631206

Order 2816.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082258C211yesmaximal, characteristic, complemented
2#13080926C212yesmaximal, complemented
3#13080915C212yesmaximal, complemented
4#13080826C212yesmaximal, complemented
5#13080811C212yesmaximal, complemented
6#13080706C212yesmaximal, complemented
7#13080691C212yesmaximal, complemented
8#13080586C212yesmaximal, complemented
9#13080571C212yesmaximal, complemented
10#13078986C211yesmaximal, characteristic, complemented
11#13078585C211yesmaximal, characteristic, complemented
12#13078539C211yesmaximal, characteristic, complemented
13#13078441C211yesmaximal, characteristic, complemented
14#13078309C211yesmaximal, characteristic, complemented
15#13078222C211yesmaximal, characteristic, complemented
16#13078166C211yesmaximal, characteristic, complemented
17#13077917C211yesmaximal, characteristic, complemented
18#13077856C211yesmaximal, characteristic, complemented
19#13077444C211yesmaximal, characteristic, complemented
20#13077320C211yesmaximal, characteristic, complemented
21#13077139C211yesmaximal, characteristic, complemented
22C2×#10622579C211yesmaximal, characteristic, complemented
23C11×#3492C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C11×#554—21no—
27C11×#554C2212yescomplemented
28C11×#553—21no—
29C11×#553C2212yescomplemented
30C11×#552—21no—
31C11×#552C2212yescomplemented
32C11×#547—21no—
33C11×#547C2212yescomplemented
34C11×#544C2211yescharacteristic, complemented
35C11×#539—22no—
36C11×#537C2211yescharacteristic
37C11×#525—22no—
38C11×#525C2211yescharacteristic
39C11×#525C2211yescharacteristic, complemented
40C11×#520C2211yescharacteristic
41C11×#520C2211yescharacteristic, complemented
42C22×C11×C4⋊C4C2211yescharacteristic, complemented
43#10623356C2211yescharacteristic
44C2×#67004C2211yescharacteristic, complemented
45C2×#67003C2211yescharacteristic
46C2×#67002C2211yescharacteristic
47C2×#67001C2211yescharacteristic
48#10623322C2211yescharacteristic
49C22×#4318C2211yescharacteristic, complemented
50D11×#123—22no—
51#10623162—21no—
52#10623162—21no—
53#10623143—21no—
54#10623143—21no—
55#10623120—22no—
56#10623082C2212yes—
57#10623082C2212yes—
58#10623081C2212yes—
59#10623081C2212yes—
60#10623057C2211yescharacteristic
61#10623052C2211yescharacteristic
62#10622847C2211yescharacteristic
63#10622846C2211yescharacteristic, complemented
64#10622820C2211yescharacteristic, complemented
65#10622706C2212yescomplemented
66#10622702C2212yescomplemented
67#10622700C2212yescomplemented
68#10622697C2212yescomplemented
69#10622682C2212yescomplemented
70#10622681C2212yescomplemented
71#10622679C2212yescomplemented
72#10622679C2212yescomplemented
73#10622665C2212yescomplemented
74#10622665C2211yescharacteristic, complemented
75#10622665C2211yescharacteristic, complemented
76#10622664C2212yescomplemented
77#10622662C2211yescharacteristic, complemented
78#10622662C2211yescharacteristic, complemented
79#10622660C2212yescomplemented
80#10622660C2212yescomplemented
81#10622660C2212yescomplemented
82#10622659C2212yescomplemented
83#10622655C2211yescharacteristic, complemented
84#10622655C2212yescomplemented
85#10622655C2211yescharacteristic, complemented
86#10622654C2212yescomplemented
87#10622652C2211yescharacteristic, complemented
88#10622652C2211yescharacteristic, complemented
89#10622650C2212yescomplemented
90#10622650C2212yescomplemented
91#10622650C2212yescomplemented
92#10622649C2212yescomplemented
93#10622644C2212yescomplemented
94#10622641C2212yescomplemented
95#10622639C2212yescomplemented
96C4×#4325C2212yescomplemented
97#10622632C2212yescomplemented
98#10622629C2212yescomplemented
99#10622627C2212yescomplemented
100C4×#4323C2212yescomplemented
101#10622625C2212yescomplemented
102#10622625C2212yescomplemented
103#10622624C2212yescomplemented
104#10622624C2212yescomplemented
105#10622617C2211yescharacteristic, complemented
106#10622615C2211yescharacteristic
107#10622615C2212yescomplemented
108#10622614C2211yescharacteristic
109#10622614C2212yescomplemented
110#10622612C2211yescharacteristic, complemented
111#10622611C2211yescharacteristic, complemented
112#10622610C2211yescharacteristic, complemented
113#10622609C2212yescomplemented
114#10622609C2212yescomplemented
115#10622584C2212yescomplemented
116#10622584C2212yescomplemented
117#10622583C2212yescomplemented
118#10622583C2212yescomplemented
119C2×#66874C2211yescharacteristic, complemented
120C2×#66874C2211yescharacteristic, complemented
121#10622581C2212yescomplemented
122#10622580C2212yescomplemented
123#10622579C2211yescharacteristic
124#10622579C2211yescharacteristic
125#10622579C2212yescomplemented
126#10622579C2212yescomplemented
127#10622579C2212yescomplemented
128#10622579C2212yescomplemented
129#10622579C2212yescomplemented
130C2×#66873C2211yescharacteristic
131C2×#66873C2211yescharacteristic
132C2×#66873C2212yescomplemented
133#10622577C2211yescharacteristic, complemented
134#10622577C2211yescharacteristic, complemented
135C2×C11×#41—22no—
136C2×C11×#41C2311yescharacteristic
137C2×C11×#41C2311yescharacteristic
138C23×C4×C11—21no—
139C23×C4×C11C2311yescharacteristic
140C22×C22⋊D11—21no—
141#67042—24no—
142#67042—42no—
143C2×#4343—21no—
144C2×D4×D11—22no—
145C2×D4×D11—21no—
146C2×#4339—21no—
147C2×#4339—21no—
148C2×#4339—24no—
149C2×#4339—42no—
150C2×#4339C2311yescharacteristic
151C2×#4339C2312yes—
152C2×#4339C2312yes—
153C2×#4339C2312yes—
154C22×D44C2312yes—
155C22×D44C2311yescharacteristic
156C22×C4×D11—21no—
157C22×Dic22C2311yescharacteristic
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8C2312yes—
160C11×#126—22no—
161C11×#126—22no—
162C11×#125—22no—
163C11×#125—22no—
164C11×#125—21no—
165C11×#125C2312yes—
166C11×#123—22no—
167C11×#123—21no—
168C11×#123—22no—
169C11×#123—22no—
170C11×#123—22no—
171C11×#123D412yes—
172C11×C22⋊Q8—21no—
173C11×C22⋊Q8—22no—
174C11×C22⋊Q8—22no—
175C11×C22⋊Q8—22no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8D411yescharacteristic
178C11×C22⋊Q8D411yescharacteristic
179C11×C22⋊Q8C2311yescharacteristic
180C11×C22⋊Q8C2311yescharacteristic
181C11×C22⋊Q8C2312yes—
182C11×#121—22no—
183C11×#121—22no—
184C11×#121—21no—
185C11×#121D411yescharacteristic
186C11×#121D411yescharacteristic
187C11×#121C2311yescharacteristic
188C11×#121C2311yescharacteristic
189C11×#121C2312yes—
190C11×#120—21no—
191C11×#120D412yes—
192C4×Q8×C11—21no—
193C4×Q8×C11C2312yes—
194C4×D4×C11—22no—
195C4×D4×C11—21no—
196C4×D4×C11—22no—
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11—22no—
201C4×D4×C11C2312yes—
202C4×D4×C11C2312yes—
203C4×D4×C11C2312yes—
204C11×#117—21no—
205C11×#117—22no—
206C11×#117C2312yes—
207C11×#117C2311yescharacteristic
208C11×#117C2311yescharacteristic
209C2×C11×C4⋊C4—21no—
210C2×C11×C4⋊C4—21no—
211C2×C11×C4⋊C4—21no—
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C11×C4⋊C4C2311yescharacteristic
215C2×C11×C4⋊C4C2312yes—
216C2×C11×C4⋊C4C2312yes—
217C2×C11×C4⋊C4C2312yes—
218#67006—21no—
219#67004—42no—
220#67003—42no—
221#67002—24no—
222#67001—42no—
223#66997—21no—
224C2×#4326C2311yescharacteristic
225C2×#4326C2312yes—
226C2×#4325C2312yes—
227C2×#4325C2311yescharacteristic
228#66991—22no—
229#66991—22no—
230#66990—22no—
231#66990—22no—
232#66989—21no—
233#66988—22no—
234C2×#4324C2311yescharacteristic
235C2×#4324C2312yes—
236C2×#4323C2312yes—
237C2×#4323C2311yescharacteristic
238#66983C2311yescharacteristic
239#66983C2311yescharacteristic
240#66982—21no—
241C4×C22⋊D11—21no—
242C4×C22⋊D11—21no—
243#66979C2311yescharacteristic
244#66977C2311yescharacteristic
245#66977C2311yescharacteristic
246#66977C2312yes—
247#66977C2312yes—
248C2×#4318—42no—
249C2×#4318C2311yescharacteristic
250C2×#4318C2311yescharacteristic
251C2×#4318C2311yescharacteristic
252C2×#4318C2311yescharacteristic
253C2×#4318C2311yescharacteristic
254C2×#4318C2311yescharacteristic
255C2×#4318C2312yes—
256C22×C11⋊C8C2311yescharacteristic
257C22×C11⋊C8C2311yescharacteristic
258C22×C11⋊C8C2312yes—
259#66950—21no—
260#66950—21no—
261#66947—22no—
262#66947—22no—
263#66946—21no—
264#66946—21no—
265C4⋊C4×D11—22no—
266C4⋊C4×D11—22no—
267#66939—22no—
268#66937—22no—
269#66937—22no—
270#66936—22no—
271#66936—22no—
272#66936—22no—
273#66936—22no—
274C22⋊C4×D11—22no—
275C22⋊C4×D11—22no—
276C22⋊C4×D11—22no—
277#66928C2312yes—
278C4×D44C2312yes—
279C4×D44C2312yes—
280#66922C2312yes—
281#66899C2311yescharacteristic
282#66899C2311yescharacteristic
283#66896C2311yescharacteristic
284#66896C2311yescharacteristic
285C22⋊(C11⋊C8)C2312yes—
286C22⋊(C11⋊C8)C2312yes—
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289#66874C2312yes—
290#66874C2312yes—
291#66874C2312yes—
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66874C2311yescharacteristic
296#66874C2312yes—
297#66874C2312yes—
298#66874C2311yescharacteristic
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66873C2312yes—
303#66873C2311yescharacteristic
304#66873C2312yes—
305#66873C2312yes—
306#66873C2312yes—
307#66873C2312yes—
308#66873C2311yescharacteristic
309#66872C2312yes—
310#66872C2312yes—
311#66872C2311yescharacteristic
312#66872C2311yescharacteristic
313#66871C2312yes—
314#66871C2312yes—
315#66871C2311yescharacteristic
316#66871C2311yescharacteristic
317C4⋊(C11⋊C8)C2312yes—
318C4⋊(C11⋊C8)C2312yes—
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321#61177—111nomaximal, Sylow
322C24×C11C2×D411yescharacteristic
323C23×D11—21no—
324C23×D11—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—84no—
330C2×Q8×C11—22no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2411yescharacteristic
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11C2×D412yes—
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2×D412yes—
341C2×D4×C11C2411yescharacteristic
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—21no—
348C22×C4×C11—22no—
349C22×C4×C11—21no—
350C22×C4×C11—22no—
351C22×C4×C11—82no—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D411yescharacteristic
354C22×C4×C11C2×D411yescharacteristic
355C22×C4×C11C2412yes—
356C22×C4×C11C2411yescharacteristic
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—21no—
363C2×C22⋊D11—21no—
364C2×C22⋊D11—21no—
365C2×C22⋊D11—44no—
366C22×Dic11—21no—
367#4343—44no—
368D4×D11—48no—
369D4×D11—44no—
370#4339—24no—
371#4339—24no—
372#4339—24no—
373#4339—22no—
374#4339—22no—
375#4339—42no—
376#4339—42no—
377#4339—42no—
378#4339—44no—
379#4339—44no—
380C2×D44—24no—
381C2×D44—21no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—42no—
385C2×D44#4114yescomplemented
386C2×D44C2411yescharacteristic
387C2×D44C2412yes—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×C4×D11—21no—
392C2×C4×D11—22no—
393C2×C4×D11—22no—
394C2×C4×D11—44no—
395C2×Dic22—21no—
396C2×Dic22—22no—
397C2×Dic22—22no—
398C2×Dic22C2411yescharacteristic
399C2×Dic22C2412yes—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—21no—
412C11×C4⋊C4C2×D412yes—
413C11×C4⋊C4C2×D412yes—
414C11×C4⋊C4C2×D411yescharacteristic
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2412yes—
418C11×C4⋊C4C2411yescharacteristic
419C11×C4⋊C4C2411yescharacteristic
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—22no—
435C42×C11—22no—
436C42×C11—21no—
437C42×C11C2412yes—
438C22⋊Dic11—21no—
439C22⋊Dic11—22no—
440C22⋊Dic11—22no—
441C22⋊Dic11—21no—
442C22⋊Dic11—21no—
443#4326—41no—
444#4326—42no—
445#4325—24no—
446#4325—41no—
447#4324—41no—
448#4324—42no—
449#4323—24no—
450#4323—41no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—21no—
457C4⋊Dic11—22no—
458C4⋊Dic11—22no—
459C4⋊Dic11C2411yescharacteristic
460C4⋊Dic11C2411yescharacteristic
461Dic11⋊C4—21no—
462Dic11⋊C4—21no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465C4×Dic11—21no—
466#4318—22no—
467#4318—22no—
468#4318—41no—
469#4318—41no—
470#4318—41no—
471#4318—41no—
472#4318—42no—
473C2×C11⋊C8—22no—
474C2×C11⋊C8—22no—
475C2×C11⋊C8—42no—
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2412yes—
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2411yescharacteristic
480C2×C11⋊C8C2412yes—
481C2×C11⋊C8C2411yescharacteristic
482#3492D1111yescharacteristic, complemented
483#3485—111no—
484#3331—112no—
485#3330—112no—
486#3323—112no—
487#3322—112no—
488#3315—112no—
489#3314—112no—
490#3307—112no—
491#3306—112no—
492#3137—111no—
493#3097—111no—
494#3092—111no—
495#3081—111no—
496#3063—111no—
497#3054—111no—
498#3046—111no—
499#3012—111no—
500#3005—111no—
501#2946—111no—
502#2930—111no—
503#2897—111no—
504C2×#417—111no—
505C23×C11—22no—
506C23×C11—21no—
507C23×C11—41no—
508C23×C11—41no—
509C23×C11C22×D412yes—
510C23×C11C22×D411yescharacteristic
511C23×C11C22×D411yescharacteristic
512C23×C11C22×D411yescharacteristic
513C22×D11—22no—
514C22×D11—24no—
515C22×D11—21no—
516C22×D11—44no—
517C22×D11—81no—
518C22×D11—81no—
519C22×D11—82no—
520C22×D11—82no—
521Q8×C11—22no—
522Q8×C11—21no—
523Q8×C11—21no—
524Q8×C11—82no—
525D4×C11—24no—
526D4×C11—22no—
527D4×C11—21no—
528D4×C11—21no—
529D4×C11—42no—
530D4×C11—42no—
531D4×C11—42no—
532D4×C11—42no—
533D4×C11—42no—
534D4×C11—82no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—22no—
547C2×C4×C11—21no—
548C2×C4×C11—22no—
549C2×C4×C11—44no—
550C2×C4×C11—42no—
551C2×C4×C11—82no—
552C2×C4×C11—81no—
553C2×C4×C11—82no—
554C2×C4×C11—81no—
555C2×C4×C11—82no—
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D412yes—
560C2×C4×C11C22×D412yes—
561C2×C4×C11C22×D411yescharacteristic
562C2×C4×C11C2×#4112yes—
563C2×C4×C11H(5,𝔽2)12yes—
564C2×C4×C11C2511yescharacteristic
565C22⋊D11—44no—
566C22⋊D11—44no—
567C22⋊D11—44no—
568C22⋊D11—42no—
569C22⋊D11—81no—
570C22⋊D11—81no—
571C2×Dic11—21no—
572C2×Dic11—21no—
573C2×Dic11—21no—
574C2×Dic11—22no—
575C2×Dic11—42no—
576D44—24no—
577D44—21no—
578D44—22no—
579D44—21no—
580D44—44no—
581D44C2×#4114yes—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—44no—
585C4×D11—42no—
586C4×D11—82no—
587C4×D11—82no—
588Dic22—22no—
589Dic22—21no—
590Dic22—22no—
591Dic22—21no—
592Dic22—42no—
593C11⋊C8—22no—
594C11⋊C8—21no—
595C11⋊C8—21no—
596C11⋊C8—21no—
597C11⋊C8—21no—
598C11⋊C8—22no—
599C2×H(5,𝔽2)—111no—
600C22×#41—111no—
601C2×#137—111no—
602C2×AGL(1,ℤ/8)—111no—
603C2×#135—111no—
604C2×#131—111no—
605C22×M16—111no—
606#554—21no—
607#554C2×D1112yescomplemented
608#553—21no—
609#553C2×D1112yescomplemented
610#552—21no—
611#552C2×D1112yescomplemented
612#547—21no—
613#547—112no—
614#547—112no—
615#547—221no—
616#547—221no—
617#547C2×D1112yescomplemented
618#546—112no—
619#546—112no—
620#546—221no—
621#546—221no—
622#544C2×D1111yescharacteristic, complemented
623#539—22no—
624#537C2×D1111yescharacteristic
625#536—111no—
626#536—111no—
627#534—222no—
628#525—22no—
629#525—111no—
630#525C2×D1111yescharacteristic
631#525C2×D1111yescharacteristic, complemented
632C2×#123—222no—
633#520C2×D1111yescharacteristic
634#520C2×D1111yescharacteristic, complemented
635#518—111no—
636C22×C4⋊C4C2×D1111yescharacteristic, complemented
637#491—112no—
638#489—112no—
639#488—112no—
640#487—112no—
641#485—112no—
642#485—112no—
643#484—112no—
644#484—112no—
645#483—112no—
646#483—112no—
647#481—112no—
648#480—112no—
649#478—112no—
650#478—112no—
651#476—112no—
652#474—112no—
653#470—111no—
654#470—112no—
655#470—111no—
656#469—111no—
657#469—111no—
658#468—111no—
659#468—111no—
660#468—111no—
661#468—112no—
662#468—111no—
663#467—112no—
664#465—112no—
665#464—112no—
666#463—112no—
667#462—112no—
668#461—112no—
669#452—112no—
670#452—112no—
671#452—112no—
672#450—112no—
673#449—112no—
674#449—112no—
675#449—112no—
676#447—112no—
677#442—112no—
678#440—112no—
679C4×SD16—112no—
680C4×D8—112no—
681#436—112no—
682#436—112no—
683#435—112no—
684#435—112no—
685#428—111no—
686#428—111no—
687#427—111no—
688#424—111no—
689#419—111no—
690#418—111no—
691#418—112no—
692#417—112no—
693#417—112no—
694#417—112no—
695#417—111no—
696#417—111no—
697#417—112no—
698#417—112no—
699#416—111no—
700#416—111no—
701#416—112no—
702C2×#103—111no—
703C2×#103—111no—
704C2×#102—111no—
705C2×#102—111no—
706C2×#102—112no—
707#408—111no—
708#407—111no—
709#405—111no—
710C22×C11—21no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—21no—
714C22×C11—22no—
715C22×C11—21no—
716C22×C11—22no—
717C22×C11—21no—
718C22×C11—21no—
719C22×C11—21no—
720C22×C11—22no—
721C22×C11—44no—
722C22×C11—41no—
723C22×C11—41no—
724C22×C11—41no—
725C22×C11#54612yes—
726C22×C11C23×D411yescharacteristic
727C2×D11—24no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—84no—
734C2×D11—164no—
735C4×C11—22no—
736C4×C11—22no—
737C4×C11—21no—
738C4×C11—21no—
739C4×C11—22no—
740C4×C11—42no—
741C4×C11—42no—
742C4×C11—41no—
743C4×C11—41no—
744C4×C11—41no—
745C4×C11#54612yes—
746C4×C11C22×#4111yescharacteristic
747C4×C11C2×H(5,𝔽2)11yescharacteristic
748Dic11—41no—
749Dic11—41no—
750Dic11—42no—
751Dic11—41no—
752H(5,𝔽2)—224no—
753H(5,𝔽2)—442no—
754C2×#41—22no—
755C2×#41—111no—
756C2×#41—112no—
757C2×#41—112no—
758C2×#41—112no—
759C2×#41—224no—
760C2×#41—221no—
761C2×#41—221no—
762C2×#41—221no—
763C2×#41—442no—
764C2×#41C22×D1111yescharacteristic
765C2×#41C22×D1111yescharacteristic
766C22×Q8—111no—
767C22×D4—111no—
768C22×D4—112no—
769C22×D4—221no—
770C22×D4—222no—
771C22×D4—221no—
772C23×C4—21no—
773C23×C4—221no—
774C23×C4C22×D1111yescharacteristic
775#137—442no—
776AGL(1,ℤ/8)—224no—
777#135—442no—
778C2×Q16—111no—
779C2×Q16—112no—
780C2×SD16—112no—
781C2×SD16—111no—
782C2×SD16—111no—
783C2×SD16—112no—
784C2×D8—112no—
785C2×D8—111no—
786#131—442no—
787C2×M16—111no—
788C2×M16—111no—
789C2×M16—111no—
790C2×M16—111no—
791C2×M16—111no—
792C2×M16—111no—
793C2×M16—112no—
794C2×M16—442no—
795C22×C8—111no—
796C22×C8—111no—
797C22×C8—112no—
798C4⋊Q8—21no—
799C4⋊Q8—112no—
800C4⋊Q8—221no—
801C4⋊Q8C22×D1112yes—
802#126—22no—
803#126—22no—
804#125—22no—
805#125—22no—
806#125—21no—
807#125C22×D1112yes—
808#124—112no—
809#124—221no—
810#123—22no—
811#123—21no—
812#123—22no—
813#123—22no—
814#123—22no—
815#123—222no—
816#123—221no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824#123C22⋊D1112yes—
825C22⋊Q8—21no—
826C22⋊Q8—22no—
827C22⋊Q8—22no—
828C22⋊Q8—22no—
829C22⋊Q8—22no—
830C22⋊Q8—111no—
831C22⋊Q8—111no—
832C22⋊Q8—112no—
833C22⋊Q8—112no—
834C22⋊Q8—221no—
835C22⋊Q8—221no—
836C22⋊Q8C22⋊D1111yescharacteristic
837C22⋊Q8C22⋊D1111yescharacteristic
838C22⋊Q8C22×D1111yescharacteristic
839C22⋊Q8C22×D1111yescharacteristic
840C22⋊Q8C22×D1112yes—
841#121—22no—
842#121—22no—
843#121—21no—
844#121—111no—
845#121—111no—
846#121—222no—
847#121—222no—
848#121—222no—
849#121—222no—
850#121C22⋊D1111yescharacteristic
851#121C22⋊D1111yescharacteristic
852#121C22×D1111yescharacteristic
853#121C22×D1111yescharacteristic
854#121C22×D1112yes—
855#120—21no—
856#120—221no—
857#120—222no—
858#120—222no—
859#120C22⋊D1112yes—
860C4×Q8—21no—
861C4×Q8C22×D1112yes—
862C4×D4—22no—
863C4×D4—21no—
864C4×D4—22no—
865C4×D4—21no—
866C4×D4—21no—
867C4×D4—22no—
868C4×D4—22no—
869C4×D4—112no—
870C4×D4—112no—
871C4×D4—221no—
872C4×D4—221no—
873C4×D4—221no—
874C4×D4—221no—
875C4×D4C22×D1112yes—
876C4×D4C22×D1112yes—
877C4×D4C22×D1112yes—
878#117—21no—
879#117—22no—
880#117—111no—
881#117C22×D1111yescharacteristic
882#117C22×D1112yes—
883#117C22×D1111yescharacteristic
884C2×C4⋊C4—21no—
885C2×C4⋊C4—21no—
886C2×C4⋊C4—21no—
887C2×C4⋊C4—21no—
888C2×C4⋊C4—222no—
889C2×C4⋊C4—222no—
890C2×C4⋊C4C22×D1111yescharacteristic
891C2×C4⋊C4C22×D1111yescharacteristic
892C2×C4⋊C4C22×D1112yes—
893C2×C4⋊C4C22×D1112yes—
894C2×C4⋊C4C22×D1112yes—
895C2×C22⋊C4—222no—
896C2×C22⋊C4—222no—
897C2×C22⋊C4—222no—
898#107—111no—
899#107—111no—
900#107—112no—
901#107—112no—
902#106—111no—
903#106—111no—
904#106—112no—
905#106—112no—
906C4⋊C8—112no—
907C4⋊C8—112no—
908#103—111no—
909#103—111no—
910#103—112no—
911#103—112no—
912#103—112no—
913#103—112no—
914#103—111no—
915#103—112no—
916#103—111no—
917#103—112no—
918#103—112no—
919#103—112no—
920#102—111no—
921#102—111no—
922#102—112no—
923#102—111no—
924#102—112no—
925#102—112no—
926#102—112no—
927#102—112no—
928#102—112no—
929#102—112no—
930#102—111no—
931#102—112no—
932C22⋊C8—112no—
933C22⋊C8—112no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936#97—112no—
937C4×C8—112no—
938C2×C11—22no—
939C2×C11—42no—
940C2×C11—41no—
941C2×C11—41no—
942C2×C11—81no—
943C2×C11C2×#54611yescharacteristic
944C2×C11#358511yescharacteristic
945C2×C11#358611yescharacteristic
946D11—44no—
947D11—81no—
948C24—221no—
949C24—222no—
950C24C2×C22⋊D1111yescharacteristic
951#41—22no—
952#41—22no—
953#41—22no—
954#41—22no—
955#41—84no—
956#41—224no—
957#41—224no—
958#41—224no—
959#41—222no—
960#41—222no—
961#41—442no—
962#41—442no—
963#41—442no—
964#41—444no—
965#41—444no—
966#41—444no—
967C2×Q8—22no—
968C2×Q8—112no—
969C2×Q8—111no—
970C2×Q8—221no—
971C2×Q8—222no—
972C2×Q8—222no—
973C2×Q8C2×C22⋊D1111yescharacteristic
974C2×Q8C23×D1111yescharacteristic
975C2×D4—21no—
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—22no—
979C2×D4—114no—
980C2×D4—112no—
981C2×D4—111no—
982C2×D4—224no—
983C2×D4—222no—
984C2×D4—222no—
985C2×D4—221no—
986C2×D4—222no—
987C2×D4—221no—
988C2×D4—221no—
989C2×D4—222no—
990C2×D4—221no—
991C2×D4—222no—
992C2×D4—442no—
993C2×D4—444no—
994C2×D4—448no—
995C2×D4—444no—
996C2×D4C2×C22⋊D1112yes—
997C2×D4C2×C22⋊D1111yescharacteristic
998C2×D4C2×C22⋊D1112yes—
999C2×D4C2×C22⋊D1112yes—
1000C2×D4C23×D1111yescharacteristic
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—21no—
1005C22×C4—22no—
1006C22×C4—21no—
1007C22×C4—22no—
1008C22×C4—21no—
1009C22×C4—22no—
1010C22×C4—82no—
1011C22×C4—221no—
1012C22×C4—222no—
1013C22×C4—222no—
1014C22×C4—222no—
1015C22×C4—221no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—444no—
1019C22×C4C2×C22⋊D1111yescharacteristic
1020C22×C4C2×C22⋊D1111yescharacteristic
1021C22×C4C2×C22⋊D1111yescharacteristic
1022C22×C4C23×D1111yescharacteristic
1023C22×C4C23×D1111yescharacteristic
1024C22×C4C23×D1112yes—
1025C22×C4C23×D1111yescharacteristic
1026Q16—441no—
1027Q16—442no—
1028SD16—224no—
1029SD16—441no—
1030SD16—442no—
1031SD16—441no—
1032D8—224no—
1033D8—441no—
1034M16—222no—
1035M16—222no—
1036M16—441no—
1037M16—441no—
1038M16—441no—
1039M16—441no—
1040M16—442no—
1041C2×C8—111no—
1042C2×C8—112no—
1043C2×C8—111no—
1044C2×C8—112no—
1045C2×C8—111no—
1046C2×C8—111no—
1047C2×C8—222no—
1048C2×C8—222no—
1049C2×C8—442no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—21no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—21no—
1062C4⋊C4—111no—
1063C4⋊C4—111no—
1064C4⋊C4—221no—
1065C4⋊C4—221no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4C2×C22⋊D1111yescharacteristic
1071C4⋊C4C2×C22⋊D1112yes—
1072C4⋊C4C2×C22⋊D1112yes—
1073C4⋊C4C2×C22⋊D1111yescharacteristic
1074C4⋊C4C23×D1112yes—
1075C4⋊C4C23×D1112yes—
1076C4⋊C4C23×D1111yescharacteristic
1077C4⋊C4C23×D1111yescharacteristic
1078C22⋊C4—21no—
1079C22⋊C4—21no—
1080C22⋊C4—22no—
1081C22⋊C4—21no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—221no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4—221no—
1091C22⋊C4—221no—
1092C22⋊C4—221no—
1093C22⋊C4—221no—
1094C22⋊C4—222no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4C2×C22⋊D1112yes—
1099C22⋊C4C2×C22⋊D1112yes—
1100C22⋊C4C2×C22⋊D1112yes—
1101C22⋊C4C2×C22⋊D1112yes—
1102C22⋊C4C2×C22⋊D1112yes—
1103C42—22no—
1104C42—22no—
1105C42—21no—
1106C42—221no—
1107C42C23×D1112yes—
1108C11#6117711yescharacteristic, complemented, Sylow
1109C23—22no—
1110C23—21no—
1111C23—41no—
1112C23—41no—
1113C23—222no—
1114C23—224no—
1115C23—221no—
1116C23—444no—
1117C23—881no—
1118C23—881no—
1119C23—882no—
1120C23—882no—
1121C23C22×C22⋊D1112yes—
1122C23C22×C22⋊D1111yescharacteristic
1123C23C22×C22⋊D1111yescharacteristic
1124C23C22×C22⋊D1111yescharacteristic
1125Q8—22no—
1126Q8—21no—
1127Q8—21no—
1128Q8—82no—
1129Q8—222no—
1130Q8—221no—
1131Q8—222no—
1132Q8—221no—
1133Q8—442no—
1134D4—24no—
1135D4—22no—
1136D4—21no—
1137D4—21no—
1138D4—42no—
1139D4—42no—
1140D4—42no—
1141D4—42no—
1142D4—42no—
1143D4—82no—
1144D4—114no—
1145D4—224no—
1146D4—221no—
1147D4—222no—
1148D4—221no—
1149D4—444no—
1150D4—444no—
1151D4—444no—
1152D4—444no—
1153D4—442no—
1154D4—881no—
1155D4—881no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—44no—
1171C2×C4—42no—
1172C2×C4—82no—
1173C2×C4—81no—
1174C2×C4—82no—
1175C2×C4—81no—
1176C2×C4—82no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—222no—
1180C2×C4—221no—
1181C2×C4—444no—
1182C2×C4—444no—
1183C2×C4—444no—
1184C2×C4—442no—
1185C2×C4—442no—
1186C2×C4—882no—
1187C2×C4—882no—
1188C2×C4#41×D1112yes—
1189C2×C4#6704212yes—
1190C2×C4C22×C22⋊D1112yes—
1191C2×C4C22×C22⋊D1112yes—
1192C2×C4C22×C22⋊D1112yes—
1193C2×C4C22×C22⋊D1111yescharacteristic
1194C2×C4C22×C22⋊D1111yescharacteristic
1195C2×C4C22×C22⋊D1111yescharacteristic
1196C2×C4C24×D1111yescharacteristic
1197C8—222no—
1198C8—221no—
1199C8—221no—
1200C8—221no—
1201C8—221no—
1202C8—222no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—22no—
1208C22—21no—
1209C22—22no—
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—22no—
1214C22—44no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—224no—
1219C22—442no—
1220C22—442no—
1221C22—441no—
1222C22—441no—
1223C22—441no—
1224C22—884no—
1225C22—1764no—
1226C22#1062336012yes—
1227C22C23×C22⋊D1111yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—21no—
1231C4—21no—
1232C4—22no—
1233C4—42no—
1234C4—42no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—441no—
1239C4—441no—
1240C4—441no—
1241C4—442no—
1242C4#1062336012yes—
1243C4C2×#41×D1111yescharacteristic
1244C4C2×#6704211yescharacteristic
1245C2—22no—
1246C2—41no—
1247C2—41no—
1248C2—42no—
1249C2—81no—
1250C2—444no—
1251C2—881no—
1252C2C2×#1062336011yescharacteristic
1253C2#1308339611yescharacteristic
1254C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3492C2
socleC22×C11C23×D4
hypercenter#3492D11
hypocenterC11#61177
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #13082258C2semidirect
2. #13080926C2semidirect
3. #13080915C2semidirect
4. #13080826C2semidirect
5. #13080811C2semidirect
6. #13080706C2semidirect
7. #13080691C2semidirect
8. #13080586C2semidirect
9. #13080571C2semidirect
10. #13078986C2semidirect
11. #13078585C2semidirect
12. #13078539C2semidirect
13. #13078441C2semidirect
14. #13078309C2semidirect
15. #13078222C2semidirect
16. #13078166C2semidirect
17. #13077917C2semidirect
18. #13077856C2semidirect
19. #13077444C2semidirect
20. #13077320C2semidirect
21. #13077139C2semidirect
22. C2×#10622579C2semidirect
23. C11×#3492C2semidirect
27. C11×#554C22semidirect
29. C11×#553C22semidirect
31. C11×#552C22semidirect
33. C11×#547C22semidirect
34. C11×#544C22semidirect
39. C11×#525C22semidirect
41. C11×#520C22semidirect
42. C22×C11×C4⋊C4C22semidirect
44. C2×#67004C22semidirect
49. C22×#4318C22semidirect
63. #10622846C22semidirect
64. #10622820C22semidirect
65. #10622706C22semidirect
66. #10622702C22semidirect
67. #10622700C22semidirect
68. #10622697C22semidirect
69. #10622682C22semidirect
70. #10622681C22semidirect
71. #10622679C22semidirect
72. #10622679C22semidirect
73. #10622665C22semidirect
74. #10622665C22semidirect
75. #10622665C22semidirect
76. #10622664C22semidirect
77. #10622662C22semidirect
78. #10622662C22semidirect
79. #10622660C22semidirect
80. #10622660C22semidirect
81. #10622660C22semidirect
82. #10622659C22semidirect
83. #10622655C22semidirect
84. #10622655C22semidirect
85. #10622655C22semidirect
86. #10622654C22semidirect
87. #10622652C22semidirect
88. #10622652C22semidirect
89. #10622650C22semidirect
90. #10622650C22semidirect
91. #10622650C22semidirect
92. #10622649C22semidirect
93. #10622644C22semidirect
94. #10622641C22semidirect
95. #10622639C22semidirect
96. C4×#4325C22semidirect
97. #10622632C22semidirect
98. #10622629C22semidirect
99. #10622627C22semidirect
100. C4×#4323C22semidirect
101. #10622625C22semidirect
102. #10622625C22semidirect
103. #10622624C22semidirect
104. #10622624C22semidirect
105. #10622617C22semidirect
107. #10622615C22semidirect
109. #10622614C22semidirect
110. #10622612C22semidirect
111. #10622611C22semidirect
112. #10622610C22semidirect
113. #10622609C22semidirect
114. #10622609C22semidirect
115. #10622584C22semidirect
116. #10622584C22semidirect
117. #10622583C22semidirect
118. #10622583C22semidirect
119. C2×#66874C22semidirect
120. C2×#66874C22semidirect
121. #10622581C22semidirect
122. #10622580C22semidirect
125. #10622579C22semidirect
126. #10622579C22semidirect
127. #10622579C22semidirect
128. #10622579C22semidirect
129. #10622579C22semidirect
132. C2×#66873C22semidirect
133. #10622577C22semidirect
134. #10622577C22semidirect
385. C2×D44#41semidirect
482. #3492D11semidirect
607. #554C2×D11semidirect
609. #553C2×D11semidirect
611. #552C2×D11semidirect
617. #547C2×D11semidirect
622. #544C2×D11semidirect
631. #525C2×D11semidirect
634. #520C2×D11semidirect
636. C22×C4⋊C4C2×D11semidirect
1108. C11#61177semidirect

Maximal subgroups

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

subgroupindex
#130822582
#130809262
#130809152
#130808262
#130808112
#130807062
#130806912
#130805862
#130805712
#130789862
#130785852
#130785392
#130784412
#130783092
#130782222
#130781662
#130779172
#130778562
#130774442
#130773202
#130771392
C2×#106225792
C11×#34922
#6117711