Finite Group Databasebeta

← #15640414

Subgroups — #15640414

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082378C211yesmaximal, characteristic, complemented
2#13080915C211yesmaximal, characteristic, complemented
3#13080841C211yesmaximal, characteristic, complemented
4#13080811C212yesmaximal, complemented
5#13080527C211yesmaximal, characteristic, complemented
6#13080460C212yesmaximal, complemented
7#13080423C211yesmaximal, characteristic, complemented
8#13080346C211yesmaximal, characteristic, complemented
9#13080297C212yesmaximal, complemented
10D4×#4323C211yesmaximal, characteristic, complemented
11#13080236C211yesmaximal, characteristic, complemented
12#13080223C212yesmaximal, complemented
13#13080212C211yesmaximal, characteristic, complemented
14#13079588C211yesmaximal, characteristic, complemented
15#13079545C211yesmaximal, characteristic, complemented
16#13079513C212yesmaximal, complemented
17#13079468C212yesmaximal, complemented
18#13078659C211yesmaximal, characteristic, complemented
19#13078612C211yesmaximal, characteristic, complemented
20#13077917C212yesmaximal, complemented
21#13077882C212yesmaximal, complemented
22#13077683C211yesmaximal, characteristic, complemented
23C11×#3546C211yesmaximal, characteristic, complemented
24C2×#67042C2212yescomplemented
25C11×#560—22no—
26C11×#556C2211yescharacteristic, complemented
27C11×#553C2212yescomplemented
28C11×#550—21no—
29C11×#550C2211yescharacteristic, complemented
30C11×#547C2211yescharacteristic, complemented
31C11×#546—21no—
32C11×#546C2212yescomplemented
33D42×C11C2211yescharacteristic, complemented
34C11×#542—21no—
35C11×#538—22no—
36C11×#537C2212yescomplemented
37C11×#535—21no—
38C11×#535C2212yescomplemented
39C11×#532C2211yescharacteristic
40C11×#532C2211yescharacteristic, complemented
41C11×#529C2211yescharacteristic, complemented
42#10623364C2212yescomplemented
43C2×#67003C2212yescomplemented
44C2×#67002C2212yescomplemented
45C2×#66985C2212yescomplemented
46C22×#4323C2212yescomplemented
47#10623257—21no—
48#10623248—21no—
49#10623207—22no—
50#10623136—22no—
51D11×#121—21no—
52D11×#121—21no—
53#10623082C2211yescharacteristic
54#10623082C2211yescharacteristic, complemented
55#10623081C2212yescomplemented
56#10623081C2212yescomplemented
57D4×D44C2211yescharacteristic
58D4×D44C2211yescharacteristic, complemented
59#10623008C2211yescharacteristic, complemented
60C2×C4×D44C2211yescharacteristic, complemented
61#10622852C2212yescomplemented
62#10622851C2212yescomplemented
63#10622847C2212yescomplemented
64#10622847C2212yescomplemented
65#10622831C2212yescomplemented
66#10622830C2212yescomplemented
67#10622706C2211yescharacteristic, complemented
68#10622701C2211yescharacteristic, complemented
69#10622700C2211yescharacteristic, complemented
70#10622700C2211yescharacteristic, complemented
71#10622689C2211yescharacteristic, complemented
72#10622686C2211yescharacteristic, complemented
73#10622685C2211yescharacteristic, complemented
74#10622685C2211yescharacteristic, complemented
75#10622681C2212yescomplemented
76#10622679C2211yescharacteristic, complemented
77#10622679C2211yescharacteristic, complemented
78#10622672C2212yescomplemented
79#10622670C2211yescharacteristic, complemented
80#10622670C2211yescharacteristic, complemented
81#10622664C2212yescomplemented
82#10622662C2212yescomplemented
83#10622660C2212yescomplemented
84#10622660C2212yescomplemented
85#10622659C2212yescomplemented
86#10622659C2211yescharacteristic, complemented
87#10622657C2211yescharacteristic, complemented
88#10622655C2212yescomplemented
89#10622655C2212yescomplemented
90#10622654C2212yescomplemented
91#10622652C2212yescomplemented
92#10622651C2212yescomplemented
93#10622651C2212yescomplemented
94#10622650C2212yescomplemented
95#10622650C2212yescomplemented
96#10622650C2212yescomplemented
97#10622650C2212yescomplemented
98#10622650C2212yescomplemented
99#10622650C2212yescomplemented
100#10622649C2211yescharacteristic
101#10622649C2212yescomplemented
102#10622649C2212yescomplemented
103#10622649C2212yescomplemented
104#10622649C2212yescomplemented
105#10622647C2211yescharacteristic, complemented
106#10622646C2212yescomplemented
107#10622644C2211yescharacteristic, complemented
108#10622640C2211yescharacteristic, complemented
109C4×#4325C2211yescharacteristic, complemented
110C4×#4325C2211yescharacteristic, complemented
111#10622632C2211yescharacteristic, complemented
112#10622629C2212yescomplemented
113#10622629C2212yescomplemented
114#10622628C2211yescharacteristic, complemented
115C4×#4323C2211yescharacteristic, complemented
116C4×#4323C2212yescomplemented
117C4×#4323C2212yescomplemented
118C4×#4323C2211yescharacteristic, complemented
119#10622625C2211yescharacteristic, complemented
120#10622625C2211yescharacteristic, complemented
121#10622625C2212yescomplemented
122D4×C11⋊C8C2211yescharacteristic, complemented
123D4×C11⋊C8C2212yescomplemented
124D4×C11⋊C8C2211yescharacteristic, complemented
125#10622616C2212yescomplemented
126#10622615C2212yescomplemented
127#10622614C2212yescomplemented
128#10622609C2212yescomplemented
129#10622583C2212yescomplemented
130#10622580C2212yescomplemented
131#10622579C2212yescomplemented
132C2×#66873C2212yescomplemented
133#10622538C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41C2312yes—
138C2×C11×#41C2312yes—
139C22×D4×C11—21no—
140C22×D4×C11C2312yes—
141#67042—44no—
142#67042—44no—
143C2×#4343—22no—
144C2×D4×D11—22no—
145C2×D4×D11—22no—
146C2×D4×D11—22no—
147C2×D4×D11—21no—
148C2×D4×D11—21no—
149C2×#4339C2312yes—
150C2×#4339C2312yes—
151C2×#4339C2312yes—
152C22×D44C2311yescharacteristic
153C22×D44C2312yes—
154C22×D44C2312yes—
155C22×C4×D11—21no—
156C11×C4⋊Q8D411yescharacteristic
157C11×C4⋊Q8C2311yescharacteristic
158C11×#127—21no—
159C11×#127—22no—
160C11×#127D411yescharacteristic
161C11×#127C2311yescharacteristic
162C11×#126—22no—
163C11×#126—22no—
164C11×#126—21no—
165C11×#125C2311yescharacteristic
166C11×#124—22no—
167C11×#124—21no—
168C11×#124—21no—
169C11×#124D412yes—
170C11×#124C2311yescharacteristic
171C11×#123—21no—
172C11×#123—22no—
173C11×#123—22no—
174C11×#123—22no—
175C11×C22⋊Q8—22no—
176C11×C22⋊Q8—21no—
177C11×C22⋊Q8C2311yescharacteristic
178C11×C22⋊Q8C2312yes—
179C11×#121—22no—
180C11×#121—22no—
181C11×#121—22no—
182C11×#121—22no—
183C11×#121—21no—
184C11×#121—21no—
185C11×#121—22no—
186C11×#121—22no—
187C11×#121D411yescharacteristic
188C11×#121D411yescharacteristic
189C11×#121D412yes—
190C11×#121C2311yescharacteristic
191C11×#121C2312yes—
192C11×#121C2312yes—
193C11×#121C2312yes—
194C11×#121C2312yes—
195C11×#120—22no—
196C11×#120—22no—
197C11×#120—22no—
198C11×#120—22no—
199C4×Q8×C11—21no—
200C4×Q8×C11C2311yescharacteristic
201C4×D4×C11—21no—
202C4×D4×C11—21no—
203C4×D4×C11—22no—
204C4×D4×C11—21no—
205C4×D4×C11C2311yescharacteristic
206C4×D4×C11C2312yes—
207C4×D4×C11C2311yescharacteristic
208C4×D4×C11C2311yescharacteristic
209C4×D4×C11C2312yes—
210C11×#117—21no—
211C11×#117C2312yes—
212C2×C11×C4⋊C4C2312yes—
213C2×C11×C22⋊C4—22no—
214C2×C42×C11C2311yescharacteristic
215#67003—44no—
216#67002—44no—
217#66999—22no—
218C2×#4326C2312yes—
219C2×#4325C2311yescharacteristic
220C2×#4325C2311yescharacteristic
221C2×#4325C2312yes—
222#66992—22no—
223#66992—22no—
224#66991—21no—
225#66991—21no—
226#66991—22no—
227#66990—22no—
228#66990—22no—
229C2×#4324C2312yes—
230C2×#4324C2312yes—
231C2×#4324C2312yes—
232#66985—44no—
233C2×#4323—44no—
234C2×#4323C2311yescharacteristic
235C2×#4323C2312yes—
236C2×#4323C2311yescharacteristic
237C2×#4323C2312yes—
238C2×#4323C2312yes—
239C2×#4323C2312yes—
240C2×#4323C2312yes—
241#66983—21no—
242#66983—21no—
243#66983C2312yes—
244#66983C2312yes—
245C2×(C2×D11)⋊C4—21no—
246C2×C4⋊Dic11C2311yescharacteristic
247#66977C2312yes—
248#66977C2312yes—
249C2×#4318C2312yes—
250C2×#4318C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66948—21no—
254#66948—21no—
255#66947—22no—
256#66947—22no—
257C4⋊C4×D11—21no—
258C4⋊C4×D11—21no—
259#66937—22no—
260#66937—22no—
261#66936—22no—
262#66936—22no—
263#66935—22no—
264#66935—22no—
265C22⋊C4×D11—22no—
266C22⋊C4×D11—22no—
267#66928C2312yes—
268#66927C2311yescharacteristic
269C4×D44—21no—
270C4×D44—21no—
271C4×D44—21no—
272C4×D44—21no—
273C4×D44C2311yescharacteristic
274C4×D44C2311yescharacteristic
275C4×D44C2311yescharacteristic
276C4×D44C2311yescharacteristic
277#66922C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2311yescharacteristic
280#66896C2311yescharacteristic
281#66896C2312yes—
282#66896C2311yescharacteristic
283#66896C2312yes—
284C22⋊(C11⋊C8)C2312yes—
285C22⋊(C11⋊C8)C2311yescharacteristic
286C22⋊(C11⋊C8)C2311yescharacteristic
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291#66874C2312yes—
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66873C2311yescharacteristic
296#66873C2312yes—
297#66873C2312yes—
298#66873C2312yes—
299#66873C2311yescharacteristic
300#66873C2312yes—
301#66873C2312yes—
302#66873C2311yescharacteristic
303#66873C2312yes—
304#66873C2311yescharacteristic
305#66872C2311yescharacteristic
306#66872C2311yescharacteristic
307#66871C2311yescharacteristic
308#66871C2312yes—
309#66871C2311yescharacteristic
310#66871C2312yes—
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4×C11⋊C8C2312yes—
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61657—111nomaximal, Sylow
319C24×C11—22no—
320C23×D11—21no—
321C23×D11—22no—
322C23×D11—22no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—42no—
326C11×#41—42no—
327C11×#41—82no—
328C11×#41—82no—
329C2×Q8×C11—21no—
330C2×Q8×C11C2×D412yes—
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—21no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—22no—
338C2×D4×C11—21no—
339C2×D4×C11—21no—
340C2×D4×C11—22no—
341C2×D4×C11—42no—
342C2×D4×C11—42no—
343C2×D4×C11—82no—
344C2×D4×C11C2×D411yescharacteristic
345C2×D4×C11C2×D411yescharacteristic
346C2×D4×C11C2×D412yes—
347C2×D4×C11C2×D412yes—
348C2×D4×C11C2×D412yes—
349C2×D4×C11C2×D412yes—
350C2×D4×C11C2411yescharacteristic
351C2×D4×C11C2412yes—
352C22×C4×C11—22no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2412yes—
360C22×C4×C11C2412yes—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—22no—
363C2×C22⋊D11—22no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—22no—
366C22×Dic11—21no—
367#4343—48no—
368D4×D11—48no—
369D4×D11—48no—
370D4×D11—48no—
371D4×D11—82no—
372D4×D11—82no—
373#4339—24no—
374#4339—24no—
375#4339—42no—
376#4339—42no—
377#4339—42no—
378#4339—42no—
379C2×D44—22no—
380C2×D44—22no—
381C2×D44—24no—
382C2×D44—24no—
383C2×D44—21no—
384C2×D44—21no—
385C2×D44—22no—
386C2×D44—22no—
387C2×D44—21no—
388C2×D44—42no—
389C2×D44—42no—
390C2×D44C2412yes—
391C2×D44C2411yescharacteristic
392C2×D44C2411yescharacteristic
393C2×C4×D11—22no—
394C2×C4×D11—21no—
395C2×C4×D11—21no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×C4×D11—21no—
400C2×C4×D11—82no—
401C2×Dic22C2412yes—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2×D412yes—
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2412yes—
414C11×C4⋊C4C2411yescharacteristic
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4C2×D412yes—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C42×C11—21no—
432C42×C11—22no—
433C42×C11C2×D411yescharacteristic
434C42×C11C2×D411yescharacteristic
435C42×C11C2411yescharacteristic
436C42×C11C2411yescharacteristic
437C22⋊Dic11—22no—
438C22⋊Dic11—22no—
439#4326—42no—
440#4325—22no—
441#4325—22no—
442#4325—42no—
443#4324—42no—
444#4324—42no—
445#4324—42no—
446#4323—22no—
447#4323—24no—
448#4323—22no—
449#4323—24no—
450#4323—42no—
451#4323—42no—
452#4323—42no—
453(C2×D11)⋊C4—21no—
454(C2×D11)⋊C4—21no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—21no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—22no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461C4⋊Dic11—21no—
462C4⋊Dic11—21no—
463C4⋊Dic11—21no—
464C4⋊Dic11C2411yescharacteristic
465C4⋊Dic11C2411yescharacteristic
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468#4318—42no—
469#4318—42no—
470C2×C11⋊C8—42no—
471C2×C11⋊C8—42no—
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2412yes—
474C2×C11⋊C8C2412yes—
475C2×C11⋊C8C2411yescharacteristic
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2411yescharacteristic
478#3546D1111yescharacteristic, complemented
479#3496—111no—
480#3330—111no—
481#3324—111no—
482#3322—112no—
483#3302—111no—
484#3297—112no—
485#3294—111no—
486#3284—111no—
487#3280—112no—
488D4×D8—111no—
489#3274—111no—
490#3273—112no—
491#3272—111no—
492#3212—111no—
493#3207—111no—
494#3203—112no—
495#3198—112no—
496#3105—111no—
497#3100—111no—
498#3012—112no—
499#3008—112no—
500#2979—111no—
501C23×C11—21no—
502C23×C11—22no—
503C23×C11—82no—
504C23×C11—82no—
505C23×C11—82no—
506C23×C11C22×D412yes—
507C23×C11C22×D412yes—
508C23×C11C22×D411yescharacteristic
509C22×D11—21no—
510C22×D11—21no—
511C22×D11—24no—
512C22×D11—22no—
513C22×D11—44no—
514C22×D11—44no—
515C22×D11—81no—
516C22×D11—81no—
517C22×D11—82no—
518C22×D11—82no—
519C22×D11—82no—
520C22×D11—82no—
521Q8×C11—21no—
522Q8×C11—21no—
523Q8×C11—42no—
524Q8×C11—42no—
525D4×C11—22no—
526D4×C11—22no—
527D4×C11—21no—
528D4×C11—22no—
529D4×C11—22no—
530D4×C11—21no—
531D4×C11—42no—
532D4×C11—42no—
533D4×C11—42no—
534D4×C11—42no—
535D4×C11—42no—
536D4×C11—81no—
537D4×C11—82no—
538D4×C11—81no—
539D4×C11—82no—
540D4×C11—82no—
541D4×C11—82no—
542D4×C11—82no—
543D4×C11—82no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—22no—
548C2×C4×C11—22no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—22no—
554C2×C4×C11—21no—
555C2×C4×C11—41no—
556C2×C4×C11—42no—
557C2×C4×C11—82no—
558C2×C4×C11—82no—
559C2×C4×C11—82no—
560C2×C4×C11C22×D412yes—
561C2×C4×C11C22×D412yes—
562C2×C4×C11C22×D411yescharacteristic
563C2×C4×C11C22×D411yescharacteristic
564C2×C4×C11C22×D411yescharacteristic
565C2×C4×C11C22×D411yescharacteristic
566C2×C4×C11C22×D411yescharacteristic
567C2×C4×C11C2511yescharacteristic
568C22⋊D11—44no—
569C22⋊D11—44no—
570C22⋊D11—44no—
571C22⋊D11—82no—
572C22⋊D11—82no—
573C2×Dic11—22no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—81no—
577D44—24no—
578D44—21no—
579D44—21no—
580D44—22no—
581D44—22no—
582D44—44no—
583D44—44no—
584D44—42no—
585D44—81no—
586D44H(5,𝔽2)12yes—
587D44H(5,𝔽2)12yes—
588C4×D11—44no—
589C4×D11—44no—
590C4×D11—44no—
591C4×D11—42no—
592C4×D11—42no—
593C4×D11—81no—
594C4×D11—81no—
595Dic22—22no—
596Dic22—22no—
597C11⋊C8—21no—
598C11⋊C8—22no—
599C11⋊C8—21no—
600C11⋊C8—21no—
601C11⋊C8—22no—
602C11⋊C8—21no—
603C2×H(5,𝔽2)—112no—
604C2×AGL(1,ℤ/8)—112no—
605C2×AGL(1,ℤ/8)—112no—
606C2×#135—112no—
607C22×D8—112no—
608#560—22no—
609#556C2×D1111yescharacteristic, complemented
610#553C2×D1112yescomplemented
611#550—21no—
612#550C2×D1111yescharacteristic, complemented
613#547—111no—
614#547—111no—
615#547—221no—
616#547C2×D1111yescharacteristic, complemented
617#546—21no—
618#546—112no—
619#546—112no—
620#546—222no—
621#546C2×D1112yescomplemented
622D42—111no—
623D42—111no—
624D42—221no—
625D42C2×D1111yescharacteristic, complemented
626#542—21no—
627#538—22no—
628#537—112no—
629#537C2×D1112yescomplemented
630#535—21no—
631#535C2×D1112yescomplemented
632#534—222no—
633#532—111no—
634#532C2×D1111yescharacteristic
635#532C2×D1111yescharacteristic, complemented
636#529C2×D1111yescharacteristic, complemented
637C2×#121—221no—
638C2×#121—221no—
639C2×C4×D4—111no—
640#495—112no—
641#493—111no—
642#492—111no—
643#488—112no—
644#487—111no—
645#486—111no—
646#485—112no—
647#484—111no—
648#484—112no—
649#482—112no—
650#481—111no—
651#480—112no—
652#480—112no—
653#478—111no—
654#478—111no—
655#474—111no—
656#474—111no—
657#469—112no—
658#468—112no—
659#468—112no—
660#468—112no—
661#467—112no—
662#466—112no—
663#466—112no—
664#465—112no—
665#463—111no—
666#463—111no—
667#463—112no—
668#463—112no—
669#462—111no—
670#461—111no—
671#460—111no—
672#459—111no—
673#459—111no—
674#459—111no—
675#452—112no—
676#452—112no—
677#452—112no—
678#450—112no—
679#450—111no—
680#450—112no—
681#449—112no—
682#449—112no—
683#449—112no—
684#449—112no—
685#449—112no—
686#449—112no—
687#449—112no—
688#447—112no—
689#447—112no—
690#447—111no—
691#447—112no—
692#447—112no—
693#447—112no—
694C4×SD16—111no—
695C4×SD16—111no—
696C4×D8—111no—
697C4×D8—112no—
698C4×D8—112no—
699C4×D8—111no—
700#436—111no—
701#436—111no—
702#436—112no—
703C8×D4—111no—
704C8×D4—112no—
705C8×D4—111no—
706#431—111no—
707#431—111no—
708#418—112no—
709#417—112no—
710#416—112no—
711C2×#102—112no—
712#408—112no—
713#408—112no—
714C22×C11—21no—
715C22×C11—22no—
716C22×C11—22no—
717C22×C11—21no—
718C22×C11—22no—
719C22×C11—22no—
720C22×C11—21no—
721C22×C11—22no—
722C22×C11—22no—
723C22×C11—42no—
724C22×C11—41no—
725C22×C11—42no—
726C22×C11—41no—
727C22×C11—41no—
728C22×C11—42no—
729C22×C11—164no—
730C22×C11C23×D411yescharacteristic
731C2×D11—22no—
732C2×D11—22no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—41no—
736C2×D11—41no—
737C2×D11—42no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—84no—
741C2×D11—164no—
742C2×D11—164no—
743C4×C11—21no—
744C4×C11—21no—
745C4×C11—22no—
746C4×C11—21no—
747C4×C11—22no—
748C4×C11—21no—
749C4×C11—41no—
750C4×C11—41no—
751C4×C11—41no—
752C4×C11—42no—
753C4×C11#57612yes—
754C4×C11C2×H(5,𝔽2)11yescharacteristic
755C4×C11C2×H(5,𝔽2)11yescharacteristic
756Dic11—42no—
757Dic11—41no—
758Dic11—41no—
759H(5,𝔽2)—444no—
760H(5,𝔽2)—444no—
761C2×#41—21no—
762C2×#41—21no—
763C2×#41—112no—
764C2×#41—112no—
765C2×#41—112no—
766C2×#41—222no—
767C2×#41C22×D1112yes—
768C2×#41C22×D1112yes—
769C22×D4—21no—
770C22×D4—111no—
771C22×D4—112no—
772C22×D4—112no—
773C22×D4—222no—
774C22×D4—222no—
775C22×D4—222no—
776C22×D4—221no—
777C22×D4—221no—
778C22×D4C22×D1112yes—
779C23×C4—221no—
780AGL(1,ℤ/8)—444no—
781AGL(1,ℤ/8)—444no—
782#135—444no—
783C2×Q16—112no—
784C2×SD16—111no—
785C2×SD16—111no—
786C2×SD16—112no—
787C2×SD16—112no—
788C2×SD16—112no—
789C2×SD16—112no—
790C2×D8—111no—
791C2×D8—112no—
792C2×D8—111no—
793C2×D8—112no—
794C2×D8—112no—
795C2×D8—112no—
796C2×D8—112no—
797C2×D8—444no—
798C2×M16—112no—
799C2×M16—112no—
800C22×C8—112no—
801C22×C8—112no—
802C4⋊Q8—111no—
803C4⋊Q8C22⋊D1111yescharacteristic
804C4⋊Q8C22×D1111yescharacteristic
805#127—21no—
806#127—22no—
807#127—111no—
808#127C22⋊D1111yescharacteristic
809#127C22×D1111yescharacteristic
810#126—22no—
811#126—22no—
812#126—21no—
813#125C22×D1111yescharacteristic
814#124—22no—
815#124—21no—
816#124—21no—
817#124—112no—
818#124C22⋊D1112yes—
819#124C22×D1111yescharacteristic
820#123—21no—
821#123—22no—
822#123—22no—
823#123—22no—
824#123—222no—
825#123—222no—
826#123—222no—
827#123—222no—
828C22⋊Q8—22no—
829C22⋊Q8—21no—
830C22⋊Q8—112no—
831C22⋊Q8—112no—
832C22⋊Q8—222no—
833C22⋊Q8C22×D1111yescharacteristic
834C22⋊Q8C22×D1112yes—
835#121—22no—
836#121—22no—
837#121—22no—
838#121—22no—
839#121—21no—
840#121—21no—
841#121—22no—
842#121—22no—
843#121—112no—
844#121—112no—
845#121—222no—
846#121—222no—
847#121—221no—
848#121—221no—
849#121—222no—
850#121—221no—
851#121—221no—
852#121—221no—
853#121—221no—
854#121—222no—
855#121—222no—
856#121C22⋊D1111yescharacteristic
857#121C22⋊D1111yescharacteristic
858#121C22⋊D1112yes—
859#121C22×D1111yescharacteristic
860#121C22×D1112yes—
861#121C22×D1112yes—
862#121C22×D1112yes—
863#121C22×D1112yes—
864#120—22no—
865#120—22no—
866#120—22no—
867#120—22no—
868#120—222no—
869#120—222no—
870#120—222no—
871#120—222no—
872C4×Q8—21no—
873C4×Q8C22×D1111yescharacteristic
874C4×D4—21no—
875C4×D4—21no—
876C4×D4—22no—
877C4×D4—21no—
878C4×D4—111no—
879C4×D4—111no—
880C4×D4—111no—
881C4×D4—111no—
882C4×D4—221no—
883C4×D4—221no—
884C4×D4—221no—
885C4×D4—221no—
886C4×D4C22×D1111yescharacteristic
887C4×D4C22×D1112yes—
888C4×D4C22×D1111yescharacteristic
889C4×D4C22×D1111yescharacteristic
890C4×D4C22×D1112yes—
891#117—21no—
892#117C22×D1112yes—
893C2×C4⋊C4—111no—
894C2×C4⋊C4—221no—
895C2×C4⋊C4—221no—
896C2×C4⋊C4C22×D1112yes—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—221no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—222no—
901C2×C42C22×D1111yescharacteristic
902#107—111no—
903#107—112no—
904#107—112no—
905#107—111no—
906#106—111no—
907#106—111no—
908C4⋊C8—111no—
909C4⋊C8—111no—
910C4⋊C8—111no—
911C4⋊C8—111no—
912#103—111no—
913#103—111no—
914#103—112no—
915#103—112no—
916#103—112no—
917#103—112no—
918#102—111no—
919#102—112no—
920#102—112no—
921#102—111no—
922#102—111no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—111no—
927#102—111no—
928#102—112no—
929#102—111no—
930#102—112no—
931#102—112no—
932C22⋊C8—111no—
933C22⋊C8—112no—
934C22⋊C8—111no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937C22⋊C8—112no—
938C22⋊C8—112no—
939C4×C8—112no—
940C4×C8—111no—
941C4×C8—111no—
942C2×C11—41no—
943C2×C11—42no—
944C2×C11—42no—
945C2×C11—82no—
946C2×C11—81no—
947C2×C11#348411yescharacteristic
948C2×C11C2×#57611yescharacteristic
949C2×C11#358411yescharacteristic
950D11—42no—
951D11—42no—
952D11—82no—
953C24—22no—
954C24—221no—
955C24—222no—
956C24—222no—
957#41—42no—
958#41—42no—
959#41—42no—
960#41—42no—
961#41—82no—
962#41—82no—
963#41—224no—
964#41—224no—
965#41—442no—
966#41—442no—
967#41—442no—
968#41—442no—
969#41—448no—
970C2×Q8—21no—
971C2×Q8—112no—
972C2×Q8C2×C22⋊D1112yes—
973C2×Q8C23×D1111yescharacteristic
974C2×D4—21no—
975C2×D4—22no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—22no—
979C2×D4—22no—
980C2×D4—21no—
981C2×D4—21no—
982C2×D4—22no—
983C2×D4—42no—
984C2×D4—42no—
985C2×D4—82no—
986C2×D4—111no—
987C2×D4—111no—
988C2×D4—112no—
989C2×D4—222no—
990C2×D4—222no—
991C2×D4—224no—
992C2×D4—224no—
993C2×D4—222no—
994C2×D4—222no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—221no—
999C2×D4—221no—
1000C2×D4—222no—
1001C2×D4—222no—
1002C2×D4—221no—
1003C2×D4—442no—
1004C2×D4—442no—
1005C2×D4—448no—
1006C2×D4—448no—
1007C2×D4—448no—
1008C2×D4—882no—
1009C2×D4—882no—
1010C2×D4C2×C22⋊D1111yescharacteristic
1011C2×D4C2×C22⋊D1111yescharacteristic
1012C2×D4C2×C22⋊D1112yes—
1013C2×D4C2×C22⋊D1112yes—
1014C2×D4C2×C22⋊D1112yes—
1015C2×D4C2×C22⋊D1112yes—
1016C2×D4C23×D1111yescharacteristic
1017C2×D4C23×D1112yes—
1018C22×C4—22no—
1019C22×C4—21no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—221no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—222no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—882no—
1031C22×C4C2×C22⋊D1111yescharacteristic
1032C22×C4C2×C22⋊D1111yescharacteristic
1033C22×C4C23×D1111yescharacteristic
1034C22×C4C23×D1112yes—
1035C22×C4C23×D1112yes—
1036Q16—442no—
1037SD16—222no—
1038SD16—222no—
1039SD16—442no—
1040SD16—442no—
1041SD16—442no—
1042SD16—442no—
1043D8—222no—
1044D8—224no—
1045D8—224no—
1046D8—222no—
1047D8—442no—
1048D8—442no—
1049D8—442no—
1050M16—442no—
1051M16—442no—
1052C2×C8—111no—
1053C2×C8—112no—
1054C2×C8—112no—
1055C2×C8—111no—
1056C2×C8—111no—
1057C2×C8—111no—
1058C2×C8—442no—
1059C2×C8—442no—
1060C4⋊C4—22no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—22no—
1066C4⋊C4—21no—
1067C4⋊C4—111no—
1068C4⋊C4—111no—
1069C4⋊C4—221no—
1070C4⋊C4—221no—
1071C4⋊C4—222no—
1072C4⋊C4—222no—
1073C4⋊C4—221no—
1074C4⋊C4C2×C22⋊D1111yescharacteristic
1075C4⋊C4C2×C22⋊D1111yescharacteristic
1076C4⋊C4C2×C22⋊D1112yes—
1077C4⋊C4C23×D1111yescharacteristic
1078C4⋊C4C23×D1111yescharacteristic
1079C4⋊C4C23×D1112yes—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—22no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—21no—
1091C22⋊C4—22no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—222no—
1095C22⋊C4—221no—
1096C22⋊C4—221no—
1097C22⋊C4—221no—
1098C22⋊C4—221no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—222no—
1102C22⋊C4C2×C22⋊D1112yes—
1103C22⋊C4C2×C22⋊D1112yes—
1104C22⋊C4C2×C22⋊D1112yes—
1105C22⋊C4C2×C22⋊D1112yes—
1106C42—21no—
1107C42—22no—
1108C42C2×C22⋊D1111yescharacteristic
1109C42C2×C22⋊D1111yescharacteristic
1110C42C23×D1111yescharacteristic
1111C42C23×D1111yescharacteristic
1112C11#6165711yescharacteristic, complemented, Sylow
1113C23—21no—
1114C23—22no—
1115C23—82no—
1116C23—82no—
1117C23—82no—
1118C23—224no—
1119C23—221no—
1120C23—221no—
1121C23—222no—
1122C23—444no—
1123C23—444no—
1124C23—881no—
1125C23—881no—
1126C23—882no—
1127C23—882no—
1128C23—882no—
1129C23—882no—
1130C23C22×C22⋊D1112yes—
1131C23C22×C22⋊D1111yescharacteristic
1132C23C22×C22⋊D1112yes—
1133Q8—21no—
1134Q8—21no—
1135Q8—42no—
1136Q8—42no—
1137Q8—222no—
1138Q8—222no—
1139D4—22no—
1140D4—22no—
1141D4—21no—
1142D4—22no—
1143D4—22no—
1144D4—21no—
1145D4—42no—
1146D4—42no—
1147D4—42no—
1148D4—42no—
1149D4—42no—
1150D4—81no—
1151D4—82no—
1152D4—81no—
1153D4—82no—
1154D4—82no—
1155D4—82no—
1156D4—82no—
1157D4—82no—
1158D4—112no—
1159D4—112no—
1160D4—224no—
1161D4—221no—
1162D4—221no—
1163D4—222no—
1164D4—222no—
1165D4—444no—
1166D4—444no—
1167D4—444no—
1168D4—444no—
1169D4—444no—
1170D4—442no—
1171D4—881no—
1172D4—882no—
1173D4—882no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—82no—
1188C2×C4—82no—
1189C2×C4—82no—
1190C2×C4—221no—
1191C2×C4—221no—
1192C2×C4—222no—
1193C2×C4—444no—
1194C2×C4—444no—
1195C2×C4—444no—
1196C2×C4—442no—
1197C2×C4—442no—
1198C2×C4—881no—
1199C2×C4—881no—
1200C2×C4—881no—
1201C2×C4C22×C22⋊D1112yes—
1202C2×C4C22×C22⋊D1111yescharacteristic
1203C2×C4C22×C22⋊D1111yescharacteristic
1204C2×C4C22×C22⋊D1111yescharacteristic
1205C2×C4C22×C22⋊D1111yescharacteristic
1206C2×C4C22×C22⋊D1112yes—
1207C2×C4C22×C22⋊D1111yescharacteristic
1208C2×C4C24×D1111yescharacteristic
1209C8—221no—
1210C8—222no—
1211C8—221no—
1212C8—221no—
1213C8—222no—
1214C8—221no—
1215C22—21no—
1216C22—22no—
1217C22—22no—
1218C22—21no—
1219C22—22no—
1220C22—22no—
1221C22—21no—
1222C22—22no—
1223C22—22no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—42no—
1228C22—42no—
1229C22—41no—
1230C22—164no—
1231C22—222no—
1232C22—222no—
1233C22—441no—
1234C22—441no—
1235C22—441no—
1236C22—441no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—884no—
1241C22—1764no—
1242C22—1764no—
1243C22C23×C22⋊D1111yescharacteristic
1244C4—22no—
1245C4—21no—
1246C4—22no—
1247C4—21no—
1248C4—21no—
1249C4—21no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—41no—
1254C4—442no—
1255C4—441no—
1256C4—441no—
1257C4#1062336612yes—
1258C4D11×H(5,𝔽2)11yescharacteristic
1259C4D11×H(5,𝔽2)11yescharacteristic
1260C2—42no—
1261C2—41no—
1262C2—42no—
1263C2—81no—
1264C2—82no—
1265C2—442no—
1266C2—442no—
1267C2—882no—
1268C2#1308224711yescharacteristic
1269C2C2×#1062336611yescharacteristic
1270C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3546C2
socleC22×C11C23×D4
hypercenter#3546D11
hypocenterC11#61657
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #3546

Complements

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

NH ≅ G/Ntype
1. #13082378C2semidirect
2. #13080915C2semidirect
3. #13080841C2semidirect
4. #13080811C2semidirect
5. #13080527C2semidirect
6. #13080460C2semidirect
7. #13080423C2semidirect
8. #13080346C2semidirect
9. #13080297C2semidirect
10. D4×#4323C2semidirect
11. #13080236C2semidirect
12. #13080223C2semidirect
13. #13080212C2semidirect
14. #13079588C2semidirect
15. #13079545C2semidirect
16. #13079513C2semidirect
17. #13079468C2semidirect
18. #13078659C2semidirect
19. #13078612C2semidirect
20. #13077917C2semidirect
21. #13077882C2semidirect
22. #13077683C2semidirect
23. C11×#3546C2semidirect
24. C2×#67042C22semidirect
26. C11×#556C22semidirect
27. C11×#553C22semidirect
29. C11×#550C22semidirect
30. C11×#547C22semidirect
32. C11×#546C22semidirect
33. D42×C11C22semidirect
36. C11×#537C22semidirect
38. C11×#535C22semidirect
40. C11×#532C22semidirect
41. C11×#529C22semidirect
42. #10623364C22semidirect
43. C2×#67003C22semidirect
44. C2×#67002C22semidirect
45. C2×#66985C22semidirect
46. C22×#4323C22semidirect
54. #10623082C22semidirect
55. #10623081C22semidirect
56. #10623081C22semidirect
58. D4×D44C22semidirect
59. #10623008C22semidirect
60. C2×C4×D44C22semidirect
61. #10622852C22semidirect
62. #10622851C22semidirect
63. #10622847C22semidirect
64. #10622847C22semidirect
65. #10622831C22semidirect
66. #10622830C22semidirect
67. #10622706C22semidirect
68. #10622701C22semidirect
69. #10622700C22semidirect
70. #10622700C22semidirect
71. #10622689C22semidirect
72. #10622686C22semidirect
73. #10622685C22semidirect
74. #10622685C22semidirect
75. #10622681C22semidirect
76. #10622679C22semidirect
77. #10622679C22semidirect
78. #10622672C22semidirect
79. #10622670C22semidirect
80. #10622670C22semidirect
81. #10622664C22semidirect
82. #10622662C22semidirect
83. #10622660C22semidirect
84. #10622660C22semidirect
85. #10622659C22semidirect
86. #10622659C22semidirect
87. #10622657C22semidirect
88. #10622655C22semidirect
89. #10622655C22semidirect
90. #10622654C22semidirect
91. #10622652C22semidirect
92. #10622651C22semidirect
93. #10622651C22semidirect
94. #10622650C22semidirect
95. #10622650C22semidirect
96. #10622650C22semidirect
97. #10622650C22semidirect
98. #10622650C22semidirect
99. #10622650C22semidirect
101. #10622649C22semidirect
102. #10622649C22semidirect
103. #10622649C22semidirect
104. #10622649C22semidirect
105. #10622647C22semidirect
106. #10622646C22semidirect
107. #10622644C22semidirect
108. #10622640C22semidirect
109. C4×#4325C22semidirect
110. C4×#4325C22semidirect
111. #10622632C22semidirect
112. #10622629C22semidirect
113. #10622629C22semidirect
114. #10622628C22semidirect
115. C4×#4323C22semidirect
116. C4×#4323C22semidirect
117. C4×#4323C22semidirect
118. C4×#4323C22semidirect
119. #10622625C22semidirect
120. #10622625C22semidirect
121. #10622625C22semidirect
122. D4×C11⋊C8C22semidirect
123. D4×C11⋊C8C22semidirect
124. D4×C11⋊C8C22semidirect
125. #10622616C22semidirect
126. #10622615C22semidirect
127. #10622614C22semidirect
128. #10622609C22semidirect
129. #10622583C22semidirect
130. #10622580C22semidirect
131. #10622579C22semidirect
132. C2×#66873C22semidirect
133. #10622538C22semidirect
134. #10622538C22semidirect
478. #3546D11semidirect
609. #556C2×D11semidirect
610. #553C2×D11semidirect
612. #550C2×D11semidirect
616. #547C2×D11semidirect
621. #546C2×D11semidirect
625. D42C2×D11semidirect
629. #537C2×D11semidirect
631. #535C2×D11semidirect
635. #532C2×D11semidirect
636. #529C2×D11semidirect
1112. C11#61657semidirect

Maximal subgroups

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

subgroupindex
#130823782
#130809152
#130808412
#130808112
#130805272
#130804602
#130804232
#130803462
#130802972
D4×#43232
#130802362
#130802232
#130802122
#130795882
#130795452
#130795132
#130794682
#130786592
#130786122
#130779172
#130778822
#130776832
C11×#35462
#6165711