Finite Group Databasebeta

← #15625727

Subgroups — #15625727

Order 2816.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082409C211yesmaximal, characteristic, complemented
2#13079719C212yesmaximal, complemented
3#13079704C212yesmaximal, complemented
4#13079693C212yesmaximal, complemented
5#13079682C212yesmaximal, complemented
6#13079649C212yesmaximal, complemented
7#13079615C212yesmaximal, complemented
8#13079577C212yesmaximal, complemented
9#13079568C212yesmaximal, complemented
10#13079107C211yesmaximal, characteristic, complemented
11#13079094C211yesmaximal, characteristic, complemented
12#13078986C211yesmaximal, characteristic, complemented
13#13078975C211yesmaximal, characteristic, complemented
14#13078110C211yesmaximal, characteristic, complemented
15#13078088C211yesmaximal, characteristic, complemented
16#13078071C211yesmaximal, characteristic, complemented
17C2×#10622641C211yesmaximal, characteristic, complemented
18#13077928C211yesmaximal, characteristic, complemented
19#13077917C211yesmaximal, characteristic, complemented
20#13077909C211yesmaximal, characteristic, complemented
21#13077891C211yesmaximal, characteristic, complemented
22#13077282C211yesmaximal, characteristic, complemented
23C11×#3461C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C11×#544C2211yescharacteristic, complemented
27C11×#542—21no—
28C11×#542C2212yescomplemented
29C11×#541—21no—
30C11×#541C2212yescomplemented
31C11×#539—22no—
32C11×#537C2211yescharacteristic
33C11×#536C2211yescharacteristic
34C11×#536C2211yescharacteristic, complemented
35C11×#533—21no—
36C11×#533C2212yescomplemented
37C11×#529—22no—
38C11×#529—21no—
39C11×#529C2212yescomplemented
40C4×C11×#41C2211yescharacteristic
41C4×C11×#41C2211yescharacteristic, complemented
42C2×C4×Q8×C11C2211yescharacteristic, complemented
43C2×#67004C2211yescharacteristic, complemented
44C2×#67003C2211yescharacteristic
45C2×#67003C2211yescharacteristic, complemented
46C2×#67002C2211yescharacteristic
47C22×#4326C2211yescharacteristic, complemented
48C2×#66995C2211yescharacteristic
49C2×#66995C2211yescharacteristic, complemented
50C22×#4325C2211yescharacteristic
51#10623107—21no—
52#10623107—21no—
53#10623085—21no—
54#10623085—22no—
55#10623085—22no—
56#10623085—21no—
57#10623057C2211yescharacteristic
58#10623057C2212yes—
59#10623056C2211yescharacteristic
60#10623056C2212yes—
61#10623008C2212yes—
62#10623008C2211yescharacteristic
63C2×#66928C2212yes—
64C2×#66928C2211yescharacteristic
65#10622847C2211yescharacteristic
66#10622847C2211yescharacteristic
67#10622706C2212yescomplemented
68#10622705C2212yescomplemented
69#10622702C2212yescomplemented
70#10622702C2212yescomplemented
71#10622701C2212yescomplemented
72#10622699C2212yescomplemented
73#10622699C2212yescomplemented
74#10622698C2212yescomplemented
75#10622682C2212yescomplemented
76#10622681C2212yescomplemented
77#10622681C2212yescomplemented
78#10622680C2212yescomplemented
79#10622673C2212yescomplemented
80#10622672C2212yescomplemented
81#10622672C2212yescomplemented
82#10622671C2212yescomplemented
83#10622663C2212yescomplemented
84#10622663C2212yescomplemented
85#10622663C2212yescomplemented
86#10622660C2212yes—
87#10622660C2212yes—
88#10622660C2212yes—
89#10622660C2212yescomplemented
90#10622660C2212yescomplemented
91#10622660C2212yescomplemented
92#10622659C2212yes—
93#10622659C2212yes—
94#10622659C2212yes—
95#10622653C2212yescomplemented
96#10622650C2212yes—
97#10622650C2212yescomplemented
98#10622649C2212yes—
99#10622644C2211yescharacteristic, complemented
100#10622644C2212yescomplemented
101#10622641C2211yescharacteristic, complemented
102#10622641C2212yescomplemented
103#10622641C2212yescomplemented
104#10622641C2212yescomplemented
105#10622641C2212yescomplemented
106#10622641C2212yescomplemented
107#10622641C2212yescomplemented
108#10622641C2212yescomplemented
109#10622641C2211yescharacteristic, complemented
110#10622641C2212yescomplemented
111#10622640C2211yescharacteristic, complemented
112#10622640C2212yescomplemented
113#10622632C2211yescharacteristic, complemented
114#10622629C2211yescharacteristic, complemented
115#10622629C2212yescomplemented
116#10622629C2211yescharacteristic, complemented
117#10622629C2212yescomplemented
118#10622628C2211yescharacteristic, complemented
119#10622617C2211yescharacteristic, complemented
120#10622615C2211yescharacteristic
121#10622615C2211yescharacteristic, complemented
122#10622614C2211yescharacteristic
123#10622613C2212yescomplemented
124#10622613C2212yescomplemented
125#10622610C2211yescharacteristic, complemented
126#10622610C2211yescharacteristic, complemented
127C2×#66874C2211yescharacteristic, complemented
128#10622579C2211yescharacteristic
129#10622579C2211yescharacteristic, complemented
130C2×#66873C2211yescharacteristic
131#10622539C2212yescomplemented
132#10622538C2212yescomplemented
133#10622537C2211yescharacteristic, complemented
134C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11C2311yescharacteristic
138#67043—42no—
139#67043—42no—
140#67042—42no—
141#67042—42no—
142C2×#4343—21no—
143C2×Q8×D11—21no—
144C2×#4341—22no—
145C2×#4341—21no—
146C2×D4×D11—22no—
147C2×D4×D11—21no—
148C2×#4339C2311yescharacteristic
149C2×#4339C2311yescharacteristic
150C2×#4339C2312yes—
151C2×#4339C2312yes—
152C22×D44C2311yescharacteristic
153C22×D44C2312yes—
154C22×Dic22C2311yescharacteristic
155C22×Dic22C2312yes—
156C11×C4⋊Q8—21no—
157C11×C4⋊Q8—21no—
158C11×C4⋊Q8C2312yes—
159C11×C4⋊Q8C2312yes—
160C11×#126—22no—
161C11×#126—22no—
162C11×#126—22no—
163C11×#126—22no—
164C11×#125—22no—
165C11×#125—21no—
166C11×#125—22no—
167C11×#125—22no—
168C11×#125C2312yes—
169C11×#124—21no—
170C11×#124—22no—
171C11×#124C2312yes—
172C11×#123—22no—
173C11×#123—22no—
174C11×#123—22no—
175C11×#123—22no—
176C11×C22⋊Q8—21no—
177C11×C22⋊Q8—22no—
178C11×C22⋊Q8—21no—
179C11×C22⋊Q8—21no—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8—22no—
182C11×C22⋊Q8C2312yes—
183C11×C22⋊Q8C2312yes—
184C11×C22⋊Q8C2312yes—
185C11×#121—22no—
186C11×#121—21no—
187C11×#121C2312yes—
188C4×Q8×C11—21no—
189C4×Q8×C11—21no—
190C4×Q8×C11—22no—
191C4×Q8×C11D411yescharacteristic
192C4×Q8×C11D411yescharacteristic
193C4×Q8×C11C2312yes—
194C4×Q8×C11C2312yes—
195C4×Q8×C11C2311yescharacteristic
196C4×Q8×C11C2311yescharacteristic
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11D411yescharacteristic
201C4×D4×C11D412yes—
202C4×D4×C11D412yes—
203C4×D4×C11D411yescharacteristic
204C4×D4×C11C2311yescharacteristic
205C4×D4×C11C2311yescharacteristic
206C11×#117—22no—
207C11×#117—21no—
208C11×#117—22no—
209C11×#117C2311yescharacteristic
210C11×#117C2311yescharacteristic
211C11×#117C2312yes—
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C42×C11—21no—
215C2×C42×C11—21no—
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2312yes—
218#67004—42no—
219#67003—42no—
220#67003—42no—
221#67002—42no—
222C2×#4326—42no—
223C2×#4326C2312yes—
224C2×#4326C2312yes—
225C2×#4326C2312yes—
226C2×#4326C2312yes—
227C2×#4326C2311yescharacteristic
228C2×#4326C2311yescharacteristic
229C2×#4326C2312yes—
230#66995—42no—
231#66995—42no—
232C2×#4325—42no—
233C2×#4325C2312yes—
234C2×#4325C2312yes—
235C2×#4325C2312yes—
236C2×#4325C2312yes—
237C2×#4325C2312yes—
238C2×#4325C2311yescharacteristic
239C2×#4325C2311yescharacteristic
240C2×#4324C2311yescharacteristic
241C2×#4324C2311yescharacteristic
242C2×#4324C2312yes—
243C2×#4323C2312yes—
244C2×#4323C2311yescharacteristic
245C2×#4323C2311yescharacteristic
246#66983—21no—
247#66983—21no—
248#66983—22no—
249#66983—22no—
250C2×(C2×D11)⋊C4—21no—
251C2×(C2×D11)⋊C4—21no—
252C2×(C2×D11)⋊C4—22no—
253C2×(C2×D11)⋊C4—22no—
254C2×#4318C2311yescharacteristic
255C2×#4318C2311yescharacteristic
256C22×C11⋊C8C2311yescharacteristic
257C22×C11⋊C8C2311yescharacteristic
258#66950—21no—
259#66950—22no—
260#66950—21no—
261#66950—22no—
262#66948—21no—
263#66948—22no—
264#66948—21no—
265#66948—22no—
266#66939—22no—
267#66939—22no—
268#66939—22no—
269#66935—22no—
270#66935—22no—
271#66935—22no—
272#66928—21no—
273#66928—22no—
274#66928—21no—
275#66928—22no—
276#66928C2311yescharacteristic
277#66928C2312yes—
278#66928C2312yes—
279#66928C2312yes—
280#66928C2312yes—
281#66928C2311yescharacteristic
282#66927C2311yescharacteristic
283#66927C2312yes—
284C4×D44—21no—
285C4×D44—22no—
286C4×D44—21no—
287C4×D44—22no—
288#66922C2311yescharacteristic
289#66922C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291C22⋊(C11⋊C8)C2312yes—
292C22⋊(C11⋊C8)C2312yes—
293C22⋊(C11⋊C8)C2312yes—
294#66874C2312yes—
295#66874C2312yes—
296#66874C2312yes—
297#66874C2312yes—
298#66874C2311yescharacteristic
299#66874C2311yescharacteristic
300#66874C2311yescharacteristic
301#66874C2311yescharacteristic
302#66874C2312yes—
303#66874C2312yes—
304#66873C2312yes—
305#66873C2312yes—
306#66873C2312yes—
307#66873C2312yes—
308#66873C2312yes—
309#66873C2312yes—
310#66873C2311yescharacteristic
311#66873C2311yescharacteristic
312#66873C2311yescharacteristic
313#66873C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4⋊(C11⋊C8)C2311yescharacteristic
317C4⋊(C11⋊C8)C2311yescharacteristic
318C4⋊(C11⋊C8)C2312yes—
319C4⋊(C11⋊C8)C2312yes—
320#66867C2312yes—
321#66867C2312yes—
322C4×C11⋊C8C2312yes—
323C4×C11⋊C8C2312yes—
324#60835—111nomaximal, Sylow
325C23×D11—22no—
326C23×D11—21no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C2×Q8×C11—21no—
332C2×Q8×C11—22no—
333C2×Q8×C11—22no—
334C2×Q8×C11—22no—
335C2×Q8×C11C2×D411yescharacteristic
336C2×Q8×C11C2412yes—
337C2×Q8×C11C2411yescharacteristic
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11C2×D412yes—
341C2×D4×C11C2×D411yescharacteristic
342C2×D4×C11C2411yescharacteristic
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2×D412yes—
351C22×C4×C11C2×D412yes—
352C22×C4×C11C2412yes—
353C22×C4×C11C2411yescharacteristic
354C2×C22⋊D11—22no—
355C2×C22⋊D11—21no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—21no—
358C22×Dic11—22no—
359C22×Dic11—21no—
360#4343—44no—
361Q8×D11—44no—
362#4341—48no—
363#4341—44no—
364D4×D11—48no—
365D4×D11—44no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—22no—
370#4339—42no—
371#4339—42no—
372#4339—42no—
373#4339—42no—
374C2×D44—22no—
375C2×D44—21no—
376C2×D44—21no—
377C2×D44—21no—
378C2×D44—22no—
379C2×D44—22no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—42no—
383C2×D44—42no—
384C2×D44C2411yescharacteristic
385C2×D44C2412yes—
386C2×D44C2411yescharacteristic
387C2×C4×D11—22no—
388C2×C4×D11—21no—
389C2×C4×D11—22no—
390C2×C4×D11—21no—
391C2×Dic22—22no—
392C2×Dic22—21no—
393C2×Dic22—22no—
394C2×Dic22—22no—
395C2×Dic22—42no—
396C2×Dic22—42no—
397C2×Dic22C2411yescharacteristic
398C2×Dic22C2412yes—
399C2×Dic22C2411yescharacteristic
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4C2×D412yes—
414C11×C4⋊C4C2×D411yescharacteristic
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D412yes—
417C11×C4⋊C4C2412yes—
418C11×C4⋊C4C2411yescharacteristic
419C11×C4⋊C4C2411yescharacteristic
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—22no—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—21no—
436C42×C11—22no—
437C42×C11C2×D411yescharacteristic
438C42×C11C2×D411yescharacteristic
439C42×C11C2×D412yes—
440C42×C11C2×D412yes—
441C42×C11C2412yes—
442C42×C11C2411yescharacteristic
443C42×C11C2411yescharacteristic
444#4326—42no—
445#4326—42no—
446#4326—42no—
447#4326—42no—
448#4326—41no—
449#4326—41no—
450#4326—42no—
451#4325—42no—
452#4325—42no—
453#4325—42no—
454#4325—42no—
455#4325—42no—
456#4325—41no—
457#4325—41no—
458#4324—41no—
459#4324—41no—
460#4324—42no—
461#4323—42no—
462#4323—41no—
463#4323—41no—
464(C2×D11)⋊C4—21no—
465(C2×D11)⋊C4—21no—
466(C2×D11)⋊C4—21no—
467(C2×D11)⋊C4—22no—
468(C2×D11)⋊C4—21no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—22no—
471(C2×D11)⋊C4—22no—
472(C2×D11)⋊C4—22no—
473(C2×D11)⋊C4—22no—
474(C2×D11)⋊C4—22no—
475(C2×D11)⋊C4—22no—
476C4⋊Dic11—21no—
477C4⋊Dic11—21no—
478C4⋊Dic11—22no—
479C4⋊Dic11—22no—
480#4318—22no—
481#4318—22no—
482C2×C11⋊C8—22no—
483C2×C11⋊C8—22no—
484C2×C11⋊C8C2411yescharacteristic
485C2×C11⋊C8C2411yescharacteristic
486C2×C11⋊C8C2412yes—
487C2×C11⋊C8C2412yes—
488C2×C11⋊C8C2411yescharacteristic
489C2×C11⋊C8C2411yescharacteristic
490#3500—111no—
491#3461D1111yescharacteristic, complemented
492#3225—112no—
493#3224—112no—
494#3223—112no—
495#3222—112no—
496#3219—112no—
497#3215—112no—
498#3211—112no—
499#3210—112no—
500#3156—111no—
501#3154—111no—
502#3137—111no—
503#3136—111no—
504#3040—111no—
505#3037—111no—
506#3035—111no—
507C2×#464—111no—
508#3013—111no—
509#3012—111no—
510#3011—111no—
511#3009—111no—
512#2925—111no—
513C23×C11—21no—
514C23×C11C22×D412yes—
515C23×C11C22×D411yescharacteristic
516C22×D11—21no—
517C22×D11—22no—
518C22×D11—21no—
519C22×D11—44no—
520C22×D11—42no—
521C22×D11—81no—
522C22×D11—82no—
523C22×D11—81no—
524C22×D11—82no—
525Q8×C11—22no—
526Q8×C11—22no—
527Q8×C11—22no—
528Q8×C11—21no—
529Q8×C11—21no—
530Q8×C11—42no—
531Q8×C11—82no—
532D4×C11—24no—
533D4×C11—22no—
534D4×C11—21no—
535D4×C11—21no—
536D4×C11—42no—
537D4×C11—82no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—21no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—41no—
546C2×C4×C11—42no—
547C2×C4×C11—41no—
548C2×C4×C11—42no—
549C2×C4×C11—42no—
550C2×C4×C11—42no—
551C2×C4×C11—42no—
552C2×C4×C11—81no—
553C2×C4×C11—81no—
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D412yes—
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C22×D412yes—
561C2×C4×C11C22×D411yescharacteristic
562C2×C4×C11H(5,𝔽2)12yes—
563C2×C4×C11H(5,𝔽2)12yes—
564C2×C4×C11C2511yescharacteristic
565C22⋊D11—44no—
566C22⋊D11—44no—
567C22⋊D11—42no—
568C22⋊D11—42no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—21no—
572C2×Dic11—44no—
573C2×Dic11—42no—
574D44—22no—
575D44—21no—
576D44—21no—
577D44—22no—
578D44—21no—
579D44—21no—
580D44—44no—
581D44—42no—
582D44—81no—
583D44—82no—
584D44—81no—
585D44—82no—
586C4×D11—44no—
587C4×D11—44no—
588C4×D11—42no—
589C4×D11—42no—
590Dic22—22no—
591Dic22—21no—
592Dic22—21no—
593Dic22—22no—
594Dic22—21no—
595Dic22—21no—
596Dic22—44no—
597Dic22—42no—
598C11⋊C8—21no—
599C11⋊C8—21no—
600C11⋊C8—21no—
601C11⋊C8—21no—
602C11⋊C8—22no—
603C11⋊C8—22no—
604C2×2−1+4—111no—
605C2×H(5,𝔽2)—111no—
606C2×#137—111no—
607C2×#137—111no—
608C2×#137—111no—
609C2×AGL(1,ℤ/8)—111no—
610C2×#135—111no—
611C2×#135—111no—
612C22×Q16—111no—
613C22×SD16—111no—
614#548—221no—
615#548—221no—
616#546—222no—
617#546—221no—
618#546—222no—
619#546—221no—
620#544C2×D1111yescharacteristic, complemented
621#542—21no—
622#542C2×D1112yescomplemented
623#541—21no—
624#541C2×D1112yescomplemented
625#539—22no—
626#537C2×D1111yescharacteristic
627#536—111no—
628#536—112no—
629#536C2×D1111yescharacteristic
630#536C2×D1111yescharacteristic, complemented
631#535—111no—
632#535—112no—
633#533—21no—
634#533C2×D1112yescomplemented
635#532—112no—
636#532—111no—
637#529—22no—
638#529—21no—
639#529C2×D1112yescomplemented
640C2×#124—112no—
641C2×#124—111no—
642C4×#41C2×D1111yescharacteristic
643C4×#41C2×D1111yescharacteristic, complemented
644C2×C4×Q8C2×D1111yescharacteristic, complemented
645#497—112no—
646#497—112no—
647#497—112no—
648#496—112no—
649#495—112no—
650#495—112no—
651#494—112no—
652#492—112no—
653#491—112no—
654#490—112no—
655#489—112no—
656#489—112no—
657#488—112no—
658#488—112no—
659#487—112no—
660#486—112no—
661#464—111no—
662#464—112no—
663#464—112no—
664#464—112no—
665#464—112no—
666#464—111no—
667#464—112no—
668#464—112no—
669#464—112no—
670#464—112no—
671#463—111no—
672#463—112no—
673#463—111no—
674#463—112no—
675#462—111no—
676#462—112no—
677#461—111no—
678#460—111no—
679#460—112no—
680#459—111no—
681#452—112no—
682#452—112no—
683#452—112no—
684#452—112no—
685#452—112no—
686#452—112no—
687#451—112no—
688#451—112no—
689#451—112no—
690#450—112no—
691#450—112no—
692#450—112no—
693#449—112no—
694#449—112no—
695#448—112no—
696#447—112no—
697#433—112no—
698#433—112no—
699#432—112no—
700#431—112no—
701#423—111no—
702C2×C4⋊C8—111no—
703#419—111no—
704#418—111no—
705#417—111no—
706#417—111no—
707#416—111no—
708#416—111no—
709C2×#103—111no—
710C2×#102—111no—
711#408—111no—
712#408—111no—
713#405—111no—
714#405—111no—
715C22×C11—21no—
716C22×C11—21no—
717C22×C11—22no—
718C22×C11—22no—
719C22×C11—22no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11—41no—
723C22×C11#53512yes—
724C22×C11C23×D411yescharacteristic
725C2×D11—42no—
726C2×D11—41no—
727C2×D11—41no—
728C2×D11—42no—
729C2×D11—41no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—42no—
733C2×D11—41no—
734C2×D11—162no—
735C2×D11—164no—
736C4×C11—21no—
737C4×C11—21no—
738C4×C11—22no—
739C4×C11—21no—
740C4×C11—21no—
741C4×C11—22no—
742C4×C11—22no—
743C4×C11—42no—
744C4×C11—41no—
745C4×C11—41no—
746C4×C11—41no—
747C4×C11—42no—
748C4×C11#53512yes—
749C4×C11C2×H(5,𝔽2)11yescharacteristic
750C4×C11C2×H(5,𝔽2)11yescharacteristic
751Dic11—42no—
752Dic11—41no—
753Dic11—41no—
7542−1+4—442no—
7552−1+4—442no—
756H(5,𝔽2)—442no—
757H(5,𝔽2)—442no—
758C2×#41—111no—
759C2×#41—111no—
760C2×#41—112no—
761C2×#41—112no—
762C2×#41—221no—
763C2×#41—222no—
764C2×#41—221no—
765C2×#41C22×D1111yescharacteristic
766C2×#41C22×D1111yescharacteristic
767C22×Q8—111no—
768C22×Q8—112no—
769C22×Q8—221no—
770C22×Q8C22×D1111yescharacteristic
771C22×D4—111no—
772C22×D4—112no—
773C22×D4—222no—
774C22×D4—221no—
775#137—442no—
776#137—442no—
777#137—442no—
778AGL(1,ℤ/8)—442no—
779#135—442no—
780#135—442no—
781C2×Q16—112no—
782C2×Q16—112no—
783C2×Q16—111no—
784C2×Q16—111no—
785C2×Q16—112no—
786C2×Q16—112no—
787C2×Q16—112no—
788C2×Q16—442no—
789C2×SD16—112no—
790C2×SD16—112no—
791C2×SD16—111no—
792C2×SD16—111no—
793C2×SD16—112no—
794C2×SD16—112no—
795C2×SD16—112no—
796C2×SD16—111no—
797C2×SD16—111no—
798C2×SD16—112no—
799C2×SD16—442no—
800C2×D8—111no—
801C2×D8—111no—
802C2×D8—112no—
803C2×M16—111no—
804C2×M16—111no—
805C22×C8—111no—
806C22×C8—111no—
807C4⋊Q8—21no—
808C4⋊Q8—21no—
809C4⋊Q8—111no—
810C4⋊Q8—112no—
811C4⋊Q8C22×D1112yes—
812C4⋊Q8C22×D1112yes—
813#127—111no—
814#127—112no—
815#126—22no—
816#126—22no—
817#126—22no—
818#126—22no—
819#125—22no—
820#125—21no—
821#125—22no—
822#125—22no—
823#125C22×D1112yes—
824#124—21no—
825#124—22no—
826#124—111no—
827#124—112no—
828#124—112no—
829#124—112no—
830#124—112no—
831#124—111no—
832#124—221no—
833#124—222no—
834#124—221no—
835#124—222no—
836#124C22×D1112yes—
837#123—22no—
838#123—22no—
839#123—22no—
840#123—22no—
841#123—222no—
842#123—222no—
843#123—222no—
844C22⋊Q8—21no—
845C22⋊Q8—22no—
846C22⋊Q8—21no—
847C22⋊Q8—21no—
848C22⋊Q8—22no—
849C22⋊Q8—22no—
850C22⋊Q8—221no—
851C22⋊Q8—222no—
852C22⋊Q8—221no—
853C22⋊Q8—222no—
854C22⋊Q8C22×D1112yes—
855C22⋊Q8C22×D1112yes—
856C22⋊Q8C22×D1112yes—
857#121—22no—
858#121—21no—
859#121—221no—
860#121—221no—
861#121—222no—
862#121—222no—
863#121—221no—
864#121—222no—
865#121—221no—
866#121—222no—
867#121C22×D1112yes—
868#120—222no—
869#120—222no—
870#120—222no—
871C4×Q8—21no—
872C4×Q8—21no—
873C4×Q8—22no—
874C4×Q8C22⋊D1111yescharacteristic
875C4×Q8C22⋊D1111yescharacteristic
876C4×Q8C22×D1112yes—
877C4×Q8C22×D1112yes—
878C4×Q8C22×D1111yescharacteristic
879C4×Q8C22×D1111yescharacteristic
880C4×D4—21no—
881C4×D4—21no—
882C4×D4—22no—
883C4×D4—221no—
884C4×D4—222no—
885C4×D4—221no—
886C4×D4—222no—
887C4×D4C22⋊D1111yescharacteristic
888C4×D4C22⋊D1112yes—
889C4×D4C22⋊D1112yes—
890C4×D4C22⋊D1111yescharacteristic
891C4×D4C22×D1111yescharacteristic
892C4×D4C22×D1111yescharacteristic
893#117—22no—
894#117—21no—
895#117—22no—
896#117C22×D1111yescharacteristic
897#117C22×D1111yescharacteristic
898#117C22×D1112yes—
899C2×C4⋊C4—21no—
900C2×C4⋊C4C22×D1111yescharacteristic
901C2×C22⋊C4—221no—
902C2×C22⋊C4—221no—
903C2×C22⋊C4—222no—
904C2×C22⋊C4—222no—
905C2×C42—21no—
906C2×C42—21no—
907C2×C42C22×D1111yescharacteristic
908C2×C42C22×D1112yes—
909C4⋊C8—111no—
910C4⋊C8—111no—
911C4⋊C8—111no—
912C4⋊C8—111no—
913C4⋊C8—112no—
914C4⋊C8—112no—
915#103—112no—
916#103—112no—
917#103—111no—
918#103—111no—
919#103—111no—
920#103—111no—
921#103—112no—
922#103—112no—
923#103—112no—
924#103—112no—
925#102—112no—
926#102—112no—
927#102—111no—
928#102—111no—
929#102—111no—
930#102—111no—
931#102—112no—
932#102—112no—
933#102—112no—
934#102—112no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937C22⋊C8—112no—
938C22⋊C8—112no—
939#97—112no—
940#97—112no—
941C4×C8—112no—
942C4×C8—112no—
943C2×C11—22no—
944C2×C11—42no—
945C2×C11—81no—
946C2×C11C2×#53511yescharacteristic
947C2×C11#358411yescharacteristic
948C2×C11#358611yescharacteristic
949D11—81no—
950D11—82no—
951D11—81no—
952C24—222no—
953C24—221no—
954#41—22no—
955#41—22no—
956#41—22no—
957#41—22no—
958#41—222no—
959#41—222no—
960#41—222no—
961#41—222no—
962#41—442no—
963#41—442no—
964#41—442no—
965#41—442no—
966#41—448no—
967#41—444no—
968#41—444no—
969C2×Q8—21no—
970C2×Q8—22no—
971C2×Q8—22no—
972C2×Q8—22no—
973C2×Q8—112no—
974C2×Q8—111no—
975C2×Q8—111no—
976C2×Q8—222no—
977C2×Q8—221no—
978C2×Q8—222no—
979C2×Q8—222no—
980C2×Q8—442no—
981C2×Q8—442no—
982C2×Q8—444no—
983C2×Q8C2×C22⋊D1111yescharacteristic
984C2×Q8C23×D1112yes—
985C2×Q8C23×D1111yescharacteristic
986C2×D4—21no—
987C2×D4—22no—
988C2×D4—112no—
989C2×D4—111no—
990C2×D4—111no—
991C2×D4—222no—
992C2×D4—221no—
993C2×D4—222no—
994C2×D4—221no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—221no—
999C2×D4—221no—
1000C2×D4—221no—
1001C2×D4—222no—
1002C2×D4—222no—
1003C2×D4—442no—
1004C2×D4—442no—
1005C2×D4—448no—
1006C2×D4—444no—
1007C2×D4C2×C22⋊D1112yes—
1008C2×D4C2×C22⋊D1111yescharacteristic
1009C2×D4C23×D1111yescharacteristic
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—222no—
1016C22×C4—221no—
1017C22×C4—222no—
1018C22×C4—221no—
1019C22×C4—222no—
1020C22×C4—221no—
1021C22×C4C2×C22⋊D1111yescharacteristic
1022C22×C4C2×C22⋊D1111yescharacteristic
1023C22×C4C2×C22⋊D1112yes—
1024C22×C4C2×C22⋊D1112yes—
1025C22×C4C23×D1112yes—
1026C22×C4C23×D1111yescharacteristic
1027Q16—442no—
1028Q16—442no—
1029Q16—441no—
1030Q16—441no—
1031Q16—442no—
1032Q16—442no—
1033Q16—442no—
1034SD16—441no—
1035SD16—441no—
1036SD16—442no—
1037SD16—442no—
1038SD16—442no—
1039SD16—441no—
1040SD16—441no—
1041SD16—442no—
1042SD16—442no—
1043SD16—442no—
1044D8—441no—
1045D8—441no—
1046D8—442no—
1047M16—222no—
1048M16—222no—
1049C2×C8—111no—
1050C2×C8—111no—
1051C2×C8—112no—
1052C2×C8—112no—
1053C2×C8—111no—
1054C2×C8—111no—
1055C2×C8—222no—
1056C2×C8—222no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—221no—
1071C4⋊C4—221no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4C2×C22⋊D1112yes—
1075C4⋊C4C2×C22⋊D1111yescharacteristic
1076C4⋊C4C2×C22⋊D1111yescharacteristic
1077C4⋊C4C2×C22⋊D1112yes—
1078C4⋊C4C23×D1112yes—
1079C4⋊C4C23×D1111yescharacteristic
1080C4⋊C4C23×D1111yescharacteristic
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—21no—
1084C22⋊C4—22no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—222no—
1091C22⋊C4—221no—
1092C22⋊C4—222no—
1093C22⋊C4—221no—
1094C22⋊C4—222no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—221no—
1101C22⋊C4—221no—
1102C22⋊C4C2×C22⋊D1112yes—
1103C22⋊C4C2×C22⋊D1112yes—
1104C22⋊C4C2×C22⋊D1112yes—
1105C42—22no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—22no—
1110C42C2×C22⋊D1111yescharacteristic
1111C42C2×C22⋊D1112yes—
1112C42C2×C22⋊D1111yescharacteristic
1113C42C2×C22⋊D1112yes—
1114C42C23×D1112yes—
1115C42C23×D1111yescharacteristic
1116C42C23×D1111yescharacteristic
1117C11#6083511yescharacteristic, complemented, Sylow
1118C23—21no—
1119C23—222no—
1120C23—221no—
1121C23—221no—
1122C23—444no—
1123C23—442no—
1124C23—881no—
1125C23—881no—
1126C23—882no—
1127C23—882no—
1128C23C22×C22⋊D1112yes—
1129C23C22×C22⋊D1111yescharacteristic
1130Q8—22no—
1131Q8—22no—
1132Q8—22no—
1133Q8—21no—
1134Q8—21no—
1135Q8—42no—
1136Q8—82no—
1137Q8—222no—
1138Q8—221no—
1139Q8—221no—
1140Q8—222no—
1141Q8—221no—
1142Q8—221no—
1143Q8—444no—
1144Q8—442no—
1145D4—24no—
1146D4—22no—
1147D4—21no—
1148D4—21no—
1149D4—42no—
1150D4—82no—
1151D4—222no—
1152D4—221no—
1153D4—221no—
1154D4—222no—
1155D4—221no—
1156D4—221no—
1157D4—444no—
1158D4—444no—
1159D4—444no—
1160D4—442no—
1161D4—442no—
1162D4—442no—
1163D4—881no—
1164D4—882no—
1165D4—881no—
1166D4—882no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—81no—
1182C2×C4—81no—
1183C2×C4—222no—
1184C2×C4—221no—
1185C2×C4—221no—
1186C2×C4—444no—
1187C2×C4—444no—
1188C2×C4—444no—
1189C2×C4—442no—
1190C2×C4—442no—
1191C2×C4—442no—
1192C2×C4#6704212yes—
1193C2×C4#6704212yes—
1194C2×C4C22×C22⋊D1111yescharacteristic
1195C2×C4C22×C22⋊D1111yescharacteristic
1196C2×C4C22×C22⋊D1111yescharacteristic
1197C2×C4C22×C22⋊D1111yescharacteristic
1198C2×C4C22×C22⋊D1112yes—
1199C2×C4C22×C22⋊D1112yes—
1200C2×C4C22×C22⋊D1112yes—
1201C2×C4C22×C22⋊D1111yescharacteristic
1202C2×C4C24×D1111yescharacteristic
1203C8—221no—
1204C8—221no—
1205C8—221no—
1206C8—221no—
1207C8—222no—
1208C8—222no—
1209C22—21no—
1210C22—21no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—441no—
1218C22—442no—
1219C22—441no—
1220C22—441no—
1221C22—442no—
1222C22—441no—
1223C22—441no—
1224C22—442no—
1225C22—441no—
1226C22—1762no—
1227C22—1764no—
1228C22#1062336112yes—
1229C22C23×C22⋊D1111yescharacteristic
1230C4—21no—
1231C4—21no—
1232C4—22no—
1233C4—22no—
1234C4—21no—
1235C4—21no—
1236C4—22no—
1237C4—41no—
1238C4—41no—
1239C4—42no—
1240C4—42no—
1241C4—41no—
1242C4—441no—
1243C4—442no—
1244C4—441no—
1245C4#1062336112yes—
1246C4C2×#6704211yescharacteristic
1247C4C2×#6704211yescharacteristic
1248C2—22no—
1249C2—42no—
1250C2—81no—
1251C2—882no—
1252C2—881no—
1253C2—881no—
1254C2C2×#1062336111yescharacteristic
1255C2#1308338711yescharacteristic
1256C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3461C2
socleC22×C11C23×D4
hypercenter#3461D11
hypocenterC11#60835
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13082409C2semidirect
2. #13079719C2semidirect
3. #13079704C2semidirect
4. #13079693C2semidirect
5. #13079682C2semidirect
6. #13079649C2semidirect
7. #13079615C2semidirect
8. #13079577C2semidirect
9. #13079568C2semidirect
10. #13079107C2semidirect
11. #13079094C2semidirect
12. #13078986C2semidirect
13. #13078975C2semidirect
14. #13078110C2semidirect
15. #13078088C2semidirect
16. #13078071C2semidirect
17. C2×#10622641C2semidirect
18. #13077928C2semidirect
19. #13077917C2semidirect
20. #13077909C2semidirect
21. #13077891C2semidirect
22. #13077282C2semidirect
23. C11×#3461C2semidirect
26. C11×#544C22semidirect
28. C11×#542C22semidirect
30. C11×#541C22semidirect
34. C11×#536C22semidirect
36. C11×#533C22semidirect
39. C11×#529C22semidirect
41. C4×C11×#41C22semidirect
42. C2×C4×Q8×C11C22semidirect
43. C2×#67004C22semidirect
45. C2×#67003C22semidirect
47. C22×#4326C22semidirect
49. C2×#66995C22semidirect
67. #10622706C22semidirect
68. #10622705C22semidirect
69. #10622702C22semidirect
70. #10622702C22semidirect
71. #10622701C22semidirect
72. #10622699C22semidirect
73. #10622699C22semidirect
74. #10622698C22semidirect
75. #10622682C22semidirect
76. #10622681C22semidirect
77. #10622681C22semidirect
78. #10622680C22semidirect
79. #10622673C22semidirect
80. #10622672C22semidirect
81. #10622672C22semidirect
82. #10622671C22semidirect
83. #10622663C22semidirect
84. #10622663C22semidirect
85. #10622663C22semidirect
89. #10622660C22semidirect
90. #10622660C22semidirect
91. #10622660C22semidirect
95. #10622653C22semidirect
97. #10622650C22semidirect
99. #10622644C22semidirect
100. #10622644C22semidirect
101. #10622641C22semidirect
102. #10622641C22semidirect
103. #10622641C22semidirect
104. #10622641C22semidirect
105. #10622641C22semidirect
106. #10622641C22semidirect
107. #10622641C22semidirect
108. #10622641C22semidirect
109. #10622641C22semidirect
110. #10622641C22semidirect
111. #10622640C22semidirect
112. #10622640C22semidirect
113. #10622632C22semidirect
114. #10622629C22semidirect
115. #10622629C22semidirect
116. #10622629C22semidirect
117. #10622629C22semidirect
118. #10622628C22semidirect
119. #10622617C22semidirect
121. #10622615C22semidirect
123. #10622613C22semidirect
124. #10622613C22semidirect
125. #10622610C22semidirect
126. #10622610C22semidirect
127. C2×#66874C22semidirect
129. #10622579C22semidirect
131. #10622539C22semidirect
132. #10622538C22semidirect
133. #10622537C22semidirect
134. C2×C4⋊(C11⋊C8)C22semidirect
491. #3461D11semidirect
620. #544C2×D11semidirect
622. #542C2×D11semidirect
624. #541C2×D11semidirect
630. #536C2×D11semidirect
634. #533C2×D11semidirect
639. #529C2×D11semidirect
643. C4×#41C2×D11semidirect
644. C2×C4×Q8C2×D11semidirect
1117. C11#60835semidirect

Maximal subgroups

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

subgroupindex
#130824092
#130797192
#130797042
#130796932
#130796822
#130796492
#130796152
#130795772
#130795682
#130791072
#130790942
#130789862
#130789752
#130781102
#130780882
#130780712
C2×#106226412
#130779282
#130779172
#130779092
#130778912
#130772822
C11×#34612
#6083511