Finite Group Databasebeta

← #15625704

Subgroups — #15625704

Order 2816.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 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#13079671C212yesmaximal, complemented
5#13079660C212yesmaximal, complemented
6#13079649C212yesmaximal, complemented
7#13079599C212yesmaximal, complemented
8#13079577C212yesmaximal, complemented
9#13079545C212yesmaximal, complemented
10#13079099C211yesmaximal, characteristic, complemented
11#13079088C211yesmaximal, characteristic, complemented
12#13078986C211yesmaximal, characteristic, complemented
13#13078975C211yesmaximal, characteristic, complemented
14#13078110C211yesmaximal, characteristic, complemented
15#13078080C211yesmaximal, characteristic, complemented
16#13078071C211yesmaximal, characteristic, complemented
17C2×#10622629C211yesmaximal, characteristic, complemented
18#13077928C211yesmaximal, characteristic, complemented
19#13077917C211yesmaximal, characteristic, complemented
20#13077900C211yesmaximal, characteristic, complemented
21#13077882C211yesmaximal, characteristic, complemented
22#13077282C211yesmaximal, characteristic, complemented
23C11×#3460C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C11×#544C2211yescharacteristic, complemented
27C11×#542—21no—
28C11×#542C2212yescomplemented
29C11×#540—21no—
30C11×#540C2212yescomplemented
31C11×#538—22no—
32C11×#537C2211yescharacteristic
33C11×#535C2211yescharacteristic
34C11×#535C2211yescharacteristic, complemented
35C11×#532—21no—
36C11×#532C2212yescomplemented
37C11×#529—21no—
38C11×#529C2212yescomplemented
39C11×#525—22no—
40C4×C11×#41C2211yescharacteristic
41C4×C11×#41C2211yescharacteristic, complemented
42C2×C4×D4×C11C2211yescharacteristic, complemented
43C2×#67004C2211yescharacteristic, complemented
44C2×#67003C2211yescharacteristic
45C2×#67003C2211yescharacteristic, complemented
46C2×#67002C2211yescharacteristic
47C22×#4324C2211yescharacteristic, complemented
48C2×#66985C2211yescharacteristic
49C2×#66985C2211yescharacteristic, complemented
50C22×#4323C2211yescharacteristic
51#10623107—21no—
52#10623107—21no—
53#10623085—21no—
54#10623085—21no—
55#10623085—22no—
56#10623085—22no—
57#10623057C2211yescharacteristic
58#10623057C2212yescomplemented
59#10623056C2211yescharacteristic
60#10623056C2212yescomplemented
61#10623008C2211yescharacteristic
62#10623008C2212yescomplemented
63C2×#66928C2211yescharacteristic
64C2×#66928C2212yescomplemented
65#10622847C2211yescharacteristic
66#10622847C2211yescharacteristic
67#10622706C2212yescomplemented
68#10622702C2212yescomplemented
69#10622702C2212yescomplemented
70#10622701C2212yescomplemented
71#10622689C2212yescomplemented
72#10622687C2212yescomplemented
73#10622687C2212yescomplemented
74#10622686C2212yescomplemented
75#10622682C2212yescomplemented
76#10622681C2212yescomplemented
77#10622681C2212yescomplemented
78#10622680C2212yescomplemented
79#10622673C2212yescomplemented
80#10622672C2212yescomplemented
81#10622672C2212yescomplemented
82#10622671C2212yescomplemented
83#10622663C2212yescomplemented
84#10622660C2212yescomplemented
85#10622660C2212yescomplemented
86#10622659C2212yescomplemented
87#10622653C2212yescomplemented
88#10622653C2212yescomplemented
89#10622653C2212yescomplemented
90#10622650C2212yes—
91#10622650C2212yes—
92#10622650C2212yescomplemented
93#10622650C2212yescomplemented
94#10622650C2212yescomplemented
95#10622650C2212yescomplemented
96#10622649C2212yes—
97#10622649C2212yes—
98#10622649C2212yescomplemented
99#10622644C2211yescharacteristic, complemented
100#10622641C2211yescharacteristic, complemented
101#10622641C2212yescomplemented
102#10622641C2211yescharacteristic, complemented
103#10622641C2212yescomplemented
104#10622640C2211yescharacteristic, complemented
105#10622632C2211yescharacteristic, complemented
106#10622632C2212yescomplemented
107#10622629C2212yescomplemented
108#10622629C2212yescomplemented
109#10622629C2212yescomplemented
110#10622629C2212yescomplemented
111#10622629C2212yescomplemented
112#10622629C2211yescharacteristic, complemented
113#10622629C2212yescomplemented
114#10622629C2211yescharacteristic, complemented
115#10622629C2212yescomplemented
116#10622629C2212yescomplemented
117#10622628C2211yescharacteristic, complemented
118#10622628C2212yescomplemented
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×#41—22no—
136C2×C11×#41C2311yescharacteristic
137C2×C11×#41C2311yescharacteristic
138C22×D4×C11C2311yescharacteristic
139C23×C4×C11—21no—
140#67043—42no—
141#67043—42no—
142#67042—42no—
143#67042—42no—
144C2×#4343—21no—
145C2×Q8×D11—21no—
146C2×#4341—22no—
147C2×#4341—21no—
148C2×D4×D11—22no—
149C2×D4×D11—21no—
150C2×#4339C2311yescharacteristic
151C2×#4339C2311yescharacteristic
152C2×#4339C2312yes—
153C2×#4339C2312yes—
154C22×D44C2311yescharacteristic
155C22×D44C2312yes—
156C22×Dic22C2311yescharacteristic
157C22×Dic22C2312yes—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8C2312yes—
160C11×#127—21no—
161C11×#127C2312yes—
162C11×#126—22no—
163C11×#126—22no—
164C11×#125—21no—
165C11×#125C2312yes—
166C11×#124—21no—
167C11×#124—22no—
168C11×#124—22no—
169C11×#124C2312yes—
170C11×#123—22no—
171C11×#123—22no—
172C11×#123—22no—
173C11×#123—22no—
174C11×C22⋊Q8—21no—
175C11×C22⋊Q8—22no—
176C11×C22⋊Q8—22no—
177C11×C22⋊Q8C2312yes—
178C11×#121—22no—
179C11×#121—21no—
180C11×#121—22no—
181C11×#121—21no—
182C11×#121—21no—
183C11×#121—22no—
184C11×#121—22no—
185C11×#121C2312yes—
186C11×#121C2312yes—
187C11×#121C2312yes—
188C11×#120—22no—
189C11×#120—22no—
190C4×Q8×C11D411yescharacteristic
191C4×Q8×C11D411yescharacteristic
192C4×Q8×C11C2311yescharacteristic
193C4×Q8×C11C2311yescharacteristic
194C4×D4×C11—21no—
195C4×D4×C11—21no—
196C4×D4×C11—22no—
197C4×D4×C11—21no—
198C4×D4×C11—21no—
199C4×D4×C11—22no—
200C4×D4×C11D412yes—
201C4×D4×C11D411yescharacteristic
202C4×D4×C11D412yes—
203C4×D4×C11D411yescharacteristic
204C4×D4×C11C2312yes—
205C4×D4×C11C2312yes—
206C4×D4×C11C2311yescharacteristic
207C4×D4×C11C2311yescharacteristic
208C11×#117—21no—
209C11×#117—22no—
210C11×#117C2311yescharacteristic
211C11×#117C2311yescharacteristic
212C11×#117C2312yes—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C11×C22⋊C4—21no—
215C2×C42×C11—21no—
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2312yes—
218#67004—42no—
219#67003—42no—
220#67003—42no—
221#67002—42no—
222C2×#4326C2311yescharacteristic
223C2×#4326C2311yescharacteristic
224C2×#4326C2312yes—
225C2×#4325C2312yes—
226C2×#4325C2311yescharacteristic
227C2×#4325C2311yescharacteristic
228C2×#4324—42no—
229C2×#4324C2312yes—
230C2×#4324C2312yes—
231C2×#4324C2312yes—
232C2×#4324C2312yes—
233C2×#4324C2311yescharacteristic
234C2×#4324C2311yescharacteristic
235C2×#4324C2312yes—
236#66985—42no—
237#66985—42no—
238C2×#4323—42no—
239C2×#4323C2312yes—
240C2×#4323C2312yes—
241C2×#4323C2312yes—
242C2×#4323C2312yes—
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—21no—
260#66950—22no—
261#66950—22no—
262#66948—21no—
263#66948—21no—
264#66948—22no—
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—21no—
274#66928—22no—
275#66928—22no—
276#66928C2312yes—
277#66928C2312yes—
278#66928C2311yescharacteristic
279#66928C2312yes—
280#66928C2312yes—
281#66928C2311yescharacteristic
282#66927C2311yescharacteristic
283#66927C2312yes—
284C4×D44—21no—
285C4×D44—21no—
286C4×D44—22no—
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#60834—111nomaximal, Sylow
325C24×C11—21no—
326C23×D11—22no—
327C23×D11—21no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—84no—
333C2×Q8×C11—22no—
334C2×Q8×C11C2×D411yescharacteristic
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11C2×D412yes—
346C2×D4×C11C2×D411yescharacteristic
347C2×D4×C11C2412yes—
348C2×D4×C11C2411yescharacteristic
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—21no—
352C22×C4×C11—22no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—82no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D412yes—
359C22×C4×C11C2×D412yes—
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C2×C22⋊D11—22no—
363C2×C22⋊D11—21no—
364C2×C22⋊D11—22no—
365C2×C22⋊D11—21no—
366C22×Dic11—22no—
367C22×Dic11—21no—
368#4343—44no—
369Q8×D11—44no—
370#4341—48no—
371#4341—44no—
372D4×D11—48no—
373D4×D11—44no—
374#4339—22no—
375#4339—22no—
376#4339—22no—
377#4339—22no—
378#4339—42no—
379#4339—42no—
380#4339—42no—
381#4339—42no—
382C2×D44—22no—
383C2×D44—21no—
384C2×D44—21no—
385C2×D44—22no—
386C2×D44—21no—
387C2×D44—22no—
388C2×D44—22no—
389C2×D44—22no—
390C2×D44—42no—
391C2×D44—42no—
392C2×D44C2411yescharacteristic
393C2×D44C2412yes—
394C2×D44C2411yescharacteristic
395C2×C4×D11—22no—
396C2×C4×D11—21no—
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×Dic22—22no—
400C2×Dic22—21no—
401C2×Dic22—22no—
402C2×Dic22—22no—
403C2×Dic22—42no—
404C2×Dic22—42no—
405C2×Dic22C2411yescharacteristic
406C2×Dic22C2412yes—
407C2×Dic22C2411yescharacteristic
408C11×C4⋊C4—21no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2×D412yes—
418C11×C4⋊C4C2×D412yes—
419C11×C4⋊C4C2412yes—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4C2×D412yes—
434C11×C22⋊C4C2×D412yes—
435C11×C22⋊C4C2×D412yes—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—21no—
439C42×C11C2×D411yescharacteristic
440C42×C11C2×D412yes—
441C42×C11C2×D411yescharacteristic
442C42×C11C2×D412yes—
443C42×C11C2412yes—
444C42×C11C2411yescharacteristic
445C42×C11C2411yescharacteristic
446#4326—41no—
447#4326—41no—
448#4326—42no—
449#4325—42no—
450#4325—41no—
451#4325—41no—
452#4324—42no—
453#4324—42no—
454#4324—42no—
455#4324—42no—
456#4324—41no—
457#4324—41no—
458#4324—42no—
459#4323—42no—
460#4323—42no—
461#4323—42no—
462#4323—42no—
463#4323—42no—
464#4323—41no—
465#4323—41no—
466(C2×D11)⋊C4—21no—
467(C2×D11)⋊C4—21no—
468(C2×D11)⋊C4—21no—
469(C2×D11)⋊C4—22no—
470(C2×D11)⋊C4—21no—
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—
476(C2×D11)⋊C4—22no—
477(C2×D11)⋊C4—22no—
478C4⋊Dic11—21no—
479C4⋊Dic11—22no—
480C4⋊Dic11—21no—
481C4⋊Dic11—22no—
482#4318—22no—
483#4318—22no—
484C2×C11⋊C8—22no—
485C2×C11⋊C8—22no—
486C2×C11⋊C8C2411yescharacteristic
487C2×C11⋊C8C2411yescharacteristic
488C2×C11⋊C8C2412yes—
489C2×C11⋊C8C2412yes—
490C2×C11⋊C8C2411yescharacteristic
491C2×C11⋊C8C2411yescharacteristic
492#3500—111no—
493#3460D1111yescharacteristic, complemented
494#3225—112no—
495#3224—112no—
496#3221—112no—
497#3220—112no—
498#3219—112no—
499#3213—112no—
500#3211—112no—
501#3207—112no—
502#3155—111no—
503#3154—111no—
504#3137—111no—
505#3136—111no—
506#3040—111no—
507#3036—111no—
508#3035—111no—
509C2×#463—111no—
510#3013—111no—
511#3012—111no—
512#3010—111no—
513#3008—111no—
514#2925—111no—
515C23×C11—22no—
516C23×C11—21no—
517C23×C11—42no—
518C23×C11—81no—
519C23×C11—81no—
520C23×C11C22×D412yes—
521C23×C11C22×D411yescharacteristic
522C22×D11—21no—
523C22×D11—22no—
524C22×D11—21no—
525C22×D11—44no—
526C22×D11—42no—
527C22×D11—81no—
528C22×D11—82no—
529C22×D11—81no—
530C22×D11—82no—
531Q8×C11—22no—
532Q8×C11—21no—
533Q8×C11—21no—
534Q8×C11—82no—
535D4×C11—24no—
536D4×C11—22no—
537D4×C11—22no—
538D4×C11—22no—
539D4×C11—21no—
540D4×C11—21no—
541D4×C11—42no—
542D4×C11—42no—
543D4×C11—82no—
544D4×C11—82no—
545D4×C11—82no—
546D4×C11—82no—
547D4×C11—82no—
548C2×C4×C11—22no—
549C2×C4×C11—22no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—22no—
554C2×C4×C11—41no—
555C2×C4×C11—41no—
556C2×C4×C11—42no—
557C2×C4×C11—42no—
558C2×C4×C11—44no—
559C2×C4×C11—42no—
560C2×C4×C11—42no—
561C2×C4×C11—81no—
562C2×C4×C11—82no—
563C2×C4×C11—81no—
564C2×C4×C11C22×D411yescharacteristic
565C2×C4×C11C22×D412yes—
566C2×C4×C11C22×D411yescharacteristic
567C2×C4×C11C22×D412yes—
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11C22×D412yes—
571C2×C4×C11C22×D411yescharacteristic
572C2×C4×C11H(5,𝔽2)12yes—
573C2×C4×C11H(5,𝔽2)12yes—
574C2×C4×C11C2511yescharacteristic
575C22⋊D11—44no—
576C22⋊D11—44no—
577C22⋊D11—42no—
578C22⋊D11—42no—
579C2×Dic11—21no—
580C2×Dic11—22no—
581C2×Dic11—21no—
582C2×Dic11—44no—
583C2×Dic11—42no—
584D44—22no—
585D44—21no—
586D44—21no—
587D44—22no—
588D44—21no—
589D44—21no—
590D44—44no—
591D44—42no—
592D44—81no—
593D44—82no—
594D44—81no—
595D44—82no—
596C4×D11—44no—
597C4×D11—44no—
598C4×D11—42no—
599C4×D11—42no—
600Dic22—22no—
601Dic22—21no—
602Dic22—21no—
603Dic22—22no—
604Dic22—21no—
605Dic22—21no—
606Dic22—44no—
607Dic22—42no—
608C11⋊C8—21no—
609C11⋊C8—21no—
610C11⋊C8—21no—
611C11⋊C8—21no—
612C11⋊C8—22no—
613C11⋊C8—22no—
614C2×2−1+4—111no—
615C2×H(5,𝔽2)—111no—
616C2×#137—111no—
617C2×AGL(1,ℤ/8)—111no—
618C2×AGL(1,ℤ/8)—111no—
619C2×AGL(1,ℤ/8)—111no—
620C2×#135—111no—
621C2×#135—111no—
622C22×SD16—111no—
623C22×D8—111no—
624#548—221no—
625#548—221no—
626#546—222no—
627#546—221no—
628#546—222no—
629#546—221no—
630#544C2×D1111yescharacteristic, complemented
631#542—21no—
632#542C2×D1112yescomplemented
633#540—21no—
634#540C2×D1112yescomplemented
635#538—22no—
636#537C2×D1111yescharacteristic
637#536—111no—
638#536—112no—
639#535—111no—
640#535—112no—
641#535C2×D1111yescharacteristic
642#535C2×D1111yescharacteristic, complemented
643#532—21no—
644#532—111no—
645#532—112no—
646#532C2×D1112yescomplemented
647#529—21no—
648#529C2×D1112yescomplemented
649C2×#124—111no—
650C2×#124—112no—
651#525—22no—
652C4×#41C2×D1111yescharacteristic
653C4×#41C2×D1111yescharacteristic, complemented
654C2×C4×D4C2×D1111yescharacteristic, complemented
655#497—112no—
656#496—112no—
657#496—112no—
658#496—112no—
659#495—112no—
660#495—112no—
661#493—112no—
662#492—112no—
663#491—112no—
664#490—112no—
665#489—112no—
666#489—112no—
667#488—112no—
668#488—112no—
669#487—112no—
670#486—112no—
671#464—111no—
672#464—112no—
673#464—111no—
674#464—112no—
675#463—111no—
676#463—112no—
677#463—112no—
678#463—112no—
679#463—112no—
680#463—111no—
681#463—112no—
682#463—112no—
683#463—112no—
684#463—112no—
685#462—111no—
686#461—111no—
687#461—112no—
688#460—111no—
689#459—111no—
690#459—112no—
691#452—112no—
692#452—112no—
693#451—112no—
694#450—112no—
695#449—112no—
696#449—112no—
697#449—112no—
698#449—112no—
699#449—112no—
700#449—112no—
701#448—112no—
702#448—112no—
703#448—112no—
704#447—112no—
705#447—112no—
706#447—112no—
707#433—112no—
708#433—112no—
709#432—112no—
710#431—112no—
711#423—111no—
712C2×C4⋊C8—111no—
713#419—111no—
714#418—111no—
715#417—111no—
716#417—111no—
717#416—111no—
718#416—111no—
719C2×#103—111no—
720C2×#102—111no—
721#408—111no—
722#408—111no—
723#405—111no—
724#405—111no—
725C22×C11—21no—
726C22×C11—21no—
727C22×C11—22no—
728C22×C11—22no—
729C22×C11—22no—
730C22×C11—41no—
731C22×C11—42no—
732C22×C11—42no—
733C22×C11—41no—
734C22×C11—41no—
735C22×C11—42no—
736C22×C11—84no—
737C22×C11#53512yes—
738C22×C11C23×D411yescharacteristic
739C2×D11—42no—
740C2×D11—41no—
741C2×D11—41no—
742C2×D11—42no—
743C2×D11—41no—
744C2×D11—41no—
745C2×D11—41no—
746C2×D11—42no—
747C2×D11—41no—
748C2×D11—162no—
749C2×D11—164no—
750C4×C11—21no—
751C4×C11—21no—
752C4×C11—22no—
753C4×C11—21no—
754C4×C11—21no—
755C4×C11—22no—
756C4×C11—22no—
757C4×C11—41no—
758C4×C11—42no—
759C4×C11—41no—
760C4×C11—41no—
761C4×C11#53512yes—
762C4×C11C2×H(5,𝔽2)11yescharacteristic
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764Dic11—42no—
765Dic11—41no—
766Dic11—41no—
7672−1+4—442no—
7682−1+4—442no—
769H(5,𝔽2)—442no—
770H(5,𝔽2)—442no—
771C2×#41—22no—
772C2×#41—111no—
773C2×#41—111no—
774C2×#41—112no—
775C2×#41—112no—
776C2×#41—221no—
777C2×#41—222no—
778C2×#41—221no—
779C2×#41C22×D1111yescharacteristic
780C2×#41C22×D1111yescharacteristic
781C22×Q8—111no—
782C22×Q8—112no—
783C22×Q8—221no—
784C22×D4—111no—
785C22×D4—112no—
786C22×D4—222no—
787C22×D4—221no—
788C22×D4C22×D1111yescharacteristic
789C23×C4—21no—
790#137—442no—
791AGL(1,ℤ/8)—442no—
792AGL(1,ℤ/8)—442no—
793AGL(1,ℤ/8)—442no—
794#135—442no—
795#135—442no—
796C2×Q16—111no—
797C2×Q16—111no—
798C2×Q16—112no—
799C2×SD16—111no—
800C2×SD16—111no—
801C2×SD16—112no—
802C2×SD16—112no—
803C2×SD16—112no—
804C2×SD16—111no—
805C2×SD16—111no—
806C2×SD16—112no—
807C2×SD16—112no—
808C2×SD16—112no—
809C2×SD16—442no—
810C2×D8—112no—
811C2×D8—112no—
812C2×D8—111no—
813C2×D8—111no—
814C2×D8—112no—
815C2×D8—112no—
816C2×D8—112no—
817C2×D8—442no—
818C2×M16—111no—
819C2×M16—111no—
820C22×C8—111no—
821C22×C8—111no—
822C4⋊Q8—21no—
823C4⋊Q8—111no—
824C4⋊Q8—112no—
825C4⋊Q8C22×D1112yes—
826#127—21no—
827#127—111no—
828#127—112no—
829#127C22×D1112yes—
830#126—22no—
831#126—22no—
832#125—21no—
833#125C22×D1112yes—
834#124—21no—
835#124—22no—
836#124—22no—
837#124—112no—
838#124—111no—
839#124—112no—
840#124—112no—
841#124—112no—
842#124—111no—
843#124—221no—
844#124—221no—
845#124—222no—
846#124—222no—
847#124C22×D1112yes—
848#123—22no—
849#123—22no—
850#123—22no—
851#123—22no—
852#123—222no—
853#123—222no—
854#123—222no—
855C22⋊Q8—21no—
856C22⋊Q8—22no—
857C22⋊Q8—22no—
858C22⋊Q8—221no—
859C22⋊Q8—221no—
860C22⋊Q8—222no—
861C22⋊Q8—222no—
862C22⋊Q8C22×D1112yes—
863#121—22no—
864#121—21no—
865#121—22no—
866#121—21no—
867#121—21no—
868#121—22no—
869#121—22no—
870#121—221no—
871#121—221no—
872#121—222no—
873#121—222no—
874#121—221no—
875#121—221no—
876#121—222no—
877#121—222no—
878#121C22×D1112yes—
879#121C22×D1112yes—
880#121C22×D1112yes—
881#120—22no—
882#120—22no—
883#120—222no—
884#120—222no—
885#120—222no—
886C4×Q8C22⋊D1111yescharacteristic
887C4×Q8C22⋊D1111yescharacteristic
888C4×Q8C22×D1111yescharacteristic
889C4×Q8C22×D1111yescharacteristic
890C4×D4—21no—
891C4×D4—21no—
892C4×D4—22no—
893C4×D4—21no—
894C4×D4—21no—
895C4×D4—22no—
896C4×D4—221no—
897C4×D4—221no—
898C4×D4—222no—
899C4×D4—222no—
900C4×D4C22⋊D1112yes—
901C4×D4C22⋊D1111yescharacteristic
902C4×D4C22⋊D1112yes—
903C4×D4C22⋊D1111yescharacteristic
904C4×D4C22×D1112yes—
905C4×D4C22×D1112yes—
906C4×D4C22×D1111yescharacteristic
907C4×D4C22×D1111yescharacteristic
908#117—21no—
909#117—22no—
910#117C22×D1111yescharacteristic
911#117C22×D1111yescharacteristic
912#117C22×D1112yes—
913C2×C4⋊C4C22×D1111yescharacteristic
914C2×C22⋊C4—21no—
915C2×C22⋊C4—221no—
916C2×C22⋊C4—221no—
917C2×C22⋊C4—222no—
918C2×C22⋊C4—222no—
919C2×C42—21no—
920C2×C42C22×D1111yescharacteristic
921C2×C42C22×D1112yes—
922C4⋊C8—111no—
923C4⋊C8—111no—
924C4⋊C8—111no—
925C4⋊C8—111no—
926C4⋊C8—112no—
927C4⋊C8—112no—
928#103—112no—
929#103—112no—
930#103—111no—
931#103—111no—
932#103—111no—
933#103—111no—
934#103—112no—
935#103—112no—
936#103—112no—
937#103—112no—
938#102—112no—
939#102—112no—
940#102—111no—
941#102—111no—
942#102—111no—
943#102—111no—
944#102—112no—
945#102—112no—
946#102—112no—
947#102—112no—
948C22⋊C8—112no—
949C22⋊C8—112no—
950C22⋊C8—112no—
951C22⋊C8—112no—
952#97—112no—
953#97—112no—
954C4×C8—112no—
955C4×C8—112no—
956C2×C11—22no—
957C2×C11—42no—
958C2×C11—81no—
959C2×C11—82no—
960C2×C11C2×#53511yescharacteristic
961C2×C11#358411yescharacteristic
962C2×C11#358511yescharacteristic
963D11—81no—
964D11—82no—
965D11—81no—
966C24—21no—
967C24—222no—
968C24—221no—
969#41—22no—
970#41—22no—
971#41—22no—
972#41—22no—
973#41—84no—
974#41—222no—
975#41—222no—
976#41—222no—
977#41—222no—
978#41—442no—
979#41—442no—
980#41—442no—
981#41—442no—
982#41—448no—
983#41—444no—
984#41—444no—
985C2×Q8—22no—
986C2×Q8—112no—
987C2×Q8—111no—
988C2×Q8—111no—
989C2×Q8—222no—
990C2×Q8—221no—
991C2×Q8—222no—
992C2×Q8—222no—
993C2×Q8—442no—
994C2×Q8—442no—
995C2×Q8—444no—
996C2×Q8C2×C22⋊D1111yescharacteristic
997C2×Q8C23×D1111yescharacteristic
998C2×D4—21no—
999C2×D4—22no—
1000C2×D4—22no—
1001C2×D4—22no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—112no—
1008C2×D4—111no—
1009C2×D4—111no—
1010C2×D4—222no—
1011C2×D4—221no—
1012C2×D4—222no—
1013C2×D4—221no—
1014C2×D4—222no—
1015C2×D4—222no—
1016C2×D4—222no—
1017C2×D4—221no—
1018C2×D4—221no—
1019C2×D4—222no—
1020C2×D4—221no—
1021C2×D4—222no—
1022C2×D4—442no—
1023C2×D4—442no—
1024C2×D4—448no—
1025C2×D4—444no—
1026C2×D4C2×C22⋊D1112yes—
1027C2×D4C2×C22⋊D1111yescharacteristic
1028C2×D4C23×D1112yes—
1029C2×D4C23×D1111yescharacteristic
1030C22×C4—21no—
1031C22×C4—21no—
1032C22×C4—21no—
1033C22×C4—22no—
1034C22×C4—21no—
1035C22×C4—22no—
1036C22×C4—82no—
1037C22×C4—222no—
1038C22×C4—221no—
1039C22×C4—222no—
1040C22×C4—221no—
1041C22×C4—222no—
1042C22×C4—221no—
1043C22×C4C2×C22⋊D1111yescharacteristic
1044C22×C4C2×C22⋊D1111yescharacteristic
1045C22×C4C2×C22⋊D1112yes—
1046C22×C4C2×C22⋊D1112yes—
1047C22×C4C23×D1112yes—
1048C22×C4C23×D1111yescharacteristic
1049Q16—441no—
1050Q16—441no—
1051Q16—442no—
1052SD16—442no—
1053SD16—442no—
1054SD16—441no—
1055SD16—441no—
1056SD16—442no—
1057SD16—442no—
1058SD16—442no—
1059SD16—441no—
1060SD16—441no—
1061SD16—442no—
1062D8—442no—
1063D8—442no—
1064D8—441no—
1065D8—441no—
1066D8—442no—
1067D8—442no—
1068D8—442no—
1069M16—222no—
1070M16—222no—
1071C2×C8—111no—
1072C2×C8—111no—
1073C2×C8—112no—
1074C2×C8—112no—
1075C2×C8—111no—
1076C2×C8—111no—
1077C2×C8—222no—
1078C2×C8—222no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—221no—
1087C4⋊C4—222no—
1088C4⋊C4—221no—
1089C4⋊C4—222no—
1090C4⋊C4C2×C22⋊D1111yescharacteristic
1091C4⋊C4C2×C22⋊D1111yescharacteristic
1092C4⋊C4C2×C22⋊D1112yes—
1093C4⋊C4C2×C22⋊D1112yes—
1094C4⋊C4C23×D1112yes—
1095C4⋊C4C23×D1111yescharacteristic
1096C4⋊C4C23×D1111yescharacteristic
1097C22⋊C4—21no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—21no—
1102C22⋊C4—21no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—22no—
1108C22⋊C4—222no—
1109C22⋊C4—221no—
1110C22⋊C4—222no—
1111C22⋊C4—221no—
1112C22⋊C4—222no—
1113C22⋊C4—222no—
1114C22⋊C4—222no—
1115C22⋊C4—222no—
1116C22⋊C4—222no—
1117C22⋊C4—222no—
1118C22⋊C4—221no—
1119C22⋊C4—221no—
1120C22⋊C4C2×C22⋊D1112yes—
1121C22⋊C4C2×C22⋊D1112yes—
1122C22⋊C4C2×C22⋊D1112yes—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42C2×C22⋊D1111yescharacteristic
1127C42C2×C22⋊D1112yes—
1128C42C2×C22⋊D1111yescharacteristic
1129C42C2×C22⋊D1112yes—
1130C42C23×D1112yes—
1131C42C23×D1111yescharacteristic
1132C42C23×D1111yescharacteristic
1133C11#6083411yescharacteristic, complemented, Sylow
1134C23—22no—
1135C23—21no—
1136C23—42no—
1137C23—81no—
1138C23—81no—
1139C23—222no—
1140C23—221no—
1141C23—221no—
1142C23—444no—
1143C23—442no—
1144C23—881no—
1145C23—881no—
1146C23—882no—
1147C23—882no—
1148C23C22×C22⋊D1112yes—
1149C23C22×C22⋊D1111yescharacteristic
1150Q8—22no—
1151Q8—21no—
1152Q8—21no—
1153Q8—82no—
1154Q8—222no—
1155Q8—221no—
1156Q8—221no—
1157Q8—222no—
1158Q8—221no—
1159Q8—221no—
1160Q8—444no—
1161Q8—442no—
1162D4—24no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—21no—
1167D4—21no—
1168D4—42no—
1169D4—42no—
1170D4—82no—
1171D4—82no—
1172D4—82no—
1173D4—82no—
1174D4—82no—
1175D4—222no—
1176D4—221no—
1177D4—221no—
1178D4—222no—
1179D4—221no—
1180D4—221no—
1181D4—444no—
1182D4—444no—
1183D4—444no—
1184D4—442no—
1185D4—442no—
1186D4—442no—
1187D4—881no—
1188D4—882no—
1189D4—881no—
1190D4—882no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—44no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—81no—
1205C2×C4—82no—
1206C2×C4—81no—
1207C2×C4—222no—
1208C2×C4—221no—
1209C2×C4—221no—
1210C2×C4—444no—
1211C2×C4—444no—
1212C2×C4—444no—
1213C2×C4—442no—
1214C2×C4—442no—
1215C2×C4—442no—
1216C2×C4#6704212yes—
1217C2×C4#6704212yes—
1218C2×C4C22×C22⋊D1111yescharacteristic
1219C2×C4C22×C22⋊D1111yescharacteristic
1220C2×C4C22×C22⋊D1111yescharacteristic
1221C2×C4C22×C22⋊D1112yes—
1222C2×C4C22×C22⋊D1112yes—
1223C2×C4C22×C22⋊D1111yescharacteristic
1224C2×C4C22×C22⋊D1112yes—
1225C2×C4C22×C22⋊D1111yescharacteristic
1226C2×C4C24×D1111yescharacteristic
1227C8—221no—
1228C8—221no—
1229C8—221no—
1230C8—221no—
1231C8—222no—
1232C8—222no—
1233C22—21no—
1234C22—21no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—42no—
1239C22—41no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—42no—
1244C22—84no—
1245C22—441no—
1246C22—442no—
1247C22—441no—
1248C22—441no—
1249C22—442no—
1250C22—441no—
1251C22—441no—
1252C22—442no—
1253C22—441no—
1254C22—1762no—
1255C22—1764no—
1256C22#1062336112yes—
1257C22C23×C22⋊D1111yescharacteristic
1258C4—21no—
1259C4—21no—
1260C4—22no—
1261C4—22no—
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—441no—
1270C4—442no—
1271C4—441no—
1272C4#1062336112yes—
1273C4C2×#6704211yescharacteristic
1274C4C2×#6704211yescharacteristic
1275C2—22no—
1276C2—42no—
1277C2—82no—
1278C2—81no—
1279C2—882no—
1280C2—881no—
1281C2—881no—
1282C2C2×#1062336111yescharacteristic
1283C2#1308338711yescharacteristic
1284C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3460C2
socleC22×C11C23×D4
hypercenter#3460D11
hypocenterC11#60834
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #13082409C2semidirect
2. #13079719C2semidirect
3. #13079704C2semidirect
4. #13079671C2semidirect
5. #13079660C2semidirect
6. #13079649C2semidirect
7. #13079599C2semidirect
8. #13079577C2semidirect
9. #13079545C2semidirect
10. #13079099C2semidirect
11. #13079088C2semidirect
12. #13078986C2semidirect
13. #13078975C2semidirect
14. #13078110C2semidirect
15. #13078080C2semidirect
16. #13078071C2semidirect
17. C2×#10622629C2semidirect
18. #13077928C2semidirect
19. #13077917C2semidirect
20. #13077900C2semidirect
21. #13077882C2semidirect
22. #13077282C2semidirect
23. C11×#3460C2semidirect
26. C11×#544C22semidirect
28. C11×#542C22semidirect
30. C11×#540C22semidirect
34. C11×#535C22semidirect
36. C11×#532C22semidirect
38. C11×#529C22semidirect
41. C4×C11×#41C22semidirect
42. C2×C4×D4×C11C22semidirect
43. C2×#67004C22semidirect
45. C2×#67003C22semidirect
47. C22×#4324C22semidirect
49. C2×#66985C22semidirect
58. #10623057C22semidirect
60. #10623056C22semidirect
62. #10623008C22semidirect
64. C2×#66928C22semidirect
67. #10622706C22semidirect
68. #10622702C22semidirect
69. #10622702C22semidirect
70. #10622701C22semidirect
71. #10622689C22semidirect
72. #10622687C22semidirect
73. #10622687C22semidirect
74. #10622686C22semidirect
75. #10622682C22semidirect
76. #10622681C22semidirect
77. #10622681C22semidirect
78. #10622680C22semidirect
79. #10622673C22semidirect
80. #10622672C22semidirect
81. #10622672C22semidirect
82. #10622671C22semidirect
83. #10622663C22semidirect
84. #10622660C22semidirect
85. #10622660C22semidirect
86. #10622659C22semidirect
87. #10622653C22semidirect
88. #10622653C22semidirect
89. #10622653C22semidirect
92. #10622650C22semidirect
93. #10622650C22semidirect
94. #10622650C22semidirect
95. #10622650C22semidirect
98. #10622649C22semidirect
99. #10622644C22semidirect
100. #10622641C22semidirect
101. #10622641C22semidirect
102. #10622641C22semidirect
103. #10622641C22semidirect
104. #10622640C22semidirect
105. #10622632C22semidirect
106. #10622632C22semidirect
107. #10622629C22semidirect
108. #10622629C22semidirect
109. #10622629C22semidirect
110. #10622629C22semidirect
111. #10622629C22semidirect
112. #10622629C22semidirect
113. #10622629C22semidirect
114. #10622629C22semidirect
115. #10622629C22semidirect
116. #10622629C22semidirect
117. #10622628C22semidirect
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
493. #3460D11semidirect
630. #544C2×D11semidirect
632. #542C2×D11semidirect
634. #540C2×D11semidirect
642. #535C2×D11semidirect
646. #532C2×D11semidirect
648. #529C2×D11semidirect
653. C4×#41C2×D11semidirect
654. C2×C4×D4C2×D11semidirect
1133. C11#60834semidirect

Maximal subgroups

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

subgroupindex
#130824092
#130797192
#130797042
#130796712
#130796602
#130796492
#130795992
#130795772
#130795452
#130790992
#130790882
#130789862
#130789752
#130781102
#130780802
#130780712
C2×#106226292
#130779282
#130779172
#130779002
#130778822
#130772822
C11×#34602
#6083411