Finite Group Databasebeta

← #15618689

Subgroups — #15618689

Order 2816.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D44C211yesmaximal, characteristic
2#13077694C212yesmaximal, complemented
3#13077686C212yesmaximal, complemented
4#13077677C212yesmaximal, complemented
5#13077671C212yesmaximal, complemented
6#13077662C212yesmaximal, complemented
7#13077662C212yesmaximal, complemented
8#13077653C212yesmaximal, complemented
9#13077644C212yesmaximal, complemented
10#13077362C211yesmaximal, characteristic, complemented
11M16×D44C211yesmaximal, characteristic, complemented
12#13077340C211yesmaximal, characteristic, complemented
13#13077340C211yesmaximal, characteristic, complemented
14#13077335C211yesmaximal, characteristic, complemented
15#13077318C211yesmaximal, characteristic, complemented
16#13077309C211yesmaximal, characteristic, complemented
17C2×#10622319C211yesmaximal, characteristic, complemented
18#13077282C211yesmaximal, characteristic, complemented
19#13077064C211yesmaximal, characteristic, complemented
20#13077064C211yesmaximal, characteristic, complemented
21#13077058C211yesmaximal, characteristic, complemented
22D11×#408C211yesmaximal, characteristic, complemented
23C11×#2923C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C4×C11×#41C2211yescharacteristic
27C2×#66960C2211yescharacteristic, complemented
28C2×#66960C2211yescharacteristic, complemented
29C2×M16×D11C2211yescharacteristic, complemented
30C2×M16×D11C2211yescharacteristic, complemented
31C2×#66954C2211yescharacteristic, complemented
32C2×#66954C2211yescharacteristic, complemented
33C22×#4313C2211yescharacteristic, complemented
34C22×C8×D11C2211yescharacteristic, complemented
35#10623108C411yescharacteristic
36#10623107C411yescharacteristic
37#10623107C411yescharacteristic
38Q8×D44C411yescharacteristic
39#10623086C411yescharacteristic
40#10623086C412yes—
41#10623085C411yescharacteristic
42#10623085C411yescharacteristic
43#10623085C412yes—
44#10623085C412yes—
45D4×D44C411yescharacteristic
46D4×D44C412yes—
47#10623055C2211yescharacteristic
48#10623055C2211yescharacteristic
49#10623055C2212yes—
50#10623055C2212yes—
51#10623008C2211yescharacteristic
52#10623008C2212yes—
53C2×C4×D44C2211yescharacteristic
54C2×C4×D44C2212yes—
55C11×#433C2212yescomplemented
56C11×#433C2212yescomplemented
57C11×#432C2212yescomplemented
58C11×#432C2212yescomplemented
59C11×#424C2211yescharacteristic, complemented
60C11×#424C2211yescharacteristic, complemented
61C11×#408C2211yescharacteristic
62C11×#408C2211yescharacteristic
63C4×C11×M16C2211yescharacteristic, complemented
64C2×C11×#97C2211yescharacteristic, complemented
65#10622847C2211yescharacteristic
66#10622847C2211yescharacteristic
67#10622742C2211yescharacteristic, complemented
68#10622742C2211yescharacteristic, complemented
69#10622739C2211yescharacteristic, complemented
70#10622739C2211yescharacteristic, complemented
71#10622723C2211yescharacteristic, complemented
72#10622723C2211yescharacteristic, complemented
73C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
74C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
75#10622613C2212yescomplemented
76#10622613C2212yescomplemented
77#10622610C2211yescharacteristic, complemented
78#10622610C2211yescharacteristic, complemented
79#10622539C2212yescomplemented
80#10622538C2212yescomplemented
81#10622537C2211yescharacteristic, complemented
82C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
83#10622451C2212yescomplemented
84#10622451C2212yescomplemented
85#10622451C2212yescomplemented
86#10622451C2212yescomplemented
87#10622449C2212yescomplemented
88#10622449C2212yescomplemented
89#10622449C2212yescomplemented
90#10622449C2212yescomplemented
91#10622449C2212yescomplemented
92#10622449C2212yescomplemented
93#10622449C2212yescomplemented
94#10622449C2212yescomplemented
95#10622447C2212yescomplemented
96#10622447C2212yescomplemented
97#10622447C2212yescomplemented
98#10622447C2212yescomplemented
99#10622340C2212yescomplemented
100#10622340C2212yescomplemented
101#10622340C2212yescomplemented
102#10622340C2212yescomplemented
103#10622340C2212yescomplemented
104#10622340C2212yescomplemented
105#10622340C2212yescomplemented
106#10622340C2212yescomplemented
107#10622339C2212yescomplemented
108#10622339C2212yescomplemented
109#10622339C2212yescomplemented
110#10622339C2212yescomplemented
111D11×C22⋊C8C2212yescomplemented
112D11×C22⋊C8C2212yescomplemented
113D11×C22⋊C8C2212yescomplemented
114D11×C22⋊C8C2212yescomplemented
115#10622319C2211yescharacteristic
116#10622319C2211yescharacteristic
117#10622319C2212yes—
118#10622319C2211yescharacteristic, complemented
119#10622319C2211yescharacteristic, complemented
120#10622319C2211yescharacteristic, complemented
121#10622319C2211yescharacteristic, complemented
122#10622319C2211yescharacteristic, complemented
123#10622319C2211yescharacteristic, complemented
124#10622319C2212yescomplemented
125#10622319C2212yescomplemented
126#10622319C2212yescomplemented
127#10622319C2212yescomplemented
128#10622319C2212yescomplemented
129#10622319C2212yescomplemented
130#10622319C2212yescomplemented
131#10622301C2212yescomplemented
132#10622301C2212yescomplemented
133C8×D44C2212yescomplemented
134C8×D44C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136#41×D11—42no—
137#41×D11—42no—
138#41×D11—42no—
139#41×D11—42no—
140C2×#4343C2×C411yescharacteristic
141C2×#4343C2×C411yescharacteristic
142C2×Q8×D11C2×C411yescharacteristic
143C2×Q8×D11C2×C411yescharacteristic
144C2×#4341C2×C411yescharacteristic
145C2×#4341C2×C411yescharacteristic
146C2×#4341C2×C412yes—
147C2×#4341C2×C412yes—
148C2×D4×D11C2×C411yescharacteristic
149C2×D4×D11C2×C411yescharacteristic
150C2×D4×D11C2×C412yes—
151C2×D4×D11C2×C412yes—
152C2×#4339C2311yescharacteristic
153C2×#4339C2311yescharacteristic
154C2×#4339C2312yes—
155C2×#4339C2312yes—
156C22×D44C2×C411yescharacteristic
157C22×D44C2×C412yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×C4×D11C2312yes—
162C2×C11×M16C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C22×C8×C11C2311yescharacteristic
165C22×C8×C11C2311yescharacteristic
166C4×Q8×C11C2×C411yescharacteristic
167C4×Q8×C11C2×C411yescharacteristic
168C4×D4×C11C2×C412yes—
169C4×D4×C11C2×C411yescharacteristic
170C4×D4×C11C2×C412yes—
171C4×D4×C11C2×C411yescharacteristic
172C11×#117C2311yescharacteristic
173C11×#117C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176#66983C2×C412yes—
177#66983C2×C412yes—
178#66983C2×C412yes—
179#66983C2×C412yes—
180#66983C2×C412yes—
181#66983C2×C412yes—
182C2×(C2×D11)⋊C4C2×C411yescharacteristic
183C2×(C2×D11)⋊C4C2×C411yescharacteristic
184C2×(C2×D11)⋊C4C2×C412yes—
185C2×(C2×D11)⋊C4C2×C412yes—
186C2×C4⋊Dic11C2×C411yescharacteristic
187C2×C4⋊Dic11C2×C412yes—
188C2×#4318C2311yescharacteristic
189C2×#4318C2311yescharacteristic
190C22×C11⋊C8C2311yescharacteristic
191C22×C11⋊C8C2311yescharacteristic
192#66960—42no—
193#66960—42no—
194M16×D11—42no—
195M16×D11—42no—
196#66954—42no—
197#66954—42no—
198C2×#4313—42no—
199C2×#4313C2311yescharacteristic
200C2×#4313C2311yescharacteristic
201C2×#4313C2311yescharacteristic
202C2×#4313C2311yescharacteristic
203C2×#4313C2312yes—
204C2×#4313C2312yes—
205C2×#4313C2312yes—
206C2×#4313C2312yes—
207C2×#4313C2312yes—
208C2×#4313C2312yes—
209C2×C8×D11—42no—
210C2×C8×D11C2311yescharacteristic
211C2×C8×D11C2311yescharacteristic
212C2×C8×D11C2311yescharacteristic
213C2×C8×D11C2311yescharacteristic
214C2×C8×D11C2312yes—
215C2×C8×D11C2312yes—
216C2×C8×D11C2312yes—
217C2×C8×D11C2312yes—
218C2×C8×D11C2312yes—
219C2×C8×D11C2312yes—
220#66950C2×C411yescharacteristic
221#66950C2×C411yescharacteristic
222#66950C2×C412yes—
223#66950C2×C412yes—
224#66950C2×C411yescharacteristic
225#66950C2×C411yescharacteristic
226#66950C2×C412yes—
227#66950C2×C412yes—
228#66948C2×C411yescharacteristic
229#66948C2×C411yescharacteristic
230#66948C2×C412yes—
231#66948C2×C412yes—
232#66948C2×C411yescharacteristic
233#66948C2×C411yescharacteristic
234#66948C2×C412yes—
235#66948C2×C412yes—
236#66939C2×C412yes—
237#66939C2×C412yes—
238#66939C2×C412yes—
239#66939C2×C412yes—
240#66939C2×C412yes—
241#66939C2×C412yes—
242#66935C2×C412yes—
243#66935C2×C412yes—
244#66935C2×C412yes—
245#66935C2×C412yes—
246#66935C2×C412yes—
247#66935C2×C412yes—
248#66928C2×C411yescharacteristic
249#66928C2×C411yescharacteristic
250#66928C2×C412yes—
251#66928C2×C412yes—
252#66927C2×C411yescharacteristic
253#66927C2×C412yes—
254C4×D44C2×C411yescharacteristic
255C4×D44C2×C412yes—
256C4×D44C2×C411yescharacteristic
257C4×D44C2×C411yescharacteristic
258C4×D44C2×C412yes—
259C4×D44C2×C412yes—
260C4×D44C2×C411yescharacteristic
261C4×D44C2×C412yes—
262C4×D44C2311yescharacteristic
263C4×D44C2311yescharacteristic
264C4×D44C2312yes—
265C4×D44C2311yescharacteristic
266C4×D44C2311yescharacteristic
267C4×D44C2312yes—
268C4×D44C2312yes—
269C4×D44C2312yes—
270C4×D44C2312yes—
271C4×D44C2312yes—
272#66922C2×C411yescharacteristic
273#66922C2×C412yes—
274C11×C4⋊C8C2312yes—
275C11×C4⋊C8C2312yes—
276C11×C4⋊C8C2312yes—
277C11×C4⋊C8C2312yes—
278C11×C22⋊C8C2312yes—
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×C22⋊C8C2312yes—
282C11×#97C2311yescharacteristic
283C11×#97C2311yescharacteristic
284C11×#97C2312yes—
285C11×#97C2311yescharacteristic
286C11×#97C2311yescharacteristic
287C4×C8×C11C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291C22⋊(C11⋊C8)C2312yes—
292(C2×D11)⋊C8C2311yescharacteristic
293(C2×D11)⋊C8C2311yescharacteristic
294(C2×D11)⋊C8C2311yescharacteristic
295(C2×D11)⋊C8C2311yescharacteristic
296(C2×D11)⋊C8C2311yescharacteristic
297(C2×D11)⋊C8C2311yescharacteristic
298(C2×D11)⋊C8C2311yescharacteristic
299(C2×D11)⋊C8C2311yescharacteristic
300(C2×D11)⋊C8C2312yes—
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308(C2×D11)⋊C8C2312yes—
309(C2×D11)⋊C8C2312yes—
310(C2×D11)⋊C8C2312yes—
311(C2×D11)⋊C8C2312yes—
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4⋊(C11⋊C8)C2312yes—
317C4⋊(C11⋊C8)C2312yes—
318#66867C2312yes—
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321C4×C11⋊C8C2312yes—
322#60240—111nomaximal, Sylow
323C23×D11C22×C411yescharacteristic
324C23×D11C22×C411yescharacteristic
325C23×D11C22×C412yes—
326C23×D11C22×C412yes—
327C11×#41—22no—
328C11×#41—22no—
329C2×Q8×C11C22×C411yescharacteristic
330C2×D4×C11C22×C412yes—
331C2×D4×C11C22×C411yescharacteristic
332C22×C4×C11C22×C412yes—
333C22×C4×C11C22×C411yescharacteristic
334C22×C4×C11C22×C412yes—
335C22×C4×C11C22×C411yescharacteristic
336C22×C4×C11C2412yes—
337C22×C4×C11C2411yescharacteristic
338C2×C22⋊D11C22×C412yes—
339C2×C22⋊D11C22×C412yes—
340C2×C22⋊D11C22×C412yes—
341C2×C22⋊D11C22×C412yes—
342C2×C22⋊D11C22×C412yes—
343C2×C22⋊D11C22×C412yes—
344C22×Dic11C22×C411yescharacteristic
345C22×Dic11C22×C411yescharacteristic
346C22×Dic11C22×C412yes—
347C22×Dic11C22×C412yes—
348#4343—42no—
349#4343—42no—
350Q8×D11—42no—
351Q8×D11—42no—
352#4341—42no—
353#4341—42no—
354#4341—44no—
355#4341—44no—
356D4×D11—44no—
357D4×D11—44no—
358D4×D11—42no—
359D4×D11—42no—
360#4339—22no—
361#4339—22no—
362#4339—22no—
363#4339—22no—
364#4339—42no—
365#4339—42no—
366#4339—42no—
367#4339—42no—
368C2×D44—42no—
369C2×D44—44no—
370C2×D44C22×C411yescharacteristic
371C2×D44C22×C411yescharacteristic
372C2×D44C22×C412yes—
373C2×D44C22×C411yescharacteristic
374C2×D44C22×C411yescharacteristic
375C2×D44C22×C411yescharacteristic
376C2×D44C22×C412yes—
377C2×D44C22×C411yescharacteristic
378C2×D44C22×C412yes—
379C2×D44C22×C412yes—
380C2×D44C22×C412yes—
381C2×D44C22×C412yes—
382C2×D44C22×C412yes—
383C2×D44C22×C412yes—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×C4×D11—22no—
388C2×C4×D11—42no—
389C2×C4×D11—42no—
390C2×C4×D11—42no—
391C2×C4×D11—42no—
392C2×C4×D11C22×C411yescharacteristic
393C2×C4×D11C22×C411yescharacteristic
394C2×C4×D11C22×C411yescharacteristic
395C2×C4×D11C22×C411yescharacteristic
396C2×C4×D11C22×C412yes—
397C2×C4×D11C22×C412yes—
398C2×C4×D11C22×C412yes—
399C2×C4×D11C22×C412yes—
400C2×C4×D11C2411yescharacteristic
401C2×C4×D11C2411yescharacteristic
402C2×C4×D11C2411yescharacteristic
403C2×C4×D11C2412yes—
404C2×C4×D11C2412yes—
405C2×C4×D11C2411yescharacteristic
406C2×Dic22C22×C411yescharacteristic
407C2×Dic22C22×C411yescharacteristic
408C2×Dic22C22×C412yes—
409C2×Dic22C22×C412yes—
410C11×M16—22no—
411C11×M16—22no—
412C2×C8×C11—22no—
413C2×C8×C11—22no—
414C2×C8×C11C2412yes—
415C2×C8×C11C2412yes—
416C2×C8×C11C2411yescharacteristic
417C2×C8×C11C2411yescharacteristic
418C2×C8×C11C2411yescharacteristic
419C2×C8×C11C2411yescharacteristic
420C11×C4⋊C4C22×C412yes—
421C11×C4⋊C4C22×C412yes—
422C11×C4⋊C4C22×C411yescharacteristic
423C11×C4⋊C4C22×C411yescharacteristic
424C11×C22⋊C4C22×C412yes—
425C11×C22⋊C4C22×C412yes—
426C11×C22⋊C4C22×C412yes—
427C42×C11C22×C412yes—
428C42×C11C22×C411yescharacteristic
429C42×C11C22×C412yes—
430C42×C11C22×C411yescharacteristic
431C42×C11C2412yes—
432C42×C11C2411yescharacteristic
433C42×C11C2411yescharacteristic
434(C2×D11)⋊C4C22×C411yescharacteristic
435(C2×D11)⋊C4C22×C411yescharacteristic
436(C2×D11)⋊C4C22×C411yescharacteristic
437(C2×D11)⋊C4C22×C411yescharacteristic
438(C2×D11)⋊C4C22×C412yes—
439(C2×D11)⋊C4C22×C412yes—
440(C2×D11)⋊C4C22×C411yescharacteristic
441(C2×D11)⋊C4C22×C412yes—
442(C2×D11)⋊C4C22×C411yescharacteristic
443(C2×D11)⋊C4C22×C412yes—
444(C2×D11)⋊C4C22×C411yescharacteristic
445(C2×D11)⋊C4C22×C411yescharacteristic
446(C2×D11)⋊C4C22×C412yes—
447(C2×D11)⋊C4C22×C412yes—
448(C2×D11)⋊C4C22×C412yes—
449(C2×D11)⋊C4C22×C412yes—
450(C2×D11)⋊C4C22×C412yes—
451(C2×D11)⋊C4C22×C412yes—
452(C2×D11)⋊C4C22×C412yes—
453(C2×D11)⋊C4C22×C412yes—
454C4⋊Dic11C22×C412yes—
455C4⋊Dic11C22×C411yescharacteristic
456C4⋊Dic11C22×C412yes—
457C4⋊Dic11C22×C412yes—
458C4⋊Dic11C22×C412yes—
459C4⋊Dic11C22×C411yescharacteristic
460C4⋊Dic11C22×C411yescharacteristic
461C4⋊Dic11C22×C411yescharacteristic
462C4⋊Dic11C22×C412yes—
463C4⋊Dic11C22×C412yes—
464#4318—22no—
465#4318—22no—
466C2×C11⋊C8—22no—
467C2×C11⋊C8—22no—
468C2×C11⋊C8C2411yescharacteristic
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2412yes—
471C2×C11⋊C8C2412yes—
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2411yescharacteristic
474#4313—41no—
475#4313—41no—
476#4313—41no—
477#4313—41no—
478#4313—42no—
479#4313—42no—
480#4313—42no—
481#4313—42no—
482#4313—42no—
483#4313—42no—
484C8×D11—41no—
485C8×D11—41no—
486C8×D11—41no—
487C8×D11—41no—
488C8×D11—42no—
489C8×D11—42no—
490C8×D11—42no—
491C8×D11—42no—
492C8×D11—42no—
493C8×D11—42no—
494D4×#41—111no—
495#2981—112no—
496#2980—112no—
497#2978—112no—
498#2977—112no—
499#2976—112no—
500#2976—112no—
501#2974—112no—
502#2973—112no—
503#2935—111no—
504D4×M16—111no—
505#2933—111no—
506#2933—111no—
507#2932—111no—
508#2930—111no—
509#2929—111no—
510C2×#435—111no—
511#2925—111no—
512#2923D1111yescharacteristic, complemented
513#2880—111no—
514#2880—111no—
515#2879—111no—
516C2×#408—111no—
517C23×C11C23×C412yes—
518C23×C11C23×C411yescharacteristic
519C22×D11—22no—
520C22×D11—22no—
521C22×D11—22no—
522C22×D11—24no—
523C22×D11—41no—
524C22×D11—42no—
525C22×D11—42no—
526C22×D11—41no—
527C22×D11—42no—
528C22×D11—42no—
529C22×D11—41no—
530C22×D11—42no—
531C22×D11C23×C411yescharacteristic
532C22×D11C23×C411yescharacteristic
533C22×D11C23×C411yescharacteristic
534C22×D11C23×C412yes—
535C22×D11C23×C412yes—
536C22×D11C23×C411yescharacteristic
537Q8×C11—22no—
538D4×C11—24no—
539D4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—41no—
543C2×C4×C11—42no—
544C2×C4×C11—41no—
545C2×C4×C11—42no—
546C2×C4×C11C23×C411yescharacteristic
547C2×C4×C11C23×C412yes—
548C2×C4×C11C23×C411yescharacteristic
549C2×C4×C11C23×C412yes—
550C2×C4×C11C23×C411yescharacteristic
551C2×C4×C11C23×C411yescharacteristic
552C2×C4×C11C23×C412yes—
553C2×C4×C11C23×C411yescharacteristic
554C2×C4×C11H(5,𝔽2)12yes—
555C2×C4×C11H(5,𝔽2)12yes—
556C2×C4×C11C2511yescharacteristic
557C22⋊D11—24no—
558C22⋊D11—24no—
559C22⋊D11—42no—
560C22⋊D11—42no—
561C22⋊D11—42no—
562C22⋊D11—42no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—42no—
566C2×Dic11—42no—
567C2×Dic11C23×C412yes—
568C2×Dic11C23×C412yes—
569C2×Dic11C23×C411yescharacteristic
570C2×Dic11C23×C411yescharacteristic
571C2×Dic11C23×C411yescharacteristic
572C2×Dic11C23×C411yescharacteristic
573D44—22no—
574D44—22no—
575D44—24no—
576D44—22no—
577D44—22no—
578D44—41no—
579D44—42no—
580D44—41no—
581D44—42no—
582D44—42no—
583D44—42no—
584D44—42no—
585D44—42no—
586D44—42no—
587C4×D11—22no—
588C4×D11—22no—
589C4×D11—22no—
590C4×D11—22no—
591C4×D11—21no—
592C4×D11—21no—
593C4×D11—21no—
594C4×D11—21no—
595C4×D11—22no—
596C4×D11—22no—
597C4×D11—22no—
598C4×D11—22no—
599C4×D11—21no—
600C4×D11—21no—
601C4×D11—21no—
602C4×D11—21no—
603C4×D11—42no—
604C4×D11—42no—
605C4×D11—42no—
606C4×D11—42no—
607Dic22—22no—
608Dic22—22no—
609Dic22—42no—
610Dic22—42no—
611C8×C11—21no—
612C8×C11—21no—
613C8×C11—21no—
614C8×C11—21no—
615C8×C11—22no—
616C8×C11—22no—
617C11⋊C8—21no—
618C11⋊C8—21no—
619C11⋊C8—21no—
620C11⋊C8—22no—
621C11⋊C8—22no—
622C11⋊C8—21no—
623C22×#41—111no—
624C22×#41—111no—
625C2×#131—111no—
626C2×#131—111no—
627C2×#131—111no—
628C2×#131—111no—
629C22×M16—111no—
630C22×M16—111no—
631C22×M16—111no—
632C23×C8—111no—
633#550—111no—
634D4×Q8—111no—
635#548—111no—
636#548—111no—
637#547—112no—
638#547—111no—
639#546—112no—
640#546—112no—
641#546—111no—
642#546—111no—
643D42—111no—
644D42—112no—
645#532—111no—
646#532—112no—
647#525—111no—
648#525—111no—
649#525—112no—
650#525—112no—
651C4×#41C2×D1111yescharacteristic
652C2×C4×D4—111no—
653C2×C4×D4—112no—
654#436—112no—
655#436—112no—
656#436—112no—
657#436—112no—
658#436—112no—
659#436—112no—
660#435—112no—
661#435—112no—
662#435—112no—
663#435—112no—
664#435—112no—
665#435—112no—
666#435—112no—
667#435—112no—
668#435—111no—
669#435—111no—
670#435—111no—
671#435—111no—
672#435—111no—
673#435—111no—
674#435—111no—
675#435—111no—
676#435—112no—
677#435—112no—
678#435—112no—
679#435—112no—
680#435—112no—
681#435—112no—
682#435—112no—
683#435—112no—
684C8×D4—112no—
685C8×D4—112no—
686C8×D4—112no—
687C8×D4—112no—
688C8×D4—112no—
689C8×D4—112no—
690#433—112no—
691#433—112no—
692#433C2×D1112yescomplemented
693#433C2×D1112yescomplemented
694#432—112no—
695#432C2×D1112yescomplemented
696#432C2×D1112yescomplemented
697#431—112no—
698#424C2×D1111yescharacteristic, complemented
699#424C2×D1111yescharacteristic, complemented
700#423—111no—
701C2×C4⋊C8—111no—
702#408—111no—
703#408—111no—
704#408—111no—
705#408—111no—
706#408—111no—
707#408—111no—
708#408—112no—
709#408—112no—
710#408—112no—
711#408—112no—
712#408—112no—
713#408—112no—
714#408—112no—
715#408—112no—
716#408C2×D1111yescharacteristic
717#408C2×D1111yescharacteristic
718#407—111no—
719#407—111no—
720#407—112no—
721#407—112no—
722#407—112no—
723#407—112no—
724C2×C22⋊C8—111no—
725C2×C22⋊C8—111no—
726C2×C22⋊C8—112no—
727C2×C22⋊C8—112no—
728C2×C22⋊C8—112no—
729C2×C22⋊C8—112no—
730#405—111no—
731#405—111no—
732C4×M16C2×D1111yescharacteristic, complemented
733C2×#97C2×D1111yescharacteristic, complemented
734C22×C11—21no—
735C22×C11—21no—
736C22×C11—22no—
737C22×C11—22no—
738C22×C11—22no—
739C22×C11#51812yes—
740C22×C11C24×C411yescharacteristic
741C2×D11—21no—
742C2×D11—21no—
743C2×D11—21no—
744C2×D11—21no—
745C2×D11—21no—
746C2×D11—22no—
747C2×D11—22no—
748C2×D11—21no—
749C2×D11—22no—
750C2×D11—21no—
751C2×D11—21no—
752C2×D11—22no—
753C2×D11—21no—
754C2×D11—21no—
755C2×D11—21no—
756C2×D11—22no—
757C2×D11—22no—
758C2×D11—44no—
759C2×D11—84no—
760C2×D11—82no—
761C2×D11—84no—
762C2×D11#56812yes—
763C4×C11—22no—
764C4×C11—21no—
765C4×C11—21no—
766C4×C11—22no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—22no—
770C4×C11#51812yes—
771C4×C11C2×H(5,𝔽2)11yescharacteristic
772C4×C11C2×H(5,𝔽2)11yescharacteristic
773Dic11—22no—
774Dic11—22no—
775Dic11—21no—
776Dic11—21no—
777Dic11—21no—
778Dic11—21no—
779C2×#41—111no—
780C2×#41—111no—
781C2×#41—112no—
782C2×#41—112no—
783C2×#41—111no—
784C2×#41—111no—
785C2×#41—111no—
786C2×#41—111no—
787C2×#41—112no—
788C2×#41—112no—
789C2×#41—442no—
790C2×#41—442no—
791C2×#41—442no—
792C2×#41—442no—
793C2×#41C22×D1111yescharacteristic
794C22×Q8—111no—
795C22×Q8—111no—
796C22×D4—111no—
797C22×D4—111no—
798C22×D4—112no—
799C22×D4—112no—
800C22×D4—111no—
801C22×D4—112no—
802C23×C4—111no—
803C23×C4—111no—
804C23×C4—112no—
805C23×C4—112no—
806#131—442no—
807#131—442no—
808#131—442no—
809#131—442no—
810C2×M16—111no—
811C2×M16—111no—
812C2×M16—111no—
813C2×M16—111no—
814C2×M16—112no—
815C2×M16—111no—
816C2×M16—111no—
817C2×M16—112no—
818C2×M16—112no—
819C2×M16—112no—
820C2×M16—112no—
821C2×M16—112no—
822C2×M16—442no—
823C2×M16—442no—
824C2×M16—442no—
825C2×M16C22×D1111yescharacteristic
826C2×M16C22×D1111yescharacteristic
827C22×C8—111no—
828C22×C8—111no—
829C22×C8—111no—
830C22×C8—111no—
831C22×C8—111no—
832C22×C8—111no—
833C22×C8—112no—
834C22×C8—112no—
835C22×C8—112no—
836C22×C8—112no—
837C22×C8—112no—
838C22×C8—112no—
839C22×C8—442no—
840C22×C8C22×D1111yescharacteristic
841C22×C8C22×D1111yescharacteristic
842C4⋊Q8—111no—
843C4⋊Q8—112no—
844#127—111no—
845#127—112no—
846#124—111no—
847#124—111no—
848#124—112no—
849#124—112no—
850#123—112no—
851#123—112no—
852#123—112no—
853#123—112no—
854#123—112no—
855#123—112no—
856C22⋊Q8—111no—
857C22⋊Q8—111no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—111no—
861C22⋊Q8—111no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864#121—112no—
865#121—112no—
866#121—112no—
867#121—112no—
868#121—112no—
869#121—112no—
870#121—111no—
871#121—111no—
872#121—112no—
873#121—112no—
874#121—111no—
875#121—111no—
876#121—112no—
877#121—112no—
878#120—112no—
879#120—112no—
880#120—112no—
881#120—112no—
882#120—112no—
883#120—112no—
884C4×Q8C4×D1111yescharacteristic
885C4×Q8C4×D1111yescharacteristic
886C4×D4—111no—
887C4×D4—112no—
888C4×D4—111no—
889C4×D4—111no—
890C4×D4—112no—
891C4×D4—112no—
892C4×D4—111no—
893C4×D4—112no—
894C4×D4—111no—
895C4×D4—112no—
896C4×D4—111no—
897C4×D4—112no—
898C4×D4—111no—
899C4×D4—111no—
900C4×D4—112no—
901C4×D4—112no—
902C4×D4—112no—
903C4×D4—112no—
904C4×D4C4×D1112yes—
905C4×D4C4×D1111yescharacteristic
906C4×D4C4×D1112yes—
907C4×D4C4×D1111yescharacteristic
908#117C22×D1111yescharacteristic
909#117C22×D1112yes—
910C2×C4⋊C4—111no—
911C2×C4⋊C4—112no—
912C2×C22⋊C4—111no—
913C2×C22⋊C4—111no—
914C2×C22⋊C4—112no—
915C2×C22⋊C4—112no—
916C2×C42C22×D1111yescharacteristic
917C2×C42C22×D1112yes—
918C4⋊C8—111no—
919C4⋊C8—111no—
920C4⋊C8—111no—
921C4⋊C8—111no—
922C4⋊C8—112no—
923C4⋊C8—112no—
924C4⋊C8C22×D1112yes—
925C4⋊C8C22×D1112yes—
926C4⋊C8C22×D1112yes—
927C4⋊C8C22×D1112yes—
928C22⋊C8—112no—
929C22⋊C8—112no—
930C22⋊C8—112no—
931C22⋊C8—112no—
932C22⋊C8—111no—
933C22⋊C8—111no—
934C22⋊C8—111no—
935C22⋊C8—112no—
936C22⋊C8—111no—
937C22⋊C8—112no—
938C22⋊C8—111no—
939C22⋊C8—112no—
940C22⋊C8—111no—
941C22⋊C8—111no—
942C22⋊C8—112no—
943C22⋊C8—112no—
944C22⋊C8—112no—
945C22⋊C8—111no—
946C22⋊C8—112no—
947C22⋊C8—112no—
948C22⋊C8—112no—
949C22⋊C8—112no—
950C22⋊C8—112no—
951C22⋊C8—112no—
952C22⋊C8C22×D1112yes—
953C22⋊C8C22×D1112yes—
954C22⋊C8C22×D1112yes—
955C22⋊C8C22×D1112yes—
956#97—112no—
957#97—112no—
958#97C22×D1111yescharacteristic
959#97C22×D1111yescharacteristic
960#97C22×D1111yescharacteristic
961#97C22×D1111yescharacteristic
962#97C22×D1112yes—
963C4×C8—112no—
964C4×C8—112no—
965C4×C8C22×D1112yes—
966C2×C11—22no—
967C2×C11—42no—
968C2×C11C2×#51811yescharacteristic
969C2×C11C2×#56811yescharacteristic
970C2×C11#357311yescharacteristic
971D11—22no—
972D11—41no—
973D11—41no—
974D11—42no—
975D11—42no—
976D11—41no—
977C24—111no—
978C24—112no—
979C24—111no—
980C24—112no—
981#41—22no—
982#41—22no—
983#41—222no—
984#41—222no—
985#41—222no—
986#41—222no—
987#41—442no—
988#41—442no—
989#41—442no—
990#41—442no—
991#41—444no—
992#41—444no—
993#41—442no—
994#41—442no—
995#41—442no—
996#41—442no—
997C2×Q8—111no—
998C2×Q8—111no—
999C2×Q8—112no—
1000C2×Q8—112no—
1001C2×Q8—442no—
1002C2×Q8—442no—
1003C2×Q8C2×C4×D1111yescharacteristic
1004C2×D4—112no—
1005C2×D4—112no—
1006C2×D4—112no—
1007C2×D4—112no—
1008C2×D4—112no—
1009C2×D4—112no—
1010C2×D4—111no—
1011C2×D4—112no—
1012C2×D4—111no—
1013C2×D4—111no—
1014C2×D4—111no—
1015C2×D4—112no—
1016C2×D4—111no—
1017C2×D4—111no—
1018C2×D4—112no—
1019C2×D4—112no—
1020C2×D4—112no—
1021C2×D4—112no—
1022C2×D4—112no—
1023C2×D4—112no—
1024C2×D4—442no—
1025C2×D4—444no—
1026C2×D4—442no—
1027C2×D4—442no—
1028C2×D4—444no—
1029C2×D4—444no—
1030C2×D4C2×C4×D1112yes—
1031C2×D4C2×C4×D1111yescharacteristic
1032C22×C4—111no—
1033C22×C4—111no—
1034C22×C4—112no—
1035C22×C4—112no—
1036C22×C4—111no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—111no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—112no—
1044C22×C4—112no—
1045C22×C4—111no—
1046C22×C4—112no—
1047C22×C4—112no—
1048C22×C4—112no—
1049C22×C4—112no—
1050C22×C4—222no—
1051C22×C4—222no—
1052C22×C4—222no—
1053C22×C4—222no—
1054C22×C4—442no—
1055C22×C4—442no—
1056C22×C4—442no—
1057C22×C4—442no—
1058C22×C4C2×C4×D1112yes—
1059C22×C4C2×C4×D1111yescharacteristic
1060C22×C4C2×C4×D1112yes—
1061C22×C4C2×C4×D1111yescharacteristic
1062C22×C4C23×D1112yes—
1063C22×C4C23×D1111yescharacteristic
1064M16—22no—
1065M16—22no—
1066M16—222no—
1067M16—222no—
1068M16—441no—
1069M16—441no—
1070M16—441no—
1071M16—441no—
1072M16—442no—
1073M16—442no—
1074M16—442no—
1075M16—442no—
1076M16—442no—
1077M16—442no—
1078C2×C8—22no—
1079C2×C8—22no—
1080C2×C8—111no—
1081C2×C8—111no—
1082C2×C8—112no—
1083C2×C8—112no—
1084C2×C8—111no—
1085C2×C8—111no—
1086C2×C8—222no—
1087C2×C8—222no—
1088C2×C8—441no—
1089C2×C8—441no—
1090C2×C8—441no—
1091C2×C8—441no—
1092C2×C8—442no—
1093C2×C8—442no—
1094C2×C8—442no—
1095C2×C8—442no—
1096C2×C8—442no—
1097C2×C8—442no—
1098C2×C8C23×D1112yes—
1099C2×C8C23×D1112yes—
1100C2×C8C23×D1111yescharacteristic
1101C2×C8C23×D1111yescharacteristic
1102C2×C8C23×D1111yescharacteristic
1103C2×C8C23×D1111yescharacteristic
1104C4⋊C4—111no—
1105C4⋊C4—111no—
1106C4⋊C4—112no—
1107C4⋊C4—111no—
1108C4⋊C4—112no—
1109C4⋊C4—111no—
1110C4⋊C4—112no—
1111C4⋊C4—112no—
1112C4⋊C4—112no—
1113C4⋊C4—112no—
1114C4⋊C4C2×C4×D1112yes—
1115C4⋊C4C2×C4×D1112yes—
1116C4⋊C4C2×C4×D1111yescharacteristic
1117C4⋊C4C2×C4×D1111yescharacteristic
1118C22⋊C4—111no—
1119C22⋊C4—111no—
1120C22⋊C4—111no—
1121C22⋊C4—112no—
1122C22⋊C4—111no—
1123C22⋊C4—112no—
1124C22⋊C4—112no—
1125C22⋊C4—111no—
1126C22⋊C4—112no—
1127C22⋊C4—111no—
1128C22⋊C4—111no—
1129C22⋊C4—111no—
1130C22⋊C4—112no—
1131C22⋊C4—112no—
1132C22⋊C4—112no—
1133C22⋊C4—112no—
1134C22⋊C4—112no—
1135C22⋊C4—112no—
1136C22⋊C4—112no—
1137C22⋊C4—112no—
1138C22⋊C4C2×C4×D1112yes—
1139C22⋊C4C2×C4×D1112yes—
1140C22⋊C4C2×C4×D1112yes—
1141C42C2×C4×D1112yes—
1142C42C2×C4×D1111yescharacteristic
1143C42C2×C4×D1112yes—
1144C42C2×C4×D1111yescharacteristic
1145C42C23×D1112yes—
1146C42C23×D1111yescharacteristic
1147C42C23×D1111yescharacteristic
1148C11#6024011yescharacteristic, complemented, Sylow
1149C23—111no—
1150C23—111no—
1151C23—111no—
1152C23—112no—
1153C23—111no—
1154C23—112no—
1155C23—222no—
1156C23—224no—
1157C23—222no—
1158C23—222no—
1159C23—441no—
1160C23—442no—
1161C23—442no—
1162C23—441no—
1163C23—442no—
1164C23—441no—
1165C23—442no—
1166C23—442no—
1167C23C22×C4×D1112yes—
1168C23C22×C4×D1111yescharacteristic
1169Q8—22no—
1170Q8—222no—
1171Q8—222no—
1172Q8—442no—
1173Q8—442no—
1174D4—24no—
1175D4—22no—
1176D4—222no—
1177D4—222no—
1178D4—224no—
1179D4—224no—
1180D4—224no—
1181D4—222no—
1182D4—222no—
1183D4—442no—
1184D4—442no—
1185D4—441no—
1186D4—442no—
1187D4—441no—
1188D4—442no—
1189D4—442no—
1190D4—442no—
1191D4—442no—
1192D4—442no—
1193D4—442no—
1194D4—442no—
1195D4—442no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—111no—
1203C2×C4—111no—
1204C2×C4—111no—
1205C2×C4—111no—
1206C2×C4—112no—
1207C2×C4—112no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—221no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—221no—
1225C2×C4—221no—
1226C2×C4—442no—
1227C2×C4—442no—
1228C2×C4—442no—
1229C2×C4—442no—
1230C2×C4—442no—
1231C2×C4—442no—
1232C2×C4C22×C4×D1111yescharacteristic
1233C2×C4C22×C4×D1111yescharacteristic
1234C2×C4C22×C4×D1112yes—
1235C2×C4C22×C4×D1112yes—
1236C2×C4C22×C4×D1111yescharacteristic
1237C2×C4C22×C4×D1112yes—
1238C2×C4C22×C4×D1111yescharacteristic
1239C2×C4C22×C4×D1111yescharacteristic
1240C2×C4#6704212yes—
1241C2×C4#6704212yes—
1242C2×C4C24×D1111yescharacteristic
1243C8—21no—
1244C8—21no—
1245C8—21no—
1246C8—21no—
1247C8—22no—
1248C8—22no—
1249C8—221no—
1250C8—221no—
1251C8—221no—
1252C8—221no—
1253C8—222no—
1254C8—222no—
1255C22—21no—
1256C22—21no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—112no—
1261C22—221no—
1262C22—221no—
1263C22—221no—
1264C22—221no—
1265C22—222no—
1266C22—221no—
1267C22—222no—
1268C22—221no—
1269C22—221no—
1270C22—222no—
1271C22—222no—
1272C22—221no—
1273C22—221no—
1274C22—221no—
1275C22—221no—
1276C22—222no—
1277C22—222no—
1278C22—444no—
1279C22—882no—
1280C22—884no—
1281C22—884no—
1282C22#1062305212yes—
1283C22C23×C4×D1111yescharacteristic
1284C4—21no—
1285C4—21no—
1286C4—22no—
1287C4—21no—
1288C4—21no—
1289C4—22no—
1290C4—22no—
1291C4—221no—
1292C4—221no—
1293C4—221no—
1294C4—221no—
1295C4—222no—
1296C4—222no—
1297C4#1062305212yes—
1298C4C2×#6704211yescharacteristic
1299C4C2×#6704211yescharacteristic
1300C2—22no—
1301C2—42no—
1302C2—222no—
1303C2—441no—
1304C2—441no—
1305C2—441no—
1306C2—442no—
1307C2—442no—
1308C2C2×#1062305211yescharacteristic
1309C2D11×#56811yescharacteristic
1310C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2923C2
prime radical#41×D44C2
cosocleC2×C4×C11C25
hypercenter#2923D11
hypocenterC11#60240
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13077694C2semidirect
3. #13077686C2semidirect
4. #13077677C2semidirect
5. #13077671C2semidirect
6. #13077662C2semidirect
7. #13077662C2semidirect
8. #13077653C2semidirect
9. #13077644C2semidirect
10. #13077362C2semidirect
11. M16×D44C2semidirect
12. #13077340C2semidirect
13. #13077340C2semidirect
14. #13077335C2semidirect
15. #13077318C2semidirect
16. #13077309C2semidirect
17. C2×#10622319C2semidirect
18. #13077282C2semidirect
19. #13077064C2semidirect
20. #13077064C2semidirect
21. #13077058C2semidirect
22. D11×#408C2semidirect
23. C11×#2923C2semidirect
27. C2×#66960C22semidirect
28. C2×#66960C22semidirect
29. C2×M16×D11C22semidirect
30. C2×M16×D11C22semidirect
31. C2×#66954C22semidirect
32. C2×#66954C22semidirect
33. C22×#4313C22semidirect
34. C22×C8×D11C22semidirect
55. C11×#433C22semidirect
56. C11×#433C22semidirect
57. C11×#432C22semidirect
58. C11×#432C22semidirect
59. C11×#424C22semidirect
60. C11×#424C22semidirect
63. C4×C11×M16C22semidirect
64. C2×C11×#97C22semidirect
67. #10622742C22semidirect
68. #10622742C22semidirect
69. #10622739C22semidirect
70. #10622739C22semidirect
71. #10622723C22semidirect
72. #10622723C22semidirect
73. C2×(C2×D11)⋊C8C22semidirect
74. C2×(C2×D11)⋊C8C22semidirect
75. #10622613C22semidirect
76. #10622613C22semidirect
77. #10622610C22semidirect
78. #10622610C22semidirect
79. #10622539C22semidirect
80. #10622538C22semidirect
81. #10622537C22semidirect
82. C2×C4⋊(C11⋊C8)C22semidirect
83. #10622451C22semidirect
84. #10622451C22semidirect
85. #10622451C22semidirect
86. #10622451C22semidirect
87. #10622449C22semidirect
88. #10622449C22semidirect
89. #10622449C22semidirect
90. #10622449C22semidirect
91. #10622449C22semidirect
92. #10622449C22semidirect
93. #10622449C22semidirect
94. #10622449C22semidirect
95. #10622447C22semidirect
96. #10622447C22semidirect
97. #10622447C22semidirect
98. #10622447C22semidirect
99. #10622340C22semidirect
100. #10622340C22semidirect
101. #10622340C22semidirect
102. #10622340C22semidirect
103. #10622340C22semidirect
104. #10622340C22semidirect
105. #10622340C22semidirect
106. #10622340C22semidirect
107. #10622339C22semidirect
108. #10622339C22semidirect
109. #10622339C22semidirect
110. #10622339C22semidirect
111. D11×C22⋊C8C22semidirect
112. D11×C22⋊C8C22semidirect
113. D11×C22⋊C8C22semidirect
114. D11×C22⋊C8C22semidirect
118. #10622319C22semidirect
119. #10622319C22semidirect
120. #10622319C22semidirect
121. #10622319C22semidirect
122. #10622319C22semidirect
123. #10622319C22semidirect
124. #10622319C22semidirect
125. #10622319C22semidirect
126. #10622319C22semidirect
127. #10622319C22semidirect
128. #10622319C22semidirect
129. #10622319C22semidirect
130. #10622319C22semidirect
131. #10622301C22semidirect
132. #10622301C22semidirect
133. C8×D44C22semidirect
134. C8×D44C22semidirect
512. #2923D11semidirect
692. #433C2×D11semidirect
693. #433C2×D11semidirect
695. #432C2×D11semidirect
696. #432C2×D11semidirect
698. #424C2×D11semidirect
699. #424C2×D11semidirect
732. C4×M16C2×D11semidirect
733. C2×#97C2×D11semidirect
1148. C11#60240semidirect

Maximal subgroups

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

subgroupindex
#41×D442
#130776942
#130776862
#130776772
#130776712
#130776622
#130776532
#130776442
#130773622
M16×D442
#130773402
#130773352
#130773182
#130773092
C2×#106223192
#130772822
#130770642
#130770582
D11×#4082
C11×#29232
#6024011