Finite Group Databasebeta

← #14907155

Subgroups — #14907155

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622529C211yesmaximal, characteristic
2#13077491C211yesmaximal, characteristic, complemented
3#13077486C211yesmaximal, characteristic, complemented
4#13070482C211yesmaximal, characteristic, complemented
5#13070481C211yesmaximal, characteristic, complemented
6#13070479C211yesmaximal, characteristic, complemented
7C4×#66893C211yesmaximal, characteristic, complemented
8#13070472C211yesmaximal, characteristic, complemented
9C4×#66890C211yesmaximal, characteristic, complemented
10#13070460C211yesmaximal, characteristic, complemented
11D11×#366C211yesmaximal, characteristic, complemented
12#13070327C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14#13070214C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18#10623105—21no—
19#10623077—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622639—21no—
28#10622631—21no—
29#10622529C418yescomplemented
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622430—21no—
38#10622416—21no—
39#10622384—21no—
40#10622370—21no—
41C4×Dic44C2211yescharacteristic
42C4×D88C2211yescharacteristic
43#10622302C2211yescharacteristic
44C11×#366C2211yescharacteristic
45C11×#358C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C11×#346C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C4×C11⋊C16C2211yescharacteristic
60C2×#4343—21no—
61C2×#4341—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66Q8×Dic11—21no—
67C2×#4325—21no—
68D4×Dic11—21no—
69C2×#4324—21no—
70C4×C22⋊D11—41no—
71C2×Dic11⋊C4—41no—
72#66972—22no—
73#66972C2×C414yescomplemented
74#66965—22no—
75#66965C2×C414yescomplemented
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78C2×#4313D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66946—21no—
81#66946—41no—
82C4⋊C4×D11—21no—
83C4⋊C4×D11—21no—
84C4⋊C4×D11—41no—
85#66940—21no—
86(C22⋊D11)⋊C4—41no—
87#66930—41no—
88C4×D44—21no—
89C4×D44—41no—
90#66925—41no—
91#66925D411yescharacteristic
92C4×Dic22—21no—
93C11×SD32C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66896—21no—
103#66893C2×C414yescomplemented
104#66890C2×C414yescomplemented
105#66885—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66873—21no—
115#66871—21no—
116#66871—21no—
117#66867D411yescharacteristic
118#66864C2×C414yescomplemented
119#66862—22no—
120C16×D11C2×C414yescomplemented
121#33459—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×D4×C11—21no—
124C22×C4×C11—41no—
125C2×C22⋊D11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128#4343—24no—
129#4343—42no—
130#4341—24no—
131#4341—42no—
132C2×D44—21no—
133C2×D44—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11C2×D411yescharacteristic
140C2×Dic22—21no—
141C11×Q16—21no—
142C11×Q16C22×C412yes—
143C11×D8—21no—
144C11×D8C22×C412yes—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—41no—
154#4325—24no—
155#4324—24no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4D811yescharacteristic
159(C2×D11)⋊C4D811yescharacteristic
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4D811yescharacteristic
168Dic11⋊C4D811yescharacteristic
169C4×Dic11—41no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44C22×C412yes—
177D88—21no—
178D88C22×C412yes—
179#4313—22no—
180C8×D11C22×C412yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16C22×C412yes—
184C11⋊C16—21no—
185C11⋊C16C22×C412yes—
186C2×#508—111no—
187#2951—111no—
188#2951—111no—
189#2175—111no—
190#2175—111no—
191#2175—111no—
192#2175D1111yescharacteristic, complemented
193C4×Q32—111no—
194C4×Q32—111no—
195C4×D16—111no—
196C4×D16—111no—
197C2×#366—111no—
198#2139—111no—
199#2139—111no—
200#2108—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11C2×D811yescharacteristic
204Q8×C11—22no—
205Q8×C11—41no—
206D4×C11—22no—
207D4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—161no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—44no—
216C2×Dic11—41no—
217C2×Dic11—44no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—161no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224D44—22no—
225D44—44no—
226D44—41no—
227C4×D11—44no—
228C4×D11—161no—
229C4×D11—161no—
230C4×D11—161no—
231C4×D11—161no—
232C4×D11C4×D412yes—
233C4×D11#13512yes—
234Dic22—22no—
235Dic22—41no—
236C8×C11—21no—
237C8×C11C23×C411yescharacteristic
238C8×C11C2×#4111yescharacteristic
239C11⋊C8—21no—
240C11⋊C8C4×D412yes—
241C2×#135—111no—
242C2×#135—111no—
243#520—221no—
244#520—221no—
245#508—118no—
246C2×Q32—111no—
247C2×SD32—111no—
248C2×SD32C2×D1111yescharacteristic
249C2×D16—111no—
250C2×M32—111no—
251C22×C16—111no—
252#440—221no—
253#440—221no—
254#440—221no—
255#440—221no—
256C4×Q16—111no—
257C4×Q16—111no—
258C4×Q16—111no—
259C4×Q16C2×D1111yescharacteristic
260C4×D8—111no—
261C4×D8—111no—
262C4×D8—111no—
263C4×D8C2×D1111yescharacteristic
264C2×#107—111no—
265C2×#107—111no—
266#417—221no—
267#417—221no—
268#405—111no—
269#366—111no—
270#366—111no—
271#366—111no—
272#366C2×D1111yescharacteristic
273#358—111no—
274#358—111no—
275#358—111no—
276#358C2×D1111yescharacteristic
277#357—111no—
278#357—111no—
279#357—111no—
280#357C2×D1111yescharacteristic
281#346—111no—
282#346C2×D1111yescharacteristic
283C4×C16—111no—
284C4×C16—111no—
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11C22×D811yescharacteristic
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—42no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11C4×D812yes—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11C2×C4×D411yescharacteristic
301C4×C11C2×#13511yescharacteristic
302Dic11—21no—
303Dic11—21no—
304Dic11—42no—
305Dic11—81no—
306Dic11—81no—
307Dic11C4×D812yes—
308C2×#41—221no—
309C2×#41—221no—
310#135—114no—
311#135—114no—
312#135—222no—
313#135—222no—
314C2×Q16—111no—
315C2×Q16C22×D1111yescharacteristic
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—111no—
319C2×D8C22×D1111yescharacteristic
320C2×M16—111no—
321C22×C8—111no—
322C4×Q8—21no—
323C4×Q8—221no—
324C4×Q8—221no—
325C4×Q8—221no—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—441no—
331C4×D4—441no—
332C4×D4—441no—
333C4×D4—441no—
334#117—111no—
335#117—441no—
336#117—441no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—441no—
340C2×C4⋊C4—441no—
341Q32—114no—
342SD32—114no—
343SD32C4×D1114yescomplemented
344D16—114no—
345M32—222no—
346C2×C16—111no—
347C2×C16—114no—
348C2×C16—111no—
349C2×C16C22×D1111yescharacteristic
350C2×C16C22×D1111yescharacteristic
351#107—111no—
352#107—111no—
353#107—221no—
354#107—221no—
355#107C22×D1111yescharacteristic
356#107C22×D1111yescharacteristic
357#103—21no—
358#103—221no—
359#103—221no—
360#103—221no—
361#102—21no—
362#102—221no—
363#102—221no—
364#102—221no—
365#97—111no—
366#97—111no—
367C4×C8—111no—
368C4×C8C22×D1111yescharacteristic
369C2×C11—82no—
370C2×C11C2×C4×D811yescharacteristic
371C2×C11#341511yescharacteristic
372C2×C11#341711yescharacteristic
373D11—22no—
374D11—82no—
375#41—224no—
376#41—224no—
377#41—442no—
378#41—442no—
379C2×Q8—21no—
380C2×Q8—221no—
381C2×D4—21no—
382C2×D4—221no—
383C2×D4—441no—
384C2×D4—441no—
385C22×C4—41no—
386C22×C4—111no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394Q16—21no—
395Q16—112no—
396Q16—221no—
397Q16C2×C4×D1112yes—
398SD16—224no—
399SD16—224no—
400D8—21no—
401D8—112no—
402D8—221no—
403D8C2×C4×D1112yes—
404M16—222no—
405C2×C8—111no—
406C2×C8—112no—
407C2×C8—112no—
408C2×C8—111no—
409C2×C8D4×D1111yescharacteristic
410C2×C8C23×D1111yescharacteristic
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—111no—
415C4⋊C4—111no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C22⋊C4—41no—
424C22⋊C4—111no—
425C22⋊C4—111no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C42—41no—
430C42—111no—
431C42—441no—
432C42—441no—
433C42—441no—
434C42D4×D1111yescharacteristic
435C16—21no—
436C16—112no—
437C16—221no—
438C16C2×C4×D1112yes—
439C11#3345911yescharacteristic, complemented, Sylow
440C23—41no—
441C23—111no—
442C23—441no—
443Q8—22no—
444Q8—41no—
445Q8—222no—
446Q8—441no—
447D4—22no—
448D4—41no—
449D4—222no—
450D4—444no—
451D4—444no—
452D4—441no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—111no—
457C2×C4—112no—
458C2×C4—112no—
459C2×C4—111no—
460C2×C4—111no—
461C2×C4—161no—
462C2×C4—444no—
463C2×C4—444no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—1761no—
468C2×C4—1761no—
469C2×C4—1761no—
470C2×C4—1761no—
471C2×C4—1761no—
472C2×C4D8×D1111yescharacteristic
473C2×C4D8×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C8—21no—
476C8—112no—
477C8—221no—
478C8C22×C4×D1111yescharacteristic
479C8#41×D1111yescharacteristic
480C22—42no—
481C22—81no—
482C22—81no—
483C22—112no—
484C22—221no—
485C22—221no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22C2×D8×D1111yescharacteristic
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—112no—
496C4—221no—
497C4—221no—
498C4—442no—
499C4—881no—
500C4—881no—
501C4C4×D4×D1111yescharacteristic
502C4D11×#13511yescharacteristic
503C2—82no—
504C2—222no—
505C2—882no—
506C2C4×D8×D1111yescharacteristic
507C2#1308175611yescharacteristic
508C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
prime radicalC2×#10622529C2
cosocleC2×C8×C11C24
hypercenter#2175D11
hypocenterC11#33459
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. #13077491C2semidirect
3. #13077486C2semidirect
4. #13070482C2semidirect
5. #13070481C2semidirect
6. #13070479C2semidirect
7. C4×#66893C2semidirect
8. #13070472C2semidirect
9. C4×#66890C2semidirect
10. #13070460C2semidirect
11. D11×#366C2semidirect
12. #13070327C2semidirect
13. #13070325C2semidirect
14. #13070214C2semidirect
15. C11×#2175C2semidirect
29. #10622529C4semidirect
73. #66972C2×C4semidirect
75. #66965C2×C4semidirect
93. C11×SD32C2×C4semidirect
103. #66893C2×C4semidirect
104. #66890C2×C4semidirect
118. #66864C2×C4semidirect
120. C16×D11C2×C4semidirect
192. #2175D11semidirect
343. SD32C4×D11semidirect
439. C11#33459semidirect

Maximal subgroups

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

subgroupindex
C2×#106225292
#130774912
#130774862
#130704822
#130704812
#130704792
C4×#668932
#130704722
C4×#668902
#130704602
D11×#3662
#130703272
#130703252
#130702142
C11×#21752
#3345911