Finite Group Databasebeta

← #34111681

Subgroups — #34111681

Order 20096.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097799C211yesmaximal, characteristic, complemented
2C2×#19097793C211yesmaximal, characteristic, complemented
3#23757944C211yesmaximal, characteristic, complemented
4#23757919C211yesmaximal, characteristic, complemented
5#23757662C211yesmaximal, characteristic, complemented
6#23757519C211yesmaximal, characteristic, complemented
7#23757509C211yesmaximal, characteristic, complemented
8#23757496C211yesmaximal, characteristic, complemented
9#23757469C211yesmaximal, characteristic, complemented
10#23757437C211yesmaximal, characteristic, complemented
11#23757420C211yesmaximal, characteristic, complemented
12#23757420C211yesmaximal, characteristic, complemented
13#23757409C211yesmaximal, characteristic, complemented
14#23757375C211yesmaximal, characteristic, complemented
15#435×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578954C2211yescharacteristic, complemented
19C22×D628C2211yescharacteristic
20#19097799—24no—
21#19097793—24no—
22C2×Dic628C2211yescharacteristic, complemented
23C2×#14578943C2211yescharacteristic
24C2×#14578943C2211yescharacteristic
25C2×#14578943C2211yescharacteristic, complemented
26C2×#14578943C2211yescharacteristic, complemented
27C2×D1256C2211yescharacteristic
28C2×D1256C2211yescharacteristic
29C2×D1256C2211yescharacteristic
30C2×D1256C2211yescharacteristic
31#19097768C2211yescharacteristic, complemented
32#19097767—21no—
33#19097759C2211yescharacteristic
34#19097756—21no—
35#19097750C2211yescharacteristic
36#19097745C2211yescharacteristic
37#19097745C2211yescharacteristic
38#19097745C2211yescharacteristic, complemented
39#19097744—21no—
40#19097744—21no—
41#19097744—21no—
42#19097739—21no—
43C4×Dic314C2211yescharacteristic, complemented
44C4×D628C2211yescharacteristic
45#19097733—21no—
46C22⋊C4×D157—21no—
47#19097705C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097696C2211yescharacteristic, complemented
50#19097693C2211yescharacteristic
51#19097693C2211yescharacteristic
52#19097693C2211yescharacteristic, complemented
53#19097693C2211yescharacteristic, complemented
54C2×M16×C157C2211yescharacteristic
55C22×C8×C157C2211yescharacteristic, complemented
56C4×D4×C157C2211yescharacteristic
57C4⋊C8×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic
59C22⋊C8×C157C2211yescharacteristic, complemented
60#97×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62#14578954—22no—
63#14578954—22no—
64#14578954—22no—
65#14578954—41no—
66#14578954—41no—
67#14578954—41no—
68C2×Dic314C2311yescharacteristic
69C2×Dic314C2311yescharacteristic
70C2×D628—22no—
71C2×D628—21no—
72C2×D628—21no—
73C2×D628—21no—
74C2×D628—41no—
75C2×D628C2311yescharacteristic
76C2×D628C2311yescharacteristic
77C2×D628C2311yescharacteristic
78C2×D628C2311yescharacteristic
79C2×C22⋊D157—21no—
80C2×C22⋊D157—21no—
81C2×C22⋊D157—21no—
82C2×C22⋊D157—21no—
83C2×C22⋊D157—21no—
84C2×C22⋊D157—21no—
85C2×C4×D157—21no—
86C2×C4×D157—21no—
87C2×C4×D157—21no—
88C2×C4×D157—21no—
89Dic628—22no—
90#14578943—22no—
91#14578943—22no—
92#14578943—41no—
93#14578943D414yescomplemented
94D1256—22no—
95D1256—22no—
96D1256—22no—
97D1256—41no—
98C4⋊Dic157C2311yescharacteristic
99C4⋊Dic157C2311yescharacteristic
100#14578933—21no—
101#14578933—21no—
102C22⋊Dic157—21no—
103#14578931—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931—21no—
107#14578931—21no—
108#14578931—21no—
109C4×Dic157—21no—
110C2×D4×C157D411yescharacteristic
111C22×C4×C157C2311yescharacteristic
112C22×C4×C157C2311yescharacteristic
113M16×C157—22no—
114C2×C8×C157—22no—
115C2×C8×C157C2311yescharacteristic
116C2×C8×C157C2311yescharacteristic
117C2×C8×C157C2311yescharacteristic
118C2×C8×C157C2311yescharacteristic
119C4⋊C4×C157D411yescharacteristic
120C22⋊C4×C157D411yescharacteristic
121C22⋊C4×C157D411yescharacteristic
122C42×C157C2311yescharacteristic
123C22×D157—21no—
124C22×D157—21no—
125C22×D157—21no—
126C22×D157—21no—
127C22×D157—42no—
128C22×D157—42no—
129C22×D157—81no—
130Dic314—21no—
131Dic314—21no—
132Dic314—21no—
133Dic314C2×D412yes—
134D628—21no—
135D628—21no—
136D628—21no—
137D628—21no—
138D628—21no—
139D628—21no—
140D628—21no—
141D628—42no—
142D628—42no—
143D628—81no—
144D628C2×D412yes—
145C22⋊D157—42no—
146C22⋊D157—42no—
147C22⋊D157—42no—
148C22⋊D157—81no—
149C22⋊D157—81no—
150C22⋊D157—81no—
151C2×Dic157—21no—
152C2×Dic157—21no—
153C2×Dic157—21no—
154C2×Dic157—21no—
155C4×D157—42no—
156C4×D157—42no—
157C4×D157—42no—
158C4×D157—81no—
159C23×C157C2×D411yescharacteristic
160C23×C157C2×D411yescharacteristic
161D4×C157—41no—
162C2×C4×C157—21no—
163C2×C4×C157—21no—
164C2×C4×C157—21no—
165C2×C4×C157—21no—
166C2×C4×C157C2×D411yescharacteristic
167C2×C4×C157C2×D411yescharacteristic
168C2×C4×C157C2×D411yescharacteristic
169C2×C4×C157C2×D411yescharacteristic
170C2×C4×C157C2411yescharacteristic
171C8×C157—21no—
172C8×C157—21no—
173C8×C157—21no—
174C8×C157C2×D412yes—
175C22×C157—21no—
176C22×C157—21no—
177C22×C157—21no—
178C22×C157—21no—
179C22×C157—21no—
180C22×C157—21no—
181C22×C157C22×D411yescharacteristic
182C2×D157—22no—
183C2×D157—41no—
184C2×D157—41no—
185C2×D157—41no—
186C2×D157—41no—
187C2×D157—41no—
188C2×D157—41no—
189C2×D157—41no—
190C2×D157—41no—
191C2×D157—41no—
192C2×D157—41no—
193C2×D157—41no—
194C2×D157—84no—
195C4×C157—21no—
196C4×C157—21no—
197C4×C157—21no—
198C4×C157—21no—
199C4×C157C22×D411yescharacteristic
200C4×C157H(5,𝔽2)11yescharacteristic
201Dic157—22no—
202Dic157—41no—
203Dic157—41no—
204Dic157—41no—
205C2×C157—41no—
206C2×C157—41no—
207C2×C157D4211yescharacteristic
208C2×C157#57511yescharacteristic
209C2×C157#57611yescharacteristic
210D157—42no—
211D157—81no—
212D157—81no—
213D157—81no—
214C157#326811yescharacteristic, complemented, Sylow
215#3268—1571nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1571no—
217C2×#135—1571no—
218#550—1571no—
219#546—1571no—
220#496—1571no—
221#468—1571no—
222#466—1571no—
223#464—1571no—
224#459—1571no—
225#452—1571no—
226#449—1571no—
227#449—1571no—
228#447—1571no—
229#440—1571no—
230#435D15711yescharacteristic, complemented
231C2×#41—1571no—
232C2×#41—1571no—
233C2×#41—1571no—
234C22×D4—1571no—
235AGL(1,ℤ/8)—3144no—
236#135—3144no—
237C2×Q16—1571no—
238C2×SD16—1571no—
239C2×SD16—1571no—
240C2×SD16—1571no—
241C2×SD16—1571no—
242C2×D8—1571no—
243C2×D8—1571no—
244C2×D8—1571no—
245C2×D8—1571no—
246C2×M16C2×D15711yescharacteristic
247C22×C8C2×D15711yescharacteristic, complemented
248#127—3141no—
249#127—1571no—
250#124—1571no—
251#123—3141no—
252C22⋊Q8—1571no—
253#121—3141no—
254#121—3141no—
255#121—3141no—
256#121—1571no—
257#121—1571no—
258#121—1571no—
259#120—3141no—
260C4×Q8—1571no—
261C4×D4—3141no—
262C4×D4—1571no—
263C4×D4C2×D15711yescharacteristic
264C2×C22⋊C4—3141no—
265#107—1571no—
266C4⋊C8C2×D15711yescharacteristic, complemented
267#103—1571no—
268#103—1571no—
269#102—1571no—
270#102—1571no—
271#102—1571no—
272#102—1571no—
273C22⋊C8C2×D15711yescharacteristic
274C22⋊C8C2×D15711yescharacteristic, complemented
275#97C2×D15711yescharacteristic, complemented
276C24—3141no—
277#41—3142no—
278#41—3142no—
279#41—3142no—
280#41—6281no—
281#41—6281no—
282#41—6281no—
283C2×Q8—1571no—
284C2×Q8—1571no—
285C2×D4—3142no—
286C2×D4—3141no—
287C2×D4—3141no—
288C2×D4—3141no—
289C2×D4—3141no—
290C2×D4—3141no—
291C2×D4—3141no—
292C2×D4—3141no—
293C2×D4—3141no—
294C2×D4—3141no—
295C2×D4—6281no—
296C2×D4—1571no—
297C2×D4—1571no—
298C2×D4—1571no—
299C2×D4—1571no—
300C2×D4D62811yescharacteristic
301C22×C4—3141no—
302C22×C4—3141no—
303C22×C4—3141no—
304C22×C4—3141no—
305C22×C4C22×D15711yescharacteristic
306C22×C4C22×D15711yescharacteristic
307Q16—3142no—
308SD16—3142no—
309SD16—3142no—
310SD16—6281no—
311SD16—1574no—
312D8—3142no—
313D8—3142no—
314D8—3142no—
315D8—6281no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D15711yescharacteristic
319C2×C8C22×D15711yescharacteristic
320C2×C8C22×D15711yescharacteristic
321C2×C8C22×D15711yescharacteristic
322C4⋊C4—3141no—
323C4⋊C4—3141no—
324C4⋊C4—1571no—
325C4⋊C4—1571no—
326C4⋊C4D62811yescharacteristic
327C22⋊C4—3141no—
328C22⋊C4—3141no—
329C22⋊C4—3141no—
330C22⋊C4—3141no—
331C22⋊C4—3141no—
332C22⋊C4—3141no—
333C22⋊C4—3141no—
334C22⋊C4D62811yescharacteristic
335C22⋊C4D62811yescharacteristic
336C42—3141no—
337C42C22×D15711yescharacteristic
338C23—3141no—
339C23—3141no—
340C23—3141no—
341C23—3141no—
342C23—6282no—
343C23—6282no—
344C23—12561no—
345C23C2×D62811yescharacteristic
346C23C2×D62811yescharacteristic
347Q8—3141no—
348Q8—3141no—
349Q8—3141no—
350Q8—1572no—
351D4—41no—
352D4—3141no—
353D4—3141no—
354D4—3141no—
355D4—3141no—
356D4—3141no—
357D4—3141no—
358D4—3141no—
359D4—6282no—
360D4—6282no—
361D4—6282no—
362D4—6282no—
363D4—6282no—
364D4—1572no—
365D4—12561no—
366D4—12561no—
367D4—12561no—
368D4—12561no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—3141no—
374C2×C4—3141no—
375C2×C4—3141no—
376C2×C4—3141no—
377C2×C4—6282no—
378C2×C4—6282no—
379C2×C4—6282no—
380C2×C4—12561no—
381C2×C4C2×D62811yescharacteristic
382C2×C4C2×D62811yescharacteristic
383C2×C4C2×D62811yescharacteristic
384C2×C4C2×D62811yescharacteristic
385C2×C4C23×D15711yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D15712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—3142no—
397C22—6281no—
398C22—6281no—
399C22—6281no—
400C22—6281no—
401C22—6281no—
402C22—6281no—
403C22—6281no—
404C22—6281no—
405C22—6281no—
406C22—6281no—
407C22—6281no—
408C22—12564no—
409C22C22×D62811yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—3142no—
415C4—6281no—
416C4—6281no—
417C4—6281no—
418C4C2×D4×D15711yescharacteristic
419C4#1909781711yescharacteristic
420C2—41no—
421C2—41no—
422C2—6282no—
423C2—12561no—
424C2—12561no—
425C2—12561no—
426C2D4×D62811yescharacteristic
427C2#2375807311yescharacteristic
428C2#2375807811yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#435×C157C2
socleC22×C157C22×D4
hypercenter#435D157
hypocenterC157#3268
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#19097799C2semidirect
2. C2×#19097793C2semidirect
3. #23757944C2semidirect
4. #23757919C2semidirect
5. #23757662C2semidirect
6. #23757519C2semidirect
7. #23757509C2semidirect
8. #23757496C2semidirect
9. #23757469C2semidirect
10. #23757437C2semidirect
11. #23757420C2semidirect
12. #23757420C2semidirect
13. #23757409C2semidirect
14. #23757375C2semidirect
15. #435×C157C2semidirect
18. C2×#14578954C22semidirect
22. C2×Dic628C22semidirect
25. C2×#14578943C22semidirect
26. C2×#14578943C22semidirect
31. #19097768C22semidirect
38. #19097745C22semidirect
43. C4×Dic314C22semidirect
47. #19097705C22semidirect
48. #19097696C22semidirect
49. #19097696C22semidirect
52. #19097693C22semidirect
53. #19097693C22semidirect
55. C22×C8×C157C22semidirect
57. C4⋊C8×C157C22semidirect
59. C22⋊C8×C157C22semidirect
60. #97×C157C22semidirect
93. #14578943D4semidirect
214. C157#3268semidirect
230. #435D157semidirect
247. C22×C8C2×D157semidirect
266. C4⋊C8C2×D157semidirect
274. C22⋊C8C2×D157semidirect
275. #97C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977992
C2×#190977932
#237579442
#237579192
#237576622
#237575192
#237575092
#237574962
#237574692
#237574372
#237574202
#237574092
#237573752
#435×C1572
#3268157