Finite Group Databasebeta

← #34112129

Subgroups — #34112129

Order 20096.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757932C211yesmaximal, characteristic, complemented
2#23757927C211yesmaximal, characteristic, complemented
3#23757633C211yesmaximal, characteristic, complemented
4#23757609C211yesmaximal, characteristic, complemented
5#23757587C211yesmaximal, characteristic, complemented
6#23757569C211yesmaximal, characteristic, complemented
7#23757519C211yesmaximal, characteristic, complemented
8#23757509C211yesmaximal, characteristic, complemented
9#23757489C211yesmaximal, characteristic, complemented
10#23757420C211yesmaximal, characteristic, complemented
11#23757414C211yesmaximal, characteristic, complemented
12#23757375C211yesmaximal, characteristic, complemented
13#23757275C211yesmaximal, characteristic, complemented
14C2×#19097696C211yesmaximal, characteristic, complemented
15#435×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578953—21no—
18C22×Dic314C2211yescharacteristic
19C2×#14578943C2211yescharacteristic
20C2×#14578943C2211yescharacteristic
21C2×D1256C2211yescharacteristic
22#19097771C2211yescharacteristic
23#19097759C2211yescharacteristic
24#19097757—21no—
25#19097755—21no—
26#19097755—21no—
27#19097751—21no—
28#19097750C2211yescharacteristic
29#19097749—21no—
30#19097745C2211yescharacteristic
31#19097745C2211yescharacteristic
32#19097745C2211yescharacteristic
33#19097743—21no—
34C4×Dic314C2211yescharacteristic
35C4×D628C2211yescharacteristic
36#19097731—21no—
37C2×C4⋊Dic157C2211yescharacteristic
38C2×C4⋊Dic157C2211yescharacteristic
39#19097705C2211yescharacteristic
40#19097705C2211yescharacteristic
41#19097705C2211yescharacteristic
42#19097696C2211yescharacteristic
43#19097696C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097696C2211yescharacteristic
47#19097696C2211yescharacteristic
48#19097693C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097693C2211yescharacteristic
51#19097693C2211yescharacteristic
52C2×M16×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55C4⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57C22⋊C8×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—41no—
61#14578953—44no—
62C2×Dic314—22no—
63C2×Dic314—21no—
64C2×Dic314—21no—
65C2×Dic314—41no—
66C2×Dic314C2311yescharacteristic
67C2×Dic314C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×D628C2311yescharacteristic
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157—21no—
74C22×Dic157—21no—
75C22×Dic157—21no—
76C22×Dic157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79#14578943—22no—
80#14578943—41no—
81D1256—41no—
82C4⋊Dic157—21no—
83C4⋊Dic157—21no—
84C4⋊Dic157—21no—
85C4⋊Dic157C2311yescharacteristic
86C4⋊Dic157C2311yescharacteristic
87C4⋊Dic157C2311yescharacteristic
88C4⋊Dic157C2311yescharacteristic
89#14578933—21no—
90#14578933—21no—
91C22⋊Dic157—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96#14578931—21no—
97#14578931—21no—
98C4×Dic157—21no—
99C2×D4×C157D411yescharacteristic
100C22×C4×C157C2311yescharacteristic
101C22×C4×C157C2311yescharacteristic
102M16×C157—41no—
103C2×C8×C157—41no—
104C2×C8×C157C2311yescharacteristic
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C2×C8×C157C2311yescharacteristic
108C4⋊C4×C157D411yescharacteristic
109C22⋊C4×C157D411yescharacteristic
110C22⋊C4×C157D411yescharacteristic
111C42×C157C2311yescharacteristic
112C22×D157—21no—
113C22×D157—21no—
114Dic314—21no—
115Dic314—21no—
116Dic314—21no—
117Dic314—42no—
118Dic314—42no—
119Dic314#4112yescomplemented
120D628—21no—
121D628—21no—
122D628—21no—
123D628—21no—
124C22⋊D157—42no—
125C22⋊D157—42no—
126C22⋊D157—42no—
127C22⋊D157—42no—
128C2×Dic157—21no—
129C2×Dic157—21no—
130C2×Dic157—21no—
131C2×Dic157—21no—
132C2×Dic157—21no—
133C2×Dic157—21no—
134C2×Dic157—42no—
135C2×Dic157—42no—
136C2×Dic157—42no—
137C4×D157—42no—
138C4×D157—42no—
139C23×C157C2×D411yescharacteristic
140C23×C157C2×D411yescharacteristic
141D4×C157—22no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2411yescharacteristic
151C8×C157—21no—
152C8×C157—21no—
153C8×C157—21no—
154C8×C157—21no—
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—21no—
159C22×C157—21no—
160C22×C157AGL(1,ℤ/8)12yes—
161C22×C157C22×D411yescharacteristic
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—41no—
168C4×C157—21no—
169C4×C157—21no—
170C4×C157—21no—
171C4×C157—21no—
172C4×C157C2×#4111yescharacteristic
173C4×C157H(5,𝔽2)11yescharacteristic
174Dic157—22no—
175Dic157—41no—
176Dic157—41no—
177Dic157—41no—
178Dic157—41no—
179Dic157—41no—
180C2×C157—22no—
181C2×C157—41no—
182C2×C157#54611yescharacteristic
183C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C157#57811yescharacteristic
185D157—81no—
186D157—81no—
187C157#330811yescharacteristic, complemented, Sylow
188#3308—1571nomaximal, Sylow
189#548—1571no—
190#547—1571no—
191#489—1571no—
192#484—1571no—
193#480—1571no—
194#477—1571no—
195#468—1571no—
196#466—1571no—
197#463—1571no—
198#449—1571no—
199#448—1571no—
200#440—1571no—
201#435D15711yescharacteristic, complemented
202#417—1571no—
203C2×#103—1571no—
204C2×#41—3141no—
205C2×#41—1571no—
206C22×Q8—1571no—
207C2×SD16—1571no—
208C2×SD16—1571no—
209C2×D8—1571no—
210C2×M16C2×D15711yescharacteristic
211C22×C8C2×D15711yescharacteristic
212C4⋊Q8—1571no—
213#124—3141no—
214#124—1571no—
215#123—3141no—
216#123—3141no—
217C22⋊Q8—3141no—
218C22⋊Q8—3141no—
219C22⋊Q8—1571no—
220#121—3141no—
221#121—1571no—
222#121—1571no—
223#121—1571no—
224C4×Q8—1571no—
225C4×D4—3141no—
226C4×D4—1571no—
227C4×D4C2×D15711yescharacteristic
228C2×C4⋊C4—1571no—
229C2×C4⋊C4—1571no—
230#107—1571no—
231#107—1571no—
232#107—1571no—
233C4⋊C8C2×D15711yescharacteristic
234#103—1571no—
235#103—1571no—
236#103—1571no—
237#103—1571no—
238#103—1571no—
239#103—1571no—
240#102—1571no—
241#102—1571no—
242#102—1571no—
243#102—1571no—
244C22⋊C8C2×D15711yescharacteristic
245C22⋊C8C2×D15711yescharacteristic
246#97C2×D15711yescharacteristic
247#41—3142no—
248#41—6281no—
249#41—6284no—
250C2×Q8—3142no—
251C2×Q8—3141no—
252C2×Q8—3141no—
253C2×Q8—6281no—
254C2×Q8—1571no—
255C2×Q8—1571no—
256C2×D4—3141no—
257C2×D4—3141no—
258C2×D4—3141no—
259C2×D4—3141no—
260C2×D4—1571no—
261C2×D4—1571no—
262C2×D4D62811yescharacteristic
263C22×C4—3141no—
264C22×C4—3141no—
265C22×C4—3141no—
266C22×C4—3141no—
267C22×C4—3141no—
268C22×C4C22×D15711yescharacteristic
269C22×C4C22×D15711yescharacteristic
270SD16—3142no—
271SD16—6281no—
272D8—6281no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D15711yescharacteristic
276C2×C8C22×D15711yescharacteristic
277C2×C8C22×D15711yescharacteristic
278C2×C8C22×D15711yescharacteristic
279C4⋊C4—3141no—
280C4⋊C4—3141no—
281C4⋊C4—3141no—
282C4⋊C4—3141no—
283C4⋊C4—3141no—
284C4⋊C4—1571no—
285C4⋊C4—1571no—
286C4⋊C4—1571no—
287C4⋊C4—1571no—
288C4⋊C4D62811yescharacteristic
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4D62811yescharacteristic
297C22⋊C4D62811yescharacteristic
298C42—3141no—
299C42C22×D15711yescharacteristic
300C23—3141no—
301C23—3141no—
302C23C2×D62811yescharacteristic
303C23C2×D62811yescharacteristic
304Q8—3141no—
305Q8—3141no—
306Q8—3141no—
307Q8—6282no—
308Q8—6282no—
309Q8—1572no—
310D4—22no—
311D4—3141no—
312D4—3141no—
313D4—3141no—
314D4—3141no—
315D4—6282no—
316D4—6282no—
317D4—6282no—
318D4—6282no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3141no—
324C2×C4—3141no—
325C2×C4—3141no—
326C2×C4—3141no—
327C2×C4—3141no—
328C2×C4—3141no—
329C2×C4—6282no—
330C2×C4—6282no—
331C2×C4—6282no—
332C2×C4—6282no—
333C2×C4—6282no—
334C2×C4C2×D62811yescharacteristic
335C2×C4C2×D62811yescharacteristic
336C2×C4C2×D62811yescharacteristic
337C2×C4C2×D62811yescharacteristic
338C2×C4C23×D15711yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—6281no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22—6281no—
354C22#1909779912yes—
355C22C22×D62811yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—3142no—
361C4—6281no—
362C4—6281no—
363C4—6281no—
364C4—6281no—
365C4—6281no—
366C4#41×D15711yescharacteristic
367C4#1909781611yescharacteristic
368C2—22no—
369C2—41no—
370C2—12561no—
371C2—12561no—
372C2#2375791811yescharacteristic
373C2C2×#1909779911yescharacteristic
374C2#2375809011yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#435×C157C2
socleC22×C157C22×D4
hypercenter#435D157
hypocenterC157#3308
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. #23757932C2semidirect
2. #23757927C2semidirect
3. #23757633C2semidirect
4. #23757609C2semidirect
5. #23757587C2semidirect
6. #23757569C2semidirect
7. #23757519C2semidirect
8. #23757509C2semidirect
9. #23757489C2semidirect
10. #23757420C2semidirect
11. #23757414C2semidirect
12. #23757375C2semidirect
13. #23757275C2semidirect
14. C2×#19097696C2semidirect
15. #435×C157C2semidirect
119. Dic314#41semidirect
187. C157#3308semidirect
201. #435D157semidirect

Maximal subgroups

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

subgroupindex
#237579322
#237579272
#237576332
#237576092
#237575872
#237575692
#237575192
#237575092
#237574892
#237574202
#237574142
#237573752
#237572752
C2×#190976962
#435×C1572
#3308157