Finite Group Databasebeta

← #34109302

Subgroups — #34109302

Order 20096.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757805C211yesmaximal, characteristic
2#23757402C211yesmaximal, characteristic, complemented
3#23757401C211yesmaximal, characteristic, complemented
4#23757349C211yesmaximal, characteristic, complemented
5#23757348C211yesmaximal, characteristic, complemented
6#23757345C211yesmaximal, characteristic, complemented
7#23757344C211yesmaximal, characteristic, complemented
8#23757341C211yesmaximal, characteristic, complemented
9#23757331C211yesmaximal, characteristic, complemented
10#23757331C211yesmaximal, characteristic, complemented
11#23757328C211yesmaximal, characteristic, complemented
12#23757301C211yesmaximal, characteristic, complemented
13#23757299C211yesmaximal, characteristic, complemented
14#23757295C211yesmaximal, characteristic, complemented
15#435×C157C211yesmaximal, characteristic, complemented
16C2×#14578938C2211yescharacteristic
17C2×#14578937C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C22×#11929434C2211yescharacteristic
20#19097764C411yescharacteristic
21#19097764C411yescharacteristic
22#19097762C411yescharacteristic
23#19097758C411yescharacteristic
24#19097753C411yescharacteristic
25#19097753C411yescharacteristic
26#19097751C411yescharacteristic
27#19097742C411yescharacteristic
28C4×Dic314C2211yescharacteristic
29C4×C22⋊D157C2211yescharacteristic
30C4×C22⋊D157C2211yescharacteristic
31#19097730C2211yescharacteristic
32#19097730C2211yescharacteristic
33C42×D157C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35#19097700C2211yescharacteristic
36#19097700C2211yescharacteristic
37#19097700C2211yescharacteristic
38#19097700C2211yescharacteristic
39#19097700C2211yescharacteristic
40#19097700C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097700C2211yescharacteristic
43C22⋊#11929434C2211yescharacteristic
44C22⋊#11929434C2211yescharacteristic
45#19097683C2211yescharacteristic
46#19097683C2211yescharacteristic
47#19097682C2211yescharacteristic
48#19097681C2211yescharacteristic
49#19097681C2211yescharacteristic
50C8×Dic157C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×M16×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55C4⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57C22⋊C8×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59C2×Dic314C2×C411yescharacteristic
60C2×C22⋊D157C2×C411yescharacteristic
61C2×C22⋊D157C2×C411yescharacteristic
62C2×C4×D157C2×C411yescharacteristic
63C2×C4×D157C2×C411yescharacteristic
64C2×C4×D157C2311yescharacteristic
65#14578938—41no—
66#14578937—41no—
67#14578937—41no—
68C2×#11929434—41no—
69C2×#11929434C2311yescharacteristic
70C2×#11929434C2311yescharacteristic
71C2×#11929434C2311yescharacteristic
72C2×#11929434C2311yescharacteristic
73C4⋊Dic157C2×C411yescharacteristic
74C4⋊Dic157C2×C411yescharacteristic
75C4⋊Dic157C2×C411yescharacteristic
76C4⋊Dic157C2×C411yescharacteristic
77C4⋊Dic157C2×C411yescharacteristic
78#14578933C2×C411yescharacteristic
79#14578933C2×C411yescharacteristic
80#14578933C2×C411yescharacteristic
81#14578933C2×C411yescharacteristic
82C22⋊Dic157C2×C411yescharacteristic
83C22⋊Dic157C2×C411yescharacteristic
84C22⋊Dic157C2×C411yescharacteristic
85C22⋊Dic157C2×C411yescharacteristic
86C22⋊Dic157C2×C411yescharacteristic
87C22⋊Dic157C2×C411yescharacteristic
88#14578931C2×C411yescharacteristic
89#14578931C2×C411yescharacteristic
90C4×Dic157C2×C411yescharacteristic
91C4×Dic157C2×C411yescharacteristic
92C4×Dic157C2311yescharacteristic
93C4×Dic157C2311yescharacteristic
94C4×Dic157C2311yescharacteristic
95C2×D4×C157C2×C411yescharacteristic
96C22×C4×C157C2311yescharacteristic
97C22×C4×C157C2311yescharacteristic
98M16×C157—41no—
99C2×C8×C157—41no—
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C2×C8×C157C2311yescharacteristic
104C4⋊C4×C157C2×C411yescharacteristic
105C22⋊C4×C157C2×C411yescharacteristic
106C22⋊C4×C157C2×C411yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157C22×C411yescharacteristic
109Dic314—41no—
110C22⋊D157—41no—
111C22⋊D157—41no—
112C2×Dic157C22×C411yescharacteristic
113C2×Dic157C22×C411yescharacteristic
114C2×Dic157C22×C411yescharacteristic
115C2×Dic157C22×C411yescharacteristic
116C2×Dic157C22×C411yescharacteristic
117C2×Dic157C22×C411yescharacteristic
118C2×Dic157C22×C411yescharacteristic
119C4×D157—21no—
120C4×D157—21no—
121C4×D157—41no—
122C4×D157—41no—
123#11929434—21no—
124#11929434—21no—
125#11929434—21no—
126#11929434—21no—
127C23×C157C22×C411yescharacteristic
128C23×C157C22×C411yescharacteristic
129D4×C157—41no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157C22×C411yescharacteristic
135C2×C4×C157C22×C411yescharacteristic
136C2×C4×C157C22×C411yescharacteristic
137C2×C4×C157C22×C411yescharacteristic
138C2×C4×C157C2411yescharacteristic
139C8×C157—21no—
140C8×C157—21no—
141C8×C157—21no—
142C8×C157—21no—
143C22×C157—21no—
144C22×C157—21no—
145C22×C157—21no—
146C22×C157—21no—
147C22×C157—21no—
148C22×C157—21no—
149C22×C157C23×C411yescharacteristic
150C2×D157—21no—
151C2×D157—21no—
152C2×D157—21no—
153C4×C157—21no—
154C4×C157—21no—
155C4×C157—21no—
156C4×C157—21no—
157C4×C157H(5,𝔽2)11yescharacteristic
158C4×C1572−1+411yescharacteristic
159Dic157—21no—
160Dic157—21no—
161Dic157—21no—
162Dic157—21no—
163Dic157—21no—
164Dic157—21no—
165Dic157—21no—
166C2×C157—41no—
167C2×C157—41no—
168C2×C157#52011yescharacteristic
169C2×C157#56811yescharacteristic
170C2×C157#56811yescharacteristic
171D157—41no—
172C157#299511yescharacteristic, complemented, Sylow
173#2995—1571nomaximal, Sylow
174#529—1571no—
175#446—1571no—
176#446—1571no—
177#436—1571no—
178#436—1571no—
179#435—1571no—
180#435—1571no—
181#435—1571no—
182#435D15711yescharacteristic, complemented
183#433—1571no—
184#433—1571no—
185#432—1571no—
186#424—1571no—
187#424—1571no—
188#423—1571no—
189C2×M16—1571no—
190C2×M16—1571no—
191C2×M16—1571no—
192C2×M16C2×D15711yescharacteristic
193C22×C8—1571no—
194C22×C8C2×D15711yescharacteristic
195#126—1571no—
196#126—1571no—
197#125—1571no—
198#124—1571no—
199#123—1571no—
200#123—1571no—
201C22⋊Q8—1571no—
202#121—1571no—
203C4×Q8—1571no—
204C4×D4—1571no—
205C4×D4—1571no—
206C4×D4C2×D15711yescharacteristic
207#117—1571no—
208#117—1571no—
209C2×C42—1571no—
210C4⋊C8—1571no—
211C4⋊C8—1571no—
212C4⋊C8—1571no—
213C4⋊C8—1571no—
214C4⋊C8—1571no—
215C4⋊C8—1571no—
216C4⋊C8—1571no—
217C4⋊C8—1571no—
218C4⋊C8—1571no—
219C4⋊C8C2×D15711yescharacteristic
220C22⋊C8—1571no—
221C22⋊C8—1571no—
222C22⋊C8—1571no—
223C22⋊C8—1571no—
224C22⋊C8C2×D15711yescharacteristic
225C22⋊C8C2×D15711yescharacteristic
226#97—1571no—
227#97—1571no—
228#97—1571no—
229#97C2×D15711yescharacteristic
230C4×C8—1571no—
231C4×C8—1571no—
232C2×Q8—1571no—
233C2×D4—1571no—
234C2×D4—1571no—
235C2×D4C4×D15711yescharacteristic
236C22×C4—1571no—
237C22×C4—1571no—
238C22×C4—1571no—
239C22×C4C22×D15711yescharacteristic
240C22×C4C22×D15711yescharacteristic
241M16—41no—
242M16—6281no—
243M16—6281no—
244M16—6281no—
245C2×C8—41no—
246C2×C8—6281no—
247C2×C8—1571no—
248C2×C8—1571no—
249C2×C8—1571no—
250C2×C8—1571no—
251C2×C8C22×D15711yescharacteristic
252C2×C8C22×D15711yescharacteristic
253C2×C8C22×D15711yescharacteristic
254C2×C8C22×D15711yescharacteristic
255C4⋊C4—1571no—
256C4⋊C4—1571no—
257C4⋊C4—1571no—
258C4⋊C4—1571no—
259C4⋊C4—1571no—
260C4⋊C4—1571no—
261C4⋊C4—1571no—
262C4⋊C4—1571no—
263C4⋊C4—1571no—
264C4⋊C4C4×D15711yescharacteristic
265C22⋊C4—1571no—
266C22⋊C4—1571no—
267C22⋊C4—1571no—
268C22⋊C4—1571no—
269C22⋊C4—1571no—
270C22⋊C4—1571no—
271C22⋊C4—1571no—
272C22⋊C4—1571no—
273C22⋊C4C4×D15711yescharacteristic
274C22⋊C4C4×D15711yescharacteristic
275C42—1571no—
276C42—1571no—
277C42—1571no—
278C42—1571no—
279C42—1571no—
280C42C22×D15711yescharacteristic
281C23—1571no—
282C23C2×C4×D15711yescharacteristic
283C23C2×C4×D15711yescharacteristic
284Q8—6281no—
285D4—41no—
286D4—6281no—
287D4—6281no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3141no—
293C2×C4—3141no—
294C2×C4—6281no—
295C2×C4—6281no—
296C2×C4—1571no—
297C2×C4—1571no—
298C2×C4—1571no—
299C2×C4—1571no—
300C2×C4—1571no—
301C2×C4—1571no—
302C2×C4—1571no—
303C2×C4C2×C4×D15711yescharacteristic
304C2×C4C2×C4×D15711yescharacteristic
305C2×C4C2×C4×D15711yescharacteristic
306C2×C4C2×C4×D15711yescharacteristic
307C2×C4C23×D15711yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—3141no—
313C8—3141no—
314C8—3141no—
315C8—3141no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—3141no—
323C22—3141no—
324C22—3141no—
325C22C22×C4×D15711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—3141no—
331C4—3141no—
332C4—3141no—
333C4—3141no—
334C4—3141no—
335C4—3141no—
336C4—3141no—
337C4#1909781611yescharacteristic
338C4#1909781811yescharacteristic
339C2—41no—
340C2—41no—
341C2—6281no—
342C2#2375775211yescharacteristic
343C2#2375803811yescharacteristic
344C2#2375803911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D157
commutator, socleC22×C157C23×C4
Fitting#435×C157C2
prime radical#19097742C4
cosocleC2×C4×C157C24
hypercenter#435D157
hypocenterC157#2995
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #23757402C2semidirect
3. #23757401C2semidirect
4. #23757349C2semidirect
5. #23757348C2semidirect
6. #23757345C2semidirect
7. #23757344C2semidirect
8. #23757341C2semidirect
9. #23757331C2semidirect
10. #23757331C2semidirect
11. #23757328C2semidirect
12. #23757301C2semidirect
13. #23757299C2semidirect
14. #23757295C2semidirect
15. #435×C157C2semidirect
172. C157#2995semidirect
182. #435D157semidirect

Maximal subgroups

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

subgroupindex
#237578052
#237574022
#237574012
#237573492
#237573482
#237573452
#237573442
#237573412
#237573312
#237573282
#237573012
#237572992
#237572952
#435×C1572
#2995157