Finite Group Databasebeta

← #34109204

Subgroups — #34109204

Order 20096.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757820C211yesmaximal, characteristic
2#23757347C211yesmaximal, characteristic, complemented
3#23757346C211yesmaximal, characteristic, complemented
4#23757345C211yesmaximal, characteristic, complemented
5#23757344C211yesmaximal, characteristic, complemented
6#23757343C211yesmaximal, characteristic, complemented
7#23757342C211yesmaximal, characteristic, complemented
8#23757341C211yesmaximal, characteristic, complemented
9#23757329C211yesmaximal, characteristic, complemented
10#23757328C211yesmaximal, characteristic, complemented
11#23757241C211yesmaximal, characteristic, complemented
12#23757239C211yesmaximal, characteristic, complemented
13#23757238C211yesmaximal, characteristic, complemented
14#23757238C211yesmaximal, characteristic, complemented
15#435×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578938C2211yescharacteristic
19C2×#14578937C2211yescharacteristic
20C2×#14578937C2211yescharacteristic
21C22×#11929434C2211yescharacteristic
22C2×C8×D157C2211yescharacteristic
23C2×C8×D157C2211yescharacteristic
24#19097770C411yescharacteristic
25#19097767C411yescharacteristic
26#19097757C411yescharacteristic
27#19097757C411yescharacteristic
28#19097746C411yescharacteristic
29#19097744C411yescharacteristic
30#19097744C411yescharacteristic
31#19097742C411yescharacteristic
32C4×D628C2211yescharacteristic
33C4×C22⋊D157C2211yescharacteristic
34C4×C22⋊D157C2211yescharacteristic
35C42×D157C2211yescharacteristic
36C4⋊#11929434C2211yescharacteristic
37#19097700C2211yescharacteristic
38#19097700C2211yescharacteristic
39C22⋊#11929434C2211yescharacteristic
40C22⋊#11929434C2211yescharacteristic
41#19097683C2211yescharacteristic
42#19097683C2211yescharacteristic
43#19097683C2211yescharacteristic
44#19097683C2211yescharacteristic
45#19097683C2211yescharacteristic
46#19097683C2211yescharacteristic
47#19097683C2211yescharacteristic
48#19097683C2211yescharacteristic
49#19097682C2211yescharacteristic
50#19097681C2211yescharacteristic
51#19097681C2211yescharacteristic
52C2×M16×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55C4⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57C22⋊C8×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578954—41no—
60#14578954—41no—
61#14578954—41no—
62#14578954—41no—
63C2×Dic314C2×C411yescharacteristic
64C2×Dic314C2×C411yescharacteristic
65C2×D628C2×C411yescharacteristic
66C2×D628C2×C411yescharacteristic
67C2×D628C2×C411yescharacteristic
68C2×C22⋊D157C2×C411yescharacteristic
69C2×C22⋊D157C2×C411yescharacteristic
70C2×C22⋊D157C2×C411yescharacteristic
71C2×C22⋊D157C2×C411yescharacteristic
72C2×C22⋊D157C2×C411yescharacteristic
73C2×C22⋊D157C2×C411yescharacteristic
74C2×C4×D157C2×C411yescharacteristic
75C2×C4×D157C2×C411yescharacteristic
76C2×C4×D157C2311yescharacteristic
77C2×C4×D157C2311yescharacteristic
78C2×C4×D157C2311yescharacteristic
79#14578938—41no—
80#14578937—41no—
81#14578937—41no—
82C2×#11929434—41no—
83C2×#11929434C2311yescharacteristic
84C2×#11929434C2311yescharacteristic
85C2×#11929434C2311yescharacteristic
86C2×#11929434C2311yescharacteristic
87C8×D157—41no—
88C8×D157—41no—
89C4⋊Dic157C2×C411yescharacteristic
90#14578933C2×C411yescharacteristic
91#14578933C2×C411yescharacteristic
92C22⋊Dic157C2×C411yescharacteristic
93C22⋊Dic157C2×C411yescharacteristic
94#14578931C2×C411yescharacteristic
95#14578931C2×C411yescharacteristic
96#14578931C2×C411yescharacteristic
97#14578931C2×C411yescharacteristic
98C4×Dic157C2×C411yescharacteristic
99C4×Dic157C2×C411yescharacteristic
100C4×Dic157C2311yescharacteristic
101C2×D4×C157C2×C411yescharacteristic
102C22×C4×C157C2311yescharacteristic
103C22×C4×C157C2311yescharacteristic
104M16×C157—41no—
105C2×C8×C157—41no—
106C2×C8×C157C2311yescharacteristic
107C2×C8×C157C2311yescharacteristic
108C2×C8×C157C2311yescharacteristic
109C2×C8×C157C2311yescharacteristic
110C4⋊C4×C157C2×C411yescharacteristic
111C22⋊C4×C157C2×C411yescharacteristic
112C22⋊C4×C157C2×C411yescharacteristic
113C42×C157C2311yescharacteristic
114C22×D157C22×C411yescharacteristic
115C22×D157C22×C411yescharacteristic
116C22×D157C22×C411yescharacteristic
117Dic314—41no—
118Dic314—41no—
119D628—41no—
120D628—41no—
121D628—41no—
122C22⋊D157—41no—
123C22⋊D157—41no—
124C22⋊D157—41no—
125C22⋊D157—41no—
126C22⋊D157—41no—
127C22⋊D157—41no—
128C2×Dic157C22×C411yescharacteristic
129C2×Dic157C22×C411yescharacteristic
130C2×Dic157C22×C411yescharacteristic
131C2×Dic157C22×C411yescharacteristic
132C2×Dic157C22×C411yescharacteristic
133C4×D157—21no—
134C4×D157—21no—
135C4×D157—21no—
136C4×D157—21no—
137C4×D157—21no—
138C4×D157—21no—
139C4×D157—41no—
140C4×D157—41no—
141#11929434—21no—
142#11929434—21no—
143#11929434—21no—
144#11929434—21no—
145C23×C157C22×C411yescharacteristic
146C23×C157C22×C411yescharacteristic
147D4×C157—41no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157C22×C411yescharacteristic
153C2×C4×C157C22×C411yescharacteristic
154C2×C4×C157C22×C411yescharacteristic
155C2×C4×C157C22×C411yescharacteristic
156C2×C4×C157C2411yescharacteristic
157C8×C157—21no—
158C8×C157—21no—
159C8×C157—21no—
160C8×C157—21no—
161C22×C157—21no—
162C22×C157—21no—
163C22×C157—21no—
164C22×C157—21no—
165C22×C157—21no—
166C22×C157—21no—
167C22×C157C23×C411yescharacteristic
168C2×D157—21no—
169C2×D157—21no—
170C2×D157—21no—
171C2×D157—21no—
172C2×D157—21no—
173C2×D157—21no—
174C2×D157—21no—
175C2×D157—21no—
176C2×D157—21no—
177C4×C157—21no—
178C4×C157—21no—
179C4×C157—21no—
180C4×C157—21no—
181C4×C157H(5,𝔽2)11yescharacteristic
182C4×C157H(5,𝔽2)11yescharacteristic
183Dic157—21no—
184Dic157—21no—
185Dic157—21no—
186Dic157—21no—
187Dic157—21no—
188C2×C157—41no—
189C2×C157—41no—
190C2×C157#51811yescharacteristic
191C2×C157#56811yescharacteristic
192C2×C157#56811yescharacteristic
193D157—41no—
194D157—41no—
195D157—41no—
196C157#298011yescharacteristic, complemented, Sylow
197#2980—1571nomaximal, Sylow
198#532—1571no—
199#435—1571no—
200#435—1571no—
201#435—1571no—
202#435—1571no—
203#435—1571no—
204#435—1571no—
205#435—1571no—
206#435D15711yescharacteristic, complemented
207#432—1571no—
208#432—1571no—
209#408—1571no—
210#408—1571no—
211#408—1571no—
212#408—1571no—
213C2×#41—1571no—
214C2×#41—1571no—
215C2×M16—1571no—
216C2×M16—1571no—
217C2×M16—1571no—
218C2×M16C2×D15711yescharacteristic
219C22×C8—1571no—
220C22×C8—1571no—
221C22×C8—1571no—
222C22×C8C2×D15711yescharacteristic
223C4⋊Q8—1571no—
224#127—1571no—
225#124—1571no—
226#124—1571no—
227#121—1571no—
228#121—1571no—
229#121—1571no—
230#121—1571no—
231C4×D4—1571no—
232C4×D4—1571no—
233C4×D4—1571no—
234C4×D4C2×D15711yescharacteristic
235C2×C42—1571no—
236C4⋊C8—1571no—
237C4⋊C8—1571no—
238C4⋊C8—1571no—
239C4⋊C8C2×D15711yescharacteristic
240C22⋊C8—1571no—
241C22⋊C8—1571no—
242C22⋊C8—1571no—
243C22⋊C8—1571no—
244C22⋊C8—1571no—
245C22⋊C8—1571no—
246C22⋊C8—1571no—
247C22⋊C8—1571no—
248C22⋊C8—1571no—
249C22⋊C8—1571no—
250C22⋊C8C2×D15711yescharacteristic
251C22⋊C8C2×D15711yescharacteristic
252#97—1571no—
253#97—1571no—
254#97—1571no—
255#97C2×D15711yescharacteristic
256#41—6281no—
257#41—6281no—
258#41—6281no—
259#41—6281no—
260C2×Q8—1571no—
261C2×Q8—1571no—
262C2×D4—1571no—
263C2×D4—1571no—
264C2×D4—1571no—
265C2×D4—1571no—
266C2×D4—1571no—
267C2×D4—1571no—
268C2×D4—1571no—
269C2×D4—1571no—
270C2×D4—1571no—
271C2×D4C4×D15711yescharacteristic
272C22×C4—1571no—
273C22×C4—1571no—
274C22×C4—1571no—
275C22×C4—1571no—
276C22×C4—1571no—
277C22×C4C22×D15711yescharacteristic
278C22×C4C22×D15711yescharacteristic
279M16—41no—
280M16—6281no—
281M16—6281no—
282M16—6281no—
283C2×C8—41no—
284C2×C8—6281no—
285C2×C8—6281no—
286C2×C8—6281no—
287C2×C8—1571no—
288C2×C8—1571no—
289C2×C8—1571no—
290C2×C8—1571no—
291C2×C8C22×D15711yescharacteristic
292C2×C8C22×D15711yescharacteristic
293C2×C8C22×D15711yescharacteristic
294C2×C8C22×D15711yescharacteristic
295C4⋊C4—1571no—
296C4⋊C4—1571no—
297C4⋊C4—1571no—
298C4⋊C4C4×D15711yescharacteristic
299C22⋊C4—1571no—
300C22⋊C4—1571no—
301C22⋊C4—1571no—
302C22⋊C4—1571no—
303C22⋊C4—1571no—
304C22⋊C4—1571no—
305C22⋊C4C4×D15711yescharacteristic
306C22⋊C4C4×D15711yescharacteristic
307C42—1571no—
308C42—1571no—
309C42—1571no—
310C42C22×D15711yescharacteristic
311C23—1571no—
312C23—1571no—
313C23—1571no—
314C23C2×C4×D15711yescharacteristic
315C23C2×C4×D15711yescharacteristic
316Q8—6281no—
317Q8—6281no—
318D4—41no—
319D4—6281no—
320D4—6281no—
321D4—6281no—
322D4—6281no—
323D4—6281no—
324D4—6281no—
325D4—6281no—
326D4—6281no—
327D4—6281no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3141no—
333C2×C4—3141no—
334C2×C4—3141no—
335C2×C4—3141no—
336C2×C4—3141no—
337C2×C4—3141no—
338C2×C4—6281no—
339C2×C4—6281no—
340C2×C4—1571no—
341C2×C4—1571no—
342C2×C4—1571no—
343C2×C4—1571no—
344C2×C4—1571no—
345C2×C4C2×C4×D15711yescharacteristic
346C2×C4C2×C4×D15711yescharacteristic
347C2×C4C2×C4×D15711yescharacteristic
348C2×C4C2×C4×D15711yescharacteristic
349C2×C4C23×D15711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—3141no—
355C8—3141no—
356C8—3141no—
357C8—3141no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—3141no—
365C22—3141no—
366C22—3141no—
367C22—3141no—
368C22—3141no—
369C22—3141no—
370C22—3141no—
371C22—3141no—
372C22—3141no—
373C22C22×C4×D15711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—3141no—
379C4—3141no—
380C4—3141no—
381C4—3141no—
382C4—3141no—
383C4#1909781611yescharacteristic
384C4#1909781711yescharacteristic
385C2—41no—
386C2—41no—
387C2—6281no—
388C2—6281no—
389C2—6281no—
390C2#2375774511yescharacteristic
391C2#2375803811yescharacteristic
392C2#2375803911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D157
commutator, socleC22×C157C23×C4
Fitting#435×C157C2
prime radical#23757820C2
cosocleC2×C4×C157C24
hypercenter#435D157
hypocenterC157#2980
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #23757347C2semidirect
3. #23757346C2semidirect
4. #23757345C2semidirect
5. #23757344C2semidirect
6. #23757343C2semidirect
7. #23757342C2semidirect
8. #23757341C2semidirect
9. #23757329C2semidirect
10. #23757328C2semidirect
11. #23757241C2semidirect
12. #23757239C2semidirect
13. #23757238C2semidirect
14. #23757238C2semidirect
15. #435×C157C2semidirect
196. C157#2980semidirect
206. #435D157semidirect

Maximal subgroups

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

subgroupindex
#237578202
#237573472
#237573462
#237573452
#237573442
#237573432
#237573422
#237573412
#237573292
#237573282
#237572412
#237572392
#237572382
#435×C1572
#2980157