Finite Group Databasebeta

← #34103298

Subgroups — #34103298

Order 20096.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097749C211yesmaximal, characteristic
2#23757178C211yesmaximal, characteristic, complemented
3#23757177C211yesmaximal, characteristic, complemented
4#23757170C211yesmaximal, characteristic, complemented
5#23757164C211yesmaximal, characteristic
6#23757163C211yesmaximal, characteristic
7#23757163C211yesmaximal, characteristic
8#23757162C211yesmaximal, characteristic
9#23757159C211yesmaximal, characteristic, complemented
10#23757157C211yesmaximal, characteristic, complemented
11#23757154C211yesmaximal, characteristic, complemented
12#23757154C211yesmaximal, characteristic, complemented
13#23757135C211yesmaximal, characteristic
14#23757130C211yesmaximal, characteristic
15#389×C157C211yesmaximal, characteristic, complemented
16C22×Dic314C2211yescharacteristic
17C22×C4×D157C2211yescharacteristic
18#19097749C418yescomplemented
19C2×C4⋊Dic157C2211yescharacteristic
20C2×#14578933C2211yescharacteristic
21C2×#14578933C2211yescharacteristic
22C2×#14578933C2211yescharacteristic
23C2×#14578933C2211yescharacteristic
24C2×#14578931C2211yescharacteristic
25C2×#14578931C2211yescharacteristic
26C2×#14578931C2211yescharacteristic
27C2×#14578931C2211yescharacteristic
28C2×#14578931C2211yescharacteristic
29C2×#14578931C2211yescharacteristic
30C2×C4×Dic157C2211yescharacteristic
31C2×C4×Dic157C2211yescharacteristic
32C2×C4×Dic157C2211yescharacteristic
33#19097678C2211yescharacteristic
34#19097678C2211yescharacteristic
35#19097678C2211yescharacteristic
36#19097678C2211yescharacteristic
37#19097678C2211yescharacteristic
38#19097678C2211yescharacteristic
39#19097678C2211yescharacteristic
40#19097678C2211yescharacteristic
41#19097678C2211yescharacteristic
42#19097678C2211yescharacteristic
43#19097678C2211yescharacteristic
44#19097678C2211yescharacteristic
45C2×C4⋊C4×C157C2211yescharacteristic
46C2×C4⋊C4×C157C2211yescharacteristic
47C2×C4⋊C4×C157C2211yescharacteristic
48C2×C4⋊C4×C157C2211yescharacteristic
49C2×C42×C157C2211yescharacteristic
50#95×C157C2211yescharacteristic
51#95×C157C2211yescharacteristic
52C23×D157C2311yescharacteristic
53C2×Dic314—41no—
54C2×Dic314—41no—
55C2×Dic314C2×C414yes—
56C22×Dic157C2311yescharacteristic
57C22×Dic157C2311yescharacteristic
58C22×Dic157C2311yescharacteristic
59C22×Dic157C2311yescharacteristic
60C22×Dic157C2311yescharacteristic
61C22×Dic157C2311yescharacteristic
62C22×Dic157C2311yescharacteristic
63C2×C4×D157—41no—
64C2×C4×D157—41no—
65C2×C4×D157C2×C414yes—
66C4⋊Dic157—41no—
67#14578933—41no—
68#14578933—41no—
69#14578933C2×C414yes—
70#14578933C2×C414yes—
71#14578931—41no—
72#14578931—41no—
73#14578931—41no—
74#14578931—41no—
75#14578931C2×C414yes—
76#14578931C2×C414yes—
77C4×Dic157—41no—
78C4×Dic157—41no—
79C4×Dic157—41no—
80C22×C4×C157C2311yescharacteristic
81C22×C4×C157C2311yescharacteristic
82C22×C4×C157C2311yescharacteristic
83C22×C4×C157C2311yescharacteristic
84C22×C4×C157C2311yescharacteristic
85C22×C4×C157C2311yescharacteristic
86C22×C4×C157C2311yescharacteristic
87C4⋊C4×C157—41no—
88C4⋊C4×C157—41no—
89C4⋊C4×C157—41no—
90C4⋊C4×C157C2×C414yes—
91C42×C157—41no—
92C22×D157—21no—
93C22×D157—21no—
94C22×D157—21no—
95C22×D157—21no—
96C22×D157—21no—
97C22×D157—21no—
98C22×D157C22×C412yes—
99Dic314—44no—
100C2×Dic157—21no—
101C2×Dic157—21no—
102C2×Dic157—21no—
103C2×Dic157—21no—
104C2×Dic157—21no—
105C2×Dic157—21no—
106C2×Dic157—21no—
107C2×Dic157—21no—
108C2×Dic157—21no—
109C2×Dic157—21no—
110C2×Dic157—21no—
111C2×Dic157—21no—
112C2×Dic157—21no—
113C2×Dic157—21no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C2×Dic157—21no—
118C2×Dic157C22×C412yes—
119C2×Dic157C22×C412yes—
120C2×Dic157C22×C412yes—
121C4×D157—44no—
122C23×C157C2411yescharacteristic
123C2×C4×C157—21no—
124C2×C4×C157—21no—
125C2×C4×C157—21no—
126C2×C4×C157—21no—
127C2×C4×C157—21no—
128C2×C4×C157—21no—
129C2×C4×C157—21no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157C22×C412yes—
142C2×C4×C157C22×C412yes—
143C2×C4×C157C22×C412yes—
144C22×C157C23×C411yescharacteristic
145C22×C157H(5,𝔽2)11yescharacteristic
146C22×C157H(5,𝔽2)11yescharacteristic
147C22×C157H(5,𝔽2)11yescharacteristic
148C22×C1572−1+411yescharacteristic
149C22×C1572−1+411yescharacteristic
150C22×C1572−1+411yescharacteristic
151C2×D157—22no—
152C2×D157—22no—
153C2×D157—22no—
154C2×D157—41no—
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
158C4×C157—22no—
159C4×C157—22no—
160C4×C157—22no—
161C4×C157—41no—
162C4×C157—41no—
163C4×C157—41no—
164C4×C157—41no—
165Dic157—22no—
166Dic157—22no—
167Dic157—22no—
168Dic157—41no—
169Dic157—41no—
170Dic157—41no—
171Dic157—41no—
172C2×C157#51811yescharacteristic
173C2×C157#51911yescharacteristic
174C2×C157#52011yescharacteristic
175C2×C157#56211yescharacteristic
176C2×C157#56211yescharacteristic
177C2×C157#56311yescharacteristic
178C2×C157#56311yescharacteristic
179D157—42no—
180C157#237811yescharacteristic, complemented, Sylow
181#2378—1571nomaximal, Sylow
182C2×C22⋊Q8—1571no—
183#391—1571no—
184#391—1571no—
185#389—1571no—
186#389D15711yescharacteristic, complemented
187#388—1571no—
188#388—1571no—
189#388—1571no—
190#388—1571no—
191#387—1571no—
192#387—1571no—
193#387—1571no—
194#387—1571no—
195#381—1571no—
196#380—1571no—
197C22×Q8—1571no—
198C23×C4—1571no—
199C22⋊Q8—1578no—
200C2×C4⋊C4—1571no—
201C2×C4⋊C4—1571no—
202C2×C4⋊C4—1571no—
203C2×C4⋊C4—1571no—
204C2×C4⋊C4—1571no—
205C2×C4⋊C4C2×D15711yescharacteristic
206C2×C4⋊C4C2×D15711yescharacteristic
207C2×C4⋊C4C2×D15711yescharacteristic
208C2×C4⋊C4C2×D15711yescharacteristic
209C2×C22⋊C4—1571no—
210C2×C22⋊C4—1571no—
211C2×C22⋊C4—1571no—
212C2×C22⋊C4—1571no—
213C2×C22⋊C4—1571no—
214C2×C22⋊C4—1571no—
215C2×C42—1571no—
216C2×C42—1571no—
217C2×C42—1571no—
218C2×C42C2×D15711yescharacteristic
219#95—1571no—
220#95—1571no—
221#95—1571no—
222#95—1571no—
223#95—1571no—
224#95—1571no—
225#95—1571no—
226#95—1571no—
227#95—1571no—
228#95—1571no—
229#95—1571no—
230#95—1571no—
231#95C2×D15711yescharacteristic
232#95C2×D15711yescharacteristic
233C24—1571no—
234C2×Q8—6281no—
235C2×Q8—6281no—
236C2×Q8—1574no—
237C22×C4—6281no—
238C22×C4—6281no—
239C22×C4—1571no—
240C22×C4—1571no—
241C22×C4—1571no—
242C22×C4—1571no—
243C22×C4—1571no—
244C22×C4—1571no—
245C22×C4—1571no—
246C22×C4—1574no—
247C22×C4C22×D15711yescharacteristic
248C22×C4C22×D15711yescharacteristic
249C22×C4C22×D15711yescharacteristic
250C22×C4C22×D15711yescharacteristic
251C22×C4C22×D15711yescharacteristic
252C22×C4C22×D15711yescharacteristic
253C22×C4C22×D15711yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—6281no—
258C4⋊C4—6281no—
259C4⋊C4—6281no—
260C4⋊C4—1574no—
261C4⋊C4—1574no—
262C4⋊C4C4×D15714yes—
263C22⋊C4—6281no—
264C22⋊C4—6281no—
265C22⋊C4—6281no—
266C22⋊C4—6281no—
267C22⋊C4—1574no—
268C22⋊C4—1574no—
269C42—41no—
270C42—6281no—
271C42—6281no—
272C42—6281no—
273C23—3141no—
274C23—3141no—
275C23—3141no—
276C23—3141no—
277C23—3141no—
278C23—3141no—
279C23—1572no—
280C23C23×D15711yescharacteristic
281Q8—6284no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—3141no—
301C2×C4—3141no—
302C2×C4—3141no—
303C2×C4—3141no—
304C2×C4—3141no—
305C2×C4—3141no—
306C2×C4—3141no—
307C2×C4—3141no—
308C2×C4—3141no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—3141no—
318C2×C4—6284no—
319C2×C4—1572no—
320C2×C4—1572no—
321C2×C4—1572no—
322C2×C4C2×C4×D15712yes—
323C2×C4C2×C4×D15712yes—
324C2×C4C2×C4×D15712yes—
325C22—3142no—
326C22—3142no—
327C22—3142no—
328C22—6281no—
329C22—6281no—
330C22—6281no—
331C22—6281no—
332C22C22×C4×D15711yescharacteristic
333C22#1909781611yescharacteristic
334C22#1909781611yescharacteristic
335C22#1909781711yescharacteristic
336C22#1909781811yescharacteristic
337C22#1909781911yescharacteristic
338C22#1909781911yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3142no—
347C4—3142no—
348C4—3142no—
349C4—6281no—
350C4—6281no—
351C4—6281no—
352C4—6281no—
353C2—6282no—
354C2#2375774511yescharacteristic
355C2#2375774911yescharacteristic
356C2#2375775411yescharacteristic
357C2#2375801811yescharacteristic
358C2#2375801911yescharacteristic
359C2#2375802211yescharacteristic
360C2#2375802711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#389×C157C2
socle, cosocleC23×C157C24
prime radicalC23×D157C23
hypercenter#389D157
hypocenterC157#2378
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #23757178C2semidirect
3. #23757177C2semidirect
4. #23757170C2semidirect
9. #23757159C2semidirect
10. #23757157C2semidirect
11. #23757154C2semidirect
12. #23757154C2semidirect
15. #389×C157C2semidirect
18. #19097749C4semidirect
180. C157#2378semidirect
186. #389D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977492
#237571782
#237571772
#237571702
#237571642
#237571632
#237571622
#237571592
#237571572
#237571542
#237571352
#237571302
#389×C1572
#2378157