Finite Group Databasebeta

← #34103010

Subgroups — #34103010

Order 20096.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D157C211yesmaximal, characteristic
2#23757170C211yesmaximal, characteristic, complemented
3#23757168C211yesmaximal, characteristic, complemented
4#23757159C211yesmaximal, characteristic, complemented
5#23757158C211yesmaximal, characteristic, complemented
6#23757156C211yesmaximal, characteristic, complemented
7#23757132C211yesmaximal, characteristic
8#23757132C211yesmaximal, characteristic
9#23757130C211yesmaximal, characteristic
10C4×#14578933C211yesmaximal, characteristic, complemented
11#23757124C211yesmaximal, characteristic, complemented
12C4×#14578931C211yesmaximal, characteristic
13#23757120C211yesmaximal, characteristic
14#23757120C211yesmaximal, characteristic
15#387×C157C211yesmaximal, characteristic, complemented
16C22×C4×D157C2211yescharacteristic
17C22×C4×D157C2211yescharacteristic
18C22×C4×D157C2211yescharacteristic
19C2×C4⋊Dic157C2211yescharacteristic
20C2×C4⋊Dic157C2211yescharacteristic
21C2×#14578933C2211yescharacteristic
22C2×#14578933C2211yescharacteristic
23C2×#14578933C2211yescharacteristic
24C2×#14578933C2211yescharacteristic
25C2×#14578933C2211yescharacteristic
26C2×#14578933C2211yescharacteristic
27C4⋊C4×D157C418yescomplemented
28C2×#14578931C2211yescharacteristic
29C2×#14578931C2211yescharacteristic
30C2×#14578931C2211yescharacteristic
31C2×#14578931C2211yescharacteristic
32C2×C4×Dic157C2211yescharacteristic
33C2×C4×Dic157C2211yescharacteristic
34C2×C4×Dic157C2211yescharacteristic
35C2×C4×Dic157C2211yescharacteristic
36C2×C4×Dic157C2211yescharacteristic
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×C42×C157C2211yescharacteristic
48#95×C157C2211yescharacteristic
49#95×C157C2211yescharacteristic
50#95×C157C2211yescharacteristic
51#95×C157C2211yescharacteristic
52C23×D157C2311yescharacteristic
53C22×Dic157C2311yescharacteristic
54C22×Dic157C2311yescharacteristic
55C22×Dic157C2311yescharacteristic
56C22×Dic157C2311yescharacteristic
57C22×Dic157C2311yescharacteristic
58C22×Dic157C2311yescharacteristic
59C22×Dic157C2311yescharacteristic
60C2×C4×D157—22no—
61C2×C4×D157—22no—
62C2×C4×D157—41no—
63C2×C4×D157—41no—
64C2×C4×D157—41no—
65C2×C4×D157—41no—
66C2×C4×D157C2×C414yes—
67C2×C4×D157C2×C414yes—
68C2×C4×D157C2×C414yes—
69C4⋊Dic157—41no—
70C4⋊Dic157C2×C414yes—
71#14578933—22no—
72#14578933—22no—
73#14578933—41no—
74#14578933—41no—
75#14578933C2×C414yes—
76#14578933C2×C414yes—
77#14578931—22no—
78#14578931—22no—
79#14578931—22no—
80#14578931Q814yes—
81C4×Dic157—22no—
82C4×Dic157—22no—
83C4×Dic157—41no—
84C4×Dic157—41no—
85C4×Dic157—41no—
86C22×C4×C157C2311yescharacteristic
87C22×C4×C157C2311yescharacteristic
88C22×C4×C157C2311yescharacteristic
89C22×C4×C157C2311yescharacteristic
90C22×C4×C157C2311yescharacteristic
91C22×C4×C157C2311yescharacteristic
92C22×C4×C157C2311yescharacteristic
93C4⋊C4×C157—41no—
94C4⋊C4×C157C2×C414yes—
95C42×C157—41no—
96C22×D157—21no—
97C22×D157—21no—
98C22×D157—21no—
99C22×D157—21no—
100C22×D157C22×C412yes—
101C22×D157C2×Q812yes—
102C22×D157#4112yes—
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—
121C2×Dic157C2×Q812yes—
122C2×Dic157#4112yes—
123C2×Dic157#4112yes—
124C4×D157—28no—
125C4×D157—44no—
126C4×D157—44no—
127C23×C157C2411yescharacteristic
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×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157C22×C412yes—
146C2×C4×C157C22×C412yes—
147C2×C4×C157C22×C412yes—
148C2×C4×C157C2×Q812yes—
149C22×C157C23×C411yescharacteristic
150C22×C157C22×Q811yescharacteristic
151C22×C157C2×#4111yescharacteristic
152C22×C157C2×#4111yescharacteristic
153C22×C157C2×#4111yescharacteristic
154C22×C157H(5,𝔽2)11yescharacteristic
155C22×C157H(5,𝔽2)11yescharacteristic
156C2×D157—22no—
157C2×D157—22no—
158C2×D157—22no—
159C2×D157—22no—
160C2×D157—22no—
161C2×D157—22no—
162C2×D157C4×Q814yes—
163C4×C157—22no—
164C4×C157—22no—
165C4×C157—22no—
166C4×C157—22no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157—41no—
170Dic157—22no—
171Dic157—22no—
172Dic157—22no—
173Dic157—41no—
174Dic157—41no—
175Dic157—41no—
176Dic157#11714yes—
177C2×C157C2×#11711yescharacteristic
178C2×C157C2×C4×Q811yescharacteristic
179C2×C157#51811yescharacteristic
180C2×C157#55311yescharacteristic
181C2×C157#55311yescharacteristic
182C2×C157#55411yescharacteristic
183C2×C157#55411yescharacteristic
184D157—24no—
185C157#234511yescharacteristic, complemented, Sylow
186#2345—1571nomaximal, Sylow
187C22×C4⋊C4—1571no—
188#389—1571no—
189#389—1571no—
190#387—1571no—
191#387—1571no—
192#387—1571no—
193#387D15711yescharacteristic, complemented
194#380—1571no—
195#380—1571no—
196#380—1571no—
197C4×C4⋊C4—1571no—
198C4×C4⋊C4—1571no—
199C4×C22⋊C4—1571no—
200C4×C22⋊C4—1571no—
201C4×C22⋊C4—1571no—
202C23×C4—1571no—
203C23×C4—1571no—
204C23×C4—1571no—
205C2×C4⋊C4—1571no—
206C2×C4⋊C4—1571no—
207C2×C4⋊C4—1571no—
208C2×C4⋊C4—1571no—
209C2×C4⋊C4—1571no—
210C2×C4⋊C4—1571no—
211C2×C4⋊C4—1571no—
212C2×C4⋊C4—1571no—
213C2×C4⋊C4—1578no—
214C2×C4⋊C4C2×D15711yescharacteristic
215C2×C4⋊C4C2×D15711yescharacteristic
216C2×C22⋊C4—1571no—
217C2×C22⋊C4—1571no—
218C2×C22⋊C4—1571no—
219C2×C22⋊C4—1571no—
220C2×C42—1571no—
221C2×C42—1571no—
222C2×C42—1571no—
223C2×C42—1571no—
224C2×C42—1571no—
225C2×C42C2×D15711yescharacteristic
226#95—1571no—
227#95—1571no—
228#95—1571no—
229#95—1571no—
230#95—1571no—
231#95—1571no—
232#95—1571no—
233#95—1571no—
234#95C2×D15711yescharacteristic
235#95C2×D15711yescharacteristic
236#95C2×D15711yescharacteristic
237#95C2×D15711yescharacteristic
238C24—1571no—
239C22×C4—3142no—
240C22×C4—3142no—
241C22×C4—6281no—
242C22×C4—6281no—
243C22×C4—6281no—
244C22×C4—6281no—
245C22×C4—1571no—
246C22×C4—1571no—
247C22×C4—1571no—
248C22×C4—1571no—
249C22×C4—1571no—
250C22×C4—1571no—
251C22×C4—1574no—
252C22×C4—1574no—
253C22×C4—1574no—
254C22×C4—1571no—
255C22×C4C22×D15711yescharacteristic
256C22×C4C22×D15711yescharacteristic
257C22×C4C22×D15711yescharacteristic
258C22×C4C22×D15711yescharacteristic
259C22×C4C22×D15711yescharacteristic
260C22×C4C22×D15711yescharacteristic
261C22×C4C22×D15711yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—3142no—
264C4⋊C4—3142no—
265C4⋊C4—6281no—
266C4⋊C4—6281no—
267C4⋊C4—6281no—
268C4⋊C4—1574no—
269C4⋊C4—1574no—
270C4⋊C4—1574no—
271C4⋊C4C4×D15714yes—
272C22⋊C4—3142no—
273C22⋊C4—3142no—
274C22⋊C4—3142no—
275C22⋊C4—1574no—
276C42—41no—
277C42—3142no—
278C42—3142no—
279C42—6281no—
280C42—6281no—
281C42—6281no—
282C23—3141no—
283C23—3141no—
284C23—3141no—
285C23—3141no—
286C23—1572no—
287C23—1572no—
288C23—1572no—
289C23C23×D15711yescharacteristic
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—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—3148no—
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—3141no—
319C2×C4—3141no—
320C2×C4—3141no—
321C2×C4—3141no—
322C2×C4—3141no—
323C2×C4—6284no—
324C2×C4—6284no—
325C2×C4—1572no—
326C2×C4—1572no—
327C2×C4—1572no—
328C2×C4—1572no—
329C2×C4—1572no—
330C2×C4—1572no—
331C2×C4C2×C4×D15712yes—
332C2×C4C2×C4×D15712yes—
333C2×C4C2×C4×D15712yes—
334C2×C4Q8×D15712yes—
335C22—3142no—
336C22—3142no—
337C22—3142no—
338C22—3142no—
339C22—3142no—
340C22—3142no—
341C22—1574no—
342C22C22×C4×D15711yescharacteristic
343C22C2×Q8×D15711yescharacteristic
344C22#41×D15711yescharacteristic
345C22#41×D15711yescharacteristic
346C22#41×D15711yescharacteristic
347C22#1909781611yescharacteristic
348C22#1909781711yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3142no—
357C4—3142no—
358C4—3142no—
359C4—6281no—
360C4—6281no—
361C4—6281no—
362C4—1574no—
363C2—3144no—
364C2#117×D15711yescharacteristic
365C2C4×Q8×D15711yescharacteristic
366C2#2375774511yescharacteristic
367C2#2375796811yescharacteristic
368C2#2375797411yescharacteristic
369C2#2375797711yescharacteristic
370C2#2375797911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#387×C157C2
socle, cosocleC23×C157C24
prime radicalC23×D157C23
hypercenter#387D157
hypocenterC157#2345
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #23757170C2semidirect
3. #23757168C2semidirect
4. #23757159C2semidirect
5. #23757158C2semidirect
6. #23757156C2semidirect
10. C4×#14578933C2semidirect
11. #23757124C2semidirect
15. #387×C157C2semidirect
27. C4⋊C4×D157C4semidirect
185. C157#2345semidirect
193. #387D157semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1572
#237571702
#237571682
#237571592
#237571582
#237571562
#237571322
#237571302
C4×#145789332
#237571242
C4×#145789312
#237571202
#387×C1572
#2345157