Finite Group Databasebeta

← #34100588

Subgroups — #34100588

Order 20096.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097741C211yesmaximal, characteristic
2C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
3C2×#19097685C211yesmaximal, characteristic, complemented
4C2×#19097685C211yesmaximal, characteristic, complemented
5#23757128C211yesmaximal, characteristic, complemented
6#23757040C211yesmaximal, characteristic, complemented
7#342×C157C211yesmaximal, characteristic, complemented
8C24×D157C2211yescharacteristic
9C22×D628C412yescomplemented
10C22×C22⋊D157C2211yescharacteristic
11C22×C4×D157—21no—
12#19097741—21no—
13#19097741—22no—
14#19097741—21no—
15C2×C22⋊Dic157C2211yescharacteristic
16C2×C22⋊Dic157C2211yescharacteristic
17C2×#14578931—21no—
18C2×#14578931—22no—
19C2×#14578931C412yescomplemented
20C22⋊C4×D157—22no—
21C22⋊C4×D157—22no—
22#19097685—22no—
23#19097685—22no—
24C2×C22⋊C4×C157C2211yescharacteristic
25C2×C22⋊C4×C157C2211yescharacteristic
26C2×C22⋊C4×C157C2211yescharacteristic
27C23×D157—21no—
28C23×D157—21no—
29C23×D157—21no—
30C23×D157—21no—
31C23×D157—44no—
32C23×D157C2×C412yes—
33C23×D157C2×C411yescharacteristic, complemented
34C23×D157D411yescharacteristic
35C23×D157D412yes—
36C23×D157D411yescharacteristic
37C2×D628—22no—
38C2×D628—22no—
39C2×D628—44no—
40C2×C22⋊D157—21no—
41C2×C22⋊D157—21no—
42C2×C22⋊D157—21no—
43C2×C22⋊D157—21no—
44C2×C22⋊D157—21no—
45C2×C22⋊D157—21no—
46C22×Dic157—21no—
47C22×Dic157—21no—
48C22×Dic157C2×C411yescharacteristic, complemented
49C2×C4×D157—24no—
50C2×C4×D157—44no—
51C22⋊Dic157—21no—
52C22⋊Dic157—21no—
53C22⋊Dic157—21no—
54C22⋊Dic157D412yescomplemented
55#14578931—24no—
56#14578931—22no—
57#14578931—22no—
58#14578931—44no—
59C24×C157C2311yescharacteristic
60C22×C4×C157—21no—
61C22×C4×C157—21no—
62C22×C4×C157C2×C412yescomplemented
63C22⋊C4×C157—21no—
64C22⋊C4×C157—21no—
65C22⋊C4×C157—21no—
66C22⋊C4×C157—21no—
67C22⋊C4×C157—21no—
68C22⋊C4×C157D412yescomplemented
69C22×D157—21no—
70C22×D157—21no—
71C22×D157—24no—
72C22×D157—22no—
73C22×D157—22no—
74C22×D157—21no—
75C22×D157—22no—
76C22×D157—22no—
77C22×D157—21no—
78C22×D157—24no—
79C22×D157—24no—
80C22×D157—21no—
81C22×D157—21no—
82C22×D157—21no—
83C22×D157—42no—
84C22×D157—42no—
85C22×D157—42no—
86C22×D157—44no—
87C22×D157—44no—
88C22×D157—44no—
89C22×D157—44no—
90C22×D157—42no—
91C22×D157C22⋊C412yes—
92C22×D157C22⋊C412yes—
93D628—44no—
94D628—44no—
95C22⋊D157—41no—
96C22⋊D157—41no—
97C22⋊D157—41no—
98C22⋊D157—41no—
99C2×Dic157—21no—
100C2×Dic157—21no—
101C2×Dic157—21no—
102C2×Dic157—22no—
103C2×Dic157—42no—
104C2×Dic157—42no—
105C2×Dic157—41no—
106C4×D157—48no—
107C23×C157—42no—
108C23×C157C22×C411yescharacteristic
109C23×C157C2×D411yescharacteristic
110C23×C157C2×D411yescharacteristic
111C23×C157C2×D411yescharacteristic
112C23×C157C2×D411yescharacteristic
113C23×C157#4111yescharacteristic
114C23×C157#4111yescharacteristic
115C2×C4×C157—22no—
116C2×C4×C157—22no—
117C2×C4×C157—42no—
118C2×C4×C157—42no—
119C2×C4×C157—42no—
120C2×C4×C157—41no—
121C22×C157—22no—
122C22×C157—22no—
123C22×C157—22no—
124C22×C157—41no—
125C22×C157—41no—
126C22×C157—41no—
127C22×C157—41no—
128C22×C157C2×C22⋊C411yescharacteristic
129C22×C157C4×D411yescharacteristic
130C22×C157C4×D411yescharacteristic
131C22×C157#12011yescharacteristic
132C22×C157#12111yescharacteristic
133C22×C157#12111yescharacteristic
134C22×C157#12311yescharacteristic
135C2×D157—24no—
136C2×D157—24no—
137C2×D157—22no—
138C2×D157—22no—
139C2×D157—22no—
140C2×D157—22no—
141C2×D157—22no—
142C2×D157—44no—
143C2×D157—44no—
144C2×D157—44no—
145C2×D157—44no—
146C2×D157—42no—
147C2×D157—42no—
148C2×D157—41no—
149C2×D157—42no—
150C2×D157—81no—
151C2×D157—81no—
152C2×D157#9914yescomplemented
153C4×C157—42no—
154C4×C157—42no—
155C4×C157—81no—
156Dic157—42no—
157Dic157—41no—
158Dic157—81no—
159C2×C157—21no—
160C2×C157—21no—
161C2×C157—21no—
162C2×C157—21no—
163C2×C157—21no—
164C2×C157—21no—
165C2×C157#38611yescharacteristic
166C2×C157C2×#9912yes—
167D157—24no—
168D157—42no—
169D157—81no—
170C157#189811yescharacteristic, complemented, Sylow
171#1898—1571nomaximal, Sylow
172C2×#120—1571no—
173C22×C22⋊C4—1571no—
174C2×#99—1571no—
175C2×#99—1571no—
176#379—1571no—
177#342—1571no—
178#342D15711yescharacteristic, complemented
179C25—1571no—
180C22×D4—1571no—
181C22×D4—1572no—
182C23×C4—3141no—
183#120—3141no—
184#120—3142no—
185#120—3141no—
186C2×C22⋊C4—3142no—
187C2×C22⋊C4—3141no—
188C2×C22⋊C4—3142no—
189C2×C22⋊C4—3142no—
190C2×C22⋊C4—1571no—
191C2×C22⋊C4—1572no—
192C2×C22⋊C4—1571no—
193C2×C22⋊C4C2×D15711yescharacteristic
194C2×C22⋊C4C2×D15711yescharacteristic
195C2×C22⋊C4C2×D15711yescharacteristic
196#99—3142no—
197#99—3142no—
198C24—3141no—
199C24—3141no—
200C24—3141no—
201C24—3141no—
202C24—6284no—
203C24—1571no—
204C24—1572no—
205C24—1572no—
206C24—1571no—
207C24—1571no—
208C24C22×D15711yescharacteristic
209C2×D4—3142no—
210C2×D4—3142no—
211C2×D4—3141no—
212C2×D4—3141no—
213C2×D4—3141no—
214C2×D4—3141no—
215C2×D4—3141no—
216C2×D4—3141no—
217C2×D4—6284no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—3144no—
221C22×C4—3141no—
222C22×C4—3141no—
223C22×C4—6284no—
224C22×C4—1571no—
225C22×C4C4×D15712yescomplemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—3144no—
232C22⋊C4—3142no—
233C22⋊C4—3142no—
234C22⋊C4—3141no—
235C22⋊C4—3141no—
236C22⋊C4—3141no—
237C22⋊C4—6284no—
238C22⋊C4—1572no—
239C22⋊C4D62812yescomplemented
240C23—42no—
241C23—3144no—
242C23—3144no—
243C23—3144no—
244C23—3141no—
245C23—3141no—
246C23—3142no—
247C23—3142no—
248C23—3141no—
249C23—3142no—
250C23—3142no—
251C23—3141no—
252C23—3141no—
253C23—3141no—
254C23—3141no—
255C23—6282no—
256C23—6282no—
257C23—6282no—
258C23—6282no—
259C23—6284no—
260C23—6284no—
261C23—6284no—
262C23—6284no—
263C23—1572no—
264C23—1572no—
265C23C2×C4×D15711yescharacteristic
266C23D4×D15711yescharacteristic
267C23D4×D15711yescharacteristic
268C23D4×D15711yescharacteristic
269C23C2×D62811yescharacteristic
270C23#1457895411yescharacteristic
271C23#1457895511yescharacteristic
272D4—6284no—
273D4—6284no—
274D4—6281no—
275D4—6281no—
276D4—6281no—
277D4—6281no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—3141no—
285C2×C4—3141no—
286C2×C4—3141no—
287C2×C4—3142no—
288C2×C4—6288no—
289C2×C4—6282no—
290C2×C4—6282no—
291C2×C4—6281no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—3144no—
300C22—3144no—
301C22—3142no—
302C22—3142no—
303C22—3142no—
304C22—3142no—
305C22—3142no—
306C22—6284no—
307C22—6284no—
308C22—6284no—
309C22—6284no—
310C22—6282no—
311C22—6282no—
312C22—6281no—
313C22—6282no—
314C22—1574no—
315C22—12561no—
316C22—12561no—
317C22C22⋊C4×D15711yescharacteristic
318C22#1909773311yescharacteristic
319C22C4×D62811yescharacteristic
320C22#1909774111yescharacteristic
321C22#1909774411yescharacteristic
322C22#1909774611yescharacteristic
323C22#1909775611yescharacteristic
324C4—42no—
325C4—42no—
326C4—81no—
327C4—6282no—
328C4—6281no—
329C4—12561no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—3144no—
337C2—6282no—
338C2—12561no—
339C2#2375715111yescharacteristic
340C2#99×D15712yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×#19097741C2
cosocleC24×C157C23
hypercenter#342D157
hypocenterC157#1898
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D157C2semidirect
3. C2×#19097685C2semidirect
4. C2×#19097685C2semidirect
5. #23757128C2semidirect
6. #23757040C2semidirect
7. #342×C157C2semidirect
9. C22×D628C4semidirect
19. C2×#14578931C4semidirect
33. C23×D157C2×C4semidirect
48. C22×Dic157C2×C4semidirect
54. C22⋊Dic157D4semidirect
62. C22×C4×C157C2×C4semidirect
68. C22⋊C4×C157D4semidirect
152. C2×D157#99semidirect
170. C157#1898semidirect
178. #342D157semidirect
225. C22×C4C4×D157semidirect
239. C22⋊C4D628semidirect

Maximal subgroups

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

subgroupindex
C2×#190977412
C2×C22⋊C4×D1572
C2×#190976852
#237571282
#237570402
#342×C1572
#1898157