Finite Group Databasebeta

← C101×#8191 #38790342

Subgroups — C101×#8191 #38790342

Order 25856.

498 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C101C211yesmaximal, characteristic
2C4×#104×C101C211yesmaximal, characteristic
3C101×#1744C211yesmaximal, characteristic, complemented
4C101×#1476C211yesmaximal, characteristic
5C8×M16×C101C211yesmaximal, characteristic, complemented
6C101×#1278C211yesmaximal, characteristic, complemented
7C101×#1276C211yesmaximal, characteristic, complemented
8C4×#41×C101C2211yescharacteristic
9C8×Q8×C101C412yescomplemented
10C8×D4×C101—22no—
11C8×D4×C101C412yescomplemented
12#431×C101—21no—
13#431×C101C2211yescharacteristic
14#431×C101C2211yescharacteristic
15C2×#104×C101C412yes—
16C4×M16×C101C2211yescharacteristic
17C2×C4×C8×C101—21no—
18C2×C4×C8×C101C2211yescharacteristic
19C2×C4×C8×C101C2211yescharacteristic
20C43×C101C2211yescharacteristic
21#339×C101C412yes—
22#336×C101—22no—
23Q8⋊C8×C101C412yescomplemented
24D4⋊C8×C101C412yescomplemented
25#322×C101—21no—
26C82×C101—21no—
27C2×#41×C101C2×C411yescharacteristic
28C2×M16×C101C2×C412yes—
29C22×C8×C101—21no—
30C22×C8×C101—22no—
31C22×C8×C101D412yes—
32C4×Q8×C101C2×C411yescharacteristic
33C4×Q8×C101C2×C411yescharacteristic
34C4×D4×C101—21no—
35C4×D4×C101—21no—
36C4×D4×C101C2×C411yescharacteristic
37C4×D4×C101C2×C411yescharacteristic
38#117×C101—21no—
39#117×C101C2×C411yescharacteristic
40C2×C42×C101—21no—
41C2×C42×C101—21no—
42C2×C42×C101—21no—
43C2×C42×C101C2×C412yes—
44C2×C42×C101C2311yescharacteristic
45C4⋊C8×C101—22no—
46C4⋊C8×C101C2×C412yes—
47C4⋊C8×C101C2×C412yes—
48#104×C101C818yescomplemented
49C22⋊C8×C101—21no—
50C22⋊C8×C101—21no—
51C22⋊C8×C101—22no—
52#97×C101—21no—
53C4×C8×C101—22no—
54C4×C8×C101—21no—
55C4×C8×C101—21no—
56C4×C8×C101—21no—
57C4×C8×C101—21no—
58C4×C8×C101C2×C412yes—
59C4×C8×C101C2×C412yes—
60C4×C8×C101D411yescharacteristic
61C4×C8×C101D411yescharacteristic
62#41×C101—22no—
63#41×C101C2×C814yes—
64C2×Q8×C101C4211yescharacteristic
65C2×D4×C101—21no—
66C2×D4×C101C4211yescharacteristic
67C22×C4×C101—21no—
68C22×C4×C101—22no—
69C22×C4×C101—21no—
70C22×C4×C101—21no—
71C22×C4×C101C22×C411yescharacteristic
72C22×C4×C101C2×D411yescharacteristic
73C22×C4×C101#4111yescharacteristic
74M16×C101—22no—
75M16×C101C2×C814yescomplemented
76C2×C8×C101—22no—
77C2×C8×C101—22no—
78C2×C8×C101—22no—
79C2×C8×C101—22no—
80C2×C8×C101—42no—
81C2×C8×C101—44no—
82C2×C8×C101—42no—
83C2×C8×C101C22⋊C412yes—
84C2×C8×C101C22⋊C412yes—
85C4⋊C4×C101—21no—
86C4⋊C4×C101—21no—
87C4⋊C4×C101C4211yescharacteristic
88C4⋊C4×C101C4211yescharacteristic
89C22⋊C4×C101—21no—
90C22⋊C4×C101—21no—
91C22⋊C4×C101—21no—
92C42×C101—21no—
93C42×C101—21no—
94C42×C101—21no—
95C42×C101—22no—
96C42×C101—42no—
97C42×C101—42no—
98C42×C101C2×C814yescomplemented
99C42×C101C22×C411yescharacteristic
100C42×C101C22×C411yescharacteristic
101C42×C101C2×D411yescharacteristic
102C42×C101#4111yescharacteristic
103C23×C101—21no—
104C23×C101C4×D411yescharacteristic
105Q8×C101—21no—
106Q8×C101C4×C812yes—
107D4×C101—24no—
108D4×C101—21no—
109D4×C101C4×C812yes—
110C2×C4×C101—21no—
111C2×C4×C101—22no—
112C2×C4×C101—24no—
113C2×C4×C101—22no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—24no—
117C2×C4×C101—42no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—42no—
121C2×C4×C101C2×C4211yescharacteristic
122C2×C4×C101C2×C22⋊C411yescharacteristic
123C2×C4×C101#11711yescharacteristic
124C2×C4×C101C4×D411yescharacteristic
125C2×C4×C101C4×D411yescharacteristic
126C2×C4×C101C4×D411yescharacteristic
127C2×C4×C101C22×C812yes—
128C2×C4×C101#13112yes—
129C8×C101—22no—
130C8×C101—22no—
131C8×C101—24no—
132C8×C101—42no—
133C8×C101—42no—
134C8×C101—42no—
135C22×C101—21no—
136C22×C101—21no—
137C22×C101—22no—
138C22×C101—41no—
139C22×C101—41no—
140C22×C101C4×C22⋊C411yescharacteristic
141C22×C101C8×D412yes—
142C4×C101—22no—
143C4×C101—21no—
144C4×C101—21no—
145C4×C101—44no—
146C4×C101—41no—
147C4×C101—41no—
148C4×C101C2×C4×C811yescharacteristic
149C4×C101#40511yescharacteristic
150C4×C101#42112yes—
151C4×C101C8×D412yes—
152C4×C101#44412yes—
153#8191C10111yesmaximal, characteristic, direct product factor, Sylow
154C2×C101—22no—
155C2×C101—42no—
156C2×C101C8×C22⋊C411yescharacteristic
157C2×C101#175911yescharacteristic
158C2×C101#176511yescharacteristic
159C8×#41C2×C10111yescharacteristic
160C4×#104C2×C10111yescharacteristic
161#1744C2×C10111yescharacteristic, complemented
162#1476C2×C10111yescharacteristic
163C8×M16C2×C10111yescharacteristic, complemented
164#1278C2×C10111yescharacteristic, complemented
165#1276C2×C10111yescharacteristic, complemented
166C101#819111yescharacteristic, direct product factor, Sylow
167C4×#41C22×C10111yescharacteristic
168C8×Q8C4×C10112yescomplemented
169C8×D4—22no—
170C8×D4C4×C10112yescomplemented
171#431—21no—
172#431C22×C10111yescharacteristic
173#431C22×C10111yescharacteristic
174C2×#104C4×C10112yes—
175C4×M16C22×C10111yescharacteristic
176C2×C4×C8—21no—
177C2×C4×C8C22×C10111yescharacteristic
178C2×C4×C8C22×C10111yescharacteristic
179C43C22×C10111yescharacteristic
180#339C4×C10112yes—
181#336—22no—
182Q8⋊C8C4×C10112yescomplemented
183D4⋊C8C4×C10112yescomplemented
184#322—21no—
185C82—21no—
186C2×#41C2×C4×C10111yescharacteristic
187C2×M16C2×C4×C10112yes—
188C22×C8—21no—
189C22×C8—22no—
190C22×C8D4×C10112yes—
191C4×Q8C2×C4×C10111yescharacteristic
192C4×Q8C2×C4×C10111yescharacteristic
193C4×D4—21no—
194C4×D4—21no—
195C4×D4C2×C4×C10111yescharacteristic
196C4×D4C2×C4×C10111yescharacteristic
197#117—21no—
198#117C2×C4×C10111yescharacteristic
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42C2×C4×C10112yes—
203C2×C42C23×C10111yescharacteristic
204C4⋊C8—22no—
205C4⋊C8C2×C4×C10112yes—
206C4⋊C8C2×C4×C10112yes—
207#104C8×C10118yescomplemented
208C22⋊C8—21no—
209C22⋊C8—21no—
210C22⋊C8—22no—
211#97—21no—
212C4×C8—22no—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8C2×C4×C10112yes—
218C4×C8C2×C4×C10112yes—
219C4×C8D4×C10111yescharacteristic
220C4×C8D4×C10111yescharacteristic
221#41—22no—
222#41C2×C8×C10114yes—
223C2×Q8C42×C10111yescharacteristic
224C2×D4—21no—
225C2×D4C42×C10111yescharacteristic
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C22×C4×C10111yescharacteristic
231C22×C4C2×D4×C10111yescharacteristic
232C22×C4#41×C10111yescharacteristic
233M16—22no—
234M16C2×C8×C10114yescomplemented
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—42no—
240C2×C8—44no—
241C2×C8—42no—
242C2×C8C22⋊C4×C10112yes—
243C2×C8C22⋊C4×C10112yes—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4C42×C10111yescharacteristic
247C4⋊C4C42×C10111yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—21no—
250C22⋊C4—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—22no—
255C42—42no—
256C42—42no—
257C42C2×C8×C10114yescomplemented
258C42C22×C4×C10111yescharacteristic
259C42C22×C4×C10111yescharacteristic
260C42C2×D4×C10111yescharacteristic
261C42#41×C10111yescharacteristic
262C23—21no—
263C23C4×D4×C10111yescharacteristic
264Q8—21no—
265Q8C4×C8×C10112yes—
266D4—24no—
267D4—21no—
268D4C4×C8×C10112yes—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4C2×C42×C10111yescharacteristic
281C2×C4C2×C22⋊C4×C10111yescharacteristic
282C2×C4#117×C10111yescharacteristic
283C2×C4C4×D4×C10111yescharacteristic
284C2×C4C4×D4×C10111yescharacteristic
285C2×C4C4×D4×C10111yescharacteristic
286C2×C4C22×C8×C10112yes—
287C2×C4#131×C10112yes—
288C8—22no—
289C8—22no—
290C8—24no—
291C8—42no—
292C8—42no—
293C8—42no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—41no—
298C22—41no—
299C22C4×C22⋊C4×C10111yescharacteristic
300C22C8×D4×C10112yes—
301C4—22no—
302C4—21no—
303C4—21no—
304C4—44no—
305C4—41no—
306C4—41no—
307C4C2×C4×C8×C10111yescharacteristic
308C4#405×C10111yescharacteristic
309C4#421×C10112yes—
310C4C8×D4×C10112yes—
311C4#444×C10112yes—
312C2—22no—
313C2—42no—
314C2C8×C22⋊C4×C10111yescharacteristic
315C2C101×#175911yescharacteristic
316C2C101×#176511yescharacteristic
subgroupG/H
centerC42×C101C2×D4
commutatorC4C2×C4×C8×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101C4×C22⋊C4
prime radicalC2×#41×C101C2×C4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C42×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1744C2semidirect
5. C8×M16×C101C2semidirect
6. C101×#1278C2semidirect
7. C101×#1276C2semidirect
9. C8×Q8×C101C4semidirect
11. C8×D4×C101C4semidirect
23. Q8⋊C8×C101C4semidirect
24. D4⋊C8×C101C4semidirect
48. #104×C101C8semidirect
75. M16×C101C2×C8semidirect
98. C42×C101C2×C8semidirect
153. #8191C101direct (N × H)
161. #1744C2×C101semidirect
163. C8×M16C2×C101semidirect
164. #1278C2×C101semidirect
165. #1276C2×C101semidirect
166. C101#8191direct (N × H)
168. C8×Q8C4×C101semidirect
170. C8×D4C4×C101semidirect
182. Q8⋊C8C4×C101semidirect
183. D4⋊C8C4×C101semidirect
207. #104C8×C101semidirect
234. M16C2×C8×C101semidirect
257. C42C2×C8×C101semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C1012
C4×#104×C1012
C101×#17442
C101×#14762
C8×M16×C1012
C101×#12782
C101×#12762
#8191101