Finite Group Databasebeta

← C101×#22691 #38804842

Subgroups — C101×#22691 #38804842

Order 25856.

846 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#443×C101C211yesmaximal, characteristic
2C101×#2952C212yesmaximal
3C101×#2913C212yesmaximal, complemented
4C101×#1951C212yesmaximal, complemented
5C101×#1860C214yesmaximal, complemented
6C101×#1846C211yesmaximal, characteristic, complemented
7C101×#1816C212yesmaximal, complemented
8C101×#1772C211yesmaximal, characteristic, complemented
9C2×#135×C101C2211yescharacteristic
10C2×#131×C101C2212yes—
11#520×C101C2214yes—
12#443×C101C418yescomplemented
13#442×C101—22no—
14#441×C101—22no—
15C4×SD16×C101—24no—
16C2×#108×C101C2211yescharacteristic
17C2×#108×C101C2211yescharacteristic
18#428×C101—24no—
19#428×C101C2214yes—
20#427×C101—22no—
21#427×C101C2211yescharacteristic
22C2×#107×C101—22no—
23C2×#107×C101C2212yes—
24C2×#106×C101C2212yes—
25C2×#104×C101C2212yes—
26#417×C101C2214yes—
27#405×C101C2212yes—
28C2×C4×C8×C101C2211yescharacteristic
29#382×C101C2212yes—
30#343×C101C2214yes—
31#339×C101C2212yes—
32C2×#41×C101C2312yes—
33#135×C101C2×C414yes—
34#135×C101Q814yes—
35C2×Q16×C101D411yescharacteristic
36C2×SD16×C101D412yes—
37C2×D8×C101D411yescharacteristic
38#131×C101—24no—
39#131×C101C2×C418yescomplemented
40C2×M16×C101—22no—
41C2×M16×C101C2312yes—
42C2×M16×C101C2312yes—
43C22×C8×C101—22no—
44C22×C8×C101C2311yescharacteristic
45C22×C8×C101C2311yescharacteristic
46C4×Q8×C101—24no—
47C4×D4×C101—24no—
48C4×D4×C101—44no—
49#117×C101—24no—
50#117×C101C2312yes—
51C2×C4⋊C4×C101—24no—
52C2×C4⋊C4×C101C2314yes—
53C2×C42×C101C2311yescharacteristic
54#108×C101—22no—
55#108×C101C2×C414yescomplemented
56#107×C101—22no—
57#107×C101—22no—
58#107×C101—24no—
59#107×C101D412yes—
60#106×C101—22no—
61#106×C101—22no—
62#106×C101—24no—
63#106×C101D412yes—
64#104×C101C2×C418yescomplemented
65#103×C101—24no—
66#102×C101—24no—
67#97×C101—22no—
68C4×C8×C101—22no—
69C4×C8×C101C2×C414yescomplemented
70#95×C101—42no—
71#41×C101—22no—
72#41×C101—22no—
73#41×C101C22×C414yes—
74#41×C101C2×Q814yes—
75C2×Q8×C101C2×D412yes—
76C2×D4×C101—22no—
77C2×D4×C101C2×D412yes—
78C22×C4×C101—22no—
79C22×C4×C101—21no—
80C22×C4×C101—24no—
81C22×C4×C101—44no—
82C22×C4×C101C2411yescharacteristic
83Q16×C101C4⋊C414yes—
84SD16×C101C4⋊C418yes—
85D8×C101C4⋊C414yes—
86M16×C101—22no—
87M16×C101—28no—
88M16×C101—22no—
89M16×C101—22no—
90M16×C101C22×C414yes—
91C2×C8×C101—22no—
92C2×C8×C101—28no—
93C2×C8×C101—22no—
94C2×C8×C101C22×C412yes—
95C2×C8×C101C22×C412yes—
96C2×C8×C101C2×D411yescharacteristic
97C2×C8×C101C2×D411yescharacteristic
98C2×C8×C101C2×D411yescharacteristic
99C2×C8×C101C2×D411yescharacteristic
100C2×C8×C101C2×Q812yes—
101C2×C8×C101#4112yes—
102C4⋊C4×C101—24no—
103C4⋊C4×C101—24no—
104C4⋊C4×C101—44no—
105C4⋊C4×C101C2×D414yes—
106C22⋊C4×C101—22no—
107C22⋊C4×C101—44no—
108C42×C101—22no—
109C42×C101—21no—
110C42×C101—44no—
111C42×C101C22×C412yes—
112C23×C101—22no—
113C23×C101H(5,𝔽2)11yescharacteristic
114Q8×C101—22no—
115Q8×C101C2×C4⋊C414yes—
116D4×C101—24no—
117D4×C101—24no—
118D4×C101—22no—
119D4×C101C2×C4⋊C414yes—
120C2×C4×C101—22no—
121C2×C4×C101—24no—
122C2×C4×C101—24no—
123C2×C4×C101—22no—
124C2×C4×C101—24no—
125C2×C4×C101—42no—
126C2×C4×C101—44no—
127C2×C4×C101—84no—
128C2×C4×C101—164no—
129C2×C4×C101C23×C411yescharacteristic
130C2×C4×C101C22×D411yescharacteristic
131C2×C4×C101C22×D411yescharacteristic
132C2×C4×C101C22×Q811yescharacteristic
133C2×C4×C101C2×#4111yescharacteristic
134C2×C4×C1012−1+411yescharacteristic
135C8×C101—24no—
136C8×C101—42no—
137C8×C101C2×C4⋊C412yes—
138C8×C101C2×C4⋊C412yes—
139C8×C101C4×D412yes—
140C8×C101C4×D412yes—
141C22×C101—22no—
142C22×C101—24no—
143C22×C101—42no—
144C22×C101—42no—
145C22×C101#52011yescharacteristic
146C22×C101D4211yescharacteristic
147C22×C101#55411yescharacteristic
148C4×C101—24no—
149C4×C101—42no—
150C4×C101—44no—
151C4×C101—84no—
152C4×C101C22×C4⋊C411yescharacteristic
153C4×C101C2×C4×D411yescharacteristic
154C4×C101#54711yescharacteristic
155C4×C101D4×Q811yescharacteristic
156#22691C10111yesmaximal, characteristic, direct product factor, Sylow
157C2×C101—21no—
158C2×C101—21no—
159C2×C101—44no—
160C2×C101D4×C4⋊C411yescharacteristic
161C2×C101#329012yes—
162C2×#443C2×C10111yescharacteristic
163#2952C2×C10112yes—
164#2913C2×C10112yescomplemented
165#1951C2×C10112yescomplemented
166#1860C2×C10114yescomplemented
167#1846C2×C10111yescharacteristic, complemented
168#1816C2×C10112yescomplemented
169#1772C2×C10111yescharacteristic, complemented
170C101#2269111yescharacteristic, direct product factor, Sylow
171C2×#135C22×C10111yescharacteristic
172C2×#131C22×C10112yes—
173#520C22×C10114yes—
174#443C4×C10118yescomplemented
175#442—22no—
176#441—22no—
177C4×SD16—24no—
178C2×#108C22×C10111yescharacteristic
179C2×#108C22×C10111yescharacteristic
180#428—24no—
181#428C22×C10114yes—
182#427—22no—
183#427C22×C10111yescharacteristic
184C2×#107—22no—
185C2×#107C22×C10112yes—
186C2×#106C22×C10112yes—
187C2×#104C22×C10112yes—
188#417C22×C10114yes—
189#405C22×C10112yes—
190C2×C4×C8C22×C10111yescharacteristic
191#382C22×C10112yes—
192#343C22×C10114yes—
193#339C22×C10112yes—
194C2×#41C23×C10112yes—
195#135C2×C4×C10114yes—
196#135Q8×C10114yes—
197C2×Q16D4×C10111yescharacteristic
198C2×SD16D4×C10112yes—
199C2×D8D4×C10111yescharacteristic
200#131—24no—
201#131C2×C4×C10118yescomplemented
202C2×M16—22no—
203C2×M16C23×C10112yes—
204C2×M16C23×C10112yes—
205C22×C8—22no—
206C22×C8C23×C10111yescharacteristic
207C22×C8C23×C10111yescharacteristic
208C4×Q8—24no—
209C4×D4—24no—
210C4×D4—44no—
211#117—24no—
212#117C23×C10112yes—
213C2×C4⋊C4—24no—
214C2×C4⋊C4C23×C10114yes—
215C2×C42C23×C10111yescharacteristic
216#108—22no—
217#108C2×C4×C10114yescomplemented
218#107—22no—
219#107—22no—
220#107—24no—
221#107D4×C10112yes—
222#106—22no—
223#106—22no—
224#106—24no—
225#106D4×C10112yes—
226#104C2×C4×C10118yescomplemented
227#103—24no—
228#102—24no—
229#97—22no—
230C4×C8—22no—
231C4×C8C2×C4×C10114yescomplemented
232#95—42no—
233#41—22no—
234#41—22no—
235#41C22×C4×C10114yes—
236#41C2×Q8×C10114yes—
237C2×Q8C2×D4×C10112yes—
238C2×D4—22no—
239C2×D4C2×D4×C10112yes—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—44no—
244C22×C4C24×C10111yescharacteristic
245Q16C4⋊C4×C10114yes—
246SD16C4⋊C4×C10118yes—
247D8C4⋊C4×C10114yes—
248M16—22no—
249M16—28no—
250M16—22no—
251M16—22no—
252M16C22×C4×C10114yes—
253C2×C8—22no—
254C2×C8—28no—
255C2×C8—22no—
256C2×C8C22×C4×C10112yes—
257C2×C8C22×C4×C10112yes—
258C2×C8C2×D4×C10111yescharacteristic
259C2×C8C2×D4×C10111yescharacteristic
260C2×C8C2×D4×C10111yescharacteristic
261C2×C8C2×D4×C10111yescharacteristic
262C2×C8C2×Q8×C10112yes—
263C2×C8#41×C10112yes—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—44no—
267C4⋊C4C2×D4×C10114yes—
268C22⋊C4—22no—
269C22⋊C4—44no—
270C42—22no—
271C42—21no—
272C42—44no—
273C42C22×C4×C10112yes—
274C23—22no—
275C23H(5,𝔽2)×C10111yescharacteristic
276Q8—22no—
277Q8C2×C4⋊C4×C10114yes—
278D4—24no—
279D4—24no—
280D4—22no—
281D4C2×C4⋊C4×C10114yes—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—84no—
290C2×C4—164no—
291C2×C4C23×C4×C10111yescharacteristic
292C2×C4C22×D4×C10111yescharacteristic
293C2×C4C22×D4×C10111yescharacteristic
294C2×C4C22×Q8×C10111yescharacteristic
295C2×C4C2×#41×C10111yescharacteristic
296C2×C42−1+4×C10111yescharacteristic
297C8—24no—
298C8—42no—
299C8C2×C4⋊C4×C10112yes—
300C8C2×C4⋊C4×C10112yes—
301C8C4×D4×C10112yes—
302C8C4×D4×C10112yes—
303C22—22no—
304C22—24no—
305C22—42no—
306C22—42no—
307C22#520×C10111yescharacteristic
308C22D42×C10111yescharacteristic
309C22#554×C10111yescharacteristic
310C4—24no—
311C4—42no—
312C4—44no—
313C4—84no—
314C4C22×C4⋊C4×C10111yescharacteristic
315C4C2×C4×D4×C10111yescharacteristic
316C4#547×C10111yescharacteristic
317C4D4×Q8×C10111yescharacteristic
318C2—21no—
319C2—21no—
320C2—44no—
321C2D4×C4⋊C4×C10111yescharacteristic
322C2C101×#329012yes—
subgroupG/H
center, socleC22×C101D42
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#135×C101C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#2913C2semidirect
4. C101×#1951C2semidirect
5. C101×#1860C2semidirect
6. C101×#1846C2semidirect
7. C101×#1816C2semidirect
8. C101×#1772C2semidirect
12. #443×C101C4semidirect
39. #131×C101C2×C4semidirect
55. #108×C101C2×C4semidirect
64. #104×C101C2×C4semidirect
69. C4×C8×C101C2×C4semidirect
156. #22691C101direct (N × H)
164. #2913C2×C101semidirect
165. #1951C2×C101semidirect
166. #1860C2×C101semidirect
167. #1846C2×C101semidirect
168. #1816C2×C101semidirect
169. #1772C2×C101semidirect
170. C101#22691direct (N × H)
174. #443C4×C101semidirect
201. #131C2×C4×C101semidirect
217. #108C2×C4×C101semidirect
226. #104C2×C4×C101semidirect
231. C4×C8C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#443×C1012
C101×#29522
C101×#29132
C101×#19512
C101×#18602
C101×#18462
C101×#18162
C101×#17722
#22691101