Finite Group Databasebeta

← C101×#12945 #38795096

Subgroups — C101×#12945 #38795096

Order 25856.

402 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2951C211yesmaximal, characteristic
2C2×#366×C101C211yesmaximal, characteristic, complemented
3C2×#359×C101C211yesmaximal, characteristic
4C101×#2139C211yesmaximal, characteristic
5C101×#1952C211yesmaximal, characteristic, complemented
6C101×#1387C211yesmaximal, characteristic, complemented
7C101×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9#520×C101—21no—
10C2×M32×C101C2211yescharacteristic
11C22×C16×C101C2211yescharacteristic
12#440×C101—22no—
13C4×Q16×C101—21no—
14C4×D8×C101—21no—
15C2×#108×C101C2211yescharacteristic
16#428×C101—21no—
17C2×#107×C101C2211yescharacteristic
18C2×#107×C101C2211yescharacteristic
19#417×C101—21no—
20#405×C101C2211yescharacteristic
21#366×C101—22no—
22#359×C101C414yescomplemented
23#358×C101—21no—
24#357×C101—21no—
25#343×C101—21no—
26C2×#41×C101—21no—
27#135×C101—21no—
28#135×C101—21no—
29#135×C101C2×C412yes—
30#135×C101Q812yes—
31C2×Q16×C101D411yescharacteristic
32C2×SD16×C101—21no—
33C2×D8×C101D411yescharacteristic
34C2×M16×C101—21no—
35C2×M16×C101D411yescharacteristic
36C22×C8×C101C2311yescharacteristic
37C4×Q8×C101—22no—
38C4×D4×C101—22no—
39C4×D4×C101—42no—
40#117×C101—41no—
41#117×C101D411yescharacteristic
42C2×C4⋊C4×C101—21no—
43C2×C4⋊C4×C101—21no—
44C2×C4⋊C4×C101—41no—
45M32×C101—21no—
46M32×C101—21no—
47C2×C16×C101—21no—
48C2×C16×C101—21no—
49C2×C16×C101—21no—
50C2×C16×C101C2×C412yescomplemented
51#108×C101—21no—
52#108×C101C2×C412yescomplemented
53#107×C101—21no—
54#107×C101—21no—
55#107×C101—21no—
56#107×C101—41no—
57#107×C101D412yes—
58#106×C101—41no—
59#103×C101—22no—
60#102×C101—22no—
61#97×C101—21no—
62C4×C8×C101—21no—
63#41×C101—22no—
64#41×C101—22no—
65#41×C101—41no—
66#41×C101—41no—
67C2×Q8×C101—21no—
68C2×D4×C101—21no—
69C2×D4×C101—41no—
70C22×C4×C101—42no—
71C22×C4×C101—41no—
72C22×C4×C101—41no—
73C22×C4×C101—41no—
74C22×C4×C101C2×D411yescharacteristic
75Q16×C101—21no—
76Q16×C101C4⋊C412yes—
77SD16×C101—22no—
78SD16×C101—22no—
79D8×C101—21no—
80D8×C101C4⋊C412yes—
81M16×C101—22no—
82M16×C101—21no—
83M16×C101—21no—
84M16×C101—41no—
85C2×C8×C101—21no—
86C2×C8×C101—41no—
87C2×C8×C101C22×C411yescharacteristic
88C2×C8×C101C2×D411yescharacteristic
89C2×C8×C101C2×D411yescharacteristic
90C2×C8×C101C2×Q811yescharacteristic
91C2×C8×C101#4111yescharacteristic
92C2×C8×C101#4111yescharacteristic
93C4⋊C4×C101—22no—
94C4⋊C4×C101—42no—
95C4⋊C4×C101—41no—
96C4⋊C4×C101—41no—
97C4⋊C4×C101—41no—
98C4⋊C4×C101D811yescharacteristic
99C4⋊C4×C101D811yescharacteristic
100C22⋊C4×C101—21no—
101C22⋊C4×C101—42no—
102C42×C101—21no—
103C42×C101—42no—
104C16×C101—22no—
105C16×C101—41no—
106C23×C101—41no—
107C23×C101AGL(1,ℤ/8)11yescharacteristic
108Q8×C101—22no—
109Q8×C101—41no—
110D4×C101—22no—
111D4×C101—42no—
112D4×C101—42no—
113D4×C101—41no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—41no—
117C2×C4×C101—42no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—81no—
121C2×C4×C101—162no—
122C2×C4×C101—161no—
123C2×C4×C101—161no—
124C2×C4×C101C4×D411yescharacteristic
125C2×C4×C101#12011yescharacteristic
126C2×C4×C101C22⋊Q811yescharacteristic
127C2×C4×C101C2×D811yescharacteristic
128C2×C4×C101#13511yescharacteristic
129C2×C4×C101#13711yescharacteristic
130C8×C101—42no—
131C8×C101—41no—
132C8×C101C2×C4⋊C411yescharacteristic
133C8×C101C4×D411yescharacteristic
134C8×C101C22⋊Q811yescharacteristic
135C8×C101#12311yescharacteristic
136C22×C101—21no—
137C22×C101—21no—
138C22×C101—42no—
139C22×C101—81no—
140C22×C101—81no—
141C22×C101#44011yescharacteristic
142C22×C101#44711yescharacteristic
143C22×C101#47811yescharacteristic
144C4×C101—42no—
145C4×C101—41no—
146C4×C101—41no—
147C4×C101—82no—
148C4×C101—161no—
149C4×C101#38511yescharacteristic
150C4×C101C4×D811yescharacteristic
151C4×C101#45211yescharacteristic
152C4×C101#47411yescharacteristic
153#12945C10111yesmaximal, characteristic, direct product factor, Sylow
154C2×C101—21no—
155C2×C101—21no—
156C2×C101—82no—
157C2×C101#186211yescharacteristic
158C2×C101#219211yescharacteristic
159C2×C101#219511yescharacteristic
160#2951C2×C10111yescharacteristic
161C2×#366C2×C10111yescharacteristic, complemented
162C2×#359C2×C10111yescharacteristic
163#2139C2×C10111yescharacteristic
164#1952C2×C10111yescharacteristic, complemented
165#1387C2×C10111yescharacteristic, complemented
166#1379C2×C10111yescharacteristic, complemented
167C101#1294511yescharacteristic, direct product factor, Sylow
168C2×#135C22×C10111yescharacteristic
169#520—21no—
170C2×M32C22×C10111yescharacteristic
171C22×C16C22×C10111yescharacteristic
172#440—22no—
173C4×Q16—21no—
174C4×D8—21no—
175C2×#108C22×C10111yescharacteristic
176#428—21no—
177C2×#107C22×C10111yescharacteristic
178C2×#107C22×C10111yescharacteristic
179#417—21no—
180#405C22×C10111yescharacteristic
181#366—22no—
182#359C4×C10114yescomplemented
183#358—21no—
184#357—21no—
185#343—21no—
186C2×#41—21no—
187#135—21no—
188#135—21no—
189#135C2×C4×C10112yes—
190#135Q8×C10112yes—
191C2×Q16D4×C10111yescharacteristic
192C2×SD16—21no—
193C2×D8D4×C10111yescharacteristic
194C2×M16—21no—
195C2×M16D4×C10111yescharacteristic
196C22×C8C23×C10111yescharacteristic
197C4×Q8—22no—
198C4×D4—22no—
199C4×D4—42no—
200#117—41no—
201#117D4×C10111yescharacteristic
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—41no—
205M32—21no—
206M32—21no—
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16C2×C4×C10112yescomplemented
211#108—21no—
212#108C2×C4×C10112yescomplemented
213#107—21no—
214#107—21no—
215#107—21no—
216#107—41no—
217#107D4×C10112yes—
218#106—41no—
219#103—22no—
220#102—22no—
221#97—21no—
222C4×C8—21no—
223#41—22no—
224#41—22no—
225#41—41no—
226#41—41no—
227C2×Q8—21no—
228C2×D4—21no—
229C2×D4—41no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C2×D4×C10111yescharacteristic
235Q16—21no—
236Q16C4⋊C4×C10112yes—
237SD16—22no—
238SD16—22no—
239D8—21no—
240D8C4⋊C4×C10112yes—
241M16—22no—
242M16—21no—
243M16—21no—
244M16—41no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8C22×C4×C10111yescharacteristic
248C2×C8C2×D4×C10111yescharacteristic
249C2×C8C2×D4×C10111yescharacteristic
250C2×C8C2×Q8×C10111yescharacteristic
251C2×C8#41×C10111yescharacteristic
252C2×C8#41×C10111yescharacteristic
253C4⋊C4—22no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4D8×C10111yescharacteristic
259C4⋊C4D8×C10111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—42no—
262C42—21no—
263C42—42no—
264C16—22no—
265C16—41no—
266C23—41no—
267C23AGL(1,ℤ/8)×C10111yescharacteristic
268Q8—22no—
269Q8—41no—
270D4—22no—
271D4—42no—
272D4—42no—
273D4—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—162no—
282C2×C4—161no—
283C2×C4—161no—
284C2×C4C4×D4×C10111yescharacteristic
285C2×C4#120×C10111yescharacteristic
286C2×C4C22⋊Q8×C10111yescharacteristic
287C2×C4C2×D8×C10111yescharacteristic
288C2×C4#135×C10111yescharacteristic
289C2×C4#137×C10111yescharacteristic
290C8—42no—
291C8—41no—
292C8C2×C4⋊C4×C10111yescharacteristic
293C8C4×D4×C10111yescharacteristic
294C8C22⋊Q8×C10111yescharacteristic
295C8#123×C10111yescharacteristic
296C22—21no—
297C22—21no—
298C22—42no—
299C22—81no—
300C22—81no—
301C22#440×C10111yescharacteristic
302C22#447×C10111yescharacteristic
303C22#478×C10111yescharacteristic
304C4—41no—
305C4—41no—
306C4—42no—
307C4—82no—
308C4—161no—
309C4#385×C10111yescharacteristic
310C4C4×D8×C10111yescharacteristic
311C4#452×C10111yescharacteristic
312C4#474×C10111yescharacteristic
313C2—21no—
314C2—21no—
315C2—82no—
316C2C101×#186211yescharacteristic
317C2C101×#219211yescharacteristic
318C2C101×#219511yescharacteristic
subgroupG/H
center, socleC22×C101#447
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
prime radicalC2×#135×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ #405×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#366×C101C2semidirect
5. C101×#1952C2semidirect
6. C101×#1387C2semidirect
7. C101×#1379C2semidirect
22. #359×C101C4semidirect
50. C2×C16×C101C2×C4semidirect
52. #108×C101C2×C4semidirect
153. #12945C101direct (N × H)
161. C2×#366C2×C101semidirect
164. #1952C2×C101semidirect
165. #1387C2×C101semidirect
166. #1379C2×C101semidirect
167. C101#12945direct (N × H)
182. #359C4×C101semidirect
210. C2×C16C2×C4×C101semidirect
212. #108C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#29512
C2×#366×C1012
C2×#359×C1012
C101×#21392
C101×#19522
C101×#13872
C101×#13792
#12945101