Finite Group Databasebeta

← C101×#12949 #38795100

Subgroups — C101×#12949 #38795100

Order 25856.

394 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2952C211yesmaximal, characteristic
2C2×#365×C101C211yesmaximal, characteristic, complemented
3C101×#2148C211yesmaximal, characteristic
4C101×#2143C211yesmaximal, characteristic
5C101×#1953C211yesmaximal, characteristic, complemented
6C101×#1383C211yesmaximal, characteristic, complemented
7C101×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9#520×C101—21no—
10C2×M32×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12#442×C101—21no—
13#441×C101—21no—
14C4×SD16×C101—22no—
15#430×C101—21no—
16C2×#108×C101C2211yescharacteristic
17C2×#108×C101C2211yescharacteristic
18C2×#106×C101C2211yescharacteristic
19#417×C101—21no—
20#405×C101C2211yescharacteristic
21#365×C101—22no—
22#362×C101—21no—
23#361×C101—21no—
24#359×C101C414yescomplemented
25#344×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×C101—21no—
36C2×M16×C101D411yescharacteristic
37C22×C8×C101C2311yescharacteristic
38C4×Q8×C101—22no—
39C4×D4×C101—22no—
40C4×D4×C101—42no—
41#117×C101—41no—
42#117×C101D411yescharacteristic
43C2×C4⋊C4×C101—21no—
44C2×C4⋊C4×C101—41no—
45M32×C101—21no—
46M32×C101—21no—
47M32×C101—21no—
48M32×C101—21no—
49C2×C16×C101—21no—
50C2×C16×C101C2×C412yescomplemented
51#108×C101—21no—
52#108×C101—21no—
53#108×C101—21no—
54#108×C101—42no—
55#108×C101C2×C412yescomplemented
56#106×C101—21no—
57#106×C101D412yes—
58#103×C101—22no—
59#102×C101—22no—
60#97×C101—21no—
61C4×C8×C101—21no—
62#41×C101—22no—
63#41×C101—22no—
64#41×C101—41no—
65#41×C101—41no—
66C2×Q8×C101—21no—
67C2×D4×C101—21no—
68C2×D4×C101—41no—
69C22×C4×C101—42no—
70C22×C4×C101—41no—
71C22×C4×C101—41no—
72C22×C4×C101C2×D411yescharacteristic
73Q16×C101—21no—
74Q16×C101C4⋊C412yes—
75SD16×C101—22no—
76SD16×C101—22no—
77D8×C101—21no—
78D8×C101C4⋊C412yes—
79M16×C101—22no—
80M16×C101—21no—
81M16×C101—21no—
82M16×C101—41no—
83M16×C101—41no—
84M16×C101—41no—
85C2×C8×C101—21no—
86C2×C8×C101—41no—
87C2×C8×C101—41no—
88C2×C8×C101C22×C411yescharacteristic
89C2×C8×C101C2×D411yescharacteristic
90C2×C8×C101C2×D411yescharacteristic
91C2×C8×C101C2×Q811yescharacteristic
92C2×C8×C101#4111yescharacteristic
93C2×C8×C101#4111yescharacteristic
94C4⋊C4×C101—21no—
95C4⋊C4×C101—22no—
96C4⋊C4×C101—42no—
97C4⋊C4×C101—41no—
98C22⋊C4×C101—42no—
99C22⋊C4×C101SD1612yes—
100C42×C101—21no—
101C42×C101—42no—
102C16×C101—22no—
103C16×C101—41no—
104C23×C101—41no—
105C23×C101C2×SD1611yescharacteristic
106Q8×C101—22no—
107Q8×C101—41no—
108D4×C101—22no—
109D4×C101—42no—
110D4×C101—42no—
111D4×C101—41no—
112C2×C4×C101—22no—
113C2×C4×C101—41no—
114C2×C4×C101—42no—
115C2×C4×C101—42no—
116C2×C4×C101—42no—
117C2×C4×C101—162no—
118C2×C4×C101—161no—
119C2×C4×C101C4×D411yescharacteristic
120C2×C4×C101#12011yescharacteristic
121C2×C4×C101C22⋊Q811yescharacteristic
122C2×C4×C101#13511yescharacteristic
123C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
125C8×C101—42no—
126C8×C101—41no—
127C8×C101—81no—
128C8×C101C2×C4⋊C411yescharacteristic
129C8×C101C4×D411yescharacteristic
130C8×C101C22⋊Q811yescharacteristic
131C8×C101#12311yescharacteristic
132C22×C101—41no—
133C22×C101—42no—
134C22×C101—81no—
135C22×C101—81no—
136C22×C101C4×SD1611yescharacteristic
137C22×C101#45011yescharacteristic
138C22×C101#47611yescharacteristic
139C4×C101—42no—
140C4×C101—42no—
141C4×C101—82no—
142C4×C101#38511yescharacteristic
143C4×C101#44211yescharacteristic
144C4×C101#44911yescharacteristic
145C4×C101#47811yescharacteristic
146#12949C10111yesmaximal, characteristic, direct product factor, Sylow
147C2×C101—21no—
148C2×C101—21no—
149C2×C101—21no—
150C2×C101—82no—
151C2×C101#186411yescharacteristic
152#2952C2×C10111yescharacteristic
153C2×#365C2×C10111yescharacteristic, complemented
154#2148C2×C10111yescharacteristic
155#2143C2×C10111yescharacteristic
156#1953C2×C10111yescharacteristic, complemented
157#1383C2×C10111yescharacteristic, complemented
158#1378C2×C10111yescharacteristic, complemented
159C101#1294911yescharacteristic, direct product factor, Sylow
160C2×#135C22×C10111yescharacteristic
161#520—21no—
162C2×M32C22×C10111yescharacteristic
163C2×M32C22×C10111yescharacteristic
164#442—21no—
165#441—21no—
166C4×SD16—22no—
167#430—21no—
168C2×#108C22×C10111yescharacteristic
169C2×#108C22×C10111yescharacteristic
170C2×#106C22×C10111yescharacteristic
171#417—21no—
172#405C22×C10111yescharacteristic
173#365—22no—
174#362—21no—
175#361—21no—
176#359C4×C10114yescomplemented
177#344—21no—
178C2×#41—21no—
179#135—21no—
180#135—21no—
181#135C2×C4×C10112yes—
182#135Q8×C10112yes—
183C2×Q16D4×C10111yescharacteristic
184C2×SD16—21no—
185C2×D8D4×C10111yescharacteristic
186C2×M16—21no—
187C2×M16—21no—
188C2×M16D4×C10111yescharacteristic
189C22×C8C23×C10111yescharacteristic
190C4×Q8—22no—
191C4×D4—22no—
192C4×D4—42no—
193#117—41no—
194#117D4×C10111yescharacteristic
195C2×C4⋊C4—21no—
196C2×C4⋊C4—41no—
197M32—21no—
198M32—21no—
199M32—21no—
200M32—21no—
201C2×C16—21no—
202C2×C16C2×C4×C10112yescomplemented
203#108—21no—
204#108—21no—
205#108—21no—
206#108—42no—
207#108C2×C4×C10112yescomplemented
208#106—21no—
209#106D4×C10112yes—
210#103—22no—
211#102—22no—
212#97—21no—
213C4×C8—21no—
214#41—22no—
215#41—22no—
216#41—41no—
217#41—41no—
218C2×Q8—21no—
219C2×D4—21no—
220C2×D4—41no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4C2×D4×C10111yescharacteristic
225Q16—21no—
226Q16C4⋊C4×C10112yes—
227SD16—22no—
228SD16—22no—
229D8—21no—
230D8C4⋊C4×C10112yes—
231M16—22no—
232M16—21no—
233M16—21no—
234M16—41no—
235M16—41no—
236M16—41no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8C22×C4×C10111yescharacteristic
241C2×C8C2×D4×C10111yescharacteristic
242C2×C8C2×D4×C10111yescharacteristic
243C2×C8C2×Q8×C10111yescharacteristic
244C2×C8#41×C10111yescharacteristic
245C2×C8#41×C10111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4SD16×C10112yes—
252C42—21no—
253C42—42no—
254C16—22no—
255C16—41no—
256C23—41no—
257C23C2×SD16×C10111yescharacteristic
258Q8—22no—
259Q8—41no—
260D4—22no—
261D4—42no—
262D4—42no—
263D4—41no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—162no—
270C2×C4—161no—
271C2×C4C4×D4×C10111yescharacteristic
272C2×C4#120×C10111yescharacteristic
273C2×C4C22⋊Q8×C10111yescharacteristic
274C2×C4#135×C10111yescharacteristic
275C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
276C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
277C8—42no—
278C8—41no—
279C8—81no—
280C8C2×C4⋊C4×C10111yescharacteristic
281C8C4×D4×C10111yescharacteristic
282C8C22⋊Q8×C10111yescharacteristic
283C8#123×C10111yescharacteristic
284C22—41no—
285C22—42no—
286C22—81no—
287C22—81no—
288C22C4×SD16×C10111yescharacteristic
289C22#450×C10111yescharacteristic
290C22#476×C10111yescharacteristic
291C4—42no—
292C4—42no—
293C4—82no—
294C4#385×C10111yescharacteristic
295C4#442×C10111yescharacteristic
296C4#449×C10111yescharacteristic
297C4#478×C10111yescharacteristic
298C2—21no—
299C2—21no—
300C2—21no—
301C2—82no—
302C2C101×#186411yescharacteristic
subgroupG/H
center, socleC2×C101#1864
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
prime radicalC2×#135×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ #405×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#365×C101C2semidirect
5. C101×#1953C2semidirect
6. C101×#1383C2semidirect
7. C101×#1378C2semidirect
24. #359×C101C4semidirect
50. C2×C16×C101C2×C4semidirect
55. #108×C101C2×C4semidirect
146. #12949C101direct (N × H)
153. C2×#365C2×C101semidirect
156. #1953C2×C101semidirect
157. #1383C2×C101semidirect
158. #1378C2×C101semidirect
159. C101#12949direct (N × H)
176. #359C4×C101semidirect
202. C2×C16C2×C4×C101semidirect
207. #108C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#29522
C2×#365×C1012
C101×#21482
C101×#21432
C101×#19532
C101×#13832
C101×#13782
#12949101