Finite Group Databasebeta

← C101×#10224 #38792375

Subgroups — C101×#10224 #38792375

Order 25856.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3230C211yesmaximal, characteristic
2C101×#3209C211yesmaximal, characteristic
3C101×#3162C211yesmaximal, characteristic
4C101×#1993C211yesmaximal, characteristic
5C101×#1518C211yesmaximal, characteristic
6C101×#1518C211yesmaximal, characteristic
7C101×#1281C211yesmaximal, characteristic
8#533×C101C2211yescharacteristic
9#533×C101C2211yescharacteristic
10C2×C4⋊Q8×C101C2211yescharacteristic
11#501×C101—21no—
12#501×C101—21no—
13#501×C101—21no—
14#501×C101—21no—
15#500×C101—21no—
16#494×C101—21no—
17#487×C101—21no—
18#487×C101—21no—
19#484×C101—22no—
20#477×C101—22no—
21#462×C101—22no—
22#451×C101—22no—
23#431×C101C2211yescharacteristic
24#431×C101C2211yescharacteristic
25#427×C101—22no—
26C2×#97×C101C2211yescharacteristic
27#382×C101C2211yescharacteristic
28#340×C101—22no—
29#328×C101—22no—
30#328×C101—22no—
31C22×Q8×C101—21no—
32C2×Q16×C101—24no—
33C22×C8×C101D412yes—
34C4⋊Q8×C101—21no—
35C4⋊Q8×C101—21no—
36C4⋊Q8×C101—21no—
37C4⋊Q8×C101D412yes—
38C4⋊Q8×C101D411yescharacteristic
39C4⋊Q8×C101D411yescharacteristic
40C4⋊Q8×C101D411yescharacteristic
41C4⋊Q8×C101D411yescharacteristic
42#125×C101—21no—
43#125×C101—21no—
44C22⋊Q8×C101—21no—
45C22⋊Q8×C101—21no—
46C22⋊Q8×C101—21no—
47C22⋊Q8×C101—21no—
48C4×Q8×C101—21no—
49C4×Q8×C101—21no—
50C4×Q8×C101—21no—
51C4×Q8×C101—21no—
52#117×C101—21no—
53#117×C101—21no—
54C2×C4⋊C4×C101—21no—
55C2×C4⋊C4×C101—21no—
56C2×C4⋊C4×C101—21no—
57C2×C42×C101C2311yescharacteristic
58#107×C101—22no—
59#107×C101—22no—
60#107×C101—24no—
61#106×C101—22no—
62#106×C101—22no—
63C4⋊C8×C101—21no—
64C4⋊C8×C101—21no—
65#103×C101—24no—
66#103×C101—24no—
67C22⋊C8×C101D412yes—
68C22⋊C8×C101D412yes—
69#97×C101—21no—
70#97×C101—21no—
71C4×C8×C101—21no—
72C4×C8×C101—21no—
73#95×C101—21no—
74#95×C101—21no—
75C2×Q8×C101—21no—
76C2×Q8×C101—22no—
77C2×Q8×C101—21no—
78C2×Q8×C101—21no—
79C2×Q8×C101—21no—
80C2×Q8×C101—41no—
81C2×Q8×C101—82no—
82C22×C4×C101—41no—
83C22×C4×C101—41no—
84C22×C4×C101C2×D411yescharacteristic
85C22×C4×C101C2×D411yescharacteristic
86C22×C4×C101C2×D411yescharacteristic
87Q16×C101—84no—
88C2×C8×C101—22no—
89C2×C8×C101—22no—
90C2×C8×C101—22no—
91C2×C8×C101—22no—
92C2×C8×C101Q1614yescomplemented
93C4⋊C4×C101—21no—
94C4⋊C4×C101—22no—
95C4⋊C4×C101—21no—
96C4⋊C4×C101—21no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101—21no—
100C4⋊C4×C101—22no—
101C4⋊C4×C101—21no—
102C4⋊C4×C101—21no—
103C4⋊C4×C101—41no—
104C4⋊C4×C101—41no—
105C4⋊C4×C101—41no—
106C4⋊C4×C101—41no—
107C4⋊C4×C101—41no—
108C4⋊C4×C101—41no—
109C4⋊C4×C101—42no—
110C22⋊C4×C101—41no—
111C22⋊C4×C101—41no—
112C42×C101—41no—
113C42×C101—41no—
114C42×C101C2×D411yescharacteristic
115C42×C101C2×D411yescharacteristic
116C42×C101C2×D411yescharacteristic
117C42×C101#4111yescharacteristic
118C23×C101#12711yescharacteristic
119Q8×C101—42no—
120Q8×C101—44no—
121Q8×C101—42no—
122Q8×C101—81no—
123Q8×C101—81no—
124Q8×C101—82no—
125C2×C4×C101—41no—
126C2×C4×C101—41no—
127C2×C4×C101—41no—
128C2×C4×C101—41no—
129C2×C4×C101—41no—
130C2×C4×C101—41no—
131C2×C4×C101—42no—
132C2×C4×C101—82no—
133C2×C4×C101—81no—
134C2×C4×C101—81no—
135C2×C4×C101—81no—
136C2×C4×C101#12011yescharacteristic
137C2×C4×C101#12011yescharacteristic
138C2×C4×C101#12011yescharacteristic
139C2×C4×C101#12111yescharacteristic
140C2×C4×C101#12111yescharacteristic
141C2×C4×C101#12111yescharacteristic
142C2×C4×C101C2×Q1612yes—
143C2×C4×C101#13712yes—
144C8×C101—24no—
145C8×C101—42no—
146C8×C101—42no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101#39211yescharacteristic
150C22×C101#49411yescharacteristic
151C22×C101#49711yescharacteristic
152C4×C101—21no—
153C4×C101—21no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—82no—
157C4×C101—81no—
158C4×C101—81no—
159C4×C101—81no—
160C4×C101—81no—
161C4×C101—161no—
162C4×C101#45112yes—
163C4×C101#46212yes—
164#10224C10111yesmaximal, characteristic, direct product factor, Sylow
165C2×C101—21no—
166C2×C101—21no—
167C2×C101#200811yescharacteristic
168C2×C101#200911yescharacteristic
169C2×C101#201611yescharacteristic
170#3230C2×C10111yescharacteristic
171#3209C2×C10111yescharacteristic
172#3162C2×C10111yescharacteristic
173#1993C2×C10111yescharacteristic
174#1518C2×C10111yescharacteristic
175#1518C2×C10111yescharacteristic
176#1281C2×C10111yescharacteristic
177C101#1022411yescharacteristic, direct product factor, Sylow
178#533C22×C10111yescharacteristic
179#533C22×C10111yescharacteristic
180C2×C4⋊Q8C22×C10111yescharacteristic
181#501—21no—
182#501—21no—
183#501—21no—
184#501—21no—
185#500—21no—
186#494—21no—
187#487—21no—
188#487—21no—
189#484—22no—
190#477—22no—
191#462—22no—
192#451—22no—
193#431C22×C10111yescharacteristic
194#431C22×C10111yescharacteristic
195#427—22no—
196C2×#97C22×C10111yescharacteristic
197#382C22×C10111yescharacteristic
198#340—22no—
199#328—22no—
200#328—22no—
201C22×Q8—21no—
202C2×Q16—24no—
203C22×C8D4×C10112yes—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C10112yes—
208C4⋊Q8D4×C10111yescharacteristic
209C4⋊Q8D4×C10111yescharacteristic
210C4⋊Q8D4×C10111yescharacteristic
211C4⋊Q8D4×C10111yescharacteristic
212#125—21no—
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C23×C10111yescharacteristic
228#107—22no—
229#107—22no—
230#107—24no—
231#106—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—24no—
236#103—24no—
237C22⋊C8D4×C10112yes—
238C22⋊C8D4×C10112yes—
239#97—21no—
240#97—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—21no—
244#95—21no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—82no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C10111yescharacteristic
255C22×C4C2×D4×C10111yescharacteristic
256C22×C4C2×D4×C10111yescharacteristic
257Q16—84no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Q16×C10114yescomplemented
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42C2×D4×C10111yescharacteristic
285C42C2×D4×C10111yescharacteristic
286C42C2×D4×C10111yescharacteristic
287C42#41×C10111yescharacteristic
288C23#127×C10111yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#120×C10111yescharacteristic
307C2×C4#120×C10111yescharacteristic
308C2×C4#120×C10111yescharacteristic
309C2×C4#121×C10111yescharacteristic
310C2×C4#121×C10111yescharacteristic
311C2×C4#121×C10111yescharacteristic
312C2×C4C2×Q16×C10112yes—
313C2×C4#137×C10112yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22#392×C10111yescharacteristic
320C22#494×C10111yescharacteristic
321C22#497×C10111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4#451×C10112yes—
333C4#462×C10112yes—
334C2—21no—
335C2—21no—
336C2C101×#200811yescharacteristic
337C2C101×#200911yescharacteristic
338C2C101×#201611yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC2×C42C23×C101
prime radicalC23×C101#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
92. C2×C8×C101Q16semidirect
164. #10224C101direct (N × H)
177. C101#10224direct (N × H)
262. C2×C8Q16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32302
C101×#32092
C101×#31622
C101×#19932
C101×#15182
C101×#12812
#10224101