Finite Group Databasebeta

← C101×#9324 #38791475

Subgroups — C101×#9324 #38791475

Order 25856.

536 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3113C211yesmaximal, characteristic
2C101×#2276C211yesmaximal, characteristic
3C101×#1986C211yesmaximal, characteristic
4C101×#1506C211yesmaximal, characteristic
5C101×#1491C211yesmaximal, characteristic
6C101×#1300C211yesmaximal, characteristic
7C101×#1285C211yesmaximal, characteristic
8#533×C101C2211yescharacteristic
9C2×C4×Q8×C101—21no—
10C2×C4×Q8×C101C2211yescharacteristic
11#483×C101—21no—
12#475×C101C412yescomplemented
13#462×C101C412yescomplemented
14#451×C101—21no—
15#441×C101—22no—
16#432×C101C2211yescharacteristic
17#432×C101C2211yescharacteristic
18C4×M16×C101C2211yescharacteristic
19C4×C4⋊C4×C101—21no—
20C4×C4⋊C4×C101—22no—
21C4×C4⋊C4×C101—21no—
22C4×C4⋊C4×C101C2211yescharacteristic
23#376×C101—21no—
24#376×C101C2211yescharacteristic
25#339×C101—22no—
26#328×C101—21no—
27#328×C101—21no—
28Q8⋊C8×C101—22no—
29C22×Q8×C101D411yescharacteristic
30C2×Q16×C101—22no—
31C2×M16×C101—21no—
32C4⋊Q8×C101C2×C411yescharacteristic
33C4⋊Q8×C101C2×C411yescharacteristic
34#125×C101—21no—
35C22⋊Q8×C101—21no—
36C22⋊Q8×C101—21no—
37C4×Q8×C101—28no—
38C4×Q8×C101—21no—
39C4×Q8×C101—21no—
40C4×Q8×C101—21no—
41C4×Q8×C101—21no—
42C4×Q8×C101C2×C412yes—
43C4×Q8×C101D412yes—
44#117×C101—21no—
45C2×C4⋊C4×C101—22no—
46C2×C4⋊C4×C101—21no—
47C2×C4⋊C4×C101—21no—
48C2×C4⋊C4×C101D411yescharacteristic
49C2×C42×C101—22no—
50C2×C42×C101—21no—
51C2×C42×C101—21no—
52C2×C42×C101—22no—
53C2×C42×C101D412yes—
54C2×C42×C101C2311yescharacteristic
55#106×C101—22no—
56C4⋊C8×C101—21no—
57C4⋊C8×C101C2×C412yes—
58#103×C101—22no—
59#103×C101—22no—
60C22⋊C8×C101—21no—
61C22⋊C8×C101—21no—
62#97×C101—21no—
63#97×C101—21no—
64#97×C101—21no—
65C4×C8×C101—21no—
66#95×C101—22no—
67#95×C101—21no—
68#95×C101—21no—
69#95×C101D411yescharacteristic
70#95×C101D411yescharacteristic
71C2×Q8×C101—24no—
72C2×Q8×C101—21no—
73C2×Q8×C101—21no—
74C2×Q8×C101—21no—
75C2×Q8×C101C22⋊C412yes—
76C22×C4×C101—21no—
77C22×C4×C101—21no—
78C22×C4×C101—21no—
79C22×C4×C101—22no—
80C22×C4×C101—21no—
81C22×C4×C101C2×D411yescharacteristic
82C22×C4×C101C2×D411yescharacteristic
83C22×C4×C101C2×D411yescharacteristic
84Q16×C101—44no—
85M16×C101—22no—
86M16×C101—41no—
87C2×C8×C101—22no—
88C2×C8×C101—41no—
89C2×C8×C101—41no—
90C4⋊C4×C101—28no—
91C4⋊C4×C101—24no—
92C4⋊C4×C101—22no—
93C4⋊C4×C101—22no—
94C4⋊C4×C101—21no—
95C4⋊C4×C101—21no—
96C4⋊C4×C101—21no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101—41no—
100C4⋊C4×C101—41no—
101C4⋊C4×C101C22⋊C412yes—
102C22⋊C4×C101—41no—
103C42×C101—28no—
104C42×C101—24no—
105C42×C101—22no—
106C42×C101—22no—
107C42×C101—42no—
108C42×C101—41no—
109C42×C101—82no—
110C42×C101C22×C411yescharacteristic
111C42×C101C2×D411yescharacteristic
112C42×C101#4111yescharacteristic
113C42×C101#4111yescharacteristic
114C23×C101#12011yescharacteristic
115Q8×C101—24no—
116Q8×C101—22no—
117Q8×C101—42no—
118Q8×C101—81no—
119Q8×C101#10414yes—
120C2×C4×C101—24no—
121C2×C4×C101—22no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—22no—
125C2×C4×C101—22no—
126C2×C4×C101—24no—
127C2×C4×C101—22no—
128C2×C4×C101—22no—
129C2×C4×C101—41no—
130C2×C4×C101—41no—
131C2×C4×C101—42no—
132C2×C4×C101—41no—
133C2×C4×C101—42no—
134C2×C4×C101—41no—
135C2×C4×C101—41no—
136C2×C4×C101—41no—
137C2×C4×C101—41no—
138C2×C4×C101—41no—
139C2×C4×C101—41no—
140C2×C4×C101C2×C22⋊C411yescharacteristic
141C2×C4×C101C4×D411yescharacteristic
142C2×C4×C101C4×D411yescharacteristic
143C2×C4×C101#12111yescharacteristic
144C2×C4×C101#12111yescharacteristic
145C2×C4×C101#12311yescharacteristic
146C8×C101—42no—
147C8×C101—42no—
148C8×C101—81no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101#38611yescharacteristic
152C22×C101#45511yescharacteristic
153C22×C101#45611yescharacteristic
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—24no—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101—44no—
161C4×C101—42no—
162C4×C101—42no—
163C4×C101—42no—
164C4×C101—81no—
165C4×C101—81no—
166C4×C101C2×#10412yes—
167#9324C10111yesmaximal, characteristic, direct product factor, Sylow
168C2×C101—21no—
169C2×C101—21no—
170C2×C101#188211yescharacteristic
171C2×C101#189611yescharacteristic
172C2×C101#190511yescharacteristic
173#3113C2×C10111yescharacteristic
174#2276C2×C10111yescharacteristic
175#1986C2×C10111yescharacteristic
176#1506C2×C10111yescharacteristic
177#1491C2×C10111yescharacteristic
178#1300C2×C10111yescharacteristic
179#1285C2×C10111yescharacteristic
180C101#932411yescharacteristic, direct product factor, Sylow
181#533C22×C10111yescharacteristic
182C2×C4×Q8—21no—
183C2×C4×Q8C22×C10111yescharacteristic
184#483—21no—
185#475C4×C10112yescomplemented
186#462C4×C10112yescomplemented
187#451—21no—
188#441—22no—
189#432C22×C10111yescharacteristic
190#432C22×C10111yescharacteristic
191C4×M16C22×C10111yescharacteristic
192C4×C4⋊C4—21no—
193C4×C4⋊C4—22no—
194C4×C4⋊C4—21no—
195C4×C4⋊C4C22×C10111yescharacteristic
196#376—21no—
197#376C22×C10111yescharacteristic
198#339—22no—
199#328—21no—
200#328—21no—
201Q8⋊C8—22no—
202C22×Q8D4×C10111yescharacteristic
203C2×Q16—22no—
204C2×M16—21no—
205C4⋊Q8C2×C4×C10111yescharacteristic
206C4⋊Q8C2×C4×C10111yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—28no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8C2×C4×C10112yes—
216C4×Q8D4×C10112yes—
217#117—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4×C10111yescharacteristic
222C2×C42—22no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—22no—
226C2×C42D4×C10112yes—
227C2×C42C23×C10111yescharacteristic
228#106—22no—
229C4⋊C8—21no—
230C4⋊C8C2×C4×C10112yes—
231#103—22no—
232#103—22no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#97—21no—
236#97—21no—
237#97—21no—
238C4×C8—21no—
239#95—22no—
240#95—21no—
241#95—21no—
242#95D4×C10111yescharacteristic
243#95D4×C10111yescharacteristic
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8C22⋊C4×C10112yes—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4C2×D4×C10111yescharacteristic
255C22×C4C2×D4×C10111yescharacteristic
256C22×C4C2×D4×C10111yescharacteristic
257Q16—44no—
258M16—22no—
259M16—41no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4C22⋊C4×C10112yes—
275C22⋊C4—41no—
276C42—28no—
277C42—24no—
278C42—22no—
279C42—22no—
280C42—42no—
281C42—41no—
282C42—82no—
283C42C22×C4×C10111yescharacteristic
284C42C2×D4×C10111yescharacteristic
285C42#41×C10111yescharacteristic
286C42#41×C10111yescharacteristic
287C23#120×C10111yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—42no—
291Q8—81no—
292Q8#104×C10114yes—
293C2×C4—24no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4C2×C22⋊C4×C10111yescharacteristic
314C2×C4C4×D4×C10111yescharacteristic
315C2×C4C4×D4×C10111yescharacteristic
316C2×C4#121×C10111yescharacteristic
317C2×C4#121×C10111yescharacteristic
318C2×C4#123×C10111yescharacteristic
319C8—42no—
320C8—42no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22#386×C10111yescharacteristic
325C22#455×C10111yescharacteristic
326C22#456×C10111yescharacteristic
327C4—21no—
328C4—21no—
329C4—24no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4—81no—
339C4C2×#104×C10112yes—
340C2—21no—
341C2—21no—
342C2C101×#188211yescharacteristic
343C2C101×#189611yescharacteristic
344C2C101×#190511yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC23×C101#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
12. #475×C101C4semidirect
13. #462×C101C4semidirect
167. #9324C101direct (N × H)
180. C101#9324direct (N × H)
185. #475C4×C101semidirect
186. #462C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31132
C101×#22762
C101×#19862
C101×#15062
C101×#14912
C101×#13002
C101×#12852
#9324101