Finite Group Databasebeta

← C101×#17550 #38799701

Subgroups — C101×#17550 #38799701

Order 25856.

1030 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3522C211yesmaximal, characteristic
2C101×#2984C211yesmaximal, characteristic, complemented
3C101×#2276C211yesmaximal, characteristic, complemented
4C101×#1509C213yesmaximal, complemented
5C101×#1505C213yesmaximal, complemented
6C101×#1502C213yesmaximal, complemented
7C101×#1500C213yesmaximal, complemented
8#559×C101C413yescomplemented
9Q82×C101C411yescharacteristic, complemented
10#554×C101C413yescomplemented
11#550×C101C411yescharacteristic, complemented
12#548×C101—21no—
13#547×C101—23no—
14#542×C101—23no—
15#532×C101C2213yes—
16#529×C101C2213yes—
17#520×C101—21no—
18C2×C4×Q8×C101—21no—
19C2×C4×Q8×C101C2211yescharacteristic
20#446×C101—23no—
21C8×Q8×C101—21no—
22#432×C101C2213yes—
23#431×C101C2213yes—
24C4×C4⋊C4×C101—23no—
25C4×C4⋊C4×C101C2213yes—
26#376×C101C2213yes—
27#328×C101C2211yescharacteristic
28#328×C101C2213yes—
29#327×C101C2213yes—
30#327×C101C2213yes—
31#327×C101C2216yes—
32C2×#41×C101—21no—
33C2×#41×C101—23no—
34C22×Q8×C101D411yescharacteristic
35C4⋊Q8×C101—23no—
36C4⋊Q8×C101C2×C413yes—
37#127×C101C2×C413yes—
38#126×C101—23no—
39#125×C101C2×C413yes—
40#124×C101—23no—
41#124×C101—23no—
42#124×C101C2×C413yes—
43#123×C101—23no—
44#123×C101—26no—
45C22⋊Q8×C101—23no—
46C22⋊Q8×C101—26no—
47C22⋊Q8×C101C2311yescharacteristic
48#121×C101—23no—
49#121×C101—23no—
50#121×C101C2313yes—
51C4×Q8×C101—28no—
52C4×Q8×C101—21no—
53C4×Q8×C101C2×C413yes—
54C4×Q8×C101C2×C411yescharacteristic
55C4×Q8×C101C2×C413yes—
56C4×Q8×C101D411yescharacteristic
57C4×Q8×C101D413yes—
58C4×D4×C101—23no—
59C4×D4×C101—23no—
60C4×D4×C101—23no—
61C4×D4×C101C2×C413yes—
62C4×D4×C101C2×C416yes—
63#117×C101—23no—
64C2×C4⋊C4×C101—23no—
65C2×C4⋊C4×C101—23no—
66C2×C4⋊C4×C101D413yes—
67C2×C42×C101—23no—
68C2×C42×C101—23no—
69C2×C42×C101C2313yes—
70C4⋊C8×C101—23no—
71C4⋊C8×C101—23no—
72C22⋊C8×C101C2311yescharacteristic
73C22⋊C8×C101C2313yes—
74#97×C101—23no—
75C4×C8×C101—23no—
76#95×C101—23no—
77#95×C101C2311yescharacteristic
78#95×C101C2313yes—
79#41×C101—44no—
80#41×C101—83no—
81#41×C101—83no—
82C2×Q8×C101—24no—
83C2×Q8×C101—23no—
84C2×Q8×C101C22⋊C413yes—
85C2×Q8×C101C22⋊C411yescharacteristic
86C2×Q8×C101C22×C411yescharacteristic
87C2×D4×C101—23no—
88C2×D4×C101—23no—
89C2×D4×C101—23no—
90C2×D4×C101C22×C413yes—
91C22×C4×C101—21no—
92C22×C4×C101—23no—
93C22×C4×C101—23no—
94C22×C4×C101—26no—
95C22×C4×C101C2×D413yes—
96C22×C4×C101C2×D413yes—
97C22×C4×C101C2411yescharacteristic
98C2×C8×C101—21no—
99C2×C8×C101—23no—
100C4⋊C4×C101—212no—
101C4⋊C4×C101—23no—
102C4⋊C4×C101—23no—
103C4⋊C4×C101—23no—
104C4⋊C4×C101—23no—
105C4⋊C4×C101—21no—
106C4⋊C4×C101C22⋊C413yes—
107C4⋊C4×C101C22⋊C413yes—
108C4⋊C4×C101C22⋊C416yes—
109C4⋊C4×C101C22×C411yescharacteristic
110C4⋊C4×C101C22×C413yes—
111C22⋊C4×C101—21no—
112C22⋊C4×C101—23no—
113C22⋊C4×C101—23no—
114C22⋊C4×C101—23no—
115C22⋊C4×C101—26no—
116C22⋊C4×C101—23no—
117C42×C101—212no—
118C42×C101—23no—
119C42×C101—83no—
120C42×C101C22×C413yes—
121C42×C101C22×C413yes—
122C42×C101C2×D413yes—
123C42×C101C2×D413yes—
124C23×C101—23no—
125C23×C101C22×D411yescharacteristic
126Q8×C101—26no—
127Q8×C101—41no—
128Q8×C101—83no—
129Q8×C101#10414yes—
130D4×C101—43no—
131D4×C101—43no—
132D4×C101—43no—
133D4×C101—46no—
134D4×C101—83no—
135C2×C4×C101—23no—
136C2×C4×C101—23no—
137C2×C4×C101—26no—
138C2×C4×C101—22no—
139C2×C4×C101—26no—
140C2×C4×C101—21no—
141C2×C4×C101—23no—
142C2×C4×C101—21no—
143C2×C4×C101—41no—
144C2×C4×C101—41no—
145C2×C4×C101—43no—
146C2×C4×C101—43no—
147C2×C4×C101—41no—
148C2×C4×C101—46no—
149C2×C4×C101—86no—
150C2×C4×C101C2×C22⋊C413yes—
151C2×C4×C101C2×C22⋊C413yes—
152C2×C4×C101C2×C22⋊C413yes—
153C2×C4×C101C2×C22⋊C413yes—
154C2×C4×C101C23×C411yescharacteristic
155C2×C4×C101C22×D411yescharacteristic
156C8×C101—41no—
157C8×C101—43no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101—43no—
161C22×C101—43no—
162C22×C101—43no—
163C22×C101C22×C22⋊C411yescharacteristic
164C22×C101#57611yescharacteristic
165C22×C101#57711yescharacteristic
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—23no—
169C4×C101—23no—
170C4×C101—23no—
171C4×C101—46no—
172C4×C101—42no—
173C4×C101—41no—
174C4×C101—43no—
175C4×C101—41no—
176C4×C101C2×#10416yes—
177#17550C10111yesmaximal, characteristic, direct product factor, Sylow
178C2×C101—21no—
179C2×C101—21no—
180C2×C101—83no—
181C2×C101#288411yescharacteristic
182C2×C101#289711yescharacteristic
183C2×C101C22×#10411yescharacteristic
184#3522C2×C10111yescharacteristic
185#2984C2×C10111yescharacteristic, complemented
186#2276C2×C10111yescharacteristic, complemented
187#1509C2×C10113yescomplemented
188#1505C2×C10113yescomplemented
189#1502C2×C10113yescomplemented
190#1500C2×C10113yescomplemented
191C101#1755011yescharacteristic, direct product factor, Sylow
192#559C4×C10113yescomplemented
193Q82C4×C10111yescharacteristic, complemented
194#554C4×C10113yescomplemented
195#550C4×C10111yescharacteristic, complemented
196#548—21no—
197#547—23no—
198#542—23no—
199#532C22×C10113yes—
200#529C22×C10113yes—
201#520—21no—
202C2×C4×Q8—21no—
203C2×C4×Q8C22×C10111yescharacteristic
204#446—23no—
205C8×Q8—21no—
206#432C22×C10113yes—
207#431C22×C10113yes—
208C4×C4⋊C4—23no—
209C4×C4⋊C4C22×C10113yes—
210#376C22×C10113yes—
211#328C22×C10111yescharacteristic
212#328C22×C10113yes—
213#327C22×C10113yes—
214#327C22×C10113yes—
215#327C22×C10116yes—
216C2×#41—21no—
217C2×#41—23no—
218C22×Q8D4×C10111yescharacteristic
219C4⋊Q8—23no—
220C4⋊Q8C2×C4×C10113yes—
221#127C2×C4×C10113yes—
222#126—23no—
223#125C2×C4×C10113yes—
224#124—23no—
225#124—23no—
226#124C2×C4×C10113yes—
227#123—23no—
228#123—26no—
229C22⋊Q8—23no—
230C22⋊Q8—26no—
231C22⋊Q8C23×C10111yescharacteristic
232#121—23no—
233#121—23no—
234#121C23×C10113yes—
235C4×Q8—28no—
236C4×Q8—21no—
237C4×Q8C2×C4×C10113yes—
238C4×Q8C2×C4×C10111yescharacteristic
239C4×Q8C2×C4×C10113yes—
240C4×Q8D4×C10111yescharacteristic
241C4×Q8D4×C10113yes—
242C4×D4—23no—
243C4×D4—23no—
244C4×D4—23no—
245C4×D4C2×C4×C10113yes—
246C4×D4C2×C4×C10116yes—
247#117—23no—
248C2×C4⋊C4—23no—
249C2×C4⋊C4—23no—
250C2×C4⋊C4D4×C10113yes—
251C2×C42—23no—
252C2×C42—23no—
253C2×C42C23×C10113yes—
254C4⋊C8—23no—
255C4⋊C8—23no—
256C22⋊C8C23×C10111yescharacteristic
257C22⋊C8C23×C10113yes—
258#97—23no—
259C4×C8—23no—
260#95—23no—
261#95C23×C10111yescharacteristic
262#95C23×C10113yes—
263#41—44no—
264#41—83no—
265#41—83no—
266C2×Q8—24no—
267C2×Q8—23no—
268C2×Q8C22⋊C4×C10113yes—
269C2×Q8C22⋊C4×C10111yescharacteristic
270C2×Q8C22×C4×C10111yescharacteristic
271C2×D4—23no—
272C2×D4—23no—
273C2×D4—23no—
274C2×D4C22×C4×C10113yes—
275C22×C4—21no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—26no—
279C22×C4C2×D4×C10113yes—
280C22×C4C2×D4×C10113yes—
281C22×C4C24×C10111yescharacteristic
282C2×C8—21no—
283C2×C8—23no—
284C4⋊C4—212no—
285C4⋊C4—23no—
286C4⋊C4—23no—
287C4⋊C4—23no—
288C4⋊C4—23no—
289C4⋊C4—21no—
290C4⋊C4C22⋊C4×C10113yes—
291C4⋊C4C22⋊C4×C10113yes—
292C4⋊C4C22⋊C4×C10116yes—
293C4⋊C4C22×C4×C10111yescharacteristic
294C4⋊C4C22×C4×C10113yes—
295C22⋊C4—21no—
296C22⋊C4—23no—
297C22⋊C4—23no—
298C22⋊C4—23no—
299C22⋊C4—26no—
300C22⋊C4—23no—
301C42—212no—
302C42—23no—
303C42—83no—
304C42C22×C4×C10113yes—
305C42C22×C4×C10113yes—
306C42C2×D4×C10113yes—
307C42C2×D4×C10113yes—
308C23—23no—
309C23C22×D4×C10111yescharacteristic
310Q8—26no—
311Q8—41no—
312Q8—83no—
313Q8#104×C10114yes—
314D4—43no—
315D4—43no—
316D4—43no—
317D4—46no—
318D4—83no—
319C2×C4—23no—
320C2×C4—23no—
321C2×C4—26no—
322C2×C4—22no—
323C2×C4—26no—
324C2×C4—21no—
325C2×C4—23no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—41no—
332C2×C4—46no—
333C2×C4—86no—
334C2×C4C2×C22⋊C4×C10113yes—
335C2×C4C2×C22⋊C4×C10113yes—
336C2×C4C2×C22⋊C4×C10113yes—
337C2×C4C2×C22⋊C4×C10113yes—
338C2×C4C23×C4×C10111yescharacteristic
339C2×C4C22×D4×C10111yescharacteristic
340C8—41no—
341C8—43no—
342C22—21no—
343C22—21no—
344C22—43no—
345C22—43no—
346C22—43no—
347C22C22×C22⋊C4×C10111yescharacteristic
348C22#576×C10111yescharacteristic
349C22#577×C10111yescharacteristic
350C4—21no—
351C4—21no—
352C4—23no—
353C4—23no—
354C4—23no—
355C4—46no—
356C4—42no—
357C4—41no—
358C4—43no—
359C4—41no—
360C4C2×#104×C10116yes—
361C2—21no—
362C2—21no—
363C2—83no—
364C2C101×#288411yescharacteristic
365C2C101×#289711yescharacteristic
366C2C22×#104×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C22×C22⋊C4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3522C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C4×Q8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2984C2semidirect
3. C101×#2276C2semidirect
4. C101×#1509C2semidirect
5. C101×#1505C2semidirect
6. C101×#1502C2semidirect
7. C101×#1500C2semidirect
8. #559×C101C4semidirect
9. Q82×C101C4semidirect
10. #554×C101C4semidirect
11. #550×C101C4semidirect
177. #17550C101direct (N × H)
185. #2984C2×C101semidirect
186. #2276C2×C101semidirect
187. #1509C2×C101semidirect
188. #1505C2×C101semidirect
189. #1502C2×C101semidirect
190. #1500C2×C101semidirect
191. C101#17550direct (N × H)
192. #559C4×C101semidirect
193. Q82C4×C101semidirect
194. #554C4×C101semidirect
195. #550C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35222
C101×#29842
C101×#22762
C101×#15092
C101×#15052
C101×#15022
C101×#15002
#17550101