Finite Group Databasebeta

← C101×#9177 #38791328

Subgroups — C101×#9177 #38791328

Order 25856.

494 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3077C211yesmaximal, characteristic
2C101×#2357C211yesmaximal, characteristic
3C101×#1518C211yesmaximal, characteristic, complemented
4C101×#1503C211yesmaximal, characteristic, complemented
5C101×#1478C211yesmaximal, characteristic
6C101×#1303C211yesmaximal, characteristic, complemented
7C101×#1286C211yesmaximal, characteristic, complemented
8#533×C101C2211yescharacteristic
9C2×C4×D4×C101C2211yescharacteristic
10#478×C101—22no—
11#476×C101C412yescomplemented
12#474×C101C412yescomplemented
13#431×C101C2211yescharacteristic
14#431×C101C2211yescharacteristic
15#428×C101—21no—
16#423×C101C2211yescharacteristic
17#418×C101—21no—
18#390×C101—21no—
19#388×C101—22no—
20#382×C101C2211yescharacteristic
21#381×C101—21no—
22C4×C4⋊C4×C101—21no—
23C4×C4⋊C4×C101C2211yescharacteristic
24C4×C22⋊C4×C101—21no—
25#328×C101—21no—
26#328×C101—21no—
27#328×C101—22no—
28D4⋊C8×C101—22no—
29C22×D4×C101D411yescharacteristic
30C23×C4×C101—21no—
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—21no—
38C4×Q8×C101—21no—
39C4×D4×C101—21no—
40C4×D4×C101—21no—
41C4×D4×C101C2×C412yes—
42C4×D4×C101D412yes—
43#117×C101—21no—
44C2×C4⋊C4×C101—21no—
45C2×C4⋊C4×C101—21no—
46C2×C4⋊C4×C101D411yescharacteristic
47C2×C22⋊C4×C101—21no—
48C2×C22⋊C4×C101—22no—
49C2×C22⋊C4×C101—22no—
50C2×C42×C101—21no—
51C2×C42×C101—22no—
52C2×C42×C101C2311yescharacteristic
53#107×C101—22no—
54#106×C101—22no—
55C4⋊C8×C101—21no—
56C4⋊C8×C101—21no—
57C4⋊C8×C101—21no—
58C4⋊C8×C101C2×C412yes—
59#102×C101—22no—
60#102×C101—22no—
61C22⋊C8×C101—21no—
62C22⋊C8×C101—21no—
63C4×C8×C101—21no—
64C4×C8×C101—21no—
65#95×C101—22no—
66#95×C101—21no—
67#95×C101D411yescharacteristic
68#95×C101D411yescharacteristic
69#95×C101D412yes—
70C24×C101—21no—
71C2×Q8×C101—21no—
72C2×Q8×C101—21no—
73C2×D4×C101—21no—
74C2×D4×C101—21no—
75C2×D4×C101—21no—
76C2×D4×C101—21no—
77C2×D4×C101—21no—
78C2×D4×C101C22⋊C412yes—
79C22×C4×C101—21no—
80C22×C4×C101—21no—
81C22×C4×C101—22no—
82C22×C4×C101—22no—
83C22×C4×C101—22no—
84C22×C4×C101—21no—
85C22×C4×C101—82no—
86C22×C4×C101C2×D411yescharacteristic
87C22×C4×C101C2×D411yescharacteristic
88C22×C4×C101C2×D411yescharacteristic
89M16×C101—41no—
90M16×C101—41no—
91C2×C8×C101—22no—
92C2×C8×C101—41no—
93C2×C8×C101—41no—
94C4⋊C4×C101—21no—
95C4⋊C4×C101—21no—
96C4⋊C4×C101—21no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101—42no—
100C4⋊C4×C101—41no—
101C4⋊C4×C101—41no—
102C4⋊C4×C101—41no—
103C4⋊C4×C101—41no—
104C4⋊C4×C101C22⋊C412yes—
105C22⋊C4×C101—22no—
106C22⋊C4×C101—22no—
107C22⋊C4×C101—44no—
108C22⋊C4×C101—41no—
109C22⋊C4×C101—82no—
110C42×C101—41no—
111C42×C101—41no—
112C42×C101—41no—
113C42×C101—82no—
114C42×C101C22×C411yescharacteristic
115C42×C101C2×D411yescharacteristic
116C42×C101#4111yescharacteristic
117C42×C101#4111yescharacteristic
118C23×C101—22no—
119C23×C101—42no—
120C23×C101—42no—
121C23×C101—41no—
122C23×C101—41no—
123C23×C101#12011yescharacteristic
124Q8×C101—81no—
125Q8×C101—81no—
126D4×C101—22no—
127D4×C101—22no—
128D4×C101—41no—
129D4×C101—41no—
130C2×C4×C101—22no—
131C2×C4×C101—22no—
132C2×C4×C101—41no—
133C2×C4×C101—41no—
134C2×C4×C101—41no—
135C2×C4×C101—42no—
136C2×C4×C101—41no—
137C2×C4×C101—42no—
138C2×C4×C101—42no—
139C2×C4×C101—41no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—41no—
143C2×C4×C101—41no—
144C2×C4×C101—42no—
145C2×C4×C101—82no—
146C2×C4×C101—82no—
147C2×C4×C101C2×C22⋊C411yescharacteristic
148C2×C4×C101C4×D411yescharacteristic
149C2×C4×C101C4×D411yescharacteristic
150C2×C4×C101#12111yescharacteristic
151C2×C4×C101#12111yescharacteristic
152C2×C4×C101#12311yescharacteristic
153C2×C4×C101#13511yescharacteristic
154C2×C4×C101#13511yescharacteristic
155C2×C4×C101#13711yescharacteristic
156C2×C4×C101#13711yescharacteristic
157C8×C101—42no—
158C8×C101—81no—
159C8×C101—81no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—42no—
163C22×C101—42no—
164C22×C101—42no—
165C22×C101—82no—
166C22×C101—82no—
167C22×C101#38611yescharacteristic
168C22×C101#45211yescharacteristic
169C22×C101#45211yescharacteristic
170C4×C101—21no—
171C4×C101—21no—
172C4×C101—21no—
173C4×C101—21no—
174C4×C101—42no—
175C4×C101—42no—
176C4×C101—81no—
177C4×C101—82no—
178C4×C101—81no—
179C4×C101—81no—
180C4×C101#41611yescharacteristic
181C4×C101#41911yescharacteristic
182C4×C101#48511yescharacteristic
183C4×C101#48511yescharacteristic
184#9177C10111yesmaximal, characteristic, direct product factor, Sylow
185C2×C101—21no—
186C2×C101—21no—
187C2×C101—82no—
188C2×C101#187311yescharacteristic
189C2×C101#190411yescharacteristic
190C2×C101#190611yescharacteristic
191#3077C2×C10111yescharacteristic
192#2357C2×C10111yescharacteristic
193#1518C2×C10111yescharacteristic, complemented
194#1503C2×C10111yescharacteristic, complemented
195#1478C2×C10111yescharacteristic
196#1303C2×C10111yescharacteristic, complemented
197#1286C2×C10111yescharacteristic, complemented
198C101#917711yescharacteristic, direct product factor, Sylow
199#533C22×C10111yescharacteristic
200C2×C4×D4C22×C10111yescharacteristic
201#478—22no—
202#476C4×C10112yescomplemented
203#474C4×C10112yescomplemented
204#431C22×C10111yescharacteristic
205#431C22×C10111yescharacteristic
206#428—21no—
207#423C22×C10111yescharacteristic
208#418—21no—
209#390—21no—
210#388—22no—
211#382C22×C10111yescharacteristic
212#381—21no—
213C4×C4⋊C4—21no—
214C4×C4⋊C4C22×C10111yescharacteristic
215C4×C22⋊C4—21no—
216#328—21no—
217#328—21no—
218#328—22no—
219D4⋊C8—22no—
220C22×D4D4×C10111yescharacteristic
221C23×C4—21no—
222C2×M16—21no—
223C4⋊Q8C2×C4×C10111yescharacteristic
224C4⋊Q8C2×C4×C10111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4C2×C4×C10112yes—
233C4×D4D4×C10112yes—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C10111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42—21no—
242C2×C42—22no—
243C2×C42C23×C10111yescharacteristic
244#107—22no—
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8C2×C4×C10112yes—
250#102—22no—
251#102—22no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256#95—22no—
257#95—21no—
258#95D4×C10111yescharacteristic
259#95D4×C10111yescharacteristic
260#95D4×C10112yes—
261C24—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4C22⋊C4×C10112yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—82no—
277C22×C4C2×D4×C10111yescharacteristic
278C22×C4C2×D4×C10111yescharacteristic
279C22×C4C2×D4×C10111yescharacteristic
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C22⋊C4×C10112yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—44no—
299C22⋊C4—41no—
300C22⋊C4—82no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—82no—
305C42C22×C4×C10111yescharacteristic
306C42C2×D4×C10111yescharacteristic
307C42#41×C10111yescharacteristic
308C42#41×C10111yescharacteristic
309C23—22no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23#120×C10111yescharacteristic
315Q8—81no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4C2×C22⋊C4×C10111yescharacteristic
339C2×C4C4×D4×C10111yescharacteristic
340C2×C4C4×D4×C10111yescharacteristic
341C2×C4#121×C10111yescharacteristic
342C2×C4#121×C10111yescharacteristic
343C2×C4#123×C10111yescharacteristic
344C2×C4#135×C10111yescharacteristic
345C2×C4#135×C10111yescharacteristic
346C2×C4#137×C10111yescharacteristic
347C2×C4#137×C10111yescharacteristic
348C8—42no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22#386×C10111yescharacteristic
359C22#452×C10111yescharacteristic
360C22#452×C10111yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4#416×C10111yescharacteristic
372C4#419×C10111yescharacteristic
373C4#485×C10111yescharacteristic
374C4#485×C10111yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2C101×#187311yescharacteristic
379C2C101×#190411yescharacteristic
380C2C101×#190611yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC22×D4×C101D4
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
3. C101×#1518C2semidirect
4. C101×#1503C2semidirect
6. C101×#1303C2semidirect
7. C101×#1286C2semidirect
11. #476×C101C4semidirect
12. #474×C101C4semidirect
184. #9177C101direct (N × H)
193. #1518C2×C101semidirect
194. #1503C2×C101semidirect
196. #1303C2×C101semidirect
197. #1286C2×C101semidirect
198. C101#9177direct (N × H)
202. #476C4×C101semidirect
203. #474C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30772
C101×#23572
C101×#15182
C101×#15032
C101×#14782
C101×#13032
C101×#12862
#9177101