Finite Group Databasebeta

← C101×#19059 #38801210

Subgroups — C101×#19059 #38801210

Order 25856.

898 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3553C211yesmaximal, characteristic, complemented
2C101×#3217C212yesmaximal, complemented
3C2×#490×C101C211yesmaximal, characteristic, complemented
4C101×#1658C212yesmaximal, complemented
5C101×#1657C214yesmaximal, complemented
6C101×#1656C212yesmaximal, complemented
7C101×#1534C211yesmaximal, characteristic, complemented
8C101×#1532C212yesmaximal, complemented
9#564×C101C2211yescharacteristic, complemented
10#563×C101C2212yescomplemented
11#562×C101C2211yescharacteristic, complemented
12#554×C101—22no—
13#553×C101—22no—
14#552×C101—22no—
15#541×C101—22no—
16#539×C101—22no—
17#539×C101—22no—
18C2×#127×C101C2211yescharacteristic
19#529×C101C2212yes—
20C2×#125×C101C2211yescharacteristic
21#496×C101C2214yes—
22#490×C101—22no—
23#490×C101C2212yes—
24#490×C101C2212yes—
25#490×C101C2214yes—
26#460×C101—22no—
27#459×C101—22no—
28#450×C101—22no—
29#447×C101—22no—
30#432×C101C2212yes—
31C2×#102×C101—22no—
32C2×#97×C101C2211yescharacteristic
33#330×C101C2212yescomplemented
34#330×C101C2212yescomplemented
35#330×C101C2214yescomplemented
36#329×C101C2214yescomplemented
37C22×D4×C101—21no—
38C22×D4×C101—22no—
39C2×SD16×C101—24no—
40C2×D8×C101—24no—
41C22×C8×C101—21no—
42C4⋊Q8×C101—22no—
43#127×C101—22no—
44#127×C101—21no—
45#127×C101C2312yes—
46#126×C101—22no—
47#126×C101—22no—
48#126×C101—22no—
49#126×C101—22no—
50#126×C101—22no—
51#125×C101—22no—
52#125×C101—22no—
53#125×C101—22no—
54#125×C101—22no—
55#125×C101—22no—
56#125×C101—22no—
57#125×C101D412yes—
58#125×C101C2311yescharacteristic
59#125×C101C2311yescharacteristic
60#125×C101C2312yes—
61#124×C101C2312yes—
62#123×C101—22no—
63#123×C101—22no—
64#123×C101—22no—
65#123×C101—22no—
66#123×C101—22no—
67C22⋊Q8×C101—22no—
68C22⋊Q8×C101—22no—
69C22⋊Q8×C101—22no—
70C22⋊Q8×C101—22no—
71C22⋊Q8×C101—22no—
72C22⋊Q8×C101—22no—
73C22⋊Q8×C101D412yes—
74#121×C101—22no—
75#121×C101—22no—
76#121×C101D412yes—
77C4×Q8×C101—22no—
78C4×Q8×C101D412yes—
79C4×D4×C101—22no—
80C4×D4×C101—22no—
81C4×D4×C101—22no—
82C4×D4×C101—22no—
83C4×D4×C101D412yes—
84#117×C101—22no—
85#117×C101—22no—
86C2×C4⋊C4×C101—22no—
87C2×C4⋊C4×C101—22no—
88C2×C4⋊C4×C101D412yes—
89C2×C42×C101C2311yescharacteristic
90C4⋊C8×C101—22no—
91#102×C101—24no—
92#102×C101—24no—
93#102×C101—24no—
94#102×C101—24no—
95C22⋊C8×C101—22no—
96#97×C101—21no—
97#97×C101C2312yes—
98#97×C101C2314yes—
99C24×C101—41no—
100C2×Q8×C101—22no—
101C2×Q8×C101C2×D412yes—
102C2×D4×C101—22no—
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101—24no—
106C2×D4×C101—44no—
107C2×D4×C101—42no—
108C2×D4×C101—41no—
109C2×D4×C101—84no—
110C2×D4×C101C2×D412yes—
111C22×C4×C101—22no—
112C22×C4×C101—22no—
113C22×C4×C101—22no—
114C22×C4×C101—22no—
115C22×C4×C101C2×D411yescharacteristic
116C22×C4×C101C2×D412yes—
117SD16×C101—84no—
118D8×C101—84no—
119C2×C8×C101—22no—
120C2×C8×C101—24no—
121C2×C8×C101—42no—
122C4⋊C4×C101—22no—
123C4⋊C4×C101—22no—
124C4⋊C4×C101—22no—
125C4⋊C4×C101—22no—
126C4⋊C4×C101—22no—
127C4⋊C4×C101—22no—
128C4⋊C4×C101—22no—
129C4⋊C4×C101—22no—
130C4⋊C4×C101—22no—
131C4⋊C4×C101—22no—
132C4⋊C4×C101—22no—
133C4⋊C4×C101—22no—
134C4⋊C4×C101—22no—
135C4⋊C4×C101—22no—
136C4⋊C4×C101—22no—
137C4⋊C4×C101C2×D412yes—
138C4⋊C4×C101C2×D412yes—
139C4⋊C4×C101C2×D412yes—
140C4⋊C4×C101C2×D412yes—
141C22⋊C4×C101—22no—
142C22⋊C4×C101—22no—
143C22⋊C4×C101—22no—
144C22⋊C4×C101—22no—
145C22⋊C4×C101—22no—
146C22⋊C4×C101—22no—
147C22⋊C4×C101—22no—
148C22⋊C4×C101—22no—
149C22⋊C4×C101—22no—
150C42×C101—22no—
151C42×C101—22no—
152C42×C101—22no—
153C42×C101C2×D411yescharacteristic
154C42×C101C2×D412yes—
155C42×C101C2411yescharacteristic
156C23×C101—22no—
157C23×C101—42no—
158C23×C101—84no—
159C23×C101—82no—
160C23×C101#12011yescharacteristic
161Q8×C101—42no—
162Q8×C101—82no—
163D4×C101—42no—
164D4×C101—44no—
165D4×C101—44no—
166D4×C101—44no—
167D4×C101—44no—
168D4×C101—82no—
169D4×C101—84no—
170D4×C101—82no—
171C2×C4×C101—22no—
172C2×C4×C101—22no—
173C2×C4×C101—22no—
174C2×C4×C101—22no—
175C2×C4×C101—22no—
176C2×C4×C101—22no—
177C2×C4×C101—42no—
178C2×C4×C101—82no—
179C2×C4×C101—82no—
180C2×C4×C101—82no—
181C2×C4×C101—82no—
182C2×C4×C101#12012yes—
183C2×C4×C101#12011yescharacteristic
184C2×C4×C101C22×D411yescharacteristic
185C2×C4×C101C22×D412yes—
186C8×C101—42no—
187C8×C101—44no—
188C22×C101—22no—
189C22×C101—42no—
190C22×C101—42no—
191C22×C101—42no—
192C22×C101—82no—
193C22×C101—84no—
194C22×C101—164no—
195C22×C101#45412yes—
196C22×C101C2×#12011yescharacteristic
197C4×C101—21no—
198C4×C101—21no—
199C4×C101—22no—
200C4×C101—22no—
201C4×C101—42no—
202C4×C101—42no—
203C4×C101—42no—
204C4×C101—42no—
205C4×C101—42no—
206#19059C10111yesmaximal, characteristic, direct product factor, Sylow
207C2×C101—22no—
208C2×C101—82no—
209C2×C101—162no—
210C2×C101C2×#45411yescharacteristic
211C2×C101#302112yes—
212#3553C2×C10111yescharacteristic, complemented
213#3217C2×C10112yescomplemented
214C2×#490C2×C10111yescharacteristic, complemented
215#1658C2×C10112yescomplemented
216#1657C2×C10114yescomplemented
217#1656C2×C10112yescomplemented
218#1534C2×C10111yescharacteristic, complemented
219#1532C2×C10112yescomplemented
220C101#1905911yescharacteristic, direct product factor, Sylow
221#564C22×C10111yescharacteristic, complemented
222#563C22×C10112yescomplemented
223#562C22×C10111yescharacteristic, complemented
224#554—22no—
225#553—22no—
226#552—22no—
227#541—22no—
228#539—22no—
229#539—22no—
230C2×#127C22×C10111yescharacteristic
231#529C22×C10112yes—
232C2×#125C22×C10111yescharacteristic
233#496C22×C10114yes—
234#490—22no—
235#490C22×C10112yes—
236#490C22×C10112yes—
237#490C22×C10114yes—
238#460—22no—
239#459—22no—
240#450—22no—
241#447—22no—
242#432C22×C10112yes—
243C2×#102—22no—
244C2×#97C22×C10111yescharacteristic
245#330C22×C10112yescomplemented
246#330C22×C10112yescomplemented
247#330C22×C10114yescomplemented
248#329C22×C10114yescomplemented
249C22×D4—21no—
250C22×D4—22no—
251C2×SD16—24no—
252C2×D8—24no—
253C22×C8—21no—
254C4⋊Q8—22no—
255#127—22no—
256#127—21no—
257#127C23×C10112yes—
258#126—22no—
259#126—22no—
260#126—22no—
261#126—22no—
262#126—22no—
263#125—22no—
264#125—22no—
265#125—22no—
266#125—22no—
267#125—22no—
268#125—22no—
269#125D4×C10112yes—
270#125C23×C10111yescharacteristic
271#125C23×C10111yescharacteristic
272#125C23×C10112yes—
273#124C23×C10112yes—
274#123—22no—
275#123—22no—
276#123—22no—
277#123—22no—
278#123—22no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8D4×C10112yes—
286#121—22no—
287#121—22no—
288#121D4×C10112yes—
289C4×Q8—22no—
290C4×Q8D4×C10112yes—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4D4×C10112yes—
296#117—22no—
297#117—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4D4×C10112yes—
301C2×C42C23×C10111yescharacteristic
302C4⋊C8—22no—
303#102—24no—
304#102—24no—
305#102—24no—
306#102—24no—
307C22⋊C8—22no—
308#97—21no—
309#97C23×C10112yes—
310#97C23×C10114yes—
311C24—41no—
312C2×Q8—22no—
313C2×Q8C2×D4×C10112yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—24no—
318C2×D4—44no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—84no—
322C2×D4C2×D4×C10112yes—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4C2×D4×C10111yescharacteristic
328C22×C4C2×D4×C10112yes—
329SD16—84no—
330D8—84no—
331C2×C8—22no—
332C2×C8—24no—
333C2×C8—42no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4C2×D4×C10112yes—
350C4⋊C4C2×D4×C10112yes—
351C4⋊C4C2×D4×C10112yes—
352C4⋊C4C2×D4×C10112yes—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C42—22no—
363C42—22no—
364C42—22no—
365C42C2×D4×C10111yescharacteristic
366C42C2×D4×C10112yes—
367C42C24×C10111yescharacteristic
368C23—22no—
369C23—42no—
370C23—84no—
371C23—82no—
372C23#120×C10111yescharacteristic
373Q8—42no—
374Q8—82no—
375D4—42no—
376D4—44no—
377D4—44no—
378D4—44no—
379D4—44no—
380D4—82no—
381D4—84no—
382D4—82no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4#120×C10112yes—
395C2×C4#120×C10111yescharacteristic
396C2×C4C22×D4×C10111yescharacteristic
397C2×C4C22×D4×C10112yes—
398C8—42no—
399C8—44no—
400C22—22no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—82no—
405C22—84no—
406C22—164no—
407C22#454×C10112yes—
408C22C2×#120×C10111yescharacteristic
409C4—21no—
410C4—21no—
411C4—22no—
412C4—22no—
413C4—42no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C2—22no—
419C2—82no—
420C2—162no—
421C2C2×#454×C10111yescharacteristic
422C2C101×#302112yes—
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
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
1. C101×#3553C2semidirect
2. C101×#3217C2semidirect
3. C2×#490×C101C2semidirect
4. C101×#1658C2semidirect
5. C101×#1657C2semidirect
6. C101×#1656C2semidirect
7. C101×#1534C2semidirect
8. C101×#1532C2semidirect
9. #564×C101C22semidirect
10. #563×C101C22semidirect
11. #562×C101C22semidirect
33. #330×C101C22semidirect
34. #330×C101C22semidirect
35. #330×C101C22semidirect
36. #329×C101C22semidirect
206. #19059C101direct (N × H)
212. #3553C2×C101semidirect
213. #3217C2×C101semidirect
214. C2×#490C2×C101semidirect
215. #1658C2×C101semidirect
216. #1657C2×C101semidirect
217. #1656C2×C101semidirect
218. #1534C2×C101semidirect
219. #1532C2×C101semidirect
220. C101#19059direct (N × H)
221. #564C22×C101semidirect
222. #563C22×C101semidirect
223. #562C22×C101semidirect
245. #330C22×C101semidirect
246. #330C22×C101semidirect
247. #330C22×C101semidirect
248. #329C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35532
C101×#32172
C2×#490×C1012
C101×#16582
C101×#16572
C101×#16562
C101×#15342
C101×#15322
#19059101