Finite Group Databasebeta

← C101×#9165 #38791316

Subgroups — C101×#9165 #38791316

Order 25856.

486 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3110C211yesmaximal, characteristic
2C101×#2974C211yesmaximal, characteristic
3C101×#1762C211yesmaximal, characteristic
4C101×#1531C211yesmaximal, characteristic, complemented
5C101×#1503C211yesmaximal, characteristic, complemented
6C101×#1302C211yesmaximal, characteristic, complemented
7C101×#1285C211yesmaximal, characteristic, complemented
8#533×C101C2211yescharacteristic
9C2×C4×D4×C101C2211yescharacteristic
10#484×C101—21no—
11#474×C101C411yescharacteristic, complemented
12#474×C101C411yescharacteristic, complemented
13#461×C101C411yescharacteristic, complemented
14#461×C101C411yescharacteristic, complemented
15#450×C101—21no—
16#440×C101—21no—
17#440×C101—21no—
18#436×C101—21no—
19#435×C101—22no—
20C8×D4×C101—21no—
21#432×C101C2211yescharacteristic
22#432×C101C2211yescharacteristic
23#431×C101C2211yescharacteristic
24C2×#102×C101—21no—
25#407×C101—21no—
26C2×C22⋊C8×C101—21no—
27C2×#97×C101C2211yescharacteristic
28C4×C4⋊C4×C101C2211yescharacteristic
29#340×C101—21no—
30#330×C101—22no—
31#328×C101—21no—
32#328×C101—21no—
33C22×D4×C101D411yescharacteristic
34C23×C4×C101—21no—
35C2×SD16×C101—21no—
36C2×SD16×C101—21no—
37C2×M16×C101—22no—
38C22×C8×C101—21no—
39C22×C8×C101—22no—
40C4⋊Q8×C101C2×C411yescharacteristic
41C4⋊Q8×C101C2×C411yescharacteristic
42#125×C101—21no—
43C22⋊Q8×C101—21no—
44C22⋊Q8×C101—21no—
45C4×Q8×C101—21no—
46C4×Q8×C101—21no—
47C4×D4×C101—21no—
48C4×D4×C101—21no—
49C4×D4×C101C2×C411yescharacteristic
50C4×D4×C101C2×C411yescharacteristic
51C4×D4×C101D411yescharacteristic
52C4×D4×C101D411yescharacteristic
53#117×C101—21no—
54C2×C4⋊C4×C101—21no—
55C2×C4⋊C4×C101D411yescharacteristic
56C2×C22⋊C4×C101—21no—
57C2×C42×C101—21no—
58C2×C42×C101C2311yescharacteristic
59#107×C101—21no—
60#107×C101—21no—
61C4⋊C8×C101—21no—
62C4⋊C8×C101—21no—
63C4⋊C8×C101C2×C411yescharacteristic
64C4⋊C8×C101C2×C411yescharacteristic
65#103×C101—21no—
66#103×C101—21no—
67#102×C101—24no—
68#102×C101—21no—
69#102×C101—21no—
70C22⋊C8×C101—22no—
71C22⋊C8×C101—22no—
72C22⋊C8×C101—21no—
73C22⋊C8×C101—21no—
74C22⋊C8×C101D411yescharacteristic
75C22⋊C8×C101D411yescharacteristic
76#97×C101—21no—
77#97×C101—21no—
78#97×C101—21no—
79#97×C101D412yes—
80C4×C8×C101—21no—
81#95×C101—21no—
82C24×C101—21no—
83C2×Q8×C101—21no—
84C2×Q8×C101—21no—
85C2×D4×C101—22no—
86C2×D4×C101—21no—
87C2×D4×C101—41no—
88C2×D4×C101C22⋊C411yescharacteristic
89C2×D4×C101C22⋊C411yescharacteristic
90C22×C4×C101—21no—
91C22×C4×C101—21no—
92C22×C4×C101—21no—
93C22×C4×C101—21no—
94C22×C4×C101—21no—
95C22×C4×C101—41no—
96C22×C4×C101—82no—
97C22×C4×C101C2×D411yescharacteristic
98C22×C4×C101C2×D411yescharacteristic
99C22×C4×C101#4111yescharacteristic
100SD16×C101—42no—
101SD16×C101—42no—
102M16×C101—82no—
103C2×C8×C101—22no—
104C2×C8×C101—21no—
105C2×C8×C101—21no—
106C2×C8×C101—21no—
107C2×C8×C101—21no—
108C2×C8×C101—22no—
109C2×C8×C101—41no—
110C2×C8×C101—41no—
111C2×C8×C101—82no—
112C4⋊C4×C101—21no—
113C4⋊C4×C101—22no—
114C4⋊C4×C101—21no—
115C4⋊C4×C101—21no—
116C4⋊C4×C101—21no—
117C4⋊C4×C101—21no—
118C4⋊C4×C101—41no—
119C4⋊C4×C101—41no—
120C4⋊C4×C101—41no—
121C4⋊C4×C101C22⋊C411yescharacteristic
122C4⋊C4×C101C22⋊C411yescharacteristic
123C22⋊C4×C101—21no—
124C22⋊C4×C101—21no—
125C22⋊C4×C101—21no—
126C22⋊C4×C101—21no—
127C22⋊C4×C101—41no—
128C42×C101—41no—
129C42×C101—81no—
130C42×C101C22×C411yescharacteristic
131C42×C101C2×D411yescharacteristic
132C42×C101C2×D411yescharacteristic
133C42×C101#4111yescharacteristic
134C23×C101—21no—
135C23×C101—21no—
136C23×C101—42no—
137C23×C101—41no—
138C23×C101—41no—
139C23×C101—81no—
140C23×C101#12111yescharacteristic
141Q8×C101—41no—
142Q8×C101—41no—
143Q8×C101—81no—
144D4×C101—21no—
145D4×C101—21no—
146D4×C101—21no—
147D4×C101—42no—
148D4×C101#10412yes—
149C2×C4×C101—21no—
150C2×C4×C101—21no—
151C2×C4×C101—21no—
152C2×C4×C101—21no—
153C2×C4×C101—21no—
154C2×C4×C101—21no—
155C2×C4×C101—41no—
156C2×C4×C101—42no—
157C2×C4×C101—42no—
158C2×C4×C101—42no—
159C2×C4×C101—41no—
160C2×C4×C101—41no—
161C2×C4×C101—81no—
162C2×C4×C101—81no—
163C2×C4×C101—81no—
164C2×C4×C101—81no—
165C2×C4×C101—81no—
166C2×C4×C101C2×C22⋊C411yescharacteristic
167C2×C4×C101C4×D411yescharacteristic
168C2×C4×C101C4×D411yescharacteristic
169C2×C4×C101#12011yescharacteristic
170C2×C4×C101#12111yescharacteristic
171C2×C4×C101#12311yescharacteristic
172C8×C101—42no—
173C8×C101—41no—
174C8×C101—42no—
175C8×C101—41no—
176C8×C101—41no—
177C8×C101—41no—
178C22×C101—21no—
179C22×C101—21no—
180C22×C101—22no—
181C22×C101—41no—
182C22×C101—41no—
183C22×C101—41no—
184C22×C101—41no—
185C22×C101—41no—
186C22×C101—82no—
187C22×C101—82no—
188C22×C101#38611yescharacteristic
189C22×C101#47111yescharacteristic
190C22×C101#47311yescharacteristic
191C4×C101—21no—
192C4×C101—21no—
193C4×C101—21no—
194C4×C101—21no—
195C4×C101—21no—
196C4×C101—41no—
197C4×C101—41no—
198C4×C101—82no—
199C4×C101—81no—
200C4×C101—81no—
201C4×C101C2×#10411yescharacteristic
202C4×C101#42111yescharacteristic
203#9165C10111yesmaximal, characteristic, direct product factor, Sylow
204C2×C101—21no—
205C2×C101—21no—
206C2×C101—42no—
207C2×C101—81no—
208C2×C101#187111yescharacteristic
209C2×C101#190411yescharacteristic
210C2×C101#190811yescharacteristic
211#3110C2×C10111yescharacteristic
212#2974C2×C10111yescharacteristic
213#1762C2×C10111yescharacteristic
214#1531C2×C10111yescharacteristic, complemented
215#1503C2×C10111yescharacteristic, complemented
216#1302C2×C10111yescharacteristic, complemented
217#1285C2×C10111yescharacteristic, complemented
218C101#916511yescharacteristic, direct product factor, Sylow
219#533C22×C10111yescharacteristic
220C2×C4×D4C22×C10111yescharacteristic
221#484—21no—
222#474C4×C10111yescharacteristic, complemented
223#474C4×C10111yescharacteristic, complemented
224#461C4×C10111yescharacteristic, complemented
225#461C4×C10111yescharacteristic, complemented
226#450—21no—
227#440—21no—
228#440—21no—
229#436—21no—
230#435—22no—
231C8×D4—21no—
232#432C22×C10111yescharacteristic
233#432C22×C10111yescharacteristic
234#431C22×C10111yescharacteristic
235C2×#102—21no—
236#407—21no—
237C2×C22⋊C8—21no—
238C2×#97C22×C10111yescharacteristic
239C4×C4⋊C4C22×C10111yescharacteristic
240#340—21no—
241#330—22no—
242#328—21no—
243#328—21no—
244C22×D4D4×C10111yescharacteristic
245C23×C4—21no—
246C2×SD16—21no—
247C2×SD16—21no—
248C2×M16—22no—
249C22×C8—21no—
250C22×C8—22no—
251C4⋊Q8C2×C4×C10111yescharacteristic
252C4⋊Q8C2×C4×C10111yescharacteristic
253#125—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C2×C4×C10111yescharacteristic
261C4×D4C2×C4×C10111yescharacteristic
262C4×D4D4×C10111yescharacteristic
263C4×D4D4×C10111yescharacteristic
264#117—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C10111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C42—21no—
269C2×C42C23×C10111yescharacteristic
270#107—21no—
271#107—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8C2×C4×C10111yescharacteristic
275C4⋊C8C2×C4×C10111yescharacteristic
276#103—21no—
277#103—21no—
278#102—24no—
279#102—21no—
280#102—21no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8D4×C10111yescharacteristic
286C22⋊C8D4×C10111yescharacteristic
287#97—21no—
288#97—21no—
289#97—21no—
290#97D4×C10112yes—
291C4×C8—21no—
292#95—21no—
293C24—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×D4—22no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4C22⋊C4×C10111yescharacteristic
300C2×D4C22⋊C4×C10111yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—82no—
308C22×C4C2×D4×C10111yescharacteristic
309C22×C4C2×D4×C10111yescharacteristic
310C22×C4#41×C10111yescharacteristic
311SD16—42no—
312SD16—42no—
313M16—82no—
314C2×C8—22no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—82no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C22⋊C4×C10111yescharacteristic
333C4⋊C4C22⋊C4×C10111yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—41no—
339C42—41no—
340C42—81no—
341C42C22×C4×C10111yescharacteristic
342C42C2×D4×C10111yescharacteristic
343C42C2×D4×C10111yescharacteristic
344C42#41×C10111yescharacteristic
345C23—21no—
346C23—21no—
347C23—42no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23#121×C10111yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—81no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4#104×C10112yes—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4C2×C22⋊C4×C10111yescharacteristic
378C2×C4C4×D4×C10111yescharacteristic
379C2×C4C4×D4×C10111yescharacteristic
380C2×C4#120×C10111yescharacteristic
381C2×C4#121×C10111yescharacteristic
382C2×C4#123×C10111yescharacteristic
383C8—42no—
384C8—41no—
385C8—42no—
386C8—41no—
387C8—41no—
388C8—41no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22#386×C10111yescharacteristic
400C22#471×C10111yescharacteristic
401C22#473×C10111yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4C2×#104×C10111yescharacteristic
413C4#421×C10111yescharacteristic
414C2—21no—
415C2—21no—
416C2—42no—
417C2—81no—
418C2C101×#187111yescharacteristic
419C2C101×#190411yescharacteristic
420C2C101×#190811yescharacteristic
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
4. C101×#1531C2semidirect
5. C101×#1503C2semidirect
6. C101×#1302C2semidirect
7. C101×#1285C2semidirect
11. #474×C101C4semidirect
12. #474×C101C4semidirect
13. #461×C101C4semidirect
14. #461×C101C4semidirect
203. #9165C101direct (N × H)
214. #1531C2×C101semidirect
215. #1503C2×C101semidirect
216. #1302C2×C101semidirect
217. #1285C2×C101semidirect
218. C101#9165direct (N × H)
222. #474C4×C101semidirect
223. #474C4×C101semidirect
224. #461C4×C101semidirect
225. #461C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31102
C101×#29742
C101×#17622
C101×#15312
C101×#15032
C101×#13022
C101×#12852
#9165101