Finite Group Databasebeta

← C101×#19657 #38801808

Subgroups — C101×#19657 #38801808

Order 25856.

700 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3230C211yesmaximal, characteristic, complemented
2C101×#3229C211yesmaximal, characteristic, complemented
3C101×#3226C211yesmaximal, characteristic
4C101×#3206C211yesmaximal, characteristic
5C101×#3131C211yesmaximal, characteristic
6C2×#487×C101C211yesmaximal, characteristic, complemented
7C101×#1719C212yesmaximal, complemented
8C101×#1718C212yesmaximal, complemented
9C101×#1710C212yesmaximal, complemented
10C101×#1708C212yesmaximal, complemented
11C101×#1450C211yesmaximal, characteristic, complemented
12#533×C101C2211yescharacteristic
13#532×C101C2211yescharacteristic
14C2×C4⋊Q8×C101C2211yescharacteristic
15C2×C4⋊Q8×C101C2211yescharacteristic
16#500×C101C2212yes—
17#500×C101C2212yes—
18#498×C101C2212yes—
19#492×C101C2212yes—
20#488×C101—22no—
21#487×C101—22no—
22#487×C101C2212yes—
23#487×C101C2212yes—
24#487×C101C2212yes—
25#487×C101C2212yes—
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#487×C101C2212yes—
29#486×C101C2212yes—
30#486×C101C2211yescharacteristic
31#486×C101C2211yescharacteristic
32#484×C101—22no—
33#483×C101—22no—
34#480×C101—22no—
35#477×C101—22no—
36#475×C101—22no—
37#474×C101—22no—
38#461×C101—22no—
39#448×C101—22no—
40#431×C101C2211yescharacteristic
41#431×C101C2211yescharacteristic
42#416×C101—22no—
43C2×#103×C101—22no—
44C2×C4×C8×C101C2211yescharacteristic
45#322×C101C2212yes—
46C82×C101C2212yes—
47C2×#41×C101—21no—
48C22×Q8×C101—21no—
49C22×Q8×C101—21no—
50C2×SD16×C101—24no—
51C22×C8×C101D412yes—
52C4⋊Q8×C101—21no—
53C4⋊Q8×C101—21no—
54C4⋊Q8×C101—21no—
55C4⋊Q8×C101—21no—
56C4⋊Q8×C101—21no—
57C4⋊Q8×C101—21no—
58C4⋊Q8×C101C2311yescharacteristic
59C4⋊Q8×C101C2312yes—
60C4⋊Q8×C101C2311yescharacteristic
61C4⋊Q8×C101C2312yes—
62C4⋊Q8×C101C2311yescharacteristic
63#127×C101C2311yescharacteristic
64#125×C101—21no—
65#124×C101—21no—
66C22⋊Q8×C101—21no—
67C22⋊Q8×C101—21no—
68#121×C101—21no—
69#121×C101—21no—
70C4×Q8×C101—21no—
71C4×Q8×C101—21no—
72C4×D4×C101—21no—
73C4×D4×C101—21no—
74#117×C101—21no—
75C2×C4⋊C4×C101—21no—
76C2×C4⋊C4×C101—21no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C42×C101C2311yescharacteristic
80#107×C101—24no—
81#107×C101—24no—
82#106×C101—24no—
83C4⋊C8×C101D412yes—
84C4⋊C8×C101D412yes—
85#103×C101—24no—
86#103×C101—24no—
87#103×C101—22no—
88#103×C101—22no—
89#103×C101—24no—
90#103×C101—24no—
91#103×C101—24no—
92#102×C101—22no—
93#102×C101—22no—
94#102×C101—24no—
95C22⋊C8×C101D412yes—
96C22⋊C8×C101D412yes—
97C4×C8×C101D412yes—
98C4×C8×C101C2311yescharacteristic
99C4×C8×C101C2311yescharacteristic
100C4×C8×C101C2312yes—
101C4×C8×C101C2312yes—
102#41×C101—44no—
103C2×Q8×C101—21no—
104C2×Q8×C101—21no—
105C2×Q8×C101—21no—
106C2×Q8×C101—22no—
107C2×Q8×C101—22no—
108C2×Q8×C101—41no—
109C2×Q8×C101—41no—
110C2×Q8×C101—44no—
111C2×Q8×C101—82no—
112C2×D4×C101—21no—
113C2×D4×C101—21no—
114C2×D4×C101—21no—
115C2×D4×C101—41no—
116C22×C4×C101—41no—
117C22×C4×C101—41no—
118C22×C4×C101—41no—
119C22×C4×C101C2×D411yescharacteristic
120C22×C4×C101C2×D411yescharacteristic
121C22×C4×C101C2×D411yescharacteristic
122SD16×C101—84no—
123C2×C8×C101—24no—
124C2×C8×C101C2×D412yes—
125C2×C8×C101C2×D412yes—
126C2×C8×C101C2×D414yes—
127C2×C8×C101C2×D414yes—
128C4⋊C4×C101—21no—
129C4⋊C4×C101—21no—
130C4⋊C4×C101—22no—
131C4⋊C4×C101—22no—
132C4⋊C4×C101—21no—
133C4⋊C4×C101—22no—
134C4⋊C4×C101—22no—
135C4⋊C4×C101—21no—
136C4⋊C4×C101—21no—
137C4⋊C4×C101—21no—
138C4⋊C4×C101—41no—
139C4⋊C4×C101—41no—
140C4⋊C4×C101—41no—
141C4⋊C4×C101—41no—
142C4⋊C4×C101—41no—
143C4⋊C4×C101—41no—
144C22⋊C4×C101—41no—
145C22⋊C4×C101—41no—
146C22⋊C4×C101—41no—
147C42×C101—41no—
148C42×C101C2×D411yescharacteristic
149C42×C101C2×D411yescharacteristic
150C42×C101C2×D411yescharacteristic
151C42×C101C2411yescharacteristic
152C23×C101—41no—
153C23×C101#12711yescharacteristic
154Q8×C101—44no—
155Q8×C101—42no—
156Q8×C101—44no—
157Q8×C101—42no—
158Q8×C101—42no—
159Q8×C101—82no—
160Q8×C101—82no—
161D4×C101—42no—
162D4×C101—42no—
163D4×C101—42no—
164D4×C101—82no—
165C2×C4×C101—22no—
166C2×C4×C101—22no—
167C2×C4×C101—41no—
168C2×C4×C101—41no—
169C2×C4×C101—41no—
170C2×C4×C101—42no—
171C2×C4×C101—42no—
172C2×C4×C101—82no—
173C2×C4×C101—82no—
174C2×C4×C101—82no—
175C2×C4×C101#12711yescharacteristic
176C2×C4×C101#12711yescharacteristic
177C2×C4×C101#12711yescharacteristic
178C2×C4×C101#13514yes—
179C2×C4×C101C22×D411yescharacteristic
180C2×C4×C101C22×D411yescharacteristic
181C2×C4×C101C22×D411yescharacteristic
182C8×C101—22no—
183C8×C101—22no—
184C8×C101—24no—
185C8×C101—24no—
186C22×C101—21no—
187C22×C101—21no—
188C22×C101—81no—
189C22×C101—81no—
190C22×C101—81no—
191C22×C101#49512yes—
192C22×C101C2×#12711yescharacteristic
193C4×C101—21no—
194C4×C101—21no—
195C4×C101—81no—
196C4×C101—82no—
197C4×C101—82no—
198C4×C101—81no—
199C4×C101—81no—
200C4×C101#49512yes—
201C4×C101C2×#13512yes—
202C4×C101#57712yes—
203C4×C101#57812yes—
204#19657C10111yesmaximal, characteristic, direct product factor, Sylow
205C2×C101—22no—
206C2×C101—161no—
207C2×C101C2×#49511yescharacteristic
208C2×C101#315411yescharacteristic
209C2×C101#315611yescharacteristic
210#3230C2×C10111yescharacteristic, complemented
211#3229C2×C10111yescharacteristic, complemented
212#3226C2×C10111yescharacteristic
213#3206C2×C10111yescharacteristic
214#3131C2×C10111yescharacteristic
215C2×#487C2×C10111yescharacteristic, complemented
216#1719C2×C10112yescomplemented
217#1718C2×C10112yescomplemented
218#1710C2×C10112yescomplemented
219#1708C2×C10112yescomplemented
220#1450C2×C10111yescharacteristic, complemented
221C101#1965711yescharacteristic, direct product factor, Sylow
222#533C22×C10111yescharacteristic
223#532C22×C10111yescharacteristic
224C2×C4⋊Q8C22×C10111yescharacteristic
225C2×C4⋊Q8C22×C10111yescharacteristic
226#500C22×C10112yes—
227#500C22×C10112yes—
228#498C22×C10112yes—
229#492C22×C10112yes—
230#488—22no—
231#487—22no—
232#487C22×C10112yes—
233#487C22×C10112yes—
234#487C22×C10111yescharacteristic
235#487C22×C10111yescharacteristic
236#487C22×C10112yes—
237#487C22×C10112yes—
238#487C22×C10112yes—
239#486C22×C10111yescharacteristic
240#486C22×C10111yescharacteristic
241#486C22×C10112yes—
242#484—22no—
243#483—22no—
244#480—22no—
245#477—22no—
246#475—22no—
247#474—22no—
248#461—22no—
249#448—22no—
250#431C22×C10111yescharacteristic
251#431C22×C10111yescharacteristic
252#416—22no—
253C2×#103—22no—
254C2×C4×C8C22×C10111yescharacteristic
255#322C22×C10112yes—
256C82C22×C10112yes—
257C2×#41—21no—
258C22×Q8—21no—
259C22×Q8—21no—
260C2×SD16—24no—
261C22×C8D4×C10112yes—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8C23×C10112yes—
269C4⋊Q8C23×C10112yes—
270C4⋊Q8C23×C10111yescharacteristic
271C4⋊Q8C23×C10111yescharacteristic
272C4⋊Q8C23×C10111yescharacteristic
273#127C23×C10111yescharacteristic
274#125—21no—
275#124—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278#121—21no—
279#121—21no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×D4—21no—
283C4×D4—21no—
284#117—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C42C23×C10111yescharacteristic
290#107—24no—
291#107—24no—
292#106—24no—
293C4⋊C8D4×C10112yes—
294C4⋊C8D4×C10112yes—
295#103—24no—
296#103—24no—
297#103—22no—
298#103—22no—
299#103—24no—
300#103—24no—
301#103—24no—
302#102—22no—
303#102—22no—
304#102—24no—
305C22⋊C8D4×C10112yes—
306C22⋊C8D4×C10112yes—
307C4×C8D4×C10112yes—
308C4×C8C23×C10111yescharacteristic
309C4×C8C23×C10112yes—
310C4×C8C23×C10112yes—
311C4×C8C23×C10111yescharacteristic
312#41—44no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×Q8—41no—
320C2×Q8—44no—
321C2×Q8—82no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×D4×C10111yescharacteristic
330C22×C4C2×D4×C10111yescharacteristic
331C22×C4C2×D4×C10111yescharacteristic
332SD16—84no—
333C2×C8—24no—
334C2×C8C2×D4×C10112yes—
335C2×C8C2×D4×C10112yes—
336C2×C8C2×D4×C10114yes—
337C2×C8C2×D4×C10114yes—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C42—41no—
358C42C2×D4×C10111yescharacteristic
359C42C2×D4×C10111yescharacteristic
360C42C2×D4×C10111yescharacteristic
361C42C24×C10111yescharacteristic
362C23—41no—
363C23#127×C10111yescharacteristic
364Q8—44no—
365Q8—42no—
366Q8—44no—
367Q8—42no—
368Q8—42no—
369Q8—82no—
370Q8—82no—
371D4—42no—
372D4—42no—
373D4—42no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4#127×C10111yescharacteristic
386C2×C4#127×C10111yescharacteristic
387C2×C4#127×C10111yescharacteristic
388C2×C4#135×C10114yes—
389C2×C4C22×D4×C10111yescharacteristic
390C2×C4C22×D4×C10111yescharacteristic
391C2×C4C22×D4×C10111yescharacteristic
392C8—22no—
393C8—22no—
394C8—24no—
395C8—24no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22#495×C10112yes—
402C22C2×#127×C10111yescharacteristic
403C4—21no—
404C4—21no—
405C4—81no—
406C4—82no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4#495×C10112yes—
411C4C2×#135×C10112yes—
412C4#577×C10112yes—
413C4#578×C10112yes—
414C2—22no—
415C2—161no—
416C2C2×#495×C10111yescharacteristic
417C2C101×#315411yescharacteristic
418C2C101×#315611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
prime radical#532×C101C22
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×#3230C2semidirect
2. C101×#3229C2semidirect
6. C2×#487×C101C2semidirect
7. C101×#1719C2semidirect
8. C101×#1718C2semidirect
9. C101×#1710C2semidirect
10. C101×#1708C2semidirect
11. C101×#1450C2semidirect
204. #19657C101direct (N × H)
210. #3230C2×C101semidirect
211. #3229C2×C101semidirect
215. C2×#487C2×C101semidirect
216. #1719C2×C101semidirect
217. #1718C2×C101semidirect
218. #1710C2×C101semidirect
219. #1708C2×C101semidirect
220. #1450C2×C101semidirect
221. C101#19657direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32302
C101×#32292
C101×#32262
C101×#32062
C101×#31312
C2×#487×C1012
C101×#17192
C101×#17182
C101×#17102
C101×#17082
C101×#14502
#19657101