Finite Group Databasebeta

← C101×#9094 #38791245

Subgroups — C101×#9094 #38791245

Order 25856.

488 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×#2983C211yesmaximal, characteristic, complemented
2C2×#440×C101C211yesmaximal, characteristic
3C101×#1479C211yesmaximal, characteristic, complemented
4C101×#1478C211yesmaximal, characteristic
5C101×#1460C211yesmaximal, characteristic
6C101×#1281C211yesmaximal, characteristic, complemented
7C101×#1275C211yesmaximal, characteristic, complemented
8C22×SD16×C101C411yescharacteristic
9C2×C4×Q8×C101C2211yescharacteristic
10C2×C4×D4×C101C2211yescharacteristic
11#446×C101—22no—
12#446×C101—22no—
13#440×C101—22no—
14#440×C101—22no—
15#432×C101—22no—
16#431×C101C2211yescharacteristic
17#431×C101C2211yescharacteristic
18#431×C101C2211yescharacteristic
19#431×C101C2211yescharacteristic
20C2×#107×C101C411yescharacteristic
21C2×#103×C101C411yescharacteristic
22C2×#102×C101C411yescharacteristic
23C2×#97×C101C2211yescharacteristic
24Q8⋊C8×C101—22no—
25D4⋊C8×C101—22no—
26#323×C101—22no—
27C22×Q8×C101C2×C411yescharacteristic
28C22×D4×C101C2×C411yescharacteristic
29C23×C4×C101—21no—
30C2×SD16×C101—22no—
31C2×SD16×C101—22no—
32C2×SD16×C101—22no—
33C22×C8×C101C2×C411yescharacteristic
34C22×C8×C101C2×C411yescharacteristic
35C4×Q8×C101—21no—
36C4×Q8×C101—21no—
37C4×Q8×C101D412yes—
38C4×Q8×C101D412yes—
39C4×D4×C101—21no—
40C4×D4×C101—21no—
41C4×D4×C101—21no—
42C4×D4×C101—21no—
43C2×C4⋊C4×C101—21no—
44C2×C4⋊C4×C101C2×C411yescharacteristic
45C2×C4⋊C4×C101C2×C411yescharacteristic
46C2×C22⋊C4×C101—21no—
47C2×C42×C101—21no—
48C2×C42×C101C2311yescharacteristic
49#107×C101—22no—
50C4⋊C8×C101—24no—
51C4⋊C8×C101—21no—
52C4⋊C8×C101—21no—
53C4⋊C8×C101—21no—
54C4⋊C8×C101—21no—
55#103×C101—22no—
56#102×C101—22no—
57C22⋊C8×C101—21no—
58C22⋊C8×C101—21no—
59C22⋊C8×C101—21no—
60C22⋊C8×C101D412yes—
61#97×C101—24no—
62#97×C101—21no—
63#97×C101—21no—
64C4×C8×C101—21no—
65C4×C8×C101—21no—
66C4×C8×C101—21no—
67C4×C8×C101D412yes—
68C24×C101—21no—
69C2×Q8×C101—21no—
70C2×Q8×C101—21no—
71C2×Q8×C101—21no—
72C2×Q8×C101—21no—
73C2×Q8×C101—21no—
74C2×Q8×C101C22⋊C412yes—
75C2×D4×C101—21no—
76C2×D4×C101—21no—
77C2×D4×C101—21no—
78C2×D4×C101—21no—
79C2×D4×C101—21no—
80C2×D4×C101M1612yes—
81C22×C4×C101—21no—
82C22×C4×C101—21no—
83C22×C4×C101—21no—
84C22×C4×C101—41no—
85C22×C4×C101—41no—
86C22×C4×C101—82no—
87C22×C4×C101C22×C411yescharacteristic
88C22×C4×C101C2×D411yescharacteristic
89C22×C4×C101#4111yescharacteristic
90SD16×C101—28no—
91C2×C8×C101—21no—
92C2×C8×C101—21no—
93C2×C8×C101—21no—
94C2×C8×C101—22no—
95C2×C8×C101—22no—
96C2×C8×C101—21no—
97C2×C8×C101—21no—
98C2×C8×C101—41no—
99C2×C8×C101—41no—
100C2×C8×C101M1612yes—
101C4⋊C4×C101—21no—
102C4⋊C4×C101—22no—
103C4⋊C4×C101—22no—
104C4⋊C4×C101—21no—
105C4⋊C4×C101—21no—
106C4⋊C4×C101C22⋊C412yes—
107C22⋊C4×C101—41no—
108C22⋊C4×C101—41no—
109C42×C101—22no—
110C42×C101—22no—
111C42×C101C2×D411yescharacteristic
112C42×C101C2×D411yescharacteristic
113C42×C101C2×D411yescharacteristic
114C42×C101#4111yescharacteristic
115C23×C101—22no—
116C23×C101—41no—
117C23×C101—41no—
118C23×C101—81no—
119C23×C101—81no—
120C23×C101C4×D411yescharacteristic
121Q8×C101—22no—
122Q8×C101—22no—
123Q8×C101—41no—
124Q8×C101—41no—
125D4×C101—22no—
126D4×C101—22no—
127D4×C101—41no—
128D4×C101—41no—
129C2×C4×C101—22no—
130C2×C4×C101—22no—
131C2×C4×C101—41no—
132C2×C4×C101—41no—
133C2×C4×C101—41no—
134C2×C4×C101—41no—
135C2×C4×C101—41no—
136C2×C4×C101—82no—
137C2×C4×C101—82no—
138C2×C4×C101—81no—
139C2×C4×C101—81no—
140C2×C4×C101C2×C22⋊C411yescharacteristic
141C2×C4×C101C4×D411yescharacteristic
142C2×C4×C101#12011yescharacteristic
143C2×C4×C101#12111yescharacteristic
144C2×C4×C101#12111yescharacteristic
145C2×C4×C101#12311yescharacteristic
146C2×C4×C101C2×M1611yescharacteristic
147C2×C4×C101C2×M1611yescharacteristic
148C2×C4×C101#13111yescharacteristic
149C2×C4×C101#13111yescharacteristic
150C8×C101—22no—
151C8×C101—42no—
152C8×C101—42no—
153C8×C101—41no—
154C8×C101—81no—
155C8×C101—81no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—42no—
159C22×C101—82no—
160C22×C101—82no—
161C22×C101—81no—
162C22×C101—81no—
163C22×C101#38611yescharacteristic
164C22×C101#43511yescharacteristic
165C22×C101#43611yescharacteristic
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—42no—
171C4×C101—42no—
172C4×C101—81no—
173C4×C101#40711yescharacteristic
174C4×C101#40811yescharacteristic
175C4×C101#43511yescharacteristic
176C4×C101#43611yescharacteristic
177#9094C10111yesmaximal, characteristic, direct product factor, Sylow
178C2×C101—21no—
179C2×C101—21no—
180C2×C101—82no—
181C2×C101#187011yescharacteristic
182C2×C101#190311yescharacteristic
183C2×C101#190511yescharacteristic
184#2983C2×C10111yescharacteristic, complemented
185C2×#440C2×C10111yescharacteristic
186#1479C2×C10111yescharacteristic, complemented
187#1478C2×C10111yescharacteristic
188#1460C2×C10111yescharacteristic
189#1281C2×C10111yescharacteristic, complemented
190#1275C2×C10111yescharacteristic, complemented
191C101#909411yescharacteristic, direct product factor, Sylow
192C22×SD16C4×C10111yescharacteristic
193C2×C4×Q8C22×C10111yescharacteristic
194C2×C4×D4C22×C10111yescharacteristic
195#446—22no—
196#446—22no—
197#440—22no—
198#440—22no—
199#432—22no—
200#431C22×C10111yescharacteristic
201#431C22×C10111yescharacteristic
202#431C22×C10111yescharacteristic
203#431C22×C10111yescharacteristic
204C2×#107C4×C10111yescharacteristic
205C2×#103C4×C10111yescharacteristic
206C2×#102C4×C10111yescharacteristic
207C2×#97C22×C10111yescharacteristic
208Q8⋊C8—22no—
209D4⋊C8—22no—
210#323—22no—
211C22×Q8C2×C4×C10111yescharacteristic
212C22×D4C2×C4×C10111yescharacteristic
213C23×C4—21no—
214C2×SD16—22no—
215C2×SD16—22no—
216C2×SD16—22no—
217C22×C8C2×C4×C10111yescharacteristic
218C22×C8C2×C4×C10111yescharacteristic
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8D4×C10112yes—
222C4×Q8D4×C10112yes—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C10111yescharacteristic
229C2×C4⋊C4C2×C4×C10111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C42—21no—
232C2×C42C23×C10111yescharacteristic
233#107—22no—
234C4⋊C8—24no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239#103—22no—
240#102—22no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8D4×C10112yes—
245#97—24no—
246#97—21no—
247#97—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8D4×C10112yes—
252C24—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8C22⋊C4×C10112yes—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4M16×C10112yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—82no—
271C22×C4C22×C4×C10111yescharacteristic
272C22×C4C2×D4×C10111yescharacteristic
273C22×C4#41×C10111yescharacteristic
274SD16—28no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8M16×C10112yes—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4C22⋊C4×C10112yes—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—22no—
294C42—22no—
295C42C2×D4×C10111yescharacteristic
296C42C2×D4×C10111yescharacteristic
297C42C2×D4×C10111yescharacteristic
298C42#41×C10111yescharacteristic
299C23—22no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23C4×D4×C10111yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309D4—22no—
310D4—22no—
311D4—41no—
312D4—41no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C22⋊C4×C10111yescharacteristic
325C2×C4C4×D4×C10111yescharacteristic
326C2×C4#120×C10111yescharacteristic
327C2×C4#121×C10111yescharacteristic
328C2×C4#121×C10111yescharacteristic
329C2×C4#123×C10111yescharacteristic
330C2×C4C2×M16×C10111yescharacteristic
331C2×C4C2×M16×C10111yescharacteristic
332C2×C4#131×C10111yescharacteristic
333C2×C4#131×C10111yescharacteristic
334C8—22no—
335C8—42no—
336C8—42no—
337C8—41no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—82no—
344C22—82no—
345C22—81no—
346C22—81no—
347C22#386×C10111yescharacteristic
348C22#435×C10111yescharacteristic
349C22#436×C10111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—81no—
357C4#407×C10111yescharacteristic
358C4#408×C10111yescharacteristic
359C4#435×C10111yescharacteristic
360C4#436×C10111yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2C101×#187011yescharacteristic
365C2C101×#190311yescharacteristic
366C2C101×#190511yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC22×D4×C101C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2983C2semidirect
3. C101×#1479C2semidirect
6. C101×#1281C2semidirect
7. C101×#1275C2semidirect
177. #9094C101direct (N × H)
184. #2983C2×C101semidirect
186. #1479C2×C101semidirect
189. #1281C2×C101semidirect
190. #1275C2×C101semidirect
191. C101#9094direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#29832
C2×#440×C1012
C101×#14792
C101×#14782
C101×#14602
C101×#12812
C101×#12752
#9094101