Finite Group Databasebeta

← C101×#12103 #38794254

Subgroups — C101×#12103 #38794254

Order 25856.

476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3189C211yesmaximal, characteristic, complemented
2C101×#2187C212yesmaximal, complemented
3C101×#1999C211yesmaximal, characteristic
4C101×#1348C212yesmaximal, complemented
5C101×#1314C211yesmaximal, characteristic, complemented
6C22×D8×C101C2211yescharacteristic
7C2×C22⋊Q8×C101—21no—
8C2×#121×C101—21no—
9C2×SD32×C101—22no—
10#484×C101—22no—
11#467×C101—21no—
12#467×C101C2212yes—
13#451×C101—22no—
14C2×#102×C101—21no—
15C2×C22⋊C8×C101C2211yescharacteristic
16#357×C101—22no—
17C22⋊C16×C101C2212yes—
18#340×C101C2211yescharacteristic
19C22×Q8×C101—21no—
20C22×D4×C101—21no—
21C22×D4×C101—41no—
22C23×C4×C101D411yescharacteristic
23C2×Q16×C101—21no—
24C2×Q16×C101D412yescomplemented
25C2×D8×C101—22no—
26C2×D8×C101—42no—
27C22×C8×C101D411yescharacteristic
28C22×C8×C101C2311yescharacteristic
29C22⋊Q8×C101—22no—
30C22⋊Q8×C101—22no—
31C22⋊Q8×C101—41no—
32C22⋊Q8×C101—41no—
33#121×C101—42no—
34#121×C101—42no—
35C2×C4⋊C4×C101—21no—
36C2×C4⋊C4×C101—21no—
37C2×C4⋊C4×C101—41no—
38C2×C22⋊C4×C101—41no—
39C2×C22⋊C4×C101—41no—
40SD32×C101—44no—
41C2×C16×C101—22no—
42#107×C101—21no—
43#107×C101D412yescomplemented
44#103×C101—22no—
45#103×C101—22no—
46#102×C101—42no—
47C22⋊C8×C101—22no—
48C24×C101—41no—
49C24×C101D811yescharacteristic
50C2×Q8×C101—22no—
51C2×Q8×C101—41no—
52C2×Q8×C101—81no—
53C2×Q8×C101—81no—
54C2×D4×C101—22no—
55C2×D4×C101—41no—
56C2×D4×C101—41no—
57C2×D4×C101—41no—
58C2×D4×C101—44no—
59C2×D4×C101—41no—
60C2×D4×C101—41no—
61C2×D4×C101—82no—
62C2×D4×C101—82no—
63C22×C4×C101—21no—
64C22×C4×C101—21no—
65C22×C4×C101—41no—
66C22×C4×C101—41no—
67C22×C4×C101—41no—
68C22×C4×C101—41no—
69C22×C4×C101—41no—
70C22×C4×C101D811yescharacteristic
71C22×C4×C101C2×D411yescharacteristic
72Q16×C101—42no—
73Q16×C101—81no—
74D8×C101—24no—
75D8×C101—42no—
76C2×C8×C101—21no—
77C2×C8×C101—41no—
78C2×C8×C101—41no—
79C2×C8×C101C2×D412yes—
80C4⋊C4×C101—22no—
81C4⋊C4×C101—22no—
82C4⋊C4×C101—41no—
83C4⋊C4×C101—41no—
84C4⋊C4×C101—42no—
85C4⋊C4×C101—42no—
86C22⋊C4×C101—42no—
87C22⋊C4×C101—44no—
88C22⋊C4×C101—42no—
89C16×C101—42no—
90C23×C101—21no—
91C23×C101—21no—
92C23×C101—41no—
93C23×C101—41no—
94C23×C101—42no—
95C23×C101—81no—
96C23×C101—81no—
97C23×C101—81no—
98C23×C101—81no—
99C23×C101—81no—
100C23×C101—81no—
101C23×C101SD3212yescomplemented
102C23×C101C2×D811yescharacteristic
103Q8×C101—42no—
104Q8×C101—42no—
105Q8×C101—82no—
106D4×C101—42no—
107D4×C101—42no—
108D4×C101—81no—
109D4×C101—88no—
110D4×C101—81no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—42no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—81no—
121C2×C4×C101—81no—
122C2×C4×C101—82no—
123C2×C4×C101—82no—
124C2×C4×C101—81no—
125C2×C4×C101#12011yescharacteristic
126C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
127C8×C101—22no—
128C8×C101—41no—
129C22×C101—21no—
130C22×C101—21no—
131C22×C101—22no—
132C22×C101—42no—
133C22×C101—41no—
134C22×C101—41no—
135C22×C101—81no—
136C22×C101—82no—
137C22×C101—82no—
138C22×C101—82no—
139C22×C101—161no—
140C22×C101—161no—
141C22×C101—161no—
142C22×C101—161no—
143C22×C101#44711yescharacteristic
144C22×C101C2×SD3211yescharacteristic
145C22×C101#51011yescharacteristic
146C4×C101—21no—
147C4×C101—41no—
148C4×C101—82no—
149C4×C101—82no—
150C4×C101—82no—
151C4×C101#45311yescharacteristic
152C4×C101B(4,𝔽2)11yescharacteristic
153#12103C10111yesmaximal, characteristic, direct product factor, Sylow
154C2×C101—21no—
155C2×C101—21no—
156C2×C101—42no—
157C2×C101—162no—
158C2×C101#159511yescharacteristic
159C2×C101#218511yescharacteristic
160C2×C101#219011yescharacteristic
161#3189C2×C10111yescharacteristic, complemented
162#2187C2×C10112yescomplemented
163#1999C2×C10111yescharacteristic
164#1348C2×C10112yescomplemented
165#1314C2×C10111yescharacteristic, complemented
166C101#1210311yescharacteristic, direct product factor, Sylow
167C22×D8C22×C10111yescharacteristic
168C2×C22⋊Q8—21no—
169C2×#121—21no—
170C2×SD32—22no—
171#484—22no—
172#467—21no—
173#467C22×C10112yes—
174#451—22no—
175C2×#102—21no—
176C2×C22⋊C8C22×C10111yescharacteristic
177#357—22no—
178C22⋊C16C22×C10112yes—
179#340C22×C10111yescharacteristic
180C22×Q8—21no—
181C22×D4—21no—
182C22×D4—41no—
183C23×C4D4×C10111yescharacteristic
184C2×Q16—21no—
185C2×Q16D4×C10112yescomplemented
186C2×D8—22no—
187C2×D8—42no—
188C22×C8D4×C10111yescharacteristic
189C22×C8C23×C10111yescharacteristic
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194#121—42no—
195#121—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—41no—
201SD32—44no—
202C2×C16—22no—
203#107—21no—
204#107D4×C10112yescomplemented
205#103—22no—
206#103—22no—
207#102—42no—
208C22⋊C8—22no—
209C24—41no—
210C24D8×C10111yescharacteristic
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—81no—
214C2×Q8—81no—
215C2×D4—22no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—44no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—82no—
223C2×D4—82no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4D8×C10111yescharacteristic
232C22×C4C2×D4×C10111yescharacteristic
233Q16—42no—
234Q16—81no—
235D8—24no—
236D8—42no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8C2×D4×C10112yes—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C16—42no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—42no—
256C23—81no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23SD32×C10112yescomplemented
263C23C2×D8×C10111yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267D4—42no—
268D4—42no—
269D4—81no—
270D4—88no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4#120×C10111yescharacteristic
287C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
288C8—22no—
289C8—41no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—161no—
301C22—161no—
302C22—161no—
303C22—161no—
304C22#447×C10111yescharacteristic
305C22C2×SD32×C10111yescharacteristic
306C22#510×C10111yescharacteristic
307C4—21no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4—82no—
312C4#453×C10111yescharacteristic
313C4B(4,𝔽2)×C10111yescharacteristic
314C2—21no—
315C2—21no—
316C2—42no—
317C2—162no—
318C2C101×#159511yescharacteristic
319C2C101×#218511yescharacteristic
320C2C101×#219011yescharacteristic
subgroupG/H
center, socleC22×C101#447
commutator, Frattini, cosocleC22×C8C23×C101
prime radicalC101×#1999C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ C2×C22⋊C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3189C2semidirect
2. C101×#2187C2semidirect
4. C101×#1348C2semidirect
5. C101×#1314C2semidirect
24. C2×Q16×C101D4semidirect
43. #107×C101D4semidirect
101. C23×C101SD32semidirect
153. #12103C101direct (N × H)
161. #3189C2×C101semidirect
162. #2187C2×C101semidirect
164. #1348C2×C101semidirect
165. #1314C2×C101semidirect
166. C101#12103direct (N × H)
185. C2×Q16D4×C101semidirect
204. #107D4×C101semidirect
262. C23SD32×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31892
C101×#21872
C101×#19992
C101×#13482
C101×#13142
#12103101