Finite Group Databasebeta

← C22×C31×#353 #21490111

Subgroups — C22×C31×#353 #21490111

Order 7936.

2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 382 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
1C22×C31×#127C211yesmaximal, characteristic
2C22×C31×#99C212yesmaximal, complemented
3C2×C31×#353C2112yesmaximal, direct product factor
4C23×D4×C31—22no—
5C23×D4×C31C411yescharacteristic, complemented
6C23×D4×C31C2211yescharacteristic
7C2×C31×#127—26no—
8C2×C31×#127C416yescomplemented
9C2×C31×#127C2216yes—
10C22×C22⋊C4×C31—22no—
11C22×C42×C31C411yescharacteristic, complemented
12C2×C31×#99—26no—
13C2×C31×#99C22112yescomplemented
14C31×#353C22116yesdirect product factor
15C25×C31—21no—
16C25×C31D412yes—
17C22×D4×C31—212no—
18C22×D4×C31—212no—
19C22×D4×C31—23no—
20C22×D4×C31—43no—
21C22×D4×C31—41no—
22C22×D4×C31—416no—
23C22×D4×C31—43no—
24C22×D4×C31—41no—
25C22×D4×C31C2×C413yes—
26C22×D4×C31C2×C416yescomplemented
27C22×D4×C31D416yes—
28C22×D4×C31C2313yes—
29C23×C4×C31—21no—
30C23×C4×C31—42no—
31C23×C4×C31C2×C411yescharacteristic
32C31×#127—212no—
33C31×#127—212no—
34C31×#127C2×C4112yescomplemented
35C31×#127C2314yes—
36C2×C22⋊C4×C31—212no—
37C2×C22⋊C4×C31—46no—
38C2×C42×C31—23no—
39C2×C42×C31C2×C416yescomplemented
40C31×#99—212no—
41C31×#99C2318yescomplemented
42C24×C31—22no—
43C24×C31—26no—
44C24×C31—26no—
45C24×C31—48no—
46C24×C31—48no—
47C24×C31—43no—
48C24×C31—41no—
49C24×C31C22⋊C416yes—
50C24×C31C22⋊C411yescharacteristic
51C24×C31C2×D416yes—
52C2×D4×C31—224no—
53C2×D4×C31—28no—
54C2×D4×C31—26no—
55C2×D4×C31—43no—
56C2×D4×C31—43no—
57C2×D4×C31—46no—
58C2×D4×C31—46no—
59C2×D4×C31—43no—
60C2×D4×C31—43no—
61C2×D4×C31—448no—
62C2×D4×C31—448no—
63C2×D4×C31—46no—
64C2×D4×C31—46no—
65C2×D4×C31—46no—
66C2×D4×C31—46no—
67C2×D4×C31C22⋊C416yes—
68C2×D4×C31C22×C413yes—
69C2×D4×C31C22×C414yescomplemented
70C2×D4×C31C2×D416yes—
71C2×D4×C31C2411yescharacteristic
72C22×C4×C31—28no—
73C22×C4×C31—23no—
74C22×C4×C31—21no—
75C22×C4×C31—26no—
76C22×C4×C31—412no—
77C22×C4×C31—88no—
78C22×C4×C31C22⋊C413yes—
79C22×C4×C31C22×C413yes—
80C22⋊C4×C31—28no—
81C22⋊C4×C31—412no—
82C42×C31—26no—
83C42×C31C22×C414yescomplemented
84C22×#353C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31—24no—
86C23×C31—26no—
87C23×C31—26no—
88C23×C31—26no—
89C23×C31—26no—
90C23×C31—24no—
91C23×C31—412no—
92C23×C31—412no—
93C23×C31—424no—
94C23×C31—48no—
95C23×C31—46no—
96C23×C31—46no—
97C23×C31—812no—
98C23×C31—812no—
99C23×C31—84no—
100C23×C31#9913yes—
101C23×C31#9911yescharacteristic
102C23×C31C2×C22⋊C413yes—
103C23×C31C2×C22⋊C416yes—
104C23×C31C22×D412yes—
105D4×C31—46no—
106D4×C31—43no—
107D4×C31—46no—
108D4×C31—41no—
109D4×C31—44no—
110D4×C31—448no—
111D4×C31—416no—
112D4×C31—412no—
113C2×C4×C31—224no—
114C2×C4×C31—24no—
115C2×C4×C31—23no—
116C2×C4×C31—23no—
117C2×C4×C31—23no—
118C2×C4×C31—23no—
119C2×C4×C31—48no—
120C2×C4×C31—824no—
121C2×C4×C31C2×C22⋊C413yes—
122C2×C4×C31C23×C411yescharacteristic
123C22×#127C2×C3111yescharacteristic
124C22×#99C2×C3112yescomplemented
125C2×#353C2×C31112yesdirect product factor
126C22×C31—26no—
127C22×C31—26no—
128C22×C31—22no—
129C22×C31—26no—
130C22×C31—46no—
131C22×C31—42no—
132C22×C31—48no—
133C22×C31—412no—
134C22×C31—412no—
135C22×C31—44no—
136C22×C31—86no—
137C22×C31—86no—
138C22×C31—812no—
139C22×C31—812no—
140C22×C31#35314yesdirect product factor
141C22×C31C2×#9913yes—
142C22×C31C2×#9913yes—
143C22×C31C22×C22⋊C411yescharacteristic
144C4×C31—28no—
145C4×C31—23no—
146C4×C31—21no—
147C4×C31—88no—
148C23×D4—22no—
149C23×D4C4×C3111yescharacteristic, complemented
150C23×D4C22×C3111yescharacteristic
151C2×#127—26no—
152C2×#127C4×C3116yescomplemented
153C2×#127C22×C3116yes—
154C22×C22⋊C4—22no—
155C22×C42C4×C3111yescharacteristic, complemented
156C2×#99—26no—
157C2×#99C22×C31112yescomplemented
158#353C22×C31116yesdirect product factor
159C2×C31—21no—
160C2×C31—23no—
161C2×C31—42no—
162C2×C31—46no—
163C2×C31—84no—
164C2×C31C2×#35316yesdirect product factor
165C2×C31C22×#9911yescharacteristic
166C25—21no—
167C25D4×C3112yes—
168C22×D4—212no—
169C22×D4—212no—
170C22×D4—23no—
171C22×D4—41no—
172C22×D4—43no—
173C22×D4—43no—
174C22×D4—41no—
175C22×D4—416no—
176C22×D4C2×C4×C3113yes—
177C22×D4C2×C4×C3116yescomplemented
178C22×D4D4×C3116yes—
179C22×D4C23×C3113yes—
180C23×C4—21no—
181C23×C4—42no—
182C23×C4C2×C4×C3111yescharacteristic
183#127—212no—
184#127—212no—
185#127C2×C4×C31112yescomplemented
186#127C23×C3114yes—
187C2×C22⋊C4—212no—
188C2×C22⋊C4—46no—
189C2×C42—23no—
190C2×C42C2×C4×C3116yescomplemented
191#99—212no—
192#99C23×C3118yescomplemented
193C31C22×#35311yescharacteristic, direct product factor, Sylow
194C24—22no—
195C24—26no—
196C24—26no—
197C24—48no—
198C24—48no—
199C24—43no—
200C24—41no—
201C24C22⋊C4×C3111yescharacteristic
202C24C22⋊C4×C3116yes—
203C24C2×D4×C3116yes—
204C2×D4—224no—
205C2×D4—28no—
206C2×D4—26no—
207C2×D4—43no—
208C2×D4—43no—
209C2×D4—46no—
210C2×D4—46no—
211C2×D4—43no—
212C2×D4—43no—
213C2×D4—46no—
214C2×D4—46no—
215C2×D4—448no—
216C2×D4—448no—
217C2×D4—46no—
218C2×D4—46no—
219C2×D4C22⋊C4×C3116yes—
220C2×D4C22×C4×C3113yes—
221C2×D4C22×C4×C3114yescomplemented
222C2×D4C2×D4×C3116yes—
223C2×D4C24×C3111yescharacteristic
224C22×C4—28no—
225C22×C4—23no—
226C22×C4—21no—
227C22×C4—26no—
228C22×C4—412no—
229C22×C4—88no—
230C22×C4C22⋊C4×C3113yes—
231C22×C4C22×C4×C3113yes—
232C22⋊C4—28no—
233C22⋊C4—412no—
234C42—26no—
235C42C22×C4×C3114yescomplemented
236C23—24no—
237C23—26no—
238C23—26no—
239C23—26no—
240C23—26no—
241C23—24no—
242C23—412no—
243C23—412no—
244C23—424no—
245C23—48no—
246C23—46no—
247C23—46no—
248C23—812no—
249C23—812no—
250C23—84no—
251C23C31×#9913yes—
252C23C31×#9911yescharacteristic
253C23C2×C22⋊C4×C3113yes—
254C23C2×C22⋊C4×C3116yes—
255C23C22×D4×C3112yes—
256D4—46no—
257D4—43no—
258D4—46no—
259D4—41no—
260D4—44no—
261D4—448no—
262D4—416no—
263D4—412no—
264C2×C4—224no—
265C2×C4—23no—
266C2×C4—23no—
267C2×C4—23no—
268C2×C4—23no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—824no—
272C2×C4C2×C22⋊C4×C3113yes—
273C2×C4C23×C4×C3111yescharacteristic
274C22—26no—
275C22—26no—
276C22—22no—
277C22—26no—
278C22—46no—
279C22—42no—
280C22—48no—
281C22—412no—
282C22—412no—
283C22—44no—
284C22—86no—
285C22—86no—
286C22—812no—
287C22—812no—
288C22C31×#35314yesdirect product factor
289C22C2×C31×#9913yes—
290C22C2×C31×#9913yes—
291C22C22×C22⋊C4×C3111yescharacteristic
292C4—28no—
293C4—23no—
294C4—21no—
295C4—88no—
296C2—21no—
297C2—23no—
298C2—42no—
299C2—46no—
300C2—84no—
301C2C2×C31×#35316yesdirect product factor
302C2C22×C31×#9911yescharacteristic
subgroupG/H
center, socleC23×C31#99
commutatorC2×C4C23×C4×C31
Frattini, cosocleC2×D4C24×C31
prime radicalC22×C31×#127C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C31 ◁ C23×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#99C2semidirect
3. C2×C31×#353C2direct (N × H)
5. C23×D4×C31C4semidirect
8. C2×C31×#127C4semidirect
11. C22×C42×C31C4semidirect
13. C2×C31×#99C22semidirect
14. C31×#353C22direct (N × H)
26. C22×D4×C31C2×C4semidirect
34. C31×#127C2×C4semidirect
39. C2×C42×C31C2×C4semidirect
41. C31×#99C23semidirect
69. C2×D4×C31C22×C4semidirect
83. C42×C31C22×C4semidirect
84. C22×#353C31direct (N × H)
124. C22×#99C2×C31semidirect
125. C2×#353C2×C31direct (N × H)
140. C22×C31#353direct (N × H)
149. C23×D4C4×C31semidirect
152. C2×#127C4×C31semidirect
155. C22×C42C4×C31semidirect
157. C2×#99C22×C31semidirect
158. #353C22×C31direct (N × H)
164. C2×C31C2×#353direct (N × H)
177. C22×D4C2×C4×C31semidirect
185. #127C2×C4×C31semidirect
190. C2×C42C2×C4×C31semidirect
192. #99C23×C31semidirect
193. C31C22×#353direct (N × H)
221. C2×D4C22×C4×C31semidirect
235. C42C22×C4×C31semidirect
288. C22C31×#353direct (N × H)
301. C2C2×C31×#353direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1272
C22×C31×#992
C2×C31×#3532
C22×#35331