Finite Group Databasebeta

← C31×#15467 #21472226

Subgroups — C31×#15467 #21472226

Order 7936.

2882 conjugacy classes of subgroups; only the 374 normal subgroups are shown.

normal subgroups only

This group has 2882 conjugacy classes of subgroups — too many to draw. Only its 374 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
1C2×C31×#393C213yesmaximal, complemented
2C2×C31×#379C213yesmaximal
3C31×#1440C216yesmaximal, complemented
4C31×#1437C213yesmaximal, complemented
5C26×C31C2211yescharacteristic
6C23×Q8×C31C2211yescharacteristic, complemented
7C22×C22⋊C4×C31C2213yes—
8C22×C22⋊C4×C31C2216yes—
9C22×C22⋊C4×C31C2216yes—
10C22×C22⋊C4×C31C2213yes—
11C22×C42×C31C2211yescharacteristic, complemented
12C31×#393—212no—
13C31×#379—212no—
14C2×C31×#95C2216yescomplemented
15C2×C31×#95C2213yescomplemented
16C2×C31×#95C2213yescomplemented
17C2×C31×#95C2212yescomplemented
18C25×C31—26no—
19C25×C31—212no—
20C25×C31—41no—
21C25×C31—43no—
22C25×C31—42no—
23C25×C31C2313yes—
24C22×Q8×C31—26no—
25C22×Q8×C31—43no—
26C22×Q8×C31—41no—
27C23×C4×C31C2316yes—
28C23×C4×C31C2313yes—
29C23×C4×C31C2313yes—
30C2×C22⋊C4×C31—26no—
31C2×C22⋊C4×C31—212no—
32C2×C22⋊C4×C31—212no—
33C2×C22⋊C4×C31—212no—
34C2×C22⋊C4×C31—212no—
35C2×C22⋊C4×C31—212no—
36C2×C22⋊C4×C31—43no—
37C2×C22⋊C4×C31—43no—
38C2×C22⋊C4×C31—46no—
39C2×C22⋊C4×C31—46no—
40C2×C22⋊C4×C31D4112yes—
41C2×C42×C31—41no—
42C2×C42×C31—42no—
43C31×#95—212no—
44C31×#95—26no—
45C31×#95—43no—
46C31×#95—42no—
47C24×C31—26no—
48C24×C31—26no—
49C24×C31—26no—
50C24×C31—23no—
51C24×C31—23no—
52C24×C31—26no—
53C24×C31—26no—
54C24×C31—224no—
55C24×C31—412no—
56C24×C31—424no—
57C24×C31—412no—
58C24×C31—424no—
59C24×C31—412no—
60C24×C31—424no—
61C24×C31—44no—
62C24×C31—44no—
63C24×C31—412no—
64C24×C31C2×D416yes—
65C24×C31#41112yes—
66C24×C31C2411yescharacteristic
67C2×Q8×C31—412no—
68C2×Q8×C31—412no—
69C2×Q8×C31—44no—
70C22×C4×C31—26no—
71C22×C4×C31—26no—
72C22×C4×C31—23no—
73C22×C4×C31—23no—
74C22×C4×C31—26no—
75C22×C4×C31—23no—
76C22×C4×C31—23no—
77C22×C4×C31—26no—
78C22×C4×C31—26no—
79C22×C4×C31—26no—
80C22×C4×C31—26no—
81C22×C4×C31—26no—
82C22×C4×C31—26no—
83C22×C4×C31—26no—
84C22×C4×C31—26no—
85C22×C4×C31C2×D416yes—
86C22×C4×C31C2×D416yes—
87C22⋊C4×C31—412no—
88C22⋊C4×C31—424no—
89C22⋊C4×C31—424no—
90C22⋊C4×C31—412no—
91C42×C31—44no—
92#15467C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31—26no—
94C23×C31—212no—
95C23×C31—26no—
96C23×C31—212no—
97C23×C31—212no—
98C23×C31—212no—
99C23×C31—212no—
100C23×C31—212no—
101C23×C31—212no—
102C23×C31—212no—
103C23×C31—448no—
104C23×C31—496no—
105C23×C31—416no—
106C23×C31—448no—
107C23×C31—432no—
108C23×C31—46no—
109C23×C31—46no—
110C23×C31—46no—
111C23×C31—46no—
112C23×C31—43no—
113C23×C31—46no—
114C23×C31—43no—
115C23×C31—46no—
116C23×C31—43no—
117C23×C31—43no—
118C23×C31#124112yes—
119C23×C31C22×D413yes—
120C23×C31C2×#4116yes—
121C23×C31H(5,𝔽2)11yescharacteristic
122C23×C31H(5,𝔽2)13yes—
123C23×C31H(5,𝔽2)12yes—
124Q8×C31—416no—
125C2×C4×C31—26no—
126C2×C4×C31—26no—
127C2×C4×C31—212no—
128C2×C4×C31—212no—
129C2×C4×C31—46no—
130C2×C4×C31—46no—
131C2×C4×C31—43no—
132C2×C4×C31—43no—
133C2×C4×C31—43no—
134C2×C4×C31—43no—
135C2×C4×C31—46no—
136C2×C4×C31—46no—
137C2×C4×C31—46no—
138C2×C4×C31—46no—
139C2×C4×C31—46no—
140C2×C4×C31—46no—
141C2×C4×C31—46no—
142C2×#393C2×C3113yescomplemented
143C2×#379C2×C3113yes—
144#1440C2×C3116yescomplemented
145#1437C2×C3113yescomplemented
146C22×C31—212no—
147C22×C31—224no—
148C22×C31—464no—
149C22×C31—412no—
150C22×C31—46no—
151C22×C31—46no—
152C22×C31—412no—
153C22×C31—412no—
154C22×C31—412no—
155C22×C31—412no—
156C22×C31#52513yes—
157C22×C31C2×#12413yes—
158C22×C31#53413yes—
159C22×C31#53816yes—
160C22×C31D4213yes—
161C22×C31#54616yes—
162C22×C31#55113yes—
163C22×C31#55116yes—
164C22×C31H(3,𝔽4)11yescharacteristic
165C22×C31H(3,𝔽4)11yescharacteristic
166C4×C31—46no—
167C4×C31—46no—
168C4×C31—86no—
169C26C22×C3111yescharacteristic
170C23×Q8C22×C3111yescharacteristic, complemented
171C22×C22⋊C4C22×C3113yes—
172C22×C22⋊C4C22×C3116yes—
173C22×C22⋊C4C22×C3116yes—
174C22×C22⋊C4C22×C3113yes—
175C22×C42C22×C3111yescharacteristic, complemented
176#393—212no—
177#379—212no—
178C2×#95C22×C3116yescomplemented
179C2×#95C22×C3113yescomplemented
180C2×#95C22×C3113yescomplemented
181C2×#95C22×C3112yescomplemented
182C2×C31—412no—
183C2×C31#247216yes—
184C2×C31#256113yes—
185C2×C31#267911yescharacteristic
186C2×C31#268413yes—
187C2×C31#273612yes—
188C25—26no—
189C25—212no—
190C25—41no—
191C25—43no—
192C25—42no—
193C25C23×C3113yes—
194C22×Q8—26no—
195C22×Q8—43no—
196C22×Q8—41no—
197C23×C4C23×C3116yes—
198C23×C4C23×C3113yes—
199C23×C4C23×C3113yes—
200C2×C22⋊C4—26no—
201C2×C22⋊C4—212no—
202C2×C22⋊C4—212no—
203C2×C22⋊C4—212no—
204C2×C22⋊C4—212no—
205C2×C22⋊C4—212no—
206C2×C22⋊C4—43no—
207C2×C22⋊C4—43no—
208C2×C22⋊C4—46no—
209C2×C22⋊C4—46no—
210C2×C22⋊C4D4×C31112yes—
211C2×C42—41no—
212C2×C42—42no—
213#95—212no—
214#95—26no—
215#95—43no—
216#95—42no—
217C31#1546711yescharacteristic, direct product factor, Sylow
218C24—26no—
219C24—26no—
220C24—26no—
221C24—23no—
222C24—23no—
223C24—26no—
224C24—26no—
225C24—224no—
226C24—412no—
227C24—424no—
228C24—424no—
229C24—412no—
230C24—412no—
231C24—424no—
232C24—44no—
233C24—44no—
234C24—412no—
235C24C2×D4×C3116yes—
236C24#41×C31112yes—
237C24C24×C3111yescharacteristic
238C2×Q8—412no—
239C2×Q8—412no—
240C2×Q8—44no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—26no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4—26no—
253C22×C4—26no—
254C22×C4—26no—
255C22×C4—26no—
256C22×C4C2×D4×C3116yes—
257C22×C4C2×D4×C3116yes—
258C22⋊C4—412no—
259C22⋊C4—424no—
260C22⋊C4—424no—
261C22⋊C4—412no—
262C42—44no—
263C23—26no—
264C23—212no—
265C23—26no—
266C23—212no—
267C23—212no—
268C23—212no—
269C23—212no—
270C23—212no—
271C23—212no—
272C23—212no—
273C23—496no—
274C23—448no—
275C23—416no—
276C23—448no—
277C23—432no—
278C23—46no—
279C23—46no—
280C23—46no—
281C23—46no—
282C23—43no—
283C23—46no—
284C23—43no—
285C23—46no—
286C23—43no—
287C23—43no—
288C23C31×#124112yes—
289C23C22×D4×C3113yes—
290C23C2×#41×C3116yes—
291C23C31×H(5,𝔽2)11yescharacteristic
292C23C31×H(5,𝔽2)13yes—
293C23C31×H(5,𝔽2)12yes—
294Q8—416no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—212no—
298C2×C4—212no—
299C2×C4—46no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—43no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—46no—
308C2×C4—46no—
309C2×C4—46no—
310C2×C4—46no—
311C2×C4—46no—
312C22—224no—
313C22—212no—
314C22—464no—
315C22—46no—
316C22—46no—
317C22—412no—
318C22—412no—
319C22—412no—
320C22—412no—
321C22—412no—
322C22C31×#52513yes—
323C22C2×C31×#12413yes—
324C22C31×#53413yes—
325C22C31×#53816yes—
326C22D42×C3113yes—
327C22C31×#54616yes—
328C22C31×#55113yes—
329C22C31×#55116yes—
330C22C31×H(3,𝔽4)11yescharacteristic
331C22C31×H(3,𝔽4)11yescharacteristic
332C4—46no—
333C4—46no—
334C4—86no—
335C2—412no—
336C2C31×#247216yes—
337C2C31×#256113yes—
338C2C31×#267911yescharacteristic
339C2C31×#268413yes—
340C2C31×#273612yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#393C2semidirect
3. C31×#1440C2semidirect
4. C31×#1437C2semidirect
6. C23×Q8×C31C22semidirect
11. C22×C42×C31C22semidirect
14. C2×C31×#95C22semidirect
15. C2×C31×#95C22semidirect
16. C2×C31×#95C22semidirect
17. C2×C31×#95C22semidirect
92. #15467C31direct (N × H)
142. C2×#393C2×C31semidirect
144. #1440C2×C31semidirect
145. #1437C2×C31semidirect
170. C23×Q8C22×C31semidirect
175. C22×C42C22×C31semidirect
178. C2×#95C22×C31semidirect
179. C2×#95C22×C31semidirect
180. C2×#95C22×C31semidirect
181. C2×#95C22×C31semidirect
217. C31#15467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3932
C2×C31×#3792
C31×#14402
C31×#14372
#1546731