Finite Group Databasebeta

← C31×#15480 #21472239

Subgroups — C31×#15480 #21472239

Order 7936.

2818 conjugacy classes of subgroups; only the 374 normal subgroups are shown.

normal subgroups only

This group has 2818 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×#397C213yesmaximal, complemented
2C2×C31×#379C213yesmaximal
3C31×#1439C216yesmaximal, complemented
4C31×#1437C212yesmaximal, complemented
5C31×#1437C211yesmaximal, characteristic, complemented
6C26×C31C2211yescharacteristic
7C22×C4⋊C4×C31C2213yescomplemented
8C22×C22⋊C4×C31C2213yes—
9C22×C22⋊C4×C31C2216yes—
10C22×C22⋊C4×C31C2216yes—
11C22×C22⋊C4×C31C2213yes—
12C22×C42×C31C2211yescharacteristic, complemented
13C31×#397—212no—
14C31×#379—212no—
15C2×C31×#95C2216yescomplemented
16C2×C31×#95C2213yescomplemented
17C2×C31×#95C2213yescomplemented
18C25×C31—26no—
19C25×C31—212no—
20C25×C31—43no—
21C25×C31—43no—
22C25×C31C2311yescharacteristic
23C25×C31C2312yes—
24C23×C4×C31C2316yes—
25C23×C4×C31C2313yes—
26C23×C4×C31C2313yes—
27C2×C4⋊C4×C31—26no—
28C2×C4⋊C4×C31—43no—
29C2×C4⋊C4×C31—43no—
30C2×C22⋊C4×C31—212no—
31C2×C22⋊C4×C31—26no—
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—43no—
42C31×#95—26no—
43C31×#95—212no—
44C31×#95—43no—
45C24×C31—26no—
46C24×C31—26no—
47C24×C31—26no—
48C24×C31—23no—
49C24×C31—23no—
50C24×C31—26no—
51C24×C31—26no—
52C24×C31—224no—
53C24×C31—424no—
54C24×C31—424no—
55C24×C31—412no—
56C24×C31—412no—
57C24×C31—412no—
58C24×C31—424no—
59C24×C31—44no—
60C24×C31—44no—
61C24×C31—48no—
62C24×C31—44no—
63C24×C31C2×D416yes—
64C24×C31#41112yes—
65C24×C31C2411yescharacteristic
66C22×C4×C31—26no—
67C22×C4×C31—26no—
68C22×C4×C31—23no—
69C22×C4×C31—26no—
70C22×C4×C31—23no—
71C22×C4×C31—26no—
72C22×C4×C31—23no—
73C22×C4×C31—23no—
74C22×C4×C31—26no—
75C22×C4×C31—26no—
76C22×C4×C31—26no—
77C22×C4×C31—26no—
78C22×C4×C31—26no—
79C22×C4×C31—26no—
80C22×C4×C31—26no—
81C22×C4×C31C2×D416yes—
82C22×C4×C31C2×D416yes—
83C4⋊C4×C31—412no—
84C22⋊C4×C31—412no—
85C22⋊C4×C31—424no—
86C22⋊C4×C31—424no—
87C22⋊C4×C31—412no—
88C42×C31—44no—
89#15480C3111yesmaximal, characteristic, direct product factor, Sylow
90C23×C31—26no—
91C23×C31—212no—
92C23×C31—26no—
93C23×C31—212no—
94C23×C31—212no—
95C23×C31—212no—
96C23×C31—212no—
97C23×C31—212no—
98C23×C31—212no—
99C23×C31—212no—
100C23×C31—496no—
101C23×C31—448no—
102C23×C31—448no—
103C23×C31—448no—
104C23×C31—42no—
105C23×C31—42no—
106C23×C31—42no—
107C23×C31—46no—
108C23×C31—46no—
109C23×C31—46no—
110C23×C31—46no—
111C23×C31—46no—
112C23×C31—43no—
113C23×C31—43no—
114C23×C31—41no—
115C23×C31—42no—
116C23×C31—41no—
117C23×C31—42no—
118C23×C31#12618yes—
119C23×C31#12714yes—
120C23×C31C22×D413yes—
121C23×C31C2×#4116yes—
122C23×C31H(5,𝔽2)13yes—
123C23×C31H(5,𝔽2)13yes—
124C2×C4×C31—26no—
125C2×C4×C31—26no—
126C2×C4×C31—212no—
127C2×C4×C31—212no—
128C2×C4×C31—46no—
129C2×C4×C31—46no—
130C2×C4×C31—43no—
131C2×C4×C31—43no—
132C2×C4×C31—43no—
133C2×C4×C31—43no—
134C2×C4×C31—46no—
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×#397C2×C3113yescomplemented
142C2×#379C2×C3113yes—
143#1439C2×C3116yescomplemented
144#1437C2×C3112yescomplemented
145#1437C2×C3111yescharacteristic, complemented
146C22×C31—224no—
147C22×C31—212no—
148C22×C31—464no—
149C22×C31—46no—
150C22×C31—412no—
151C22×C31—46no—
152C22×C31—412no—
153C22×C31—412no—
154C22×C31—412no—
155C22×C31—412no—
156C22×C31#52513yes—
157C22×C31C2×#12612yes—
158C22×C31C2×#12711yescharacteristic
159C22×C31#53413yes—
160C22×C31#53816yes—
161C22×C31#54616yes—
162C22×C31#54616yes—
163C22×C31#55113yes—
164C22×C31#55113yes—
165C22×C31#56011yescharacteristic
166C22×C31H(3,𝔽4)11yescharacteristic
167C4×C31—46no—
168C4×C31—46no—
169C4×C31—86no—
170C26C22×C3111yescharacteristic
171C22×C4⋊C4C22×C3113yescomplemented
172C22×C22⋊C4C22×C3113yes—
173C22×C22⋊C4C22×C3116yes—
174C22×C22⋊C4C22×C3116yes—
175C22×C22⋊C4C22×C3113yes—
176C22×C42C22×C3111yescharacteristic, complemented
177#397—212no—
178#379—212no—
179C2×#95C22×C3116yescomplemented
180C2×#95C22×C3113yescomplemented
181C2×#95C22×C3113yescomplemented
182C2×C31—48no—
183C2×C31—44no—
184C2×C31#248016yes—
185C2×C31#253913yes—
186C2×C31#268413yes—
187C2×C31#269713yes—
188C25—26no—
189C25—212no—
190C25—43no—
191C25—43no—
192C25C23×C3111yescharacteristic
193C25C23×C3112yes—
194C23×C4C23×C3116yes—
195C23×C4C23×C3113yes—
196C23×C4C23×C3113yes—
197C2×C4⋊C4—26no—
198C2×C4⋊C4—43no—
199C2×C4⋊C4—43no—
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—43no—
212#95—26no—
213#95—212no—
214#95—43no—
215C31#1548011yescharacteristic, direct product factor, Sylow
216C24—26no—
217C24—26no—
218C24—26no—
219C24—23no—
220C24—23no—
221C24—26no—
222C24—26no—
223C24—224no—
224C24—424no—
225C24—424no—
226C24—412no—
227C24—412no—
228C24—412no—
229C24—424no—
230C24—44no—
231C24—44no—
232C24—48no—
233C24—44no—
234C24C2×D4×C3116yes—
235C24#41×C31112yes—
236C24C24×C3111yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—23no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—26no—
246C22×C4—26no—
247C22×C4—26no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4C2×D4×C3116yes—
253C22×C4C2×D4×C3116yes—
254C4⋊C4—412no—
255C22⋊C4—412no—
256C22⋊C4—424no—
257C22⋊C4—424no—
258C22⋊C4—412no—
259C42—44no—
260C23—26no—
261C23—212no—
262C23—26no—
263C23—212no—
264C23—212no—
265C23—212no—
266C23—212no—
267C23—212no—
268C23—212no—
269C23—212no—
270C23—496no—
271C23—448no—
272C23—448no—
273C23—448no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—46no—
278C23—46no—
279C23—46no—
280C23—46no—
281C23—46no—
282C23—43no—
283C23—43no—
284C23—41no—
285C23—42no—
286C23—41no—
287C23—42no—
288C23C31×#12618yes—
289C23C31×#12714yes—
290C23C22×D4×C3113yes—
291C23C2×#41×C3116yes—
292C23C31×H(5,𝔽2)13yes—
293C23C31×H(5,𝔽2)13yes—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—212no—
297C2×C4—212no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—43no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—46no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—46no—
308C2×C4—46no—
309C2×C4—46no—
310C2×C4—46no—
311C22—224no—
312C22—212no—
313C22—464no—
314C22—46no—
315C22—412no—
316C22—46no—
317C22—412no—
318C22—412no—
319C22—412no—
320C22—412no—
321C22C31×#52513yes—
322C22C2×C31×#12612yes—
323C22C2×C31×#12711yescharacteristic
324C22C31×#53413yes—
325C22C31×#53816yes—
326C22C31×#54616yes—
327C22C31×#54616yes—
328C22C31×#55113yes—
329C22C31×#55113yes—
330C22C31×#56011yescharacteristic
331C22C31×H(3,𝔽4)11yescharacteristic
332C4—46no—
333C4—46no—
334C4—86no—
335C2—48no—
336C2—44no—
337C2C31×#248016yes—
338C2C31×#253913yes—
339C2C31×#268413yes—
340C2C31×#269713yes—
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×#397C2semidirect
3. C31×#1439C2semidirect
4. C31×#1437C2semidirect
5. C31×#1437C2semidirect
7. C22×C4⋊C4×C31C22semidirect
12. C22×C42×C31C22semidirect
15. C2×C31×#95C22semidirect
16. C2×C31×#95C22semidirect
17. C2×C31×#95C22semidirect
89. #15480C31direct (N × H)
141. C2×#397C2×C31semidirect
143. #1439C2×C31semidirect
144. #1437C2×C31semidirect
145. #1437C2×C31semidirect
171. C22×C4⋊C4C22×C31semidirect
176. C22×C42C22×C31semidirect
179. C2×#95C22×C31semidirect
180. C2×#95C22×C31semidirect
181. C2×#95C22×C31semidirect
215. C31#15480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3792
C31×#14392
C31×#14372
#1548031