Finite Group Databasebeta

← C31×#11735 #21468494

Subgroups — C31×#11735 #21468494

Order 7936.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C31×#2395C211yesmaximal, characteristic
2C4×C31×#100C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C31×#1353C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C2×C31×#117C411yescharacteristic
8C2×C31×#100—21no—
9C2×C31×C22⋊C8—21no—
10C4×M16×C31—21no—
11C31×#400C2211yescharacteristic
12C31×#399C411yescharacteristic
13C31×#398C2211yescharacteristic
14C31×#397—21no—
15C31×#397C411yescharacteristic
16C31×#394—21no—
17C4×C4⋊C4×C31—21no—
18C4×C22⋊C4×C31—21no—
19C4×C22⋊C4×C31C411yescharacteristic
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C2×M16×C31—22no—
27C22×C8×C31—41no—
28C4×D4×C31—41no—
29C4×D4×C31—41no—
30C31×#117—41no—
31C31×#117—41no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2311yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31D411yescharacteristic
43C2×C42×C31—21no—
44C2×C42×C31—21no—
45C2×C42×C31D411yescharacteristic
46C31×#100—24no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—41no—
49C31×#97—41no—
50C4×C8×C31—41no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31C22⋊C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C2×D4×C31—22no—
60C2×D4×C31—22no—
61C2×D4×C31—41no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—42no—
71C22×C4×C31—42no—
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22×C411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77M16×C31—24no—
78M16×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—82no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—42no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—42no—
96C42×C31—41no—
97C42×C31—41no—
98#11735C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31—21no—
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31#10412yes—
109C23×C31C2×C22⋊C411yescharacteristic
110D4×C31—44no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—22no—
114C2×C4×C31—22no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—42no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—81no—
136C2×C4×C31#9911yescharacteristic
137C2×C4×C31#9911yescharacteristic
138C2×C4×C31#13512yes—
139C8×C31—44no—
140C8×C31—82no—
141#2395C2×C3111yescharacteristic
142C4×#100C2×C3111yescharacteristic
143#1459C2×C3111yescharacteristic
144#1353C2×C3112yescomplemented
145#1346C2×C3112yescomplemented
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—22no—
149C22×C31—42no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—81no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31C2×#9911yescharacteristic
159C22×C31#41611yescharacteristic
160C22×C31C2×#10411yescharacteristic
161C4×C31—21no—
162C4×C31—22no—
163C4×C31—42no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—81no—
168C4×C31—81no—
169C4×C31—81no—
170C4×C31#35212yes—
171C2×C4×D4C22×C3111yescharacteristic
172C2×#117C4×C3111yescharacteristic
173C2×#100—21no—
174C2×C22⋊C8—21no—
175C4×M16—21no—
176#400C22×C3111yescharacteristic
177#399C4×C3111yescharacteristic
178#398C22×C3111yescharacteristic
179#397—21no—
180#397C4×C3111yescharacteristic
181#394—21no—
182C4×C4⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4C4×C3111yescharacteristic
185#343C22×C3112yes—
186#324C22×C3112yes—
187#323—21no—
188C2×C31—21no—
189C2×C31—21no—
190C2×C31—42no—
191C2×C31—81no—
192C2×C31#150111yescharacteristic
193C2×C31C2×#35211yescharacteristic
194C2×C31#213211yescharacteristic
195C22×D4D4×C3111yescharacteristic
196C23×C4C2×C4×C3111yescharacteristic
197C23×C4D4×C3111yescharacteristic
198C2×M16—22no—
199C22×C8—41no—
200C4×D4—41no—
201C4×D4—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×C4×C3111yescharacteristic
207C2×C4⋊C4C2×C4×C3111yescharacteristic
208C2×C4⋊C4C23×C3111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4C2×C4×C3111yescharacteristic
214C2×C22⋊C4D4×C3111yescharacteristic
215C2×C42—21no—
216C2×C42—21no—
217C2×C42D4×C3111yescharacteristic
218#100—24no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221#97—41no—
222C4×C8—41no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×C4×C3111yescharacteristic
228#95C2×C4×C3111yescharacteristic
229C31#1173511yescharacteristic, direct product factor, Sylow
230C24C22⋊C4×C3111yescharacteristic
231C24C22⋊C4×C3111yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4C22⋊C4×C3111yescharacteristic
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4C22×C4×C3111yescharacteristic
248C22×C4C2×D4×C3111yescharacteristic
249C22×C4C2×D4×C3111yescharacteristic
250M16—24no—
251M16—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—82no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42—41no—
270C42—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C31×#10412yes—
281C23C2×C22⋊C4×C3111yescharacteristic
282D4—44no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4C31×#9911yescharacteristic
309C2×C4C31×#9911yescharacteristic
310C2×C4C31×#13512yes—
311C8—44no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C2×C31×#9911yescharacteristic
326C22C31×#41611yescharacteristic
327C22C2×C31×#10411yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4C31×#35212yes—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2C31×#150111yescharacteristic
343C2C2×C31×#35211yescharacteristic
344C2C31×#213211yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
socleC22×C31C2×#99
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1353C2semidirect
5. C31×#1346C2semidirect
98. #11735C31direct (N × H)
144. #1353C2×C31semidirect
145. #1346C2×C31semidirect
229. C31#11735direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23952
C4×C31×#1002
C31×#14592
C31×#13532
C31×#13462
#1173531