Finite Group Databasebeta

← C31×#11878 #21468637

Subgroups — C31×#11878 #21468637

Order 7936.

472 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2547C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C31×#1344C214yesmaximal, complemented
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C31×#124—21no—
7C2×C4×D4×C31C2211yescharacteristic
8C2×C31×#99—21no—
9C2×C31×C22⋊C8—21no—
10C31×#397C412yescomplemented
11C31×#397C2212yes—
12C31×#391—21no—
13C31×#380—21no—
14C31×#380—21no—
15C31×#380—21no—
16C4×C4⋊C4×C31C411yescharacteristic, complemented
17C31×#342C2212yes—
18C31×#324—21no—
19C31×#323C2212yes—
20C22×Q8×C31—21no—
21C22×D4×C31D411yescharacteristic
22C23×C4×C31D411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C22×C8×C31—41no—
25C31×C4⋊Q8—41no—
26C31×C4⋊Q8—41no—
27C31×#124—42no—
28C31×#124—42no—
29C4×D4×C31—41no—
30C4×D4×C31—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—41no—
34C2×C4⋊C4×C31C2×C412yes—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31C2311yescharacteristic
41C2×C42×C31—21no—
42C2×C42×C31C2×C411yescharacteristic
43C31×#99—42no—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—41no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—41no—
49C31×#95C2×C412yes—
50C24×C31C22⋊C411yescharacteristic
51C24×C31C2×D411yescharacteristic
52C2×Q8×C31—42no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C2×D4×C31—41no—
56C2×D4×C31—41no—
57C2×D4×C31D812yes—
58C2×D4×C31SD1612yes—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C2×C8×C31—42no—
74C2×C8×C31—82no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—41no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—82no—
81C22⋊C4×C31—41no—
82C22⋊C4×C31—41no—
83C22⋊C4×C31—44no—
84C22⋊C4×C31—42no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—42no—
91#11878C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—41no—
97C23×C31—41no—
98C23×C31—41no—
99C23×C31—41no—
100C23×C31#10212yes—
101C23×C31C2×C22⋊C411yescharacteristic
102C23×C31C2×D811yescharacteristic
103C23×C31C2×SD1611yescharacteristic
104Q8×C31—84no—
105D4×C31—42no—
106D4×C31—42no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—81no—
125C2×C4×C31—81no—
126C2×C4×C31—82no—
127C2×C4×C31—82no—
128C2×C4×C31—82no—
129C2×C4×C31#9911yescharacteristic
130C2×C4×C31#9911yescharacteristic
131C2×C4×C31#10212yes—
132C8×C31—82no—
133#2547C2×C3111yescharacteristic
134#1799C2×C3111yescharacteristic
135#1459C2×C3111yescharacteristic
136#1344C2×C3114yescomplemented
137C22×C31—21no—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—22no—
141C22×C31—21no—
142C22×C31—42no—
143C22×C31—41no—
144C22×C31—41no—
145C22×C31—41no—
146C22×C31—41no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—81no—
150C22×C31—81no—
151C22×C31C2×#9911yescharacteristic
152C22×C31C2×#10211yescharacteristic
153C22×C31#42111yescharacteristic
154C4×C31—21no—
155C4×C31—22no—
156C4×C31—41no—
157C4×C31—41no—
158C4×C31—41no—
159C4×C31—82no—
160C4×C31—82no—
161C4×C31—162no—
162C4×C31#35412yes—
163C2×C4⋊Q8C4×C3111yescharacteristic, complemented
164C2×#124—21no—
165C2×C4×D4C22×C3111yescharacteristic
166C2×#99—21no—
167C2×C22⋊C8—21no—
168#397C4×C3112yescomplemented
169#397C22×C3112yes—
170#391—21no—
171#380—21no—
172#380—21no—
173#380—21no—
174C4×C4⋊C4C4×C3111yescharacteristic, complemented
175#342C22×C3112yes—
176#324—21no—
177#323C22×C3112yes—
178C2×C31—21no—
179C2×C31—21no—
180C2×C31—41no—
181C2×C31—42no—
182C2×C31—41no—
183C2×C31#151911yescharacteristic
184C2×C31#212311yescharacteristic
185C2×C31C2×#35411yescharacteristic
186C22×Q8—21no—
187C22×D4D4×C3111yescharacteristic
188C23×C4D4×C3111yescharacteristic
189C23×C4D4×C3111yescharacteristic
190C22×C8—41no—
191C4⋊Q8—41no—
192C4⋊Q8—41no—
193#124—42no—
194#124—42no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4C2×C4×C3112yes—
201C2×C4⋊C4D4×C3111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4C2×C4×C3111yescharacteristic
206C2×C22⋊C4C23×C3111yescharacteristic
207C2×C42—21no—
208C2×C42C2×C4×C3111yescharacteristic
209#99—42no—
210C22⋊C8—22no—
211C22⋊C8—41no—
212#95—22no—
213#95—22no—
214#95—41no—
215#95C2×C4×C3112yes—
216C31#1187811yescharacteristic, direct product factor, Sylow
217C24C22⋊C4×C3111yescharacteristic
218C24C2×D4×C3111yescharacteristic
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4D8×C3112yes—
225C2×D4SD16×C3112yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊C4×C3111yescharacteristic
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22×C4×C3111yescharacteristic
239C22×C4C2×D4×C3111yescharacteristic
240C2×C8—42no—
241C2×C8—82no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—82no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—44no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42—21no—
256C42—21no—
257C42—42no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23C31×#10212yes—
267C23C2×C22⋊C4×C3111yescharacteristic
268C23C2×D8×C3111yescharacteristic
269C23C2×SD16×C3111yescharacteristic
270Q8—84no—
271D4—42no—
272D4—42no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4C31×#9911yescharacteristic
296C2×C4C31×#9911yescharacteristic
297C2×C4C31×#10212yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22—21no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—81no—
312C22—81no—
313C22C2×C31×#9911yescharacteristic
314C22C2×C31×#10211yescharacteristic
315C22C31×#42111yescharacteristic
316C4—21no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—82no—
322C4—82no—
323C4—162no—
324C4C31×#35412yes—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—42no—
329C2—41no—
330C2C31×#151911yescharacteristic
331C2C31×#212311yescharacteristic
332C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#1344C2semidirect
5. C2×C31×C4⋊Q8C4semidirect
10. C31×#397C4semidirect
16. C4×C4⋊C4×C31C4semidirect
91. #11878C31direct (N × H)
136. #1344C2×C31semidirect
163. C2×C4⋊Q8C4×C31semidirect
168. #397C4×C31semidirect
174. C4×C4⋊C4C4×C31semidirect
216. C31#11878direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25472
C31×#17992
C31×#14592
C31×#13442
#1187831