Finite Group Databasebeta

← C31×#11778 #21468537

Subgroups — C31×#11778 #21468537

Order 7936.

446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2536C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic, complemented
3C31×#1467C211yesmaximal, characteristic, complemented
4C31×#1346C212yesmaximal, complemented
5C31×#1345C212yesmaximal
6C2×C31×C22⋊Q8—21no—
7C2×C4×Q8×C31C2211yescharacteristic
8C2×C4×D4×C31C411yescharacteristic
9C31×#432—21no—
10C2×C31×#101—21no—
11C4×M16×C31—21no—
12C31×#398C411yescharacteristic
13C31×#398C2211yescharacteristic
14C31×#394C411yescharacteristic
15C31×#394C2211yescharacteristic
16C31×#388—21no—
17C31×#388—21no—
18C31×#382C411yescharacteristic
19C31×#380—21no—
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×Q8×C31D411yescharacteristic
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C2×M16×C31—22no—
27C31×C22⋊Q8—44no—
28C4×Q8×C31—41no—
29C4×Q8×C31—41no—
30C4×D4×C31—41no—
31C4×D4×C31—41no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31C2311yescharacteristic
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C31×C4⋊C8—41no—
48C31×#101—24no—
49C31×C22⋊C8—22no—
50C31×#97—41no—
51C31×#97—41no—
52C4×C8×C31—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C2×Q8×C31—22no—
60C2×Q8×C31—22no—
61C2×Q8×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31—42no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
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—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—42no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—21no—
99C42×C31—21no—
100#11778C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—22no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31C2×C22⋊C411yescharacteristic
109Q8×C31—44no—
110D4×C31—42no—
111D4×C31—42no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—41no—
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—84no—
136C2×C4×C31#9911yescharacteristic
137C2×C4×C31#9911yescharacteristic
138C2×C4×C31#10412yes—
139C2×C4×C31AGL(1,ℤ/8)12yes—
140C8×C31—44no—
141C8×C31—82no—
142#2536C2×C3111yescharacteristic
143C4×#101C2×C3111yescharacteristic, complemented
144#1467C2×C3111yescharacteristic, complemented
145#1346C2×C3112yescomplemented
146#1345C2×C3112yes—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—42no—
150C22×C31—42no—
151C22×C31—42no—
152C22×C31—81no—
153C22×C31—81no—
154C22×C31—81no—
155C22×C31—81no—
156C22×C31C2×#9911yescharacteristic
157C22×C31#41811yescharacteristic
158C22×C31C2×#10411yescharacteristic
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—22no—
162C4×C31—22no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—81no—
168C4×C31—81no—
169C4×C31—81no—
170C2×C22⋊Q8—21no—
171C2×C4×Q8C22×C3111yescharacteristic
172C2×C4×D4C4×C3111yescharacteristic
173#432—21no—
174C2×#101—21no—
175C4×M16—21no—
176#398C4×C3111yescharacteristic
177#398C22×C3111yescharacteristic
178#394C4×C3111yescharacteristic
179#394C22×C3111yescharacteristic
180#388—21no—
181#388—21no—
182#382C4×C3111yescharacteristic
183#380—21no—
184#343C22×C3112yes—
185#324—21no—
186#324C22×C3112yes—
187C2×C31—21no—
188C2×C31—21no—
189C2×C31—82no—
190C2×C31#150711yescharacteristic
191C2×C31#212011yescharacteristic
192C2×C31#213311yescharacteristic
193C22×Q8D4×C3111yescharacteristic
194C22×D4C2×C4×C3111yescharacteristic
195C23×C4—21no—
196C2×M16—22no—
197C22⋊Q8—44no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×D4—41no—
201C4×D4—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C3111yescharacteristic
206C2×C4⋊C4C2×C4×C3111yescharacteristic
207C2×C4⋊C4D4×C3111yescharacteristic
208C2×C4⋊C4C23×C3111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×C4×C3111yescharacteristic
215C2×C42D4×C3111yescharacteristic
216C2×C42D4×C3111yescharacteristic
217C4⋊C8—41no—
218#101—24no—
219C22⋊C8—22no—
220#97—41no—
221#97—41no—
222C4×C8—41no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×C4×C3111yescharacteristic
227#95C2×C4×C3111yescharacteristic
228C31#1177811yescharacteristic, direct product factor, Sylow
229C24—21no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×D4—41no—
234C2×D4—42no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊C4×C3111yescharacteristic
242C22×C4C22⋊C4×C3111yescharacteristic
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C22⋊C4×C3111yescharacteristic
245C22×C4C22×C4×C3111yescharacteristic
246C22×C4C2×D4×C3111yescharacteristic
247C22×C4C2×D4×C3111yescharacteristic
248M16—24no—
249M16—42no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊C4×C3111yescharacteristic
279Q8—44no—
280D4—42no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
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—84no—
306C2×C4C31×#9911yescharacteristic
307C2×C4C31×#9911yescharacteristic
308C2×C4C31×#10412yes—
309C2×C4C31×AGL(1,ℤ/8)12yes—
310C8—44no—
311C8—82no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C2×C31×#9911yescharacteristic
322C22C31×#41811yescharacteristic
323C22C2×C31×#10411yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2C31×#150711yescharacteristic
339C2C31×#212011yescharacteristic
340C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#101C2semidirect
3. C31×#1467C2semidirect
4. C31×#1346C2semidirect
100. #11778C31direct (N × H)
143. C4×#101C2×C31semidirect
144. #1467C2×C31semidirect
145. #1346C2×C31semidirect
228. C31#11778direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25362
C4×C31×#1012
C31×#14672
C31×#13462
C31×#13452
#1177831