Finite Group Databasebeta

← C31×#8773 #21465532

Subgroups — C31×#8773 #21465532

Order 7936.

446 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2353C211yesmaximal, characteristic
2C4×C31×#100C211yesmaximal, characteristic
3C31×#1466C211yesmaximal, characteristic
4C31×#1300C212yesmaximal, complemented
5C31×#1288C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C31×#432C2212yes—
8C2×C31×#100—21no—
9C4×M16×C31C2212yes—
10C31×#388—21no—
11C31×#387—21no—
12C31×#386—21no—
13C31×#383C2211yescharacteristic
14C31×#381C411yescharacteristic
15C31×#380C411yescharacteristic
16C4×C22⋊C4×C31—21no—
17C4×C22⋊C4×C31C411yescharacteristic
18C31×#376C2211yescharacteristic
19C2×C31×#95C411yescharacteristic
20C31×#343—21no—
21C31×#323—21no—
22C31×#323—21no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C2×M16×C31—22no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31D411yescharacteristic
32C2×C22⋊C4×C31—21no—
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31D411yescharacteristic
37C2×C42×C31—21no—
38C2×C42×C31—21no—
39C2×C42×C31C2311yescharacteristic
40C31×C4⋊C8—22no—
41C31×#100—24no—
42C31×C22⋊C8—22no—
43C31×#97—22no—
44C31×#97—22no—
45C4×C8×C31—22no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95C2×C411yescharacteristic
52C31×#95C2×C411yescharacteristic
53C31×#95C2×C411yescharacteristic
54C31×#95C2×C411yescharacteristic
55C24×C31C22⋊C411yescharacteristic
56C24×C31C22⋊C411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—41no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
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—42no—
69C22×C4×C31—42no—
70C22×C4×C31—81no—
71C22×C4×C31—81no—
72C22×C4×C31—81no—
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78M16×C31—24no—
79M16×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—81no—
84C22⋊C4×C31—22no—
85C22⋊C4×C31—22no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—81no—
89C42×C31—42no—
90C42×C31—81no—
91C42×C31#4112yes—
92C42×C31#4112yes—
93#8773C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—21no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31#10412yes—
104C23×C31C2×C22⋊C411yescharacteristic
105D4×C31—44no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—81no—
127C2×C4×C31—81no—
128C2×C4×C31—81no—
129C2×C4×C31—81no—
130C2×C4×C31—84no—
131C2×C4×C31#11711yescharacteristic
132C2×C4×C31#11711yescharacteristic
133C2×C4×C31#12312yes—
134C2×C4×C31#12312yes—
135C8×C31—44no—
136C8×C31—82no—
137#2353C2×C3111yescharacteristic
138C4×#100C2×C3111yescharacteristic
139#1466C2×C3111yescharacteristic
140#1300C2×C3112yescomplemented
141#1288C2×C3112yescomplemented
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—22no—
145C22×C31—42no—
146C22×C31—42no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—81no—
153C22×C31—81no—
154C22×C31#38111yescharacteristic
155C22×C31C2×#10411yescharacteristic
156C22×C31#42111yescharacteristic
157C4×C31—22no—
158C4×C31—22no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—42no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—81no—
165C4×C31—81no—
166C4×C31—81no—
167C2×C4×D4C22×C3111yescharacteristic
168#432C22×C3112yes—
169C2×#100—21no—
170C4×M16C22×C3112yes—
171#388—21no—
172#387—21no—
173#386—21no—
174#383C22×C3111yescharacteristic
175#381C4×C3111yescharacteristic
176#380C4×C3111yescharacteristic
177C4×C22⋊C4—21no—
178C4×C22⋊C4C4×C3111yescharacteristic
179#376C22×C3111yescharacteristic
180C2×#95C4×C3111yescharacteristic
181#343—21no—
182#323—21no—
183#323—21no—
184C2×C31—21no—
185C2×C31—21no—
186C2×C31—42no—
187C2×C31—81no—
188C2×C31#182611yescharacteristic
189C2×C31#182711yescharacteristic
190C2×C31#182911yescharacteristic
191C22×D4D4×C3111yescharacteristic
192C23×C4—21no—
193C23×C4C2×C4×C3111yescharacteristic
194C23×C4C2×C4×C3111yescharacteristic
195C2×M16—22no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4D4×C3111yescharacteristic
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4D4×C3111yescharacteristic
204C2×C22⋊C4D4×C3111yescharacteristic
205C2×C42—21no—
206C2×C42—21no—
207C2×C42C23×C3111yescharacteristic
208C4⋊C8—22no—
209#100—24no—
210C22⋊C8—22no—
211#97—22no—
212#97—22no—
213C4×C8—22no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C2×C4×C3111yescharacteristic
220#95C2×C4×C3111yescharacteristic
221#95C2×C4×C3111yescharacteristic
222#95C2×C4×C3111yescharacteristic
223C31#877311yescharacteristic, direct product factor, Sylow
224C24C22⋊C4×C3111yescharacteristic
225C24C22⋊C4×C3111yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4C22⋊C4×C3111yescharacteristic
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C22×C4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246C22×C4C2×D4×C3111yescharacteristic
247M16—24no—
248M16—42no—
249C2×C8—42no—
250C2×C8—42no—
251C4⋊C4—22no—
252C4⋊C4—81no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—81no—
258C42—42no—
259C42—81no—
260C42#41×C3112yes—
261C42#41×C3112yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C31×#10412yes—
272C23C2×C22⋊C4×C3111yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—84no—
299C2×C4C31×#11711yescharacteristic
300C2×C4C31×#11711yescharacteristic
301C2×C4C31×#12312yes—
302C2×C4C31×#12312yes—
303C8—44no—
304C8—82no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22C31×#38111yescharacteristic
318C22C2×C31×#10411yescharacteristic
319C22C31×#42111yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2C31×#182611yescharacteristic
335C2C31×#182711yescharacteristic
336C2C31×#182911yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1300C2semidirect
5. C31×#1288C2semidirect
93. #8773C31direct (N × H)
140. #1300C2×C31semidirect
141. #1288C2×C31semidirect
223. C31#8773direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23532
C4×C31×#1002
C31×#14662
C31×#13002
C31×#12882
#877331