Finite Group Databasebeta

← C31×#11789 #21468548

Subgroups — C31×#11789 #21468548

Order 7936.

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

normal subgroups only

This group has 462 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×#2564C211yesmaximal, characteristic
2C4×C31×#99C211yesmaximal, characteristic
3C31×#1466C211yesmaximal, characteristic
4C31×#1352C212yesmaximal, complemented
5C31×#1351C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×#99—21no—
10C31×#400C411yescharacteristic, complemented
11C31×#399C2211yescharacteristic
12C31×#395C411yescharacteristic, complemented
13C31×#393C2211yescharacteristic
14C31×#387—21no—
15C31×#386—21no—
16C31×#385—21no—
17C31×#380—21no—
18C4×C22⋊C4×C31—21no—
19C2×C31×#95C411yescharacteristic, complemented
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31D411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C31×C22⋊Q8—41no—
29C31×C22⋊Q8—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×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31C2311yescharacteristic
43C2×C42×C31—41no—
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—41no—
46C31×#99—24no—
47C31×C22⋊C8—22no—
48C31×#97—41no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—41no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31C22⋊C411yescharacteristic
58C24×C31C2×D411yescharacteristic
59C2×Q8×C31—41no—
60C2×Q8×C31—81no—
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—41no—
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—21no—
71C22×C4×C31—21no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—81no—
76C22×C4×C31—81no—
77C22×C4×C31—81no—
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C2×C8×C31—42no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—81no—
90C22⋊C4×C31—24no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—81no—
97C42×C31—21no—
98C42×C31—21no—
99C42×C31—82no—
100#11789C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31#10412yes—
110C23×C31C2×C22⋊C411yescharacteristic
111C23×C31#13712yes—
112Q8×C31—82no—
113D4×C31—44no—
114C2×C4×C31—22no—
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—41no—
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—44no—
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—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31—84no—
142C2×C4×C31—82no—
143C2×C4×C31—82no—
144C2×C4×C31#9911yescharacteristic
145C2×C4×C31#9911yescharacteristic
146C8×C31—82no—
147#2564C2×C3111yescharacteristic
148C4×#99C2×C3111yescharacteristic
149#1466C2×C3111yescharacteristic
150#1352C2×C3112yescomplemented
151#1351C2×C3112yescomplemented
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—22no—
155C22×C31—22no—
156C22×C31—42no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—81no—
164C22×C31C2×#9911yescharacteristic
165C22×C31#41911yescharacteristic
166C22×C31C2×#10411yescharacteristic
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—42no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—81no—
175C4×C31—84no—
176C4×C31—81no—
177C4×C31—81no—
178C2×C22⋊Q8C4×C3111yescharacteristic, complemented
179C2×C4×D4C22×C3111yescharacteristic
180#432—21no—
181C2×#99—21no—
182#400C4×C3111yescharacteristic, complemented
183#399C22×C3111yescharacteristic
184#395C4×C3111yescharacteristic, complemented
185#393C22×C3111yescharacteristic
186#387—21no—
187#386—21no—
188#385—21no—
189#380—21no—
190C4×C22⋊C4—21no—
191C2×#95C4×C3111yescharacteristic, complemented
192#342C22×C3112yes—
193#323—21no—
194#323C22×C3112yes—
195C2×C31—21no—
196C2×C31—21no—
197C2×C31—42no—
198C2×C31—42no—
199C2×C31#150811yescharacteristic
200C2×C31#212111yescharacteristic
201C2×C31#212611yescharacteristic
202C22×Q8C2×C4×C3111yescharacteristic
203C22×D4D4×C3111yescharacteristic
204C23×C4—21no—
205C23×C4C2×C4×C3111yescharacteristic
206C23×C4D4×C3111yescharacteristic
207C22⋊Q8—41no—
208C22⋊Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C3111yescharacteristic
215C2×C4⋊C4C2×C4×C3111yescharacteristic
216C2×C22⋊C4—22no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4D4×C3111yescharacteristic
221C2×C22⋊C4C23×C3111yescharacteristic
222C2×C42—41no—
223C2×C42D4×C3111yescharacteristic
224C4⋊C8—41no—
225#99—24no—
226C22⋊C8—22no—
227#97—41no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—41no—
234#95C2×C4×C3111yescharacteristic
235#95C2×C4×C3111yescharacteristic
236C31#1178911yescharacteristic, direct product factor, Sylow
237C24C22⋊C4×C3111yescharacteristic
238C24C2×D4×C3111yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4C22⋊C4×C3111yescharacteristic
259C22×C4C22⋊C4×C3111yescharacteristic
260C22×C4C22⋊C4×C3111yescharacteristic
261C22×C4C22×C4×C3111yescharacteristic
262C22×C4C2×D4×C3111yescharacteristic
263C2×C8—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C22⋊C4—24no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—81no—
277C42—21no—
278C42—21no—
279C42—82no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C31×#10412yes—
289C23C2×C22⋊C4×C3111yescharacteristic
290C23C31×#13712yes—
291Q8—82no—
292D4—44no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—84no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4C31×#9911yescharacteristic
324C2×C4C31×#9911yescharacteristic
325C8—82no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×C31×#9911yescharacteristic
339C22C31×#41911yescharacteristic
340C22C2×C31×#10411yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—84no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2C31×#150811yescharacteristic
357C2C31×#212111yescharacteristic
358C2C31×#212611yescharacteristic
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×#1352C2semidirect
5. C31×#1351C2semidirect
6. C2×C31×C22⋊Q8C4semidirect
10. C31×#400C4semidirect
12. C31×#395C4semidirect
19. C2×C31×#95C4semidirect
100. #11789C31direct (N × H)
150. #1352C2×C31semidirect
151. #1351C2×C31semidirect
178. C2×C22⋊Q8C4×C31semidirect
182. #400C4×C31semidirect
184. #395C4×C31semidirect
191. C2×#95C4×C31semidirect
236. C31#11789direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25642
C4×C31×#992
C31×#14662
C31×#13522
C31×#13512
#1178931