Finite Group Databasebeta

← C31×#11826 #21468585

Subgroups — C31×#11826 #21468585

Order 7936.

414 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2638C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic
3C31×#1466C211yesmaximal, characteristic
4C31×#1351C212yesmaximal, complemented
5C31×#1344C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×#99—21no—
10C31×#398C411yescharacteristic, complemented
11C31×#397—21no—
12C31×#397C2211yescharacteristic
13C31×#395C411yescharacteristic, complemented
14C31×#394—21no—
15C31×#393C2211yescharacteristic
16C31×#387—21no—
17C31×#385—21no—
18C31×#381C411yescharacteristic, complemented
19C31×#380—21no—
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31D411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C31×C22⋊Q8—41no—
28C31×C22⋊Q8—41no—
29C4×D4×C31—41no—
30C4×D4×C31—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—41no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31D411yescharacteristic
43C2×C22⋊C4×C31C2311yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—41no—
46C31×#99—42no—
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—21no—
62C2×D4×C31—21no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
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—21no—
73C22×C4×C31—42no—
74C22×C4×C31—81no—
75C22×C4×C31—81no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22×C411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81C2×C8×C31—42no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—81no—
88C4⋊C4×C31—82no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—81no—
97C22⋊C4×C31—81no—
98C42×C31—21no—
99C42×C31—21no—
100#11826C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31C2×C22⋊C411yescharacteristic
111C23×C31AGL(1,ℤ/8)11yescharacteristic
112C23×C31#13711yescharacteristic
113Q8×C31—82no—
114D4×C31—42no—
115D4×C31—42no—
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—42no—
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—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31—81no—
142C2×C4×C31—82no—
143C2×C4×C31—82no—
144C2×C4×C31—82no—
145C2×C4×C31#9911yescharacteristic
146C2×C4×C31#9911yescharacteristic
147C8×C31—82no—
148#2638C2×C3111yescharacteristic
149#1799C2×C3111yescharacteristic
150#1466C2×C3111yescharacteristic
151#1351C2×C3112yescomplemented
152#1344C2×C3112yescomplemented
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31C2×#9911yescharacteristic
168C22×C31#41711yescharacteristic
169C22×C31#42111yescharacteristic
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—81no—
177C4×C31—81no—
178C4×C31—81no—
179C4×C31—81no—
180C4×C31—162no—
181C2×C22⋊Q8C4×C3111yescharacteristic, complemented
182C2×C4×D4C22×C3111yescharacteristic
183#432—21no—
184C2×#99—21no—
185#398C4×C3111yescharacteristic, complemented
186#397—21no—
187#397C22×C3111yescharacteristic
188#395C4×C3111yescharacteristic, complemented
189#394—21no—
190#393C22×C3111yescharacteristic
191#387—21no—
192#385—21no—
193#381C4×C3111yescharacteristic, complemented
194#380—21no—
195#342C22×C3112yes—
196#323—21no—
197#323C22×C3112yes—
198C2×C31—21no—
199C2×C31—21no—
200C2×C31—41no—
201C2×C31—41no—
202C2×C31—81no—
203C2×C31#151311yescharacteristic
204C2×C31#212111yescharacteristic
205C2×C31#212911yescharacteristic
206C22×Q8C2×C4×C3111yescharacteristic
207C22×D4D4×C3111yescharacteristic
208C23×C4C2×C4×C3111yescharacteristic
209C23×C4D4×C3111yescharacteristic
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C2×C4×C3111yescharacteristic
219C2×C4⋊C4C2×C4×C3111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4D4×C3111yescharacteristic
226C2×C22⋊C4C23×C3111yescharacteristic
227C2×C42D4×C3111yescharacteristic
228C4⋊C8—41no—
229#99—42no—
230C22⋊C8—22no—
231#97—41no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—41no—
238#95C2×C4×C3111yescharacteristic
239#95C2×C4×C3111yescharacteristic
240C31#1182611yescharacteristic, direct product factor, Sylow
241C24C22⋊C4×C3111yescharacteristic
242C24C2×D4×C3111yescharacteristic
243C2×Q8—41no—
244C2×Q8—81no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4C22⋊C4×C3111yescharacteristic
261C22×C4C22⋊C4×C3111yescharacteristic
262C22×C4C22⋊C4×C3111yescharacteristic
263C22×C4C22×C4×C3111yescharacteristic
264C22×C4C2×D4×C3111yescharacteristic
265C2×C8—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—82no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C42—21no—
283C42—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23C2×C22⋊C4×C3111yescharacteristic
294C23C31×AGL(1,ℤ/8)11yescharacteristic
295C23C31×#13711yescharacteristic
296Q8—82no—
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
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—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4C31×#9911yescharacteristic
329C2×C4C31×#9911yescharacteristic
330C8—82no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×C31×#9911yescharacteristic
346C22C31×#41711yescharacteristic
347C22C31×#42111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—162no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2C31×#151311yescharacteristic
365C2C31×#212111yescharacteristic
366C2C31×#212911yescharacteristic
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×#1351C2semidirect
5. C31×#1344C2semidirect
6. C2×C31×C22⋊Q8C4semidirect
10. C31×#398C4semidirect
13. C31×#395C4semidirect
18. C31×#381C4semidirect
100. #11826C31direct (N × H)
151. #1351C2×C31semidirect
152. #1344C2×C31semidirect
181. C2×C22⋊Q8C4×C31semidirect
185. #398C4×C31semidirect
188. #395C4×C31semidirect
193. #381C4×C31semidirect
240. C31#11826direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26382
C31×#17992
C31×#14662
C31×#13512
C31×#13442
#1182631