Finite Group Databasebeta

← C31×#11805 #21468564

Subgroups — C31×#11805 #21468564

Order 7936.

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

normal subgroups only

This group has 448 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×#2618C211yesmaximal, characteristic
2C31×#1821C211yesmaximal, characteristic, complemented
3C31×#1463C211yesmaximal, characteristic, complemented
4C31×#1346C212yesmaximal, complemented
5C31×#1345C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C411yescharacteristic
8C22×C4⋊C4×C31C2211yescharacteristic
9C31×#407—21no—
10C31×#407—21no—
11C31×#398C411yescharacteristic
12C31×#398C2211yescharacteristic
13C31×#396—21no—
14C31×#396—21no—
15C31×#394C411yescharacteristic
16C31×#394C2211yescharacteristic
17C31×#386—21no—
18C31×#380C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C2×M16×C31—22no—
29C2×M16×C31—41no—
30C31×#123—44no—
31C31×#121—41no—
32C31×#121—41no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—41no—
37C2×C4⋊C4×C31—41no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C4⋊C4×C31C2311yescharacteristic
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—41no—
51C31×C22⋊C8—41no—
52C31×C22⋊C8—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31—21no—
58C24×C31C22⋊C411yescharacteristic
59C2×D4×C31—41no—
60C2×D4×C31—42no—
61C2×D4×C31—42no—
62C2×D4×C31—41no—
63C2×D4×C31—41no—
64C2×D4×C31—81no—
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—22no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—41no—
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
83C22×C4×C31C2×D411yescharacteristic
84M16×C31—42no—
85M16×C31—42no—
86M16×C31—82no—
87C2×C8×C31—42no—
88C2×C8×C31—42no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—42no—
96C4⋊C4×C31—81no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—81no—
102C22⋊C4×C31—81no—
103#11805C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31#9911yescharacteristic
116C23×C31#9911yescharacteristic
117C23×C31C2×C22⋊C411yescharacteristic
118D4×C31—82no—
119D4×C31—82no—
120D4×C31—82no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
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—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—81no—
147C2×C4×C31—81no—
148C2×C4×C31—81no—
149C2×C4×C31AGL(1,ℤ/8)12yes—
150C8×C31—82no—
151C8×C31—82no—
152#2618C2×C3111yescharacteristic
153#1821C2×C3111yescharacteristic, complemented
154#1463C2×C3111yescharacteristic, complemented
155#1346C2×C3112yescomplemented
156#1345C2×C3112yescomplemented
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—42no—
166C22×C31—42no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31C2×#9911yescharacteristic
175C22×C31#41811yescharacteristic
176C22×C31#42111yescharacteristic
177C4×C31—22no—
178C4×C31—41no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31—81no—
184C4×C31—81no—
185C4×C31—81no—
186C2×#123—21no—
187C2×#121C4×C3111yescharacteristic
188C22×C4⋊C4C22×C3111yescharacteristic
189#407—21no—
190#407—21no—
191#398C4×C3111yescharacteristic
192#398C22×C3111yescharacteristic
193#396—21no—
194#396—21no—
195#394C4×C3111yescharacteristic
196#394C22×C3111yescharacteristic
197#386—21no—
198#380C4×C3111yescharacteristic
199#343—21no—
200#343C22×C3112yes—
201#324—21no—
202#324C22×C3112yes—
203C2×C31—21no—
204C2×C31—21no—
205C2×C31—41no—
206C2×C31—41no—
207C2×C31—161no—
208C2×C31#151011yescharacteristic
209C2×C31#212111yescharacteristic
210C2×C31#213311yescharacteristic
211C22×D4—21no—
212C22×D4C2×C4×C3111yescharacteristic
213C23×C4C2×C4×C3111yescharacteristic
214C23×C4D4×C3111yescharacteristic
215C23×C4D4×C3111yescharacteristic
216C2×M16—22no—
217C2×M16—41no—
218#123—44no—
219#121—41no—
220#121—41no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4C2×C4×C3111yescharacteristic
227C2×C4⋊C4C2×C4×C3111yescharacteristic
228C2×C4⋊C4D4×C3111yescharacteristic
229C2×C4⋊C4D4×C3111yescharacteristic
230C2×C4⋊C4C23×C3111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239C22⋊C8—41no—
240C22⋊C8—41no—
241#95—21no—
242#95—21no—
243#95C2×C4×C3111yescharacteristic
244#95C2×C4×C3111yescharacteristic
245C31#1180511yescharacteristic, direct product factor, Sylow
246C24—21no—
247C24C22⋊C4×C3111yescharacteristic
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4C22⋊C4×C3111yescharacteristic
268C22×C4C22⋊C4×C3111yescharacteristic
269C22×C4C22⋊C4×C3111yescharacteristic
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3111yescharacteristic
272C22×C4C2×D4×C3111yescharacteristic
273M16—42no—
274M16—42no—
275M16—82no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—81no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23C31×#9911yescharacteristic
304C23C31×#9911yescharacteristic
305C23C2×C22⋊C4×C3111yescharacteristic
306D4—82no—
307D4—82no—
308D4—82no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C31×AGL(1,ℤ/8)12yes—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C2×C31×#9911yescharacteristic
358C22C31×#41811yescharacteristic
359C22C31×#42111yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—161no—
374C2C31×#151011yescharacteristic
375C2C31×#212111yescharacteristic
376C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1821C2semidirect
3. C31×#1463C2semidirect
4. C31×#1346C2semidirect
5. C31×#1345C2semidirect
103. #11805C31direct (N × H)
153. #1821C2×C31semidirect
154. #1463C2×C31semidirect
155. #1346C2×C31semidirect
156. #1345C2×C31semidirect
245. C31#11805direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26182
C31×#18212
C31×#14632
C31×#13462
C31×#13452
#1180531