Finite Group Databasebeta

← C31×#9351 #21466110

Subgroups — C31×#9351 #21466110

Order 7936.

416 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3080C211yesmaximal, characteristic
2C31×#2970C211yesmaximal, characteristic
3C31×#1528C211yesmaximal, characteristic, complemented
4C31×#1488C211yesmaximal, characteristic
5C31×#1470C211yesmaximal, characteristic, complemented
6C31×#1307C211yesmaximal, characteristic, complemented
7C31×#1299C211yesmaximal, characteristic, complemented
8C2×C31×#125C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#479—21no—
11C31×#479—21no—
12C31×#478—21no—
13C31×#478—21no—
14C31×#446—21no—
15C31×#435—22no—
16C8×D4×C31—21no—
17C31×#432—21no—
18C31×#432C2211yescharacteristic
19C31×#432C2211yescharacteristic
20C31×#431C2211yescharacteristic
21C31×#428C411yescharacteristic
22C31×#428C411yescharacteristic
23C31×#423C2211yescharacteristic
24C31×#417C411yescharacteristic
25C31×#417C411yescharacteristic
26C4×M16×C31C2211yescharacteristic
27C2×C31×#97—21no—
28C31×#330—21no—
29C31×#330—21no—
30C31×Q8⋊C8—21no—
31C31×D4⋊C8—21no—
32C31×#324—22no—
33C2×#41×C31C2×C411yescharacteristic
34C2×M16×C31—21no—
35C2×M16×C31C2×C411yescharacteristic
36C2×M16×C31C2×C411yescharacteristic
37C22×C8×C31—22no—
38C31×#125—21no—
39C31×#125—21no—
40C31×#125—21no—
41C31×#125—21no—
42C4×Q8×C31D411yescharacteristic
43C4×Q8×C31D411yescharacteristic
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C4×D4×C31D411yescharacteristic
47C4×D4×C31D411yescharacteristic
48C31×#117—21no—
49C31×#117C2×C411yescharacteristic
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31C2×C411yescharacteristic
53C2×C4⋊C4×C31C2×C411yescharacteristic
54C2×C42×C31—21no—
55C2×C42×C31C2311yescharacteristic
56C31×#107—21no—
57C31×#107—21no—
58C31×#106—21no—
59C31×#106—21no—
60C31×C4⋊C8—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×#103—21no—
67C31×#103—21no—
68C31×#102—21no—
69C31×#102—21no—
70C31×C22⋊C8—22no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8D412yes—
74C31×#97—22no—
75C31×#97—21no—
76C31×#97—21no—
77C31×#97D411yescharacteristic
78C31×#97D411yescharacteristic
79C4×C8×C31—21no—
80C4×C8×C31—21no—
81#41×C31—22no—
82#41×C31—41no—
83C2×Q8×C31C22⋊C411yescharacteristic
84C2×D4×C31—21no—
85C2×D4×C31C22⋊C411yescharacteristic
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31C22×C411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31#4111yescharacteristic
94M16×C31—42no—
95M16×C31—41no—
96M16×C31—41no—
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—22no—
102C2×C8×C31—44no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31C22⋊C411yescharacteristic
116C4⋊C4×C31C22⋊C411yescharacteristic
117C22⋊C4×C31—21no—
118C22⋊C4×C31—21no—
119C22⋊C4×C31—21no—
120C42×C31—21no—
121C42×C31—21no—
122C42×C31—21no—
123C42×C31C2×D411yescharacteristic
124C42×C31C2×D411yescharacteristic
125C42×C31C2×D411yescharacteristic
126C42×C31#4111yescharacteristic
127#9351C3111yesmaximal, characteristic, direct product factor, Sylow
128C23×C31—21no—
129C23×C31C4×D411yescharacteristic
130Q8×C31—21no—
131Q8×C31—21no—
132D4×C31—21no—
133D4×C31—42no—
134D4×C31#10112yes—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—81no—
148C2×C4×C31—81no—
149C2×C4×C31C2×C22⋊C411yescharacteristic
150C2×C4×C31C4×D411yescharacteristic
151C2×C4×C31#12011yescharacteristic
152C2×C4×C31#12111yescharacteristic
153C2×C4×C31#12111yescharacteristic
154C2×C4×C31#12311yescharacteristic
155C8×C31—22no—
156C8×C31—42no—
157C8×C31—41no—
158C8×C31—41no—
159C8×C31—41no—
160C8×C31—81no—
161C8×C31—81no—
162#3080C2×C3111yescharacteristic
163#2970C2×C3111yescharacteristic
164#1528C2×C3111yescharacteristic, complemented
165#1488C2×C3111yescharacteristic
166#1470C2×C3111yescharacteristic, complemented
167#1307C2×C3111yescharacteristic, complemented
168#1299C2×C3111yescharacteristic, complemented
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—22no—
172C22×C31—21no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31#38611yescharacteristic
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31—41no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31C2×#10111yescharacteristic
187C4×C31#41311yescharacteristic
188C2×#125C22×C3111yescharacteristic
189C4×#41C22×C3111yescharacteristic
190#479—21no—
191#479—21no—
192#478—21no—
193#478—21no—
194#446—21no—
195#435—22no—
196C8×D4—21no—
197#432—21no—
198#432C22×C3111yescharacteristic
199#432C22×C3111yescharacteristic
200#431C22×C3111yescharacteristic
201#428C4×C3111yescharacteristic
202#428C4×C3111yescharacteristic
203#423C22×C3111yescharacteristic
204#417C4×C3111yescharacteristic
205#417C4×C3111yescharacteristic
206C4×M16C22×C3111yescharacteristic
207C2×#97—21no—
208#330—21no—
209#330—21no—
210Q8⋊C8—21no—
211D4⋊C8—21no—
212#324—22no—
213C2×C31—41no—
214C2×C31—42no—
215C2×C31#188111yescharacteristic
216C2×C31#190111yescharacteristic
217C2×C31#190611yescharacteristic
218C2×#41C2×C4×C3111yescharacteristic
219C2×M16—21no—
220C2×M16C2×C4×C3111yescharacteristic
221C2×M16C2×C4×C3111yescharacteristic
222C22×C8—22no—
223#125—21no—
224#125—21no—
225#125—21no—
226#125—21no—
227C4×Q8D4×C3111yescharacteristic
228C4×Q8D4×C3111yescharacteristic
229C4×D4—21no—
230C4×D4—21no—
231C4×D4D4×C3111yescharacteristic
232C4×D4D4×C3111yescharacteristic
233#117—21no—
234#117C2×C4×C3111yescharacteristic
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×C4×C3111yescharacteristic
238C2×C4⋊C4C2×C4×C3111yescharacteristic
239C2×C42—21no—
240C2×C42C23×C3111yescharacteristic
241#107—21no—
242#107—21no—
243#106—21no—
244#106—21no—
245C4⋊C8—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251#103—21no—
252#103—21no—
253#102—21no—
254#102—21no—
255C22⋊C8—22no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8D4×C3112yes—
259#97—22no—
260#97—21no—
261#97—21no—
262#97D4×C3111yescharacteristic
263#97D4×C3111yescharacteristic
264C4×C8—21no—
265C4×C8—21no—
266C31#935111yescharacteristic, direct product factor, Sylow
267#41—22no—
268#41—41no—
269C2×Q8C22⋊C4×C3111yescharacteristic
270C2×D4—21no—
271C2×D4C22⋊C4×C3111yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279C22×C4#41×C3111yescharacteristic
280M16—42no—
281M16—41no—
282M16—41no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—44no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C3111yescharacteristic
302C4⋊C4C22⋊C4×C3111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4×C3111yescharacteristic
310C42C2×D4×C3111yescharacteristic
311C42C2×D4×C3111yescharacteristic
312C42#41×C3111yescharacteristic
313C23—21no—
314C23C4×D4×C3111yescharacteristic
315Q8—21no—
316Q8—21no—
317D4—21no—
318D4—42no—
319D4C31×#10112yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C2×C22⋊C4×C3111yescharacteristic
335C2×C4C4×D4×C3111yescharacteristic
336C2×C4C31×#12011yescharacteristic
337C2×C4C31×#12111yescharacteristic
338C2×C4C31×#12111yescharacteristic
339C2×C4C31×#12311yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22C31×#38611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×C31×#10111yescharacteristic
365C4C31×#41311yescharacteristic
366C2—41no—
367C2—42no—
368C2C31×#188111yescharacteristic
369C2C31×#190111yescharacteristic
370C2C31×#190611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×C31C2×C4
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
3. C31×#1528C2semidirect
5. C31×#1470C2semidirect
6. C31×#1307C2semidirect
7. C31×#1299C2semidirect
127. #9351C31direct (N × H)
164. #1528C2×C31semidirect
166. #1470C2×C31semidirect
167. #1307C2×C31semidirect
168. #1299C2×C31semidirect
266. C31#9351direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30802
C31×#29702
C31×#15282
C31×#14882
C31×#14702
C31×#13072
C31×#12992
#935131