Finite Group Databasebeta

← C31×#9310 #21466069

Subgroups — C31×#9310 #21466069

Order 7936.

470 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3037C211yesmaximal, characteristic
2C31×#2983C211yesmaximal, characteristic, complemented
3C31×#1805C211yesmaximal, characteristic, complemented
4C31×#1517C211yesmaximal, characteristic
5C31×#1480C211yesmaximal, characteristic
6C31×#1301C211yesmaximal, characteristic, complemented
7C31×#1286C211yesmaximal, characteristic, complemented
8C2×C31×#137—21no—
9C31×#532C2211yescharacteristic
10C2×C4×Q8×C31C2211yescharacteristic
11C31×#464—22no—
12C31×#462C412yescomplemented
13C31×#460C412yescomplemented
14C31×#446—22no—
15C31×#446—22no—
16C31×#432—22no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C2×C31×C4⋊C8C2211yescharacteristic
21C31×#417—21no—
22C2×C31×#103—21no—
23C31×#382C2211yescharacteristic
24C31×#340—21no—
25C31×#327—22no—
26C31×D4⋊C8—22no—
27C2×#41×C31—21no—
28C22×Q8×C31D411yescharacteristic
29C31×#137—42no—
30C31×#137—42no—
31C2×Q16×C31—22no—
32C2×SD16×C31—22no—
33C2×M16×C31—21no—
34C22×C8×C31—21no—
35C31×C4⋊Q8C2×C411yescharacteristic
36C31×#127C2×C411yescharacteristic
37C31×#124—21no—
38C31×#121—21no—
39C31×#121—21no—
40C4×Q8×C31—21no—
41C4×Q8×C31—21no—
42C4×Q8×C31C2×C412yes—
43C4×Q8×C31D412yes—
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C42×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—24no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8C2×C412yes—
58C31×#103—22no—
59C31×#103—42no—
60C31×#102—22no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8D412yes—
63C31×#97—24no—
64C4×C8×C31—21no—
65C4×C8×C31D412yes—
66C31×#95—21no—
67C31×#95—21no—
68#41×C31—41no—
69#41×C31—41no—
70#41×C31—41no—
71#41×C31—41no—
72C2×Q8×C31—21no—
73C2×Q8×C31—21no—
74C2×Q8×C31—21no—
75C2×Q8×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31C22⋊C412yes—
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—41no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31#4111yescharacteristic
90Q16×C31—44no—
91SD16×C31—44no—
92M16×C31—41no—
93M16×C31—41no—
94C2×C8×C31—22no—
95C2×C8×C31—22no—
96C2×C8×C31—22no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31C22⋊C412yes—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—41no—
110C42×C31—22no—
111C42×C31—22no—
112C42×C31C22×C411yescharacteristic
113C42×C31C2×D411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31#4111yescharacteristic
116#9310C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—41no—
118C23×C31#12111yescharacteristic
119Q8×C31—22no—
120Q8×C31—22no—
121Q8×C31—41no—
122Q8×C31—41no—
123Q8×C31—41no—
124Q8×C31—41no—
125D4×C31—42no—
126D4×C31—41no—
127D4×C31—41no—
128D4×C31—81no—
129D4×C31—81no—
130D4×C31—81no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
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—81no—
142C2×C4×C31—81no—
143C2×C4×C31—81no—
144C2×C4×C31C2×C22⋊C411yescharacteristic
145C2×C4×C31C4×D411yescharacteristic
146C2×C4×C31C4×D411yescharacteristic
147C2×C4×C31#12011yescharacteristic
148C2×C4×C31#12111yescharacteristic
149C2×C4×C31#12311yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C31#13711yescharacteristic
154C8×C31—42no—
155C8×C31—42no—
156C8×C31—42no—
157C8×C31—81no—
158#3037C2×C3111yescharacteristic
159#2983C2×C3111yescharacteristic, complemented
160#1805C2×C3111yescharacteristic, complemented
161#1517C2×C3111yescharacteristic
162#1480C2×C3111yescharacteristic
163#1301C2×C3111yescharacteristic, complemented
164#1286C2×C3111yescharacteristic, complemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31#38611yescharacteristic
171C22×C31#46811yescharacteristic
172C22×C31#46911yescharacteristic
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—42no—
178C4×C31—42no—
179C4×C31—81no—
180C4×C31—161no—
181C4×C31#41711yescharacteristic
182C4×C31#41811yescharacteristic
183C4×C31#46811yescharacteristic
184C4×C31#46911yescharacteristic
185C2×#137—21no—
186#532C22×C3111yescharacteristic
187C2×C4×Q8C22×C3111yescharacteristic
188#464—22no—
189#462C4×C3112yescomplemented
190#460C4×C3112yescomplemented
191#446—22no—
192#446—22no—
193#432—22no—
194#431C22×C3111yescharacteristic
195#431C22×C3111yescharacteristic
196#423C22×C3111yescharacteristic
197C2×C4⋊C8C22×C3111yescharacteristic
198#417—21no—
199C2×#103—21no—
200#382C22×C3111yescharacteristic
201#340—21no—
202#327—22no—
203D4⋊C8—22no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—161no—
207C2×C31#188111yescharacteristic
208C2×C31#189511yescharacteristic
209C2×C31#190511yescharacteristic
210C2×#41—21no—
211C22×Q8D4×C3111yescharacteristic
212#137—42no—
213#137—42no—
214C2×Q16—22no—
215C2×SD16—22no—
216C2×M16—21no—
217C22×C8—21no—
218C4⋊Q8C2×C4×C3111yescharacteristic
219#127C2×C4×C3111yescharacteristic
220#124—21no—
221#121—21no—
222#121—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8C2×C4×C3112yes—
226C4×Q8D4×C3112yes—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4D4×C3111yescharacteristic
232C2×C42—21no—
233C2×C42C23×C3111yescharacteristic
234C4⋊C8—24no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8C2×C4×C3112yes—
241#103—22no—
242#103—42no—
243#102—22no—
244C22⋊C8—21no—
245C22⋊C8D4×C3112yes—
246#97—24no—
247C4×C8—21no—
248C4×C8D4×C3112yes—
249#95—21no—
250#95—21no—
251C31#931011yescharacteristic, direct product factor, Sylow
252#41—41no—
253#41—41no—
254#41—41no—
255#41—41no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C3112yes—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C3111yescharacteristic
272C22×C4C2×D4×C3111yescharacteristic
273C22×C4#41×C3111yescharacteristic
274Q16—44no—
275SD16—44no—
276M16—41no—
277M16—41no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C3112yes—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42C22×C4×C3111yescharacteristic
297C42C2×D4×C3111yescharacteristic
298C42C2×D4×C3111yescharacteristic
299C42#41×C3111yescharacteristic
300C23—41no—
301C23C31×#12111yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308D4—42no—
309D4—41no—
310D4—41no—
311D4—81no—
312D4—81no—
313D4—81no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C2×C22⋊C4×C3111yescharacteristic
328C2×C4C4×D4×C3111yescharacteristic
329C2×C4C4×D4×C3111yescharacteristic
330C2×C4C31×#12011yescharacteristic
331C2×C4C31×#12111yescharacteristic
332C2×C4C31×#12311yescharacteristic
333C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
334C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
335C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C31×#13711yescharacteristic
337C8—42no—
338C8—42no—
339C8—42no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22C31×#38611yescharacteristic
347C22C31×#46811yescharacteristic
348C22C31×#46911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—42no—
355C4—81no—
356C4—161no—
357C4C31×#41711yescharacteristic
358C4C31×#41811yescharacteristic
359C4C31×#46811yescharacteristic
360C4C31×#46911yescharacteristic
361C2—21no—
362C2—21no—
363C2—161no—
364C2C31×#188111yescharacteristic
365C2C31×#189511yescharacteristic
366C2C31×#190511yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2983C2semidirect
3. C31×#1805C2semidirect
6. C31×#1301C2semidirect
7. C31×#1286C2semidirect
12. C31×#462C4semidirect
13. C31×#460C4semidirect
116. #9310C31direct (N × H)
159. #2983C2×C31semidirect
160. #1805C2×C31semidirect
163. #1301C2×C31semidirect
164. #1286C2×C31semidirect
189. #462C4×C31semidirect
190. #460C4×C31semidirect
251. C31#9310direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30372
C31×#29832
C31×#18052
C31×#15172
C31×#14802
C31×#13012
C31×#12862
#931031