Finite Group Databasebeta

← C31×#9314 #21466073

Subgroups — C31×#9314 #21466073

Order 7936.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3116C211yesmaximal, characteristic
2C31×#2923C211yesmaximal, characteristic
3C31×#1531C211yesmaximal, characteristic, complemented
4C31×#1488C211yesmaximal, characteristic
5C31×#1485C211yesmaximal, characteristic, complemented
6C31×#1302C211yesmaximal, characteristic, complemented
7C31×#1291C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#485—21no—
11C31×#477C411yescharacteristic
12C31×#476C411yescharacteristic
13C31×#462C411yescharacteristic
14C31×#461C411yescharacteristic
15C31×#452—21no—
16C31×#441—21no—
17C31×#440—21no—
18C31×#433—22no—
19C31×#432—22no—
20C31×#432C2211yescharacteristic
21C31×#432C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C31×#424—21no—
24C31×#408—21no—
25C4×M16×C31C2211yescharacteristic
26C2×C31×#97C2211yescharacteristic
27C31×#330—22no—
28C31×Q8⋊C8—21no—
29C31×Q8⋊C8—22no—
30C31×D4⋊C8—21no—
31C2×#41×C31D411yescharacteristic
32C2×Q16×C31—21no—
33C2×SD16×C31—21no—
34C2×M16×C31—21no—
35C22×C8×C31—21no—
36C31×C4⋊Q8C2×C411yescharacteristic
37C31×C4⋊Q8C2×C411yescharacteristic
38C31×#125—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C4×Q8×C31—21no—
42C4×Q8×C31—21no—
43C4×Q8×C31C2×C411yescharacteristic
44C4×Q8×C31D411yescharacteristic
45C4×D4×C31—21no—
46C4×D4×C31—21no—
47C4×D4×C31C2×C411yescharacteristic
48C4×D4×C31D411yescharacteristic
49C31×#117—21no—
50C31×#117—21no—
51C31×#117D411yescharacteristic
52C2×C42×C31—21no—
53C2×C42×C31C2311yescharacteristic
54C31×#107—21no—
55C31×#106—21no—
56C31×C4⋊C8—24no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8C2×C411yescharacteristic
60C31×C4⋊C8C2×C411yescharacteristic
61C31×#103—21no—
62C31×#103—21no—
63C31×#103—21no—
64C31×#102—21no—
65C31×C22⋊C8—24no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×#97—21no—
70C31×#97—21no—
71C31×#97—21no—
72C31×#97—21no—
73C31×#97D412yes—
74C4×C8×C31—21no—
75C4×C8×C31D412yes—
76#41×C31—41no—
77#41×C31—41no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31C22⋊C411yescharacteristic
81C2×D4×C31—21no—
82C2×D4×C31C22⋊C411yescharacteristic
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31#4111yescharacteristic
88C22×C4×C31#4111yescharacteristic
89Q16×C31—42no—
90SD16×C31—42no—
91M16×C31—41no—
92M16×C31—41no—
93C2×C8×C31—21no—
94C2×C8×C31—21no—
95C2×C8×C31—22no—
96C2×C8×C31—22no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31C22⋊C411yescharacteristic
110C4⋊C4×C31C22⋊C411yescharacteristic
111C22⋊C4×C31—21no—
112C22⋊C4×C31—21no—
113C22⋊C4×C31—21no—
114C22⋊C4×C31—41no—
115C42×C31—21no—
116C42×C31—21no—
117C42×C31—21no—
118C42×C31—41no—
119C42×C31C22×C411yescharacteristic
120C42×C31C2×D411yescharacteristic
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123#9314C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—21no—
125C23×C31#12311yescharacteristic
126Q8×C31—21no—
127Q8×C31—21no—
128Q8×C31—42no—
129Q8×C31—41no—
130Q8×C31—41no—
131D4×C31—21no—
132D4×C31—21no—
133D4×C31—42no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—42no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—81no—
145C2×C4×C31—81no—
146C2×C4×C31C2×C22⋊C411yescharacteristic
147C2×C4×C31C4×D411yescharacteristic
148C2×C4×C31C4×D411yescharacteristic
149C2×C4×C31#12011yescharacteristic
150C2×C4×C31#12111yescharacteristic
151C2×C4×C31#12111yescharacteristic
152C8×C31—42no—
153C8×C31—42no—
154C8×C31—41no—
155C8×C31—41no—
156C8×C31—81no—
157C8×C31—81no—
158#3116C2×C3111yescharacteristic
159#2923C2×C3111yescharacteristic
160#1531C2×C3111yescharacteristic, complemented
161#1488C2×C3111yescharacteristic
162#1485C2×C3111yescharacteristic, complemented
163#1302C2×C3111yescharacteristic, complemented
164#1291C2×C3111yescharacteristic, complemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31#38611yescharacteristic
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31—41no—
180C4×C31—81no—
181C4×C31—81no—
182C4×C31#42111yescharacteristic
183C4×C31#42111yescharacteristic
184#533C22×C3111yescharacteristic
185C4×#41C22×C3111yescharacteristic
186#485—21no—
187#477C4×C3111yescharacteristic
188#476C4×C3111yescharacteristic
189#462C4×C3111yescharacteristic
190#461C4×C3111yescharacteristic
191#452—21no—
192#441—21no—
193#440—21no—
194#433—22no—
195#432—22no—
196#432C22×C3111yescharacteristic
197#432C22×C3111yescharacteristic
198#431C22×C3111yescharacteristic
199#424—21no—
200#408—21no—
201C4×M16C22×C3111yescharacteristic
202C2×#97C22×C3111yescharacteristic
203#330—22no—
204Q8⋊C8—21no—
205Q8⋊C8—22no—
206D4⋊C8—21no—
207C2×C31—41no—
208C2×C31—81no—
209C2×C31#188111yescharacteristic
210C2×C31#189711yescharacteristic
211C2×C31#190211yescharacteristic
212C2×#41D4×C3111yescharacteristic
213C2×Q16—21no—
214C2×SD16—21no—
215C2×M16—21no—
216C22×C8—21no—
217C4⋊Q8C2×C4×C3111yescharacteristic
218C4⋊Q8C2×C4×C3111yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8C2×C4×C3111yescharacteristic
225C4×Q8D4×C3111yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4C2×C4×C3111yescharacteristic
229C4×D4D4×C3111yescharacteristic
230#117—21no—
231#117—21no—
232#117D4×C3111yescharacteristic
233C2×C42—21no—
234C2×C42C23×C3111yescharacteristic
235#107—21no—
236#106—21no—
237C4⋊C8—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8C2×C4×C3111yescharacteristic
241C4⋊C8C2×C4×C3111yescharacteristic
242#103—21no—
243#103—21no—
244#103—21no—
245#102—21no—
246C22⋊C8—24no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250#97—21no—
251#97—21no—
252#97—21no—
253#97—21no—
254#97D4×C3112yes—
255C4×C8—21no—
256C4×C8D4×C3112yes—
257C31#931411yescharacteristic, direct product factor, Sylow
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C3111yescharacteristic
263C2×D4—21no—
264C2×D4C22⋊C4×C3111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4#41×C3111yescharacteristic
270C22×C4#41×C3111yescharacteristic
271Q16—42no—
272SD16—42no—
273M16—41no—
274M16—41no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C3111yescharacteristic
292C4⋊C4C22⋊C4×C3111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—41no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—41no—
301C42C22×C4×C3111yescharacteristic
302C42C2×D4×C3111yescharacteristic
303C42C2×D4×C3111yescharacteristic
304C42C2×D4×C3111yescharacteristic
305C23—21no—
306C23C31×#12311yescharacteristic
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—41no—
311Q8—41no—
312D4—21no—
313D4—21no—
314D4—42no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
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×#12111yescharacteristic
333C8—42no—
334C8—42no—
335C8—41no—
336C8—41no—
337C8—81no—
338C8—81no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22C31×#38611yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4C31×#42111yescharacteristic
357C4C31×#42111yescharacteristic
358C2—41no—
359C2—81no—
360C2C31×#188111yescharacteristic
361C2C31×#189711yescharacteristic
362C2C31×#190211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×C31D4
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
3. C31×#1531C2semidirect
5. C31×#1485C2semidirect
6. C31×#1302C2semidirect
7. C31×#1291C2semidirect
123. #9314C31direct (N × H)
160. #1531C2×C31semidirect
162. #1485C2×C31semidirect
163. #1302C2×C31semidirect
164. #1291C2×C31semidirect
257. C31#9314direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31162
C31×#29232
C31×#15312
C31×#14882
C31×#14852
C31×#13022
C31×#12912
#931431