Finite Group Databasebeta

← C31×#9387 #21466146

Subgroups — C31×#9387 #21466146

Order 7936.

582 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2873C211yesmaximal, characteristic, complemented
2C31×#2610C211yesmaximal, characteristic
3C31×#1527C212yesmaximal, complemented
4C31×#1464C211yesmaximal, characteristic, complemented
5C31×#1300C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C31×#124C2211yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#432C2212yes—
10C31×#405—24no—
11C4×M16×C31—21no—
12C4×M16×C31C2212yes—
13C31×#395C411yescharacteristic
14C31×#394C411yescharacteristic
15C31×#393C411yescharacteristic
16C31×#392C411yescharacteristic
17C31×#390—21no—
18C31×#388—21no—
19C31×#388—21no—
20C31×#386—21no—
21C31×#376C2211yescharacteristic
22C31×#329—24no—
23C31×#324—21no—
24C31×#323—21no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C2×M16×C31—22no—
30C2×M16×C31—24no—
31C2×M16×C31—24no—
32C2×M16×C31—22no—
33C22×C8×C31—22no—
34C31×#124—22no—
35C31×#124—22no—
36C31×#117—22no—
37C31×#117—22no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31C2×C411yescharacteristic
48C2×C22⋊C4×C31D411yescharacteristic
49C2×C42×C31—21no—
50C2×C42×C31D411yescharacteristic
51C2×C42×C31C2311yescharacteristic
52C31×C4⋊C8—22no—
53C31×C22⋊C8—22no—
54C31×#97—22no—
55C31×#97—22no—
56C31×#97D414yescomplemented
57C4×C8×C31—22no—
58C4×C8×C31—22no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95C2×C411yescharacteristic
63C31×#95C2×C411yescharacteristic
64C24×C31—21no—
65C24×C31C22⋊C411yescharacteristic
66C2×Q8×C31—22no—
67C2×Q8×C31—81no—
68C2×D4×C31—22no—
69C2×D4×C31—42no—
70C2×D4×C31—42no—
71C2×D4×C31—81no—
72C2×D4×C31—81no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22×C411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86M16×C31—28no—
87M16×C31—24no—
88M16×C31—24no—
89C2×C8×C31—28no—
90C2×C8×C31—24no—
91C2×C8×C31—42no—
92C4⋊C4×C31—22no—
93C4⋊C4×C31—22no—
94C4⋊C4×C31—81no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—81no—
103C22⋊C4×C31—81no—
104C42×C31—21no—
105C42×C31—21no—
106C42×C31—42no—
107C42×C31C2×D412yes—
108C42×C31#4112yes—
109#9387C3111yesmaximal, characteristic, direct product factor, Sylow
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31#10412yes—
122C23×C31C2×C22⋊C411yescharacteristic
123Q8×C31—82no—
124D4×C31—82no—
125D4×C31—84no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—24no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—22no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
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—41no—
147C2×C4×C31—41no—
148C2×C4×C31#10412yes—
149C2×C4×C31C4×D412yes—
150C2×C4×C31#12011yescharacteristic
151C2×C4×C31#12112yes—
152C2×C4×C31#12311yescharacteristic
153C8×C31—28no—
154C8×C31—82no—
155#2873C2×C3111yescharacteristic, complemented
156#2610C2×C3111yescharacteristic
157#1527C2×C3112yescomplemented
158#1464C2×C3111yescharacteristic, complemented
159#1300C2×C3112yescomplemented
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—22no—
163C22×C31—42no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31#38611yescharacteristic
175C22×C31C2×#10411yescharacteristic
176C22×C31C2×#10411yescharacteristic
177C4×C31—22no—
178C4×C31—21no—
179C4×C31—22no—
180C4×C31—21no—
181C4×C31—22no—
182C4×C31—42no—
183C4×C31—41no—
184C4×C31—41no—
185C4×C31—81no—
186C4×C31—81no—
187C22×M16—21no—
188C2×#124C22×C3111yescharacteristic
189C2×#117C22×C3111yescharacteristic
190#432C22×C3112yes—
191#405—24no—
192C4×M16—21no—
193C4×M16C22×C3112yes—
194#395C4×C3111yescharacteristic
195#394C4×C3111yescharacteristic
196#393C4×C3111yescharacteristic
197#392C4×C3111yescharacteristic
198#390—21no—
199#388—21no—
200#388—21no—
201#386—21no—
202#376C22×C3111yescharacteristic
203#329—24no—
204#324—21no—
205#323—21no—
206C2×C31—21no—
207C2×C31—21no—
208C2×C31—42no—
209C2×C31—161no—
210C2×C31#188411yescharacteristic
211C2×C31#189611yescharacteristic
212C2×C31#191411yescharacteristic
213C22×Q8C2×C4×C3111yescharacteristic
214C22×D4—21no—
215C22×D4C2×C4×C3111yescharacteristic
216C23×C4D4×C3111yescharacteristic
217C2×M16—22no—
218C2×M16—24no—
219C2×M16—24no—
220C2×M16—22no—
221C22×C8—22no—
222#124—22no—
223#124—22no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C3111yescharacteristic
228C2×C4⋊C4D4×C3111yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4C2×C4×C3111yescharacteristic
236C2×C22⋊C4D4×C3111yescharacteristic
237C2×C42—21no—
238C2×C42D4×C3111yescharacteristic
239C2×C42C23×C3111yescharacteristic
240C4⋊C8—22no—
241C22⋊C8—22no—
242#97—22no—
243#97—22no—
244#97D4×C3114yescomplemented
245C4×C8—22no—
246C4×C8—22no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95C2×C4×C3111yescharacteristic
251#95C2×C4×C3111yescharacteristic
252C31#938711yescharacteristic, direct product factor, Sylow
253C24—21no—
254C24C22⋊C4×C3111yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22⋊C4×C3111yescharacteristic
270C22×C4C22⋊C4×C3111yescharacteristic
271C22×C4C22⋊C4×C3111yescharacteristic
272C22×C4C22×C4×C3111yescharacteristic
273C22×C4C2×D4×C3111yescharacteristic
274C22×C4C2×D4×C3111yescharacteristic
275M16—28no—
276M16—24no—
277M16—24no—
278C2×C8—28no—
279C2×C8—24no—
280C2×C8—42no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—42no—
296C42C2×D4×C3112yes—
297C42#41×C3112yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23C31×#10412yes—
310C23C2×C22⋊C4×C3111yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
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—41no—
335C2×C4—41no—
336C2×C4C31×#10412yes—
337C2×C4C4×D4×C3112yes—
338C2×C4C31×#12011yescharacteristic
339C2×C4C31×#12112yes—
340C2×C4C31×#12311yescharacteristic
341C8—28no—
342C8—82no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C31×#38611yescharacteristic
358C22C2×C31×#10411yescharacteristic
359C22C2×C31×#10411yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2C31×#188411yescharacteristic
375C2C31×#189611yescharacteristic
376C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#392C4
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
1. C31×#2873C2semidirect
3. C31×#1527C2semidirect
4. C31×#1464C2semidirect
5. C31×#1300C2semidirect
56. C31×#97D4semidirect
109. #9387C31direct (N × H)
155. #2873C2×C31semidirect
157. #1527C2×C31semidirect
158. #1464C2×C31semidirect
159. #1300C2×C31semidirect
244. #97D4×C31semidirect
252. C31#9387direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28732
C31×#26102
C31×#15272
C31×#14642
C31×#13002
#938731