Finite Group Databasebeta

← C31×#9183 #21465942

Subgroups — C31×#9183 #21465942

Order 7936.

532 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2973C211yesmaximal, characteristic
2C31×#2638C211yesmaximal, characteristic
3C4×C31×#99C211yesmaximal, characteristic
4C31×#1508C212yesmaximal, complemented
5C31×#1284C212yesmaximal, complemented
6C2×C31×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#435—24no—
9C31×#432—21no—
10C2×C31×#99—21no—
11C31×#407C2212yes—
12C2×C31×C22⋊C8—21no—
13C31×#398C411yescharacteristic, complemented
14C31×#397—21no—
15C31×#397C411yescharacteristic, complemented
16C31×#395C411yescharacteristic, complemented
17C31×#394—21no—
18C31×#393C411yescharacteristic, complemented
19C31×#387—21no—
20C31×#385—21no—
21C31×#381C2211yescharacteristic
22C4×C22⋊C4×C31C2212yes—
23C31×#342—21no—
24C31×#328—24no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C23×C4×C31C2311yescharacteristic
29C2×M16×C31—22no—
30C22×C8×C31—22no—
31C31×C22⋊Q8—22no—
32C31×C22⋊Q8—22no—
33C4×D4×C31—22no—
34C4×D4×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31C2×C411yescharacteristic
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C42×C31—22no—
48C2×C42×C31D411yescharacteristic
49C31×C4⋊C8—22no—
50C31×#99—24no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×C22⋊C8D414yes—
54C31×#97—22no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—22no—
61C31×#95C2×C411yescharacteristic
62C31×#95C2×C411yescharacteristic
63C24×C31C22⋊C411yescharacteristic
64C24×C31C2×D411yescharacteristic
65C2×Q8×C31—22no—
66C2×Q8×C31—81no—
67C2×D4×C31—22no—
68C2×D4×C31—22no—
69C2×D4×C31—41no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—42no—
77C22×C4×C31—81no—
78C22×C4×C31—81no—
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D412yes—
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31#4112yes—
86M16×C31—82no—
87C2×C8×C31—24no—
88C2×C8×C31—82no—
89C4⋊C4×C31—22no—
90C4⋊C4×C31—22no—
91C4⋊C4×C31—42no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—81no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—24no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—81no—
102C22⋊C4×C31—81no—
103C42×C31—21no—
104C42×C31—21no—
105C42×C31—82no—
106#9183C3111yesmaximal, characteristic, direct product factor, Sylow
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31#10412yes—
116C23×C31C2×C22⋊C411yescharacteristic
117C23×C31#12112yes—
118Q8×C31—82no—
119D4×C31—44no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—44no—
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—81no—
146C2×C4×C31—82no—
147C2×C4×C31—82no—
148C2×C4×C31C4×D412yes—
149C2×C4×C31#12011yescharacteristic
150C2×C4×C31#12311yescharacteristic
151C8×C31—44no—
152#2973C2×C3111yescharacteristic
153#2638C2×C3111yescharacteristic
154C4×#99C2×C3111yescharacteristic
155#1508C2×C3112yescomplemented
156#1284C2×C3112yescomplemented
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—22no—
160C22×C31—22no—
161C22×C31—22no—
162C22×C31—22no—
163C22×C31—42no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31#38611yescharacteristic
170C22×C31C2×#10411yescharacteristic
171C22×C31#42111yescharacteristic
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—81no—
179C4×C31—81no—
180C4×C31—84no—
181C4×C31—81no—
182C4×C31—81no—
183C2×C22⋊Q8C22×C3111yescharacteristic
184C2×C4×D4C22×C3111yescharacteristic
185#435—24no—
186#432—21no—
187C2×#99—21no—
188#407C22×C3112yes—
189C2×C22⋊C8—21no—
190#398C4×C3111yescharacteristic, complemented
191#397—21no—
192#397C4×C3111yescharacteristic, complemented
193#395C4×C3111yescharacteristic, complemented
194#394—21no—
195#393C4×C3111yescharacteristic, complemented
196#387—21no—
197#385—21no—
198#381C22×C3111yescharacteristic
199C4×C22⋊C4C22×C3112yes—
200#342—21no—
201#328—24no—
202C2×C31—21no—
203C2×C31—21no—
204C2×C31—42no—
205C2×C31—42no—
206C2×C31#187111yescharacteristic
207C2×C31#190911yescharacteristic
208C2×C31#191311yescharacteristic
209C22×Q8C2×C4×C3111yescharacteristic
210C22×D4D4×C3111yescharacteristic
211C23×C4D4×C3111yescharacteristic
212C23×C4C23×C3111yescharacteristic
213C2×M16—22no—
214C22×C8—22no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C4×D4—22no—
218C4×D4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C2×C4×C3111yescharacteristic
223C2×C4⋊C4C2×C4×C3111yescharacteristic
224C2×C22⋊C4—22no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4C2×C4×C3111yescharacteristic
230C2×C22⋊C4D4×C3111yescharacteristic
231C2×C42—22no—
232C2×C42D4×C3111yescharacteristic
233C4⋊C8—22no—
234#99—24no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C22⋊C8D4×C3114yes—
238#97—22no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—22no—
245#95C2×C4×C3111yescharacteristic
246#95C2×C4×C3111yescharacteristic
247C31#918311yescharacteristic, direct product factor, Sylow
248C24C22⋊C4×C3111yescharacteristic
249C24C2×D4×C3111yescharacteristic
250C2×Q8—22no—
251C2×Q8—81no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4C22⋊C4×C3111yescharacteristic
265C22×C4C22⋊C4×C3111yescharacteristic
266C22×C4C22⋊C4×C3111yescharacteristic
267C22×C4C22×C4×C3111yescharacteristic
268C22×C4C2×D4×C3112yes—
269C22×C4C2×D4×C3111yescharacteristic
270C22×C4#41×C3112yes—
271M16—82no—
272C2×C8—24no—
273C2×C8—82no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—24no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C42—21no—
289C42—21no—
290C42—82no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C31×#10412yes—
300C23C2×C22⋊C4×C3111yescharacteristic
301C23C31×#12112yes—
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
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—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4C4×D4×C3112yes—
333C2×C4C31×#12011yescharacteristic
334C2×C4C31×#12311yescharacteristic
335C8—44no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C31×#38611yescharacteristic
349C22C2×C31×#10411yescharacteristic
350C22C31×#42111yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—84no—
360C4—81no—
361C4—81no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—42no—
366C2C31×#187111yescharacteristic
367C2C31×#190911yescharacteristic
368C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1508C2semidirect
5. C31×#1284C2semidirect
13. C31×#398C4semidirect
15. C31×#397C4semidirect
16. C31×#395C4semidirect
18. C31×#393C4semidirect
106. #9183C31direct (N × H)
155. #1508C2×C31semidirect
156. #1284C2×C31semidirect
190. #398C4×C31semidirect
192. #397C4×C31semidirect
193. #395C4×C31semidirect
195. #393C4×C31semidirect
247. C31#9183direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29732
C31×#26382
C4×C31×#992
C31×#15082
C31×#12842
#918331