Finite Group Databasebeta

← C31×#11793 #21468552

Subgroups — C31×#11793 #21468552

Order 7936.

444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2564C211yesmaximal, characteristic
2C4×C31×#100C211yesmaximal, characteristic
3C31×#1465C211yesmaximal, characteristic
4C31×#1354C212yesmaximal, complemented
5C31×#1353C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C2×C31×#100—21no—
9C31×#407—21no—
10C4×M16×C31—21no—
11C31×#400C2211yescharacteristic
12C31×#399C411yescharacteristic
13C31×#395C2211yescharacteristic
14C31×#393C411yescharacteristic
15C31×#387—21no—
16C31×#386—21no—
17C31×#385—21no—
18C31×#380—21no—
19C2×C31×#95C411yescharacteristic
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31D411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C2×M16×C31—22no—
29C2×M16×C31—41no—
30C31×C22⋊Q8—41no—
31C31×C22⋊Q8—41no—
32C4×D4×C31—41no—
33C4×D4×C31—41no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2311yescharacteristic
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×#100—24no—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—41no—
48C31×#97—41no—
49C4×C8×C31—41no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31C22⋊C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C2×Q8×C31—41no—
60C2×Q8×C31—81no—
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—41no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—81no—
75C22×C4×C31—81no—
76C22×C4×C31—81no—
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22×C411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82M16×C31—24no—
83M16×C31—42no—
84M16×C31—82no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—42no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—81no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—41no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—81no—
98C42×C31—21no—
99C42×C31—21no—
100#11793C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31#10412yes—
111C23×C31C2×C22⋊C411yescharacteristic
112Q8×C31—82no—
113D4×C31—44no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—22no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—41no—
121C2×C4×C31—42no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—81no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31—84no—
140C2×C4×C31#9911yescharacteristic
141C2×C4×C31#9911yescharacteristic
142C2×C4×C31#13712yes—
143C8×C31—44no—
144C8×C31—82no—
145#2564C2×C3111yescharacteristic
146C4×#100C2×C3111yescharacteristic
147#1465C2×C3111yescharacteristic
148#1354C2×C3112yescomplemented
149#1353C2×C3112yescomplemented
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—22no—
153C22×C31—42no—
154C22×C31—42no—
155C22×C31—42no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—81no—
162C22×C31C2×#9911yescharacteristic
163C22×C31#41911yescharacteristic
164C22×C31C2×#10411yescharacteristic
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—22no—
168C4×C31—42no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—81no—
173C4×C31—81no—
174C4×C31—81no—
175C2×C22⋊Q8C4×C3111yescharacteristic
176C2×C4×D4C22×C3111yescharacteristic
177C2×#100—21no—
178#407—21no—
179C4×M16—21no—
180#400C22×C3111yescharacteristic
181#399C4×C3111yescharacteristic
182#395C22×C3111yescharacteristic
183#393C4×C3111yescharacteristic
184#387—21no—
185#386—21no—
186#385—21no—
187#380—21no—
188C2×#95C4×C3111yescharacteristic
189#343C22×C3112yes—
190#324C22×C3112yes—
191#323—21no—
192C2×C31—21no—
193C2×C31—21no—
194C2×C31—42no—
195C2×C31—81no—
196C2×C31#150811yescharacteristic
197C2×C31#212111yescharacteristic
198C2×C31#213211yescharacteristic
199C22×Q8C2×C4×C3111yescharacteristic
200C22×D4D4×C3111yescharacteristic
201C23×C4—21no—
202C23×C4C2×C4×C3111yescharacteristic
203C23×C4D4×C3111yescharacteristic
204C2×M16—22no—
205C2×M16—41no—
206C22⋊Q8—41no—
207C22⋊Q8—41no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C3111yescharacteristic
214C2×C4⋊C4C23×C3111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C2×C4×C3111yescharacteristic
219C2×C22⋊C4D4×C3111yescharacteristic
220C2×C42D4×C3111yescharacteristic
221#100—24no—
222C22⋊C8—22no—
223C22⋊C8—41no—
224#97—41no—
225C4×C8—41no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C2×C4×C3111yescharacteristic
232#95C2×C4×C3111yescharacteristic
233C31#1179311yescharacteristic, direct product factor, Sylow
234C24C22⋊C4×C3111yescharacteristic
235C24C22⋊C4×C3111yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22×C4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4C2×D4×C3111yescharacteristic
259M16—24no—
260M16—42no—
261M16—82no—
262C2×C8—42no—
263C2×C8—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C31×#10412yes—
287C23C2×C22⋊C4×C3111yescharacteristic
288Q8—82no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—84no—
316C2×C4C31×#9911yescharacteristic
317C2×C4C31×#9911yescharacteristic
318C2×C4C31×#13712yes—
319C8—44no—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×C31×#9911yescharacteristic
334C22C31×#41911yescharacteristic
335C22C2×C31×#10411yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2C31×#150811yescharacteristic
351C2C31×#212111yescharacteristic
352C2C31×#213211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1354C2semidirect
5. C31×#1353C2semidirect
100. #11793C31direct (N × H)
148. #1354C2×C31semidirect
149. #1353C2×C31semidirect
233. C31#11793direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25642
C4×C31×#1002
C31×#14652
C31×#13542
C31×#13532
#1179331