Finite Group Databasebeta

← C31×#11555 #21468314

Subgroups — C31×#11555 #21468314

Order 7936.

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

normal subgroups only

This group has 414 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×#2502C211yesmaximal, characteristic
2C31×#1463C211yesmaximal, characteristic
3C2×C31×#324C211yesmaximal, characteristic
4C31×#1325C212yesmaximal, complemented
5C31×#1319C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic
7C22×C4⋊C4×C31C2211yescharacteristic
8C31×#407—21no—
9C2×C31×C22⋊C8—21no—
10C31×#398—21no—
11C31×#398—21no—
12C31×#391C411yescharacteristic
13C31×#391C2211yescharacteristic
14C31×#385—21no—
15C31×#385—21no—
16C31×#384C411yescharacteristic
17C31×#384C2211yescharacteristic
18C4×C22⋊C4×C31C411yescharacteristic
19C31×#324—21no—
20C31×#324—21no—
21C31×#324C2212yes—
22C31×#324C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C2×M16×C31—41no—
28C22×C8×C31—41no—
29C31×C22⋊Q8—41no—
30C31×C22⋊Q8—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—41no—
37C2×C4⋊C4×C31—41no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C4⋊C4×C31C2311yescharacteristic
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C42×C31C2×C411yescharacteristic
46C2×C42×C31C2×C411yescharacteristic
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—41no—
50C31×C22⋊C8—41no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C24×C31C22⋊C411yescharacteristic
57C2×Q8×C31—22no—
58C2×Q8×C31—41no—
59C2×Q8×C31—41no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—22no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—41no—
72C22×C4×C31—81no—
73C22×C4×C31—81no—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80M16×C31—82no—
81C2×C8×C31—42no—
82C2×C8×C31—42no—
83C2×C8×C31—82no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—42no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—81no—
91C4⋊C4×C31—81no—
92C4⋊C4×C31—81no—
93C4⋊C4×C31—81no—
94C22⋊C4×C31—24no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C42×C31—22no—
98C42×C31—41no—
99#11555C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—22no—
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—41no—
104C23×C31#9911yescharacteristic
105C23×C31#9911yescharacteristic
106C23×C31C2×C22⋊C411yescharacteristic
107Q8×C31—82no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—22no—
111C2×C4×C31—22no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
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—41no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31#13112yes—
140C8×C31—82no—
141C8×C31—82no—
142#2502C2×C3111yescharacteristic
143#1463C2×C3111yescharacteristic
144C2×#324C2×C3111yescharacteristic
145#1325C2×C3112yescomplemented
146#1319C2×C3112yescomplemented
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—42no—
155C22×C31—42no—
156C22×C31#35612yes—
157C22×C31#40811yescharacteristic
158C22×C31C2×#9911yescharacteristic
159C22×C31#41311yescharacteristic
160C4×C31—22no—
161C4×C31—42no—
162C4×C31—42no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31—81no—
169C4×C31—81no—
170C2×C22⋊Q8C4×C3111yescharacteristic
171C22×C4⋊C4C22×C3111yescharacteristic
172#407—21no—
173C2×C22⋊C8—21no—
174#398—21no—
175#398—21no—
176#391C4×C3111yescharacteristic
177#391C22×C3111yescharacteristic
178#385—21no—
179#385—21no—
180#384C4×C3111yescharacteristic
181#384C22×C3111yescharacteristic
182C4×C22⋊C4C4×C3111yescharacteristic
183#324—21no—
184#324—21no—
185#324C22×C3112yes—
186#324C22×C3112yes—
187C2×C31—21no—
188C2×C31—21no—
189C2×C31—22no—
190C2×C31—41no—
191C2×C31#146811yescharacteristic
192C2×C31#212711yescharacteristic
193C2×C31C2×#35611yescharacteristic
194C22×Q8C2×C4×C3111yescharacteristic
195C23×C4C2×C4×C3111yescharacteristic
196C23×C4D4×C3111yescharacteristic
197C23×C4D4×C3111yescharacteristic
198C2×M16—41no—
199C22×C8—41no—
200C22⋊Q8—41no—
201C22⋊Q8—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4C2×C4×C3111yescharacteristic
210C2×C4⋊C4C2×C4×C3111yescharacteristic
211C2×C4⋊C4D4×C3111yescharacteristic
212C2×C4⋊C4D4×C3111yescharacteristic
213C2×C4⋊C4C23×C3111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42C2×C4×C3111yescharacteristic
217C2×C42C2×C4×C3111yescharacteristic
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221C22⋊C8—41no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C31#1155511yescharacteristic, direct product factor, Sylow
228C24C22⋊C4×C3111yescharacteristic
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4C22⋊C4×C3111yescharacteristic
248C22×C4C22⋊C4×C3111yescharacteristic
249C22×C4C22×C4×C3111yescharacteristic
250C22×C4C2×D4×C3111yescharacteristic
251C22×C4C2×D4×C3111yescharacteristic
252M16—82no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—82no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C22⋊C4—24no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—22no—
270C42—41no—
271C23—21no—
272C23—21no—
273C23—22no—
274C23—41no—
275C23C31×#9911yescharacteristic
276C23C31×#9911yescharacteristic
277C23C2×C22⋊C4×C3111yescharacteristic
278Q8—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
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—81no—
309C2×C4—81no—
310C2×C4C31×#13112yes—
311C8—82no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22C31×#35612yes—
323C22C31×#40811yescharacteristic
324C22C2×C31×#9911yescharacteristic
325C22C31×#41311yescharacteristic
326C4—22no—
327C4—42no—
328C4—42no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2C31×#146811yescharacteristic
341C2C31×#212711yescharacteristic
342C2C2×C31×#35611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1325C2semidirect
5. C31×#1319C2semidirect
99. #11555C31direct (N × H)
145. #1325C2×C31semidirect
146. #1319C2×C31semidirect
227. C31#11555direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25022
C31×#14632
C2×C31×#3242
C31×#13252
C31×#13192
#1155531