Finite Group Databasebeta

← C31×#11905 #21468664

Subgroups — C31×#11905 #21468664

Order 7936.

372 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2581C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C31×#1461C211yesmaximal, characteristic
4C31×#1354C212yesmaximal
5C31×#1353C212yesmaximal
6C2×C4×Q8×C31C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#431—21no—
9C31×#423—21no—
10C2×C31×#101—21no—
11C31×#400C411yescharacteristic
12C31×#400C2211yescharacteristic
13C31×#395C411yescharacteristic
14C31×#395C2211yescharacteristic
15C31×#391—21no—
16C31×#389—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#382C411yescharacteristic
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×Q8×C31D411yescharacteristic
25C2×M16×C31—22no—
26C4×Q8×C31—41no—
27C4×Q8×C31—41no—
28C4×Q8×C31—41no—
29C4×Q8×C31—41no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C4⋊C4×C31C2311yescharacteristic
38C2×C42×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C31×C4⋊C8—41no—
43C31×C4⋊C8—41no—
44C31×C4⋊C8—41no—
45C31×#101—42no—
46C31×C22⋊C8—22no—
47C4×C8×C31—41no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C2×Q8×C31—41no—
58C2×Q8×C31—41no—
59C2×Q8×C31—42no—
60C2×Q8×C31—41no—
61C2×Q8×C31SD1612yes—
62C2×Q8×C31Q1612yes—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74M16×C31—42no—
75M16×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C4⋊C4×C31—41no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C42×C31—21no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31—42no—
94#11905C3111yesmaximal, characteristic, direct product factor, Sylow
95C23×C31C2×C22⋊C411yescharacteristic
96Q8×C31—42no—
97Q8×C31—42no—
98Q8×C31—42no—
99Q8×C31—42no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—42no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31#9911yescharacteristic
125C2×C4×C31#9911yescharacteristic
126C2×C4×C31#10312yes—
127C2×C4×C31#10312yes—
128C2×C4×C31C2×SD1611yescharacteristic
129C2×C4×C31C2×Q1611yescharacteristic
130C8×C31—82no—
131C8×C31—82no—
132#2581C2×C3111yescharacteristic
133#1801C2×C3111yescharacteristic
134#1461C2×C3111yescharacteristic
135#1354C2×C3112yes—
136#1353C2×C3112yes—
137C22×C31—21no—
138C22×C31—21no—
139C22×C31C2×#9911yescharacteristic
140C22×C31C2×#10311yescharacteristic
141C22×C31#42111yescharacteristic
142C4×C31—21no—
143C4×C31—21no—
144C4×C31—21no—
145C4×C31—22no—
146C4×C31—22no—
147C4×C31—21no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—42no—
151C4×C31—41no—
152C4×C31—81no—
153C4×C31—81no—
154C4×C31—81no—
155C2×C4×Q8C4×C3111yescharacteristic
156C2×C4×Q8C22×C3111yescharacteristic
157#431—21no—
158#423—21no—
159C2×#101—21no—
160#400C4×C3111yescharacteristic
161#400C22×C3111yescharacteristic
162#395C4×C3111yescharacteristic
163#395C22×C3111yescharacteristic
164#391—21no—
165#389—21no—
166#387—21no—
167#387—21no—
168#382C4×C3111yescharacteristic
169#343C22×C3112yes—
170#324—21no—
171#324C22×C3112yes—
172C2×C31—21no—
173C2×C31—21no—
174C2×C31#152011yescharacteristic
175C2×C31#212011yescharacteristic
176C2×C31#213311yescharacteristic
177C22×Q8C2×C4×C3111yescharacteristic
178C22×Q8D4×C3111yescharacteristic
179C2×M16—22no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×C4×C3111yescharacteristic
189C2×C4⋊C4C2×C4×C3111yescharacteristic
190C2×C4⋊C4D4×C3111yescharacteristic
191C2×C4⋊C4C23×C3111yescharacteristic
192C2×C42—21no—
193C2×C42C2×C4×C3111yescharacteristic
194C2×C42D4×C3111yescharacteristic
195C2×C42D4×C3111yescharacteristic
196C4⋊C8—41no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199#101—42no—
200C22⋊C8—22no—
201C4×C8—41no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×C4×C3111yescharacteristic
210#95C2×C4×C3111yescharacteristic
211C31#1190511yescharacteristic, direct product factor, Sylow
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C2×Q8SD16×C3112yes—
217C2×Q8Q16×C3112yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22×C4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C22×C4C2×D4×C3111yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—42no—
249C23C2×C22⋊C4×C3111yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4C31×#9911yescharacteristic
279C2×C4C31×#9911yescharacteristic
280C2×C4C31×#10312yes—
281C2×C4C31×#10312yes—
282C2×C4C2×SD16×C3111yescharacteristic
283C2×C4C2×Q16×C3111yescharacteristic
284C8—82no—
285C8—82no—
286C22—21no—
287C22—21no—
288C22C2×C31×#9911yescharacteristic
289C22C2×C31×#10311yescharacteristic
290C22C31×#42111yescharacteristic
291C4—21no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2C31×#152011yescharacteristic
307C2C31×#212011yescharacteristic
308C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
94. #11905C31direct (N × H)
211. C31#11905direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25812
C31×#18012
C31×#14612
C31×#13542
C31×#13532
#1190531