Finite Group Databasebeta

← C31×#10381 #21467140

Subgroups — C31×#10381 #21467140

Order 7936.

352 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2606C211yesmaximal, characteristic
2C31×#1986C211yesmaximal, characteristic
3C31×#1515C211yesmaximal, characteristic
4C31×#1506C211yesmaximal, characteristic
5C31×#1300C211yesmaximal, characteristic
6C31×#1288C211yesmaximal, characteristic
7C31×#1285C211yesmaximal, characteristic
8C31×#533C2211yescharacteristic
9C31×#432C2211yescharacteristic
10C31×#432C2211yescharacteristic
11C4×M16×C31C2211yescharacteristic
12C31×#398—21no—
13C31×#398—21no—
14C31×#389—21no—
15C31×#389—21no—
16C31×#387—21no—
17C31×#387—21no—
18C31×#383C2211yescharacteristic
19C4×C4⋊C4×C31C2211yescharacteristic
20C31×#376C2211yescharacteristic
21C31×#339—21no—
22C31×#339—21no—
23C31×#328—21no—
24C31×#328—21no—
25C31×#328—21no—
26C31×#328—21no—
27C2×M16×C31—21no—
28C31×C4⋊Q8Q811yescharacteristic
29C31×C4⋊Q8Q811yescharacteristic
30C31×#125—21no—
31C31×C22⋊Q8—21no—
32C31×C22⋊Q8—21no—
33C4×Q8×C31—21no—
34C4×Q8×C31—21no—
35C31×#117—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C42×C31—21no—
44C2×C42×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31C2311yescharacteristic
47C31×C4⋊C8—21no—
48C31×C4⋊C8—21no—
49C31×C22⋊C8—21no—
50C31×C22⋊C8—21no—
51C31×#97—21no—
52C31×#97—21no—
53C31×#97—21no—
54C4×C8×C31—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95D411yescharacteristic
62C31×#95D411yescharacteristic
63C31×#95D411yescharacteristic
64C31×#95D411yescharacteristic
65C2×Q8×C31—21no—
66C2×Q8×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—21no—
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76M16×C31—22no—
77M16×C31—41no—
78C2×C8×C31—41no—
79C2×C8×C31—41no—
80C2×C8×C31—41no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—42no—
88C4⋊C4×C31—42no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—81no—
93C4⋊C4×C31—81no—
94C22⋊C4×C31—41no—
95C42×C31—42no—
96C42×C31—41no—
97C42×C31—41no—
98C42×C31—41no—
99C42×C31C2×Q811yescharacteristic
100C42×C31#4111yescharacteristic
101C42×C31#4111yescharacteristic
102C42×C31#4111yescharacteristic
103#10381C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31#12011yescharacteristic
105Q8×C31—81no—
106Q8×C31—81no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—22no—
110C2×C4×C31—22no—
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—41no—
121C2×C4×C31—41no—
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×C31C22⋊Q811yescharacteristic
132C2×C4×C31C22⋊Q811yescharacteristic
133C2×C4×C31C22⋊Q811yescharacteristic
134C2×C4×C31#12411yescharacteristic
135C2×C4×C31#12411yescharacteristic
136C2×C4×C31#12411yescharacteristic
137C8×C31—42no—
138C8×C31—81no—
139C8×C31—81no—
140#2606C2×C3111yescharacteristic
141#1986C2×C3111yescharacteristic
142#1515C2×C3111yescharacteristic
143#1506C2×C3111yescharacteristic
144#1300C2×C3111yescharacteristic
145#1288C2×C3111yescharacteristic
146#1285C2×C3111yescharacteristic
147C22×C31—21no—
148C22×C31—21no—
149C22×C31#39311yescharacteristic
150C22×C31#45511yescharacteristic
151C22×C31#45611yescharacteristic
152C4×C31—21no—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—42no—
159C4×C31—42no—
160C4×C31—81no—
161C4×C31—81no—
162C4×C31—81no—
163C4×C31—81no—
164C4×C31—81no—
165C4×C31—81no—
166#533C22×C3111yescharacteristic
167#432C22×C3111yescharacteristic
168#432C22×C3111yescharacteristic
169C4×M16C22×C3111yescharacteristic
170#398—21no—
171#398—21no—
172#389—21no—
173#389—21no—
174#387—21no—
175#387—21no—
176#383C22×C3111yescharacteristic
177C4×C4⋊C4C22×C3111yescharacteristic
178#376C22×C3111yescharacteristic
179#339—21no—
180#339—21no—
181#328—21no—
182#328—21no—
183#328—21no—
184#328—21no—
185C2×C31—21no—
186C2×C31—21no—
187C2×C31#202811yescharacteristic
188C2×C31#203111yescharacteristic
189C2×C31#203111yescharacteristic
190C2×M16—21no—
191C4⋊Q8Q8×C3111yescharacteristic
192C4⋊Q8Q8×C3111yescharacteristic
193#125—21no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C4×Q8—21no—
197C4×Q8—21no—
198#117—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C42—21no—
207C2×C42D4×C3111yescharacteristic
208C2×C42D4×C3111yescharacteristic
209C2×C42C23×C3111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214#97—21no—
215#97—21no—
216#97—21no—
217C4×C8—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95D4×C3111yescharacteristic
225#95D4×C3111yescharacteristic
226#95D4×C3111yescharacteristic
227#95D4×C3111yescharacteristic
228C31#1038111yescharacteristic, direct product factor, Sylow
229C2×Q8—21no—
230C2×Q8—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4C2×D4×C3111yescharacteristic
238C22×C4C2×D4×C3111yescharacteristic
239C22×C4C2×D4×C3111yescharacteristic
240M16—22no—
241M16—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C22⋊C4—41no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—41no—
263C42C2×Q8×C3111yescharacteristic
264C42#41×C3111yescharacteristic
265C42#41×C3111yescharacteristic
266C42#41×C3111yescharacteristic
267C23C31×#12011yescharacteristic
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C31×C22⋊Q811yescharacteristic
295C2×C4C31×C22⋊Q811yescharacteristic
296C2×C4C31×C22⋊Q811yescharacteristic
297C2×C4C31×#12411yescharacteristic
298C2×C4C31×#12411yescharacteristic
299C2×C4C31×#12411yescharacteristic
300C8—42no—
301C8—81no—
302C8—81no—
303C22—21no—
304C22—21no—
305C22C31×#39311yescharacteristic
306C22C31×#45511yescharacteristic
307C22C31×#45611yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2C31×#202811yescharacteristic
325C2C31×#203111yescharacteristic
326C2C31×#203111yescharacteristic
subgroupG/H
center, socleC22×C31#393
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
103. #10381C31direct (N × H)
228. C31#10381direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26062
C31×#19862
C31×#15152
C31×#15062
C31×#13002
C31×#12882
C31×#12852
#1038131