Finite Group Databasebeta

← C31×#10084 #21466843

Subgroups — C31×#10084 #21466843

Order 7936.

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

normal subgroups only

This group has 484 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
1C2×C31×#501C211yesmaximal, characteristic
2C2×C31×#491C211yesmaximal, characteristic
3C31×#2822C211yesmaximal, characteristic
4C31×#1993C211yesmaximal, characteristic
5C2×C31×#330C211yesmaximal, characteristic
6C2×C31×#330C211yesmaximal, characteristic
7C31×#1295C211yesmaximal, characteristic
8C2×C31×C4⋊Q8C2211yescharacteristic
9C2×C31×#125C2211yescharacteristic
10C2×C31×#125C2211yescharacteristic
11C31×#501—22no—
12C31×#501—22no—
13C31×#491—22no—
14C31×#491—22no—
15C2×C31×#107—21no—
16C2×C31×#106—21no—
17C2×C31×#103—21no—
18C2×C31×#103—21no—
19C2×C31×#97C2211yescharacteristic
20C2×C31×#97C2211yescharacteristic
21C2×C31×#97C2211yescharacteristic
22C31×#400—21no—
23C31×#400—21no—
24C31×#398—22no—
25C31×#398—21no—
26C31×#398—21no—
27C31×#382C2211yescharacteristic
28C31×#340—22no—
29C31×#330—22no—
30C31×#330—22no—
31C22×Q8×C31—21no—
32C22×C8×C31—21no—
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8D412yes—
39C31×#125—21no—
40C31×#125—21no—
41C31×#125—21no—
42C31×#125—21no—
43C31×#125—21no—
44C31×#125—21no—
45C31×#125—21no—
46C31×#125—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C4⋊C4×C31D411yescharacteristic
58C2×C4⋊C4×C31D412yes—
59C2×C42×C31C2311yescharacteristic
60C31×#107—24no—
61C31×#106—24no—
62C31×#103—24no—
63C31×#103—24no—
64C31×#97—21no—
65C31×#97—21no—
66C31×#97—21no—
67C31×#97—21no—
68C31×#97D412yes—
69C31×#97D412yes—
70C31×#95—22no—
71C31×#95—22no—
72C31×#95—22no—
73C31×#95—21no—
74C31×#95—21no—
75C2×Q8×C31—22no—
76C2×Q8×C31—44no—
77C2×Q8×C31—41no—
78C22×C4×C31—22no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—41no—
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31C2×D411yescharacteristic
87C2×C8×C31—24no—
88C2×C8×C31—22no—
89C2×C8×C31—22no—
90C2×C8×C31—22no—
91C2×C8×C31—42no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C4⋊C4×C31—21no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—21no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—42no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—82no—
116C42×C31C2×D411yescharacteristic
117C42×C31C2×D411yescharacteristic
118C42×C31C2×D411yescharacteristic
119C42×C31#4111yescharacteristic
120#10084C3111yesmaximal, characteristic, direct product factor, Sylow
121C23×C31#12011yescharacteristic
122Q8×C31—44no—
123Q8×C31—82no—
124C2×C4×C31—22no—
125C2×C4×C31—21no—
126C2×C4×C31—22no—
127C2×C4×C31—21no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—82no—
143C2×C4×C31#12011yescharacteristic
144C2×C4×C31#12011yescharacteristic
145C2×C4×C31#12111yescharacteristic
146C2×C4×C31#12111yescharacteristic
147C2×C4×C31#12111yescharacteristic
148C2×C4×C31#12711yescharacteristic
149C8×C31—24no—
150C8×C31—42no—
151C8×C31—42no—
152C2×#501C2×C3111yescharacteristic
153C2×#491C2×C3111yescharacteristic
154#2822C2×C3111yescharacteristic
155#1993C2×C3111yescharacteristic
156C2×#330C2×C3111yescharacteristic
157C2×#330C2×C3111yescharacteristic
158#1295C2×C3111yescharacteristic
159C22×C31#39211yescharacteristic
160C22×C31#45412yes—
161C22×C31#45511yescharacteristic
162C22×C31#45611yescharacteristic
163C22×C31#45612yes—
164C4×C31—21no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—82no—
171C4×C31—81no—
172C4×C31—82no—
173C4×C31—81no—
174C4×C31—81no—
175C4×C31—81no—
176C2×C4⋊Q8C22×C3111yescharacteristic
177C2×#125C22×C3111yescharacteristic
178C2×#125C22×C3111yescharacteristic
179#501—22no—
180#501—22no—
181#491—22no—
182#491—22no—
183C2×#107—21no—
184C2×#106—21no—
185C2×#103—21no—
186C2×#103—21no—
187C2×#97C22×C3111yescharacteristic
188C2×#97C22×C3111yescharacteristic
189C2×#97C22×C3111yescharacteristic
190#400—21no—
191#400—21no—
192#398—22no—
193#398—21no—
194#398—21no—
195#382C22×C3111yescharacteristic
196#340—22no—
197#330—22no—
198#330—22no—
199C2×C31#166312yes—
200C2×C31#166412yes—
201C2×C31#200311yescharacteristic
202C2×C31#200511yescharacteristic
203C2×C31#200711yescharacteristic
204C22×Q8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C3112yes—
212#125—21no—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4D4×C3111yescharacteristic
228C2×C4⋊C4D4×C3111yescharacteristic
229C2×C4⋊C4D4×C3111yescharacteristic
230C2×C4⋊C4D4×C3111yescharacteristic
231C2×C4⋊C4D4×C3112yes—
232C2×C42C23×C3111yescharacteristic
233#107—24no—
234#106—24no—
235#103—24no—
236#103—24no—
237#97—21no—
238#97—21no—
239#97—21no—
240#97—21no—
241#97D4×C3112yes—
242#97D4×C3112yes—
243#95—22no—
244#95—22no—
245#95—22no—
246#95—21no—
247#95—21no—
248C31#1008411yescharacteristic, direct product factor, Sylow
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C2×D4×C3111yescharacteristic
259C22×C4C2×D4×C3111yescharacteristic
260C22×C4C2×D4×C3111yescharacteristic
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—82no—
290C42C2×D4×C3111yescharacteristic
291C42C2×D4×C3111yescharacteristic
292C42C2×D4×C3111yescharacteristic
293C42#41×C3111yescharacteristic
294C23C31×#12011yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—82no—
316C2×C4C31×#12011yescharacteristic
317C2×C4C31×#12011yescharacteristic
318C2×C4C31×#12111yescharacteristic
319C2×C4C31×#12111yescharacteristic
320C2×C4C31×#12111yescharacteristic
321C2×C4C31×#12711yescharacteristic
322C8—24no—
323C8—42no—
324C8—42no—
325C22C31×#39211yescharacteristic
326C22C31×#45412yes—
327C22C31×#45511yescharacteristic
328C22C31×#45611yescharacteristic
329C22C31×#45612yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—82no—
339C4—81no—
340C4—81no—
341C4—81no—
342C2C31×#166312yes—
343C2C31×#166412yes—
344C2C31×#200311yescharacteristic
345C2C31×#200511yescharacteristic
346C2C31×#200711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
120. #10084C31direct (N × H)
248. C31#10084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5012
C2×C31×#4912
C31×#28222
C31×#19932
C2×C31×#3302
C31×#12952
#1008431