Finite Group Databasebeta

← C31×#7803 #21464562

Subgroups — C31×#7803 #21464562

Order 7936.

338 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2810C211yesmaximal, characteristic
2C31×#2099C211yesmaximal, characteristic
3C31×#2084C211yesmaximal, characteristic
4C31×#2083C211yesmaximal, characteristic
5C31×#1271C211yesmaximal, characteristic
6C31×#1271C211yesmaximal, characteristic
7C31×#1271C211yesmaximal, characteristic
8C2×C31×#107—21no—
9C2×C31×#106—21no—
10C31×#400—21no—
11C31×#400—21no—
12C31×#400—21no—
13C31×#389C2211yescharacteristic
14C31×#389C2211yescharacteristic
15C31×#389C2211yescharacteristic
16C31×#387—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#384C2211yescharacteristic
20C31×#340—21no—
21C31×#340—21no—
22C31×#340—21no—
23C31×#340—21no—
24C31×#336C2211yescharacteristic
25C31×#336C2211yescharacteristic
26C31×#336C2211yescharacteristic
27C22×C8×C31—21no—
28C22×C8×C31—21no—
29C22×C8×C31—21no—
30C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C42×C31—21no—
43C2×C42×C31C2311yescharacteristic
44C31×#107—42no—
45C31×#106—42no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—41no—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66C2×C8×C31—22no—
67C2×C8×C31—22no—
68C2×C8×C31—41no—
69C2×C8×C31—41no—
70C2×C8×C31—41no—
71C2×C8×C31—41no—
72C2×C8×C31—41no—
73C2×C8×C31—41no—
74C2×C8×C31—41no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—41no—
95C42×C31—41no—
96C42×C31—81no—
97#7803C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31#12011yescharacteristic
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—41no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
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—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—81no—
124C2×C4×C31—81no—
125C2×C4×C31—81no—
126C2×C4×C31#13511yescharacteristic
127C2×C4×C31#13511yescharacteristic
128C2×C4×C31#13511yescharacteristic
129C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C31#13711yescharacteristic
132C8×C31—42no—
133C8×C31—42no—
134C8×C31—81no—
135#2810C2×C3111yescharacteristic
136#2099C2×C3111yescharacteristic
137#2084C2×C3111yescharacteristic
138#2083C2×C3111yescharacteristic
139#1271C2×C3111yescharacteristic
140#1271C2×C3111yescharacteristic
141#1271C2×C3111yescharacteristic
142C22×C31#44911yescharacteristic
143C22×C31#44911yescharacteristic
144C22×C31#45211yescharacteristic
145C22×C31#45411yescharacteristic
146C22×C31#45611yescharacteristic
147C22×C31#45611yescharacteristic
148C22×C31#45811yescharacteristic
149C4×C31—21no—
150C4×C31—21no—
151C4×C31—21no—
152C4×C31—21no—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—81no—
156C4×C31—81no—
157C4×C31—81no—
158C4×C31—81no—
159C4×C31—81no—
160C4×C31—81no—
161C4×C31—161no—
162C2×#107—21no—
163C2×#106—21no—
164#400—21no—
165#400—21no—
166#400—21no—
167#389C22×C3111yescharacteristic
168#389C22×C3111yescharacteristic
169#389C22×C3111yescharacteristic
170#387—21no—
171#387—21no—
172#387—21no—
173#384C22×C3111yescharacteristic
174#340—21no—
175#340—21no—
176#340—21no—
177#340—21no—
178#336C22×C3111yescharacteristic
179#336C22×C3111yescharacteristic
180#336C22×C3111yescharacteristic
181C2×C31#160911yescharacteristic
182C2×C31#160911yescharacteristic
183C2×C31#161511yescharacteristic
184C2×C31#162811yescharacteristic
185C2×C31#165011yescharacteristic
186C2×C31#165211yescharacteristic
187C2×C31#166311yescharacteristic
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4D4×C3111yescharacteristic
198C2×C4⋊C4D4×C3111yescharacteristic
199C2×C4⋊C4D4×C3111yescharacteristic
200C2×C4⋊C4D4×C3111yescharacteristic
201C2×C4⋊C4D4×C3111yescharacteristic
202C2×C4⋊C4D4×C3111yescharacteristic
203C2×C42—21no—
204C2×C42C23×C3111yescharacteristic
205#107—42no—
206#106—42no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C31#780311yescharacteristic, direct product factor, Sylow
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4C2×D4×C3111yescharacteristic
226C22×C4C2×D4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C42—41no—
258C42—81no—
259C23C31×#12011yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
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—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—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C31×#13511yescharacteristic
288C2×C4C31×#13511yescharacteristic
289C2×C4C31×#13511yescharacteristic
290C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
291C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
292C2×C4C31×#13711yescharacteristic
293C8—42no—
294C8—42no—
295C8—81no—
296C22C31×#44911yescharacteristic
297C22C31×#44911yescharacteristic
298C22C31×#45211yescharacteristic
299C22C31×#45411yescharacteristic
300C22C31×#45611yescharacteristic
301C22C31×#45611yescharacteristic
302C22C31×#45811yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—161no—
316C2C31×#160911yescharacteristic
317C2C31×#160911yescharacteristic
318C2C31×#161511yescharacteristic
319C2C31×#162811yescharacteristic
320C2C31×#165011yescharacteristic
321C2C31×#165211yescharacteristic
322C2C31×#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
97. #7803C31direct (N × H)
217. C31#7803direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28102
C31×#20992
C31×#20842
C31×#20832
C31×#12712
#780331