Finite Group Databasebeta

← C31×#7833 #21464592

Subgroups — C31×#7833 #21464592

Order 7936.

438 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C31×#2095C212yesmaximal, complemented
3C31×#2094C211yesmaximal, characteristic
4C31×#1272C212yesmaximal, complemented
5C31×#1270C211yesmaximal, characteristic
6C2×C31×#107—22no—
7C2×C31×#106—21no—
8C2×C31×#103—22no—
9C2×C31×#102—21no—
10C31×#400—21no—
11C31×#393—22no—
12C31×#391C2212yes—
13C31×#390C2211yescharacteristic
14C31×#386—21no—
15C31×#385—22no—
16C31×#384C2211yescharacteristic
17C31×#336C2211yescharacteristic
18C31×#336C2212yes—
19C22×Q8×C31D412yes—
20C22×D4×C31D411yescharacteristic
21C23×C4×C31—21no—
22C22×C8×C31—21no—
23C22×C8×C31—22no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31D411yescharacteristic
28C2×C4⋊C4×C31D412yes—
29C2×C22⋊C4×C31—22no—
30C2×C22⋊C4×C31—22no—
31C2×C22⋊C4×C31—21no—
32C2×C42×C31C2311yescharacteristic
33C31×#107—44no—
34C31×#106—42no—
35C31×#103—44no—
36C31×#102—42no—
37C31×#95—22no—
38C31×#95—21no—
39C31×#95—22no—
40C31×#95—22no—
41C24×C31—21no—
42C2×Q8×C31—22no—
43C2×Q8×C31—22no—
44C2×Q8×C31—42no—
45C2×Q8×C31—42no—
46C2×D4×C31—21no—
47C2×D4×C31—41no—
48C2×D4×C31—41no—
49C2×D4×C31Q1612yes—
50C22×C4×C31—22no—
51C22×C4×C31—21no—
52C22×C4×C31—22no—
53C22×C4×C31—41no—
54C22×C4×C31—82no—
55C22×C4×C31—81no—
56C22×C4×C31C2×D411yescharacteristic
57C22×C4×C31C2×D412yes—
58C2×C8×C31—22no—
59C2×C8×C31—24no—
60C2×C8×C31—41no—
61C2×C8×C31—42no—
62C2×C8×C31—42no—
63C2×C8×C31—41no—
64C4⋊C4×C31—41no—
65C4⋊C4×C31—42no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—81no—
71C22⋊C4×C31—42no—
72C22⋊C4×C31—42no—
73C22⋊C4×C31—82no—
74C22⋊C4×C31—81no—
75C42×C31—41no—
76#7833C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31—22no—
78C23×C31—42no—
79C23×C31—42no—
80C23×C31—41no—
81C23×C31—41no—
82C23×C31#12011yescharacteristic
83Q8×C31—44no—
84Q8×C31—82no—
85D4×C31—42no—
86D4×C31—81no—
87C2×C4×C31—21no—
88C2×C4×C31—22no—
89C2×C4×C31—21no—
90C2×C4×C31—22no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—41no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—84no—
100C2×C4×C31—81no—
101C2×C4×C31—82no—
102C2×C4×C31C2×Q1611yescharacteristic
103C2×C4×C31#13512yes—
104C2×C4×C31#13711yescharacteristic
105C2×C4×C31#13712yes—
106C8×C31—42no—
107C8×C31—44no—
108#2804C2×C3111yescharacteristic
109#2095C2×C3112yescomplemented
110#2094C2×C3111yescharacteristic
111#1272C2×C3112yescomplemented
112#1270C2×C3111yescharacteristic
113C22×C31—42no—
114C22×C31—44no—
115C22×C31—82no—
116C22×C31—81no—
117C22×C31—81no—
118C22×C31#45111yescharacteristic
119C22×C31#45212yes—
120C22×C31#45311yescharacteristic
121C22×C31#45312yes—
122C22×C31#45811yescharacteristic
123C4×C31—21no—
124C4×C31—21no—
125C4×C31—22no—
126C4×C31—22no—
127C4×C31—82no—
128C4×C31—81no—
129C4×C31—82no—
130C4×C31—161no—
131C2×#107—22no—
132C2×#106—21no—
133C2×#103—22no—
134C2×#102—21no—
135#400—21no—
136#393—22no—
137#391C22×C3112yes—
138#390C22×C3111yescharacteristic
139#386—21no—
140#385—22no—
141#384C22×C3111yescharacteristic
142#336C22×C3111yescharacteristic
143#336C22×C3112yes—
144C2×C31—82no—
145C2×C31#161411yescharacteristic
146C2×C31#161812yes—
147C2×C31#163011yescharacteristic
148C2×C31#163212yes—
149C2×C31#165511yescharacteristic
150C22×Q8D4×C3112yes—
151C22×D4D4×C3111yescharacteristic
152C23×C4—21no—
153C22×C8—21no—
154C22×C8—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4D4×C3112yes—
159C2×C4⋊C4D4×C3111yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C42C23×C3111yescharacteristic
164#107—44no—
165#106—42no—
166#103—44no—
167#102—42no—
168#95—22no—
169#95—21no—
170#95—22no—
171#95—22no—
172C31#783311yescharacteristic, direct product factor, Sylow
173C24—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4Q16×C3112yes—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4—82no—
187C22×C4—81no—
188C22×C4C2×D4×C3111yescharacteristic
189C22×C4C2×D4×C3112yes—
190C2×C8—22no—
191C2×C8—24no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—81no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—82no—
206C22⋊C4—81no—
207C42—41no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23C31×#12011yescharacteristic
214Q8—44no—
215Q8—82no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4C2×Q16×C3111yescharacteristic
234C2×C4C31×#13512yes—
235C2×C4C31×#13711yescharacteristic
236C2×C4C31×#13712yes—
237C8—42no—
238C8—44no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C31×#45111yescharacteristic
245C22C31×#45212yes—
246C22C31×#45311yescharacteristic
247C22C31×#45312yes—
248C22C31×#45811yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C31×#161411yescharacteristic
259C2C31×#161812yes—
260C2C31×#163011yescharacteristic
261C2C31×#163212yes—
262C2C31×#165511yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
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
2. C31×#2095C2semidirect
4. C31×#1272C2semidirect
76. #7833C31direct (N × H)
109. #2095C2×C31semidirect
111. #1272C2×C31semidirect
172. C31#7833direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28042
C31×#20952
C31×#20942
C31×#12722
C31×#12702
#783331