Finite Group Databasebeta

← C31×#9435 #21466194

Subgroups — C31×#9435 #21466194

Order 7936.

504 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3152C211yesmaximal, characteristic
2C31×#2979C211yesmaximal, characteristic
3C31×#1560C211yesmaximal, characteristic
4C31×#1549C212yesmaximal, complemented
5C31×#1299C212yesmaximal, complemented
6C2×C31×#137—22no—
7C31×#532C2211yescharacteristic
8C2×C31×C4⋊Q8C2211yescharacteristic
9C31×#497C414yes—
10C31×#494—21no—
11C31×#492—21no—
12C31×#436—22no—
13C8×D4×C31—22no—
14C31×#431C2212yes—
15C31×#423C2212yes—
16C31×#408—22no—
17C4×M16×C31C2211yescharacteristic
18C31×#333—21no—
19C31×#332—22no—
20C31×#332—22no—
21C31×#331—21no—
22C2×#41×C31D412yes—
23C22×Q8×C31—21no—
24C31×#137—44no—
25C31×#137—44no—
26C2×Q16×C31—24no—
27C2×SD16×C31—24no—
28C2×M16×C31—21no—
29C2×M16×C31—22no—
30C2×M16×C31—22no—
31C22×C8×C31—22no—
32C31×C4⋊Q8—22no—
33C31×C4⋊Q8—21no—
34C31×C4⋊Q8C2×C412yes—
35C31×C4⋊Q8D411yescharacteristic
36C31×#127D411yescharacteristic
37C31×#124C2×C412yes—
38C31×#121—22no—
39C4×D4×C31—22no—
40C2×C4⋊C4×C31—22no—
41C2×C42×C31C2311yescharacteristic
42C31×C4⋊C8—22no—
43C31×C4⋊C8—22no—
44C31×C4⋊C8D412yes—
45C31×C4⋊C8D412yes—
46C31×C22⋊C8—24no—
47C31×C22⋊C8—22no—
48C31×#97C2×C412yes—
49C4×C8×C31—21no—
50C4×C8×C31—22no—
51#41×C31—42no—
52#41×C31—42no—
53C2×Q8×C31—22no—
54C2×Q8×C31—42no—
55C2×Q8×C31—42no—
56C2×Q8×C31—41no—
57C2×Q8×C31C22⋊C412yes—
58C2×D4×C31—22no—
59C2×D4×C31—22no—
60C2×D4×C31C22⋊C412yes—
61C22×C4×C31—22no—
62C22×C4×C31—41no—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31#4112yes—
65Q16×C31—48no—
66SD16×C31—48no—
67M16×C31—22no—
68M16×C31—22no—
69M16×C31—82no—
70M16×C31—82no—
71C2×C8×C31—22no—
72C2×C8×C31—22no—
73C2×C8×C31—22no—
74C2×C8×C31—42no—
75C2×C8×C31—82no—
76C4⋊C4×C31—22no—
77C4⋊C4×C31—24no—
78C4⋊C4×C31—42no—
79C22⋊C4×C31—24no—
80C42×C31C22×C411yescharacteristic
81C42×C31C2×D411yescharacteristic
82C42×C31C2×D412yes—
83#9435C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—22no—
85C23×C31#12311yescharacteristic
86Q8×C31—42no—
87Q8×C31—44no—
88Q8×C31—81no—
89Q8×C31—81no—
90D4×C31—42no—
91D4×C31—42no—
92D4×C31—42no—
93D4×C31—82no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—22no—
97C2×C4×C31—22no—
98C2×C4×C31—22no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—82no—
103C2×C4×C31C2×C22⋊C411yescharacteristic
104C2×C4×C31C4×D412yes—
105C2×C4×C31#12011yescharacteristic
106C2×C4×C31#12112yes—
107C8×C31—24no—
108C8×C31—42no—
109C8×C31—42no—
110C8×C31—82no—
111#3152C2×C3111yescharacteristic
112#2979C2×C3111yescharacteristic
113#1560C2×C3111yescharacteristic
114#1549C2×C3112yescomplemented
115#1299C2×C3112yescomplemented
116C22×C31—21no—
117C22×C31—22no—
118C22×C31—42no—
119C22×C31—44no—
120C22×C31#38611yescharacteristic
121C4×C31—21no—
122C4×C31—22no—
123C4×C31—42no—
124C4×C31—82no—
125C4×C31#45311yescharacteristic
126C4×C31#45311yescharacteristic
127C4×C31#47112yes—
128C4×C31#47312yes—
129C2×#137—22no—
130#532C22×C3111yescharacteristic
131C2×C4⋊Q8C22×C3111yescharacteristic
132#497C4×C3114yes—
133#494—21no—
134#492—21no—
135#436—22no—
136C8×D4—22no—
137#431C22×C3112yes—
138#423C22×C3112yes—
139#408—22no—
140C4×M16C22×C3111yescharacteristic
141#333—21no—
142#332—22no—
143#332—22no—
144#331—21no—
145C2×C31—41no—
146C2×C31—82no—
147C2×C31#188711yescharacteristic
148C2×C31#190812yes—
149C2×#41D4×C3112yes—
150C22×Q8—21no—
151#137—44no—
152#137—44no—
153C2×Q16—24no—
154C2×SD16—24no—
155C2×M16—21no—
156C2×M16—22no—
157C2×M16—22no—
158C22×C8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—21no—
161C4⋊Q8C2×C4×C3112yes—
162C4⋊Q8D4×C3111yescharacteristic
163#127D4×C3111yescharacteristic
164#124C2×C4×C3112yes—
165#121—22no—
166C4×D4—22no—
167C2×C4⋊C4—22no—
168C2×C42C23×C3111yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8D4×C3112yes—
172C4⋊C8D4×C3112yes—
173C22⋊C8—24no—
174C22⋊C8—22no—
175#97C2×C4×C3112yes—
176C4×C8—21no—
177C4×C8—22no—
178C31#943511yescharacteristic, direct product factor, Sylow
179#41—42no—
180#41—42no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—41no—
185C2×Q8C22⋊C4×C3112yes—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4C22⋊C4×C3112yes—
189C22×C4—22no—
190C22×C4—41no—
191C22×C4C2×D4×C3111yescharacteristic
192C22×C4#41×C3112yes—
193Q16—48no—
194SD16—48no—
195M16—22no—
196M16—22no—
197M16—82no—
198M16—82no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—42no—
203C2×C8—82no—
204C4⋊C4—22no—
205C4⋊C4—24no—
206C4⋊C4—42no—
207C22⋊C4—24no—
208C42C22×C4×C3111yescharacteristic
209C42C2×D4×C3111yescharacteristic
210C42C2×D4×C3112yes—
211C23—22no—
212C23C31×#12311yescharacteristic
213Q8—42no—
214Q8—44no—
215Q8—81no—
216Q8—81no—
217D4—42no—
218D4—42no—
219D4—42no—
220D4—82no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4C2×C22⋊C4×C3111yescharacteristic
231C2×C4C4×D4×C3112yes—
232C2×C4C31×#12011yescharacteristic
233C2×C4C31×#12112yes—
234C8—24no—
235C8—42no—
236C8—42no—
237C8—82no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—44no—
242C22C31×#38611yescharacteristic
243C4—21no—
244C4—22no—
245C4—42no—
246C4—82no—
247C4C31×#45311yescharacteristic
248C4C31×#45311yescharacteristic
249C4C31×#47112yes—
250C4C31×#47312yes—
251C2—41no—
252C2—82no—
253C2C31×#188711yescharacteristic
254C2C31×#190812yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1549C2semidirect
5. C31×#1299C2semidirect
83. #9435C31direct (N × H)
114. #1549C2×C31semidirect
115. #1299C2×C31semidirect
178. C31#9435direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31522
C31×#29792
C31×#15602
C31×#15492
C31×#12992
#943531