Finite Group Databasebeta

← C31×#13612 #21470371

Subgroups — C31×#13612 #21470371

Order 7936.

304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3223C211yesmaximal, characteristic
2C31×#2135C211yesmaximal, characteristic
3C31×#2133C211yesmaximal, characteristic
4C31×#1413C212yesmaximal, complemented
5C31×#1411C212yesmaximal, complemented
6C31×#541C411yescharacteristic
7C31×#536C2211yescharacteristic
8C31×#497C411yescharacteristic
9C31×#494C2211yescharacteristic
10C31×#491C2211yescharacteristic
11C31×#488C411yescharacteristic
12C31×#464—21no—
13C31×#462—21no—
14C31×#452—21no—
15C31×#451—21no—
16C31×#433C411yescharacteristic
17C31×#413—21no—
18C2×C31×#101—21no—
19C31×#356—21no—
20C31×#356C2212yes—
21C31×#356C2212yes—
22C31×#355—21no—
23C2×#41×C31D411yescharacteristic
24C22×Q8×C31D411yescharacteristic
25C2×Q16×C31—21no—
26C2×Q16×C31—21no—
27C2×Q16×C31—21no—
28C2×SD16×C31—21no—
29C2×M16×C31—41no—
30C2×M16×C31—41no—
31C31×C4⋊Q8C2×C411yescharacteristic
32C31×C4⋊Q8D411yescharacteristic
33C31×C4⋊Q8C2311yescharacteristic
34C31×#126—41no—
35C31×#125—41no—
36C31×#125C2×C411yescharacteristic
37C31×#124C2×C411yescharacteristic
38C31×#124D411yescharacteristic
39C31×#123—41no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—41no—
42C4×Q8×C31—21no—
43C31×#117C2×C411yescharacteristic
44C31×C4⋊C8—21no—
45C31×#103—21no—
46C31×#103—21no—
47C31×#103—21no—
48C31×#102—21no—
49C31×#101—22no—
50C31×#101—22no—
51C31×#101—41no—
52C31×#100—41no—
53C31×C22⋊C8—21no—
54C31×#97C2×C411yescharacteristic
55C4×C8×C31C2×C411yescharacteristic
56#41×C31—81no—
57C2×Q8×C31—21no—
58C2×Q8×C31—21no—
59C2×Q8×C31—81no—
60C2×Q8×C31C22⋊C411yescharacteristic
61C2×Q8×C31C2×D411yescharacteristic
62C2×Q8×C31C2×D411yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31C22⋊C411yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31C22⋊C411yescharacteristic
68Q16×C31—81no—
69Q16×C31—81no—
70Q16×C31—81no—
71SD16×C31—81no—
72M16×C31—42no—
73M16×C31—42no—
74M16×C31—81no—
75M16×C31—81no—
76C2×C8×C31—21no—
77C2×C8×C31—21no—
78C2×C8×C31—81no—
79C2×C8×C31—81no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C22⋊C4×C31—21no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C42×C31—41no—
93C42×C31C22⋊C411yescharacteristic
94C42×C31C22×C411yescharacteristic
95#13612C3111yesmaximal, characteristic, direct product factor, Sylow
96C23×C31—21no—
97C23×C31#9911yescharacteristic
98Q8×C31—41no—
99Q8×C31—41no—
100Q8×C31—41no—
101Q8×C31—41no—
102Q8×C31—41no—
103Q8×C31—81no—
104D4×C31—41no—
105D4×C31—81no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
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#9911yescharacteristic
119C2×C4×C31C2×C22⋊C411yescharacteristic
120C8×C31—41no—
121C8×C31—41no—
122C8×C31—82no—
123C8×C31—82no—
124#3223C2×C3111yescharacteristic
125#2135C2×C3111yescharacteristic
126#2133C2×C3111yescharacteristic
127#1413C2×C3112yescomplemented
128#1411C2×C3112yescomplemented
129C22×C31—21no—
130C22×C31—41no—
131C22×C31—41no—
132C22×C31—81no—
133C22×C31C2×#9911yescharacteristic
134C4×C31—21no—
135C4×C31—21no—
136C4×C31—41no—
137C4×C31—41no—
138C4×C31—41no—
139C4×C31—41no—
140C4×C31—41no—
141C4×C31—81no—
142C4×C31—81no—
143#541C4×C3111yescharacteristic
144#536C22×C3111yescharacteristic
145#497C4×C3111yescharacteristic
146#494C22×C3111yescharacteristic
147#491C22×C3111yescharacteristic
148#488C4×C3111yescharacteristic
149#464—21no—
150#462—21no—
151#452—21no—
152#451—21no—
153#433C4×C3111yescharacteristic
154#413—21no—
155C2×#101—21no—
156#356—21no—
157#356C22×C3112yes—
158#356C22×C3112yes—
159#355—21no—
160C2×C31—21no—
161C2×C31—41no—
162C2×C31—81no—
163C2×C31#212711yescharacteristic
164C2×#41D4×C3111yescharacteristic
165C22×Q8D4×C3111yescharacteristic
166C2×Q16—21no—
167C2×Q16—21no—
168C2×Q16—21no—
169C2×SD16—21no—
170C2×M16—41no—
171C2×M16—41no—
172C4⋊Q8C2×C4×C3111yescharacteristic
173C4⋊Q8D4×C3111yescharacteristic
174C4⋊Q8C23×C3111yescharacteristic
175#126—41no—
176#125—41no—
177#125C2×C4×C3111yescharacteristic
178#124C2×C4×C3111yescharacteristic
179#124D4×C3111yescharacteristic
180#123—41no—
181C22⋊Q8—21no—
182C22⋊Q8—41no—
183C4×Q8—21no—
184#117C2×C4×C3111yescharacteristic
185C4⋊C8—21no—
186#103—21no—
187#103—21no—
188#103—21no—
189#102—21no—
190#101—22no—
191#101—22no—
192#101—41no—
193#100—41no—
194C22⋊C8—21no—
195#97C2×C4×C3111yescharacteristic
196C4×C8C2×C4×C3111yescharacteristic
197C31#1361211yescharacteristic, direct product factor, Sylow
198#41—81no—
199C2×Q8—21no—
200C2×Q8—21no—
201C2×Q8—81no—
202C2×Q8C22⋊C4×C3111yescharacteristic
203C2×Q8C2×D4×C3111yescharacteristic
204C2×Q8C2×D4×C3111yescharacteristic
205C2×D4—21no—
206C2×D4C22⋊C4×C3111yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C22⋊C4×C3111yescharacteristic
210Q16—81no—
211Q16—81no—
212Q16—81no—
213SD16—81no—
214M16—42no—
215M16—42no—
216M16—81no—
217M16—81no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—81no—
221C2×C8—81no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—41no—
235C42C22⋊C4×C3111yescharacteristic
236C42C22×C4×C3111yescharacteristic
237C23—21no—
238C23C31×#9911yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—81no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4C31×#9911yescharacteristic
260C2×C4C2×C22⋊C4×C3111yescharacteristic
261C8—41no—
262C8—41no—
263C8—82no—
264C8—82no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×C31×#9911yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2C31×#212711yescharacteristic
subgroupG/H
center, socleC2×C31#2127
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×C31
prime radicalC2×#41×C31D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C31 ◁ C22×C4×C31 ◁ C31×#536 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1413C2semidirect
5. C31×#1411C2semidirect
95. #13612C31direct (N × H)
127. #1413C2×C31semidirect
128. #1411C2×C31semidirect
197. C31#13612direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32232
C31×#21352
C31×#21332
C31×#14132
C31×#14112
#1361231