Finite Group Databasebeta

← C31×#17394 #21474153

Subgroups — C31×#17394 #21474153

Order 7936.

970 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#125C211yesmaximal, characteristic
2C31×#2920C212yesmaximal
3C31×#1470C218yesmaximal, complemented
4C31×#1463C214yesmaximal
5C2×C31×#125—22no—
6C2×C31×#125—22no—
7C2×C31×#125—22no—
8C2×C31×#125—22no—
9C2×C31×#125C414yes—
10C2×C31×#125C2214yes—
11C22×C4⋊C4×C31C411yescharacteristic
12C22×C4⋊C4×C31C411yescharacteristic
13C22×C4⋊C4×C31C412yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C42×C31C2211yescharacteristic
16C31×#432—22no—
17C31×#432C2214yes—
18C31×#431—22no—
19C31×#431C2214yes—
20C31×#423—22no—
21C31×#407C2214yes—
22C4×M16×C31—22no—
23C31×#324C22116yes—
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C412yes—
26C23×C4×C31C2×C412yes—
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31C2311yescharacteristic
29C2×M16×C31—24no—
30C31×#125—24no—
31C31×#125—24no—
32C31×#125—24no—
33C31×#125—24no—
34C31×#125—24no—
35C31×#125—24no—
36C31×#125—24no—
37C31×#125—24no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—22no—
41C2×C4⋊C4×C31—22no—
42C2×C4⋊C4×C31—22no—
43C2×C4⋊C4×C31—22no—
44C2×C4⋊C4×C31—24no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31C2×C414yes—
50C2×C4⋊C4×C31C2×C418yes—
51C2×C4⋊C4×C31C2×C414yes—
52C2×C4⋊C4×C31C2×C414yes—
53C2×C4⋊C4×C31C2314yes—
54C2×C42×C31C2×C412yes—
55C2×C42×C31D412yes—
56C2×C42×C31D412yes—
57C2×C42×C31D412yes—
58C2×C42×C31D412yes—
59C2×C42×C31C2312yes—
60C31×C4⋊C8—24no—
61C31×C4⋊C8—24no—
62C31×C22⋊C8—24no—
63C31×C22⋊C8C2318yes—
64C31×#97—24no—
65C4×C8×C31—24no—
66C24×C31C22×C411yescharacteristic
67C22×C4×C31—24no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—42no—
73C22×C4×C31—44no—
74C22×C4×C31—42no—
75C22×C4×C31—44no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C412yes—
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C412yes—
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22×C414yes—
83C22×C4×C31C22×C412yes—
84C22×C4×C31C22×C412yes—
85C22×C4×C31C22×C414yes—
86C22×C4×C31C22×C411yescharacteristic
87C22×C4×C31C2×D412yes—
88C22×C4×C31C2×D412yes—
89C22×C4×C31C2411yescharacteristic
90M16×C31—48no—
91C2×C8×C31—28no—
92C4⋊C4×C31—28no—
93C4⋊C4×C31—24no—
94C4⋊C4×C31—28no—
95C4⋊C4×C31—28no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—24no—
98C4⋊C4×C31—24no—
99C4⋊C4×C31—28no—
100C42×C31C22⋊C412yes—
101C42×C31C22⋊C412yes—
102C42×C31C22⋊C412yes—
103C42×C31C22⋊C412yes—
104C42×C31C2×D412yes—
105C42×C31C2×D412yes—
106C42×C31C2×D412yes—
107C42×C31C2×D412yes—
108#17394C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—22no—
110C23×C31—22no—
111C23×C31—22no—
112C23×C31C2×C22⋊C411yescharacteristic
113C23×C31C2×C22⋊C411yescharacteristic
114C23×C31C23×C411yescharacteristic
115C2×C4×C31—24no—
116C2×C4×C31—24no—
117C2×C4×C31—22no—
118C2×C4×C31—24no—
119C2×C4×C31—24no—
120C2×C4×C31—24no—
121C2×C4×C31—24no—
122C2×C4×C31—28no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—42no—
126C2×C4×C31—41no—
127C2×C4×C31—42no—
128C2×C4×C31—41no—
129C2×C4×C31—44no—
130C2×C4×C31—44no—
131C2×C4×C31—44no—
132C2×C4×C31—44no—
133C2×C4×C31—44no—
134C2×C4×C31#10114yes—
135C2×C4×C31C2×C22⋊C412yes—
136C2×C4×C31C2×C22⋊C412yes—
137C2×C4×C31C2×C22⋊C412yes—
138C2×C4×C31C2×C22⋊C412yes—
139C2×C4×C31C2×C22⋊C412yes—
140C2×C4×C31C22×D412yes—
141C8×C31—48no—
142C22×#125C2×C3111yescharacteristic
143#2920C2×C3112yes—
144#1470C2×C3118yescomplemented
145#1463C2×C3114yes—
146C22×C31—28no—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31#41012yes—
154C22×C31C2×#10112yes—
155C22×C31C22×C22⋊C411yescharacteristic
156C22×C31#56812yes—
157C4×C31—22no—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—22no—
161C4×C31—22no—
162C4×C31—44no—
163C4×C31—44no—
164C4×C31C2×#10114yes—
165C2×#125—22no—
166C2×#125—22no—
167C2×#125—22no—
168C2×#125—22no—
169C2×#125C4×C3114yes—
170C2×#125C22×C3114yes—
171C22×C4⋊C4C4×C3111yescharacteristic
172C22×C4⋊C4C4×C3111yescharacteristic
173C22×C4⋊C4C4×C3112yes—
174C22×C4⋊C4C22×C3112yes—
175C22×C42C22×C3111yescharacteristic
176#432—22no—
177#432C22×C3114yes—
178#431—22no—
179#431C22×C3114yes—
180#423—22no—
181#407C22×C3114yes—
182C4×M16—22no—
183#324C22×C31116yes—
184C2×C31—22no—
185C2×C31—22no—
186C2×C31—22no—
187C2×C31#287911yescharacteristic
188C2×C31C2×#41011yescharacteristic
189C2×C31C22×#10111yescharacteristic
190C23×C4C2×C4×C3111yescharacteristic
191C23×C4C2×C4×C3112yes—
192C23×C4C2×C4×C3112yes—
193C23×C4C2×C4×C3111yescharacteristic
194C23×C4C23×C3111yescharacteristic
195C2×M16—24no—
196#125—24no—
197#125—24no—
198#125—24no—
199#125—24no—
200#125—24no—
201#125—24no—
202#125—24no—
203#125—24no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4C2×C4×C3114yes—
216C2×C4⋊C4C2×C4×C3118yes—
217C2×C4⋊C4C2×C4×C3114yes—
218C2×C4⋊C4C2×C4×C3114yes—
219C2×C4⋊C4C23×C3114yes—
220C2×C42C2×C4×C3112yes—
221C2×C42D4×C3112yes—
222C2×C42D4×C3112yes—
223C2×C42D4×C3112yes—
224C2×C42D4×C3112yes—
225C2×C42C23×C3112yes—
226C4⋊C8—24no—
227C4⋊C8—24no—
228C22⋊C8—24no—
229C22⋊C8C23×C3118yes—
230#97—24no—
231C4×C8—24no—
232C31#1739411yescharacteristic, direct product factor, Sylow
233C24C22×C4×C3111yescharacteristic
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—42no—
240C22×C4—44no—
241C22×C4—42no—
242C22×C4—44no—
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C22⋊C4×C3112yes—
245C22×C4C22⋊C4×C3111yescharacteristic
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4C22⋊C4×C3112yes—
248C22×C4C22⋊C4×C3111yescharacteristic
249C22×C4C22×C4×C3114yes—
250C22×C4C22×C4×C3112yes—
251C22×C4C22×C4×C3112yes—
252C22×C4C22×C4×C3114yes—
253C22×C4C22×C4×C3111yescharacteristic
254C22×C4C2×D4×C3112yes—
255C22×C4C2×D4×C3112yes—
256C22×C4C24×C3111yescharacteristic
257M16—48no—
258C2×C8—28no—
259C4⋊C4—28no—
260C4⋊C4—24no—
261C4⋊C4—28no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—28no—
267C42C22⋊C4×C3112yes—
268C42C22⋊C4×C3112yes—
269C42C22⋊C4×C3112yes—
270C42C22⋊C4×C3112yes—
271C42C2×D4×C3112yes—
272C42C2×D4×C3112yes—
273C42C2×D4×C3112yes—
274C42C2×D4×C3112yes—
275C23—22no—
276C23—22no—
277C23—22no—
278C23C2×C22⋊C4×C3111yescharacteristic
279C23C2×C22⋊C4×C3111yescharacteristic
280C23C23×C4×C3111yescharacteristic
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—28no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4C31×#10114yes—
301C2×C4C2×C22⋊C4×C3112yes—
302C2×C4C2×C22⋊C4×C3112yes—
303C2×C4C2×C22⋊C4×C3112yes—
304C2×C4C2×C22⋊C4×C3112yes—
305C2×C4C2×C22⋊C4×C3112yes—
306C2×C4C22×D4×C3112yes—
307C8—48no—
308C22—28no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22C31×#41012yes—
316C22C2×C31×#10112yes—
317C22C22×C22⋊C4×C3111yescharacteristic
318C22C31×#56812yes—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—44no—
325C4—44no—
326C4C2×C31×#10114yes—
327C2—22no—
328C2—22no—
329C2—22no—
330C2C31×#287911yescharacteristic
331C2C2×C31×#41011yescharacteristic
332C2C22×C31×#10111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1470C2semidirect
108. #17394C31direct (N × H)
144. #1470C2×C31semidirect
232. C31#17394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1252
C31×#29202
C31×#14702
C31×#14632
#1739431