Finite Group Databasebeta

← C31×#7609 #21464368

Subgroups — C31×#7609 #21464368

Order 7936.

676 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#391C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic
3C31×#1728C211yesmaximal, characteristic
4C31×#1272C214yesmaximal, complemented
5C23×Q8×C31C411yescharacteristic
6C22×M16×C31—21no—
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C31×#391—21no—
11C31×#391—21no—
12C31×#391C412yes—
13C31×#391C2212yes—
14C2×C31×#95—21no—
15C2×C31×#95—21no—
16C31×#336—21no—
17C31×#336—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C22×Q8×C31—24no—
21C22×Q8×C31—21no—
22C22×Q8×C31—42no—
23C22×Q8×C31—42no—
24C22×Q8×C31C2×C412yes—
25C23×C4×C31—21no—
26C23×C4×C31—21no—
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C2×M16×C31—24no—
31C2×M16×C31—42no—
32C2×M16×C31—42no—
33C22×C8×C31—22no—
34C22×C8×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—42no—
37C2×C4⋊C4×C31C2×C412yes—
38C2×C42×C31—42no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31C2311yescharacteristic
43C31×C22⋊C8—42no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31C22⋊C411yescharacteristic
49C2×Q8×C31—24no—
50C2×Q8×C31—22no—
51C2×Q8×C31—416no—
52C2×Q8×C31—42no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C2×Q8×C31—42no—
56C2×Q8×C31M1614yescomplemented
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—24no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—41no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31SD1612yes—
77C22×C4×C31Q1612yes—
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81M16×C31—48no—
82C2×C8×C31—24no—
83C2×C8×C31—42no—
84C2×C8×C31—42no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—42no—
89C4⋊C4×C31—42no—
90C42×C31—41no—
91C42×C31—41no—
92C42×C31—41no—
93C42×C31—41no—
94#7609C3111yesmaximal, characteristic, direct product factor, Sylow
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—21no—
99C23×C31#9912yes—
100C23×C31#10312yes—
101C23×C31#10412yes—
102C23×C31C2×C22⋊C411yescharacteristic
103Q8×C31—44no—
104Q8×C31—48no—
105Q8×C31—44no—
106C2×C4×C31—28no—
107C2×C4×C31—24no—
108C2×C4×C31—24no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—24no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—44no—
124C2×C4×C31—48no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—84no—
131C2×C4×C31#10012yes—
132C2×C4×C31#10312yes—
133C2×C4×C31C2×M1612yes—
134C2×C4×C31C2×SD1611yescharacteristic
135C2×C4×C31C2×Q1611yescharacteristic
136C2×C4×C31#13712yes—
137C8×C31—44no—
138C8×C31—82no—
139C2×#391C2×C3111yescharacteristic
140#1817C2×C3111yescharacteristic
141#1728C2×C3111yescharacteristic
142#1272C2×C3114yescomplemented
143C22×C31—22no—
144C22×C31—22no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—22no—
148C22×C31—22no—
149C22×C31#32814yes—
150C22×C31#40711yescharacteristic
151C22×C31C2×#9911yescharacteristic
152C22×C31C2×#10011yescharacteristic
153C22×C31C2×#10311yescharacteristic
154C22×C31#41911yescharacteristic
155C22×C31C2×#10411yescharacteristic
156C22×C31#42111yescharacteristic
157C4×C31—22no—
158C4×C31—22no—
159C4×C31—21no—
160C4×C31—22no—
161C4×C31—21no—
162C4×C31—22no—
163C4×C31—44no—
164C4×C31—41no—
165C4×C31—82no—
166C23×Q8C4×C3111yescharacteristic
167C22×M16—21no—
168C22×C4⋊C4C4×C3111yescharacteristic
169C22×C42C22×C3111yescharacteristic
170C2×C22⋊C8—21no—
171#391—21no—
172#391—21no—
173#391C4×C3112yes—
174#391C22×C3112yes—
175C2×#95—21no—
176C2×#95—21no—
177#336—21no—
178#336—21no—
179#336C22×C3112yes—
180#336C22×C3112yes—
181C2×C31—24no—
182C2×C31#146211yescharacteristic
183C2×C31#148711yescharacteristic
184C2×C31#149111yescharacteristic
185C2×C31C2×#32811yescharacteristic
186C2×C31#151111yescharacteristic
187C2×C31#152711yescharacteristic
188C2×C31#154811yescharacteristic
189C22×Q8—24no—
190C22×Q8—21no—
191C22×Q8—42no—
192C22×Q8—42no—
193C22×Q8C2×C4×C3112yes—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4C2×C4×C3111yescharacteristic
197C23×C4D4×C3111yescharacteristic
198C23×C4D4×C3111yescharacteristic
199C2×M16—24no—
200C2×M16—42no—
201C2×M16—42no—
202C22×C8—22no—
203C22×C8—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4C2×C4×C3112yes—
207C2×C42—42no—
208C2×C42C2×C4×C3111yescharacteristic
209C2×C42D4×C3111yescharacteristic
210C2×C42D4×C3111yescharacteristic
211C2×C42C23×C3111yescharacteristic
212C22⋊C8—42no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—22no—
217C31#760911yescharacteristic, direct product factor, Sylow
218C24C22⋊C4×C3111yescharacteristic
219C2×Q8—24no—
220C2×Q8—22no—
221C2×Q8—416no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8M16×C3114yescomplemented
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C22⋊C4×C3111yescharacteristic
245C22×C4C22⋊C4×C3111yescharacteristic
246C22×C4SD16×C3112yes—
247C22×C4Q16×C3112yes—
248C22×C4C22×C4×C3111yescharacteristic
249C22×C4C2×D4×C3111yescharacteristic
250C22×C4C2×D4×C3111yescharacteristic
251M16—48no—
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C31×#9912yes—
269C23C31×#10312yes—
270C23C31×#10412yes—
271C23C2×C22⋊C4×C3111yescharacteristic
272Q8—44no—
273Q8—48no—
274Q8—44no—
275C2×C4—28no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—48no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—84no—
300C2×C4C31×#10012yes—
301C2×C4C31×#10312yes—
302C2×C4C2×M16×C3112yes—
303C2×C4C2×SD16×C3111yescharacteristic
304C2×C4C2×Q16×C3111yescharacteristic
305C2×C4C31×#13712yes—
306C8—44no—
307C8—82no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22C31×#32814yes—
315C22C31×#40711yescharacteristic
316C22C2×C31×#9911yescharacteristic
317C22C2×C31×#10011yescharacteristic
318C22C2×C31×#10311yescharacteristic
319C22C31×#41911yescharacteristic
320C22C2×C31×#10411yescharacteristic
321C22C31×#42111yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—22no—
326C4—21no—
327C4—22no—
328C4—44no—
329C4—41no—
330C4—82no—
331C2—24no—
332C2C31×#146211yescharacteristic
333C2C31×#148711yescharacteristic
334C2C31×#149111yescharacteristic
335C2C2×C31×#32811yescharacteristic
336C2C31×#151111yescharacteristic
337C2C31×#152711yescharacteristic
338C2C31×#154811yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1272C2semidirect
56. C2×Q8×C31M16semidirect
94. #7609C31direct (N × H)
142. #1272C2×C31semidirect
217. C31#7609direct (N × H)
226. C2×Q8M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3912
C31×#18172
C31×#17282
C31×#12722
#760931