Finite Group Databasebeta

← C31×#7573 #21464332

Subgroups — C31×#7573 #21464332

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C4×C31×C22⋊C8C211yesmaximal, characteristic
4C31×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C31—21no—
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C4×C8×C31—21no—
13C31×#389—21no—
14C31×#389—21no—
15C31×#389C412yes—
16C31×#389C2212yes—
17C2×C31×#95—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—42no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31C814yescomplemented
36C2×C4⋊C4×C31C2×C412yes—
37C2×C4⋊C4×C31C2×C412yes—
38C2×C42×C31—42no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31C2311yescharacteristic
43C31×C4⋊C8—42no—
44C31×C22⋊C8—24no—
45C31×C22⋊C8—42no—
46C4×C8×C31—42no—
47C31×#95—22no—
48C31×#95—22no—
49C24×C31C22⋊C411yescharacteristic
50C22×C4×C31—22no—
51C22×C4×C31—22no—
52C22×C4×C31—24no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C2×C812yes—
69C22×C4×C31M1612yes—
70C22×C4×C31D812yes—
71C22×C4×C31SD1612yes—
72C22×C4×C31C22×C411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C2×C8×C31—24no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C4⋊C4×C31—24no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—44no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—42no—
88C4⋊C4×C31C2×C814yes—
89C42×C31—22no—
90C42×C31—22no—
91C42×C31—41no—
92C42×C31—41no—
93#7573C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31C22⋊C812yes—
99C23×C31#10212yes—
100C23×C31#10412yes—
101C23×C31C2×C22⋊C411yescharacteristic
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—24no—
111C2×C4×C31—24no—
112C2×C4×C31—24no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—44no—
119C2×C4×C31—48no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—84no—
126C2×C4×C31C22⋊C812yes—
127C2×C4×C31#9912yes—
128C2×C4×C31#10112yes—
129C2×C4×C31#10212yes—
130C2×C4×C31C22×C811yescharacteristic
131C2×C4×C31C2×M1611yescharacteristic
132C2×C4×C31C2×D811yescharacteristic
133C2×C4×C31C2×SD1611yescharacteristic
134C2×C4×C31#13712yes—
135C8×C31—44no—
136C8×C31—82no—
137C2×#389C2×C3111yescharacteristic
138#1797C2×C3111yescharacteristic
139C4×C22⋊C8C2×C3111yescharacteristic
140#1271C2×C3114yescomplemented
141C22×C31—22no—
142C22×C31—22no—
143C22×C31—22no—
144C22×C31—22no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31D4⋊C814yes—
148C22×C31C2×C22⋊C811yescharacteristic
149C22×C31C2×#9911yescharacteristic
150C22×C31C2×#10111yescharacteristic
151C22×C31C2×#10211yescharacteristic
152C22×C31#41911yescharacteristic
153C22×C31C2×#10411yescharacteristic
154C22×C31#42111yescharacteristic
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—21no—
159C4×C31—22no—
160C4×C31—21no—
161C4×C31—44no—
162C4×C31—41no—
163C4×C31—82no—
164C4×C31#32414yes—
165C22×C4⋊C4—21no—
166C22×C4⋊C4C4×C3111yescharacteristic
167C22×C4⋊C4C4×C3111yescharacteristic
168C22×C42C22×C3111yescharacteristic
169C2×C4⋊C8—21no—
170C2×C22⋊C8—21no—
171C2×C22⋊C8—21no—
172C2×C4×C8—21no—
173#389—21no—
174#389—21no—
175#389C4×C3112yes—
176#389C22×C3112yes—
177C2×#95—21no—
178#336C22×C3112yes—
179#336C22×C3112yes—
180C2×C31—24no—
181C2×C31C2×#32411yescharacteristic
182C2×C31C2×D4⋊C811yescharacteristic
183C2×C31#147911yescharacteristic
184C2×C31#150811yescharacteristic
185C2×C31#151911yescharacteristic
186C2×C31#152811yescharacteristic
187C2×C31#154611yescharacteristic
188C23×C4—21no—
189C23×C4—21no—
190C23×C4C2×C4×C3111yescharacteristic
191C23×C4D4×C3111yescharacteristic
192C23×C4D4×C3111yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4C8×C3114yescomplemented
204C2×C4⋊C4C2×C4×C3112yes—
205C2×C4⋊C4C2×C4×C3112yes—
206C2×C42—42no—
207C2×C42C2×C4×C3111yescharacteristic
208C2×C42D4×C3111yescharacteristic
209C2×C42D4×C3111yescharacteristic
210C2×C42C23×C3111yescharacteristic
211C4⋊C8—42no—
212C22⋊C8—24no—
213C22⋊C8—42no—
214C4×C8—42no—
215#95—22no—
216#95—22no—
217C31#757311yescharacteristic, direct product factor, Sylow
218C24C22⋊C4×C3111yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4C22⋊C4×C3111yescharacteristic
235C22×C4C22⋊C4×C3111yescharacteristic
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C2×C8×C3112yes—
238C22×C4M16×C3112yes—
239C22×C4D8×C3112yes—
240C22×C4SD16×C3112yes—
241C22×C4C22×C4×C3111yescharacteristic
242C22×C4C2×D4×C3111yescharacteristic
243C22×C4C2×D4×C3111yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—24no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4C2×C8×C3114yes—
258C42—22no—
259C42—22no—
260C42—41no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23C31×C22⋊C812yes—
267C23C31×#10212yes—
268C23C31×#10412yes—
269C23C2×C22⋊C4×C3111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—48no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—84no—
294C2×C4C31×C22⋊C812yes—
295C2×C4C31×#9912yes—
296C2×C4C31×#10112yes—
297C2×C4C31×#10212yes—
298C2×C4C22×C8×C3111yescharacteristic
299C2×C4C2×M16×C3111yescharacteristic
300C2×C4C2×D8×C3111yescharacteristic
301C2×C4C2×SD16×C3111yescharacteristic
302C2×C4C31×#13712yes—
303C8—44no—
304C8—82no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22C31×D4⋊C814yes—
312C22C2×C31×C22⋊C811yescharacteristic
313C22C2×C31×#9911yescharacteristic
314C22C2×C31×#10111yescharacteristic
315C22C2×C31×#10211yescharacteristic
316C22C31×#41911yescharacteristic
317C22C2×C31×#10411yescharacteristic
318C22C31×#42111yescharacteristic
319C4—21no—
320C4—21no—
321C4—22no—
322C4—21no—
323C4—22no—
324C4—21no—
325C4—44no—
326C4—41no—
327C4—82no—
328C4C31×#32414yes—
329C2—24no—
330C2C2×C31×#32411yescharacteristic
331C2C2×C31×D4⋊C811yescharacteristic
332C2C31×#147911yescharacteristic
333C2C31×#150811yescharacteristic
334C2C31×#151911yescharacteristic
335C2C31×#152811yescharacteristic
336C2C31×#154611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C2×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×#1271C2semidirect
35. C2×C4⋊C4×C31C8semidirect
93. #7573C31direct (N × H)
140. #1271C2×C31semidirect
203. C2×C4⋊C4C8×C31semidirect
217. C31#7573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#17972
C4×C31×C22⋊C82
C31×#12712
#757331