Finite Group Databasebeta

← C31×#8374 #21465133

Subgroups — C31×#8374 #21465133

Order 7936.

712 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#557C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic
3C31×#1528C212yesmaximal
4C31×#1491C212yesmaximal
5C31×#1467C211yesmaximal, characteristic
6C31×#557—24no—
7C31×#557—24no—
8C2×C31×C4⋊Q8—21no—
9C2×C31×C4⋊Q8C411yescharacteristic
10C2×C31×#125—21no—
11C2×C31×#125—21no—
12C2×C31×#125C411yescharacteristic
13C2×C31×#125C2211yescharacteristic
14C2×C4×Q8×C31—21no—
15C2×C4×Q8×C31C411yescharacteristic
16C2×C4×Q8×C31C411yescharacteristic
17C2×C4×Q8×C31C2211yescharacteristic
18C2×C4×Q8×C31C2211yescharacteristic
19C31×#432C2212yes—
20C2×C31×#101—21no—
21C4×M16×C31C2212yes—
22C31×#343—21no—
23C31×#330—24no—
24C31×Q8⋊C8—24no—
25C31×#324—21no—
26C31×#324—21no—
27C22×Q8×C31—21no—
28C22×Q8×C31C2×C411yescharacteristic
29C22×Q8×C31D411yescharacteristic
30C2×M16×C31—22no—
31C31×C4⋊Q8—28no—
32C31×C4⋊Q8—22no—
33C31×C4⋊Q8—22no—
34C31×#125—28no—
35C31×#125—28no—
36C31×#125—22no—
37C31×#125—22no—
38C31×#125—22no—
39C31×#125D414yes—
40C4×Q8×C31—28no—
41C4×Q8×C31—22no—
42C4×Q8×C31—22no—
43C4×Q8×C31—22no—
44C4×Q8×C31—22no—
45C4×Q8×C31—22no—
46C4×Q8×C31—22no—
47C4×Q8×C31—22no—
48C4×Q8×C31D414yes—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31C2×C411yescharacteristic
59C2×C4⋊C4×C31C2×C411yescharacteristic
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C4⋊C4×C31D411yescharacteristic
62C2×C4⋊C4×C31D411yescharacteristic
63C2×C42×C31—21no—
64C2×C42×C31—21no—
65C2×C42×C31—21no—
66C2×C42×C31C2×C411yescharacteristic
67C2×C42×C31C2×C411yescharacteristic
68C2×C42×C31C2311yescharacteristic
69C31×C4⋊C8—22no—
70C31×#101—24no—
71C31×C22⋊C8—22no—
72C31×#97—22no—
73C31×#97—22no—
74C4×C8×C31—22no—
75C2×Q8×C31—24no—
76C2×Q8×C31—24no—
77C2×Q8×C31—22no—
78C2×Q8×C31—21no—
79C2×Q8×C31—22no—
80C2×Q8×C31—41no—
81C2×Q8×C31—42no—
82C2×Q8×C31—42no—
83C2×Q8×C31C22⋊C412yes—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22×C411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95M16×C31—24no—
96M16×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—42no—
99C4⋊C4×C31—24no—
100C4⋊C4×C31—24no—
101C4⋊C4×C31—24no—
102C4⋊C4×C31—24no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—24no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31C22⋊C412yes—
114C4⋊C4×C31C22⋊C412yes—
115C4⋊C4×C31C22⋊C412yes—
116C42×C31—24no—
117C42×C31—24no—
118C42×C31—21no—
119C42×C31—21no—
120C42×C31—21no—
121C42×C31—21no—
122C42×C31—24no—
123C42×C31C2×D412yes—
124C42×C31C2×D412yes—
125#8374C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31C2×C22⋊C411yescharacteristic
127Q8×C31—24no—
128Q8×C31—22no—
129Q8×C31—44no—
130Q8×C31—48no—
131Q8×C31#10114yescomplemented
132C2×C4×C31—24no—
133C2×C4×C31—22no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—22no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—22no—
142C2×C4×C31—21no—
143C2×C4×C31—22no—
144C2×C4×C31—22no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31#10412yes—
156C2×C4×C31C2×C22⋊C411yescharacteristic
157C2×C4×C31C2×C22⋊C411yescharacteristic
158C2×C4×C31#12012yes—
159C2×C4×C31#12012yes—
160C8×C31—44no—
161C8×C31—82no—
162C2×#557C2×C3111yescharacteristic
163C4×#101C2×C3111yescharacteristic
164#1528C2×C3112yes—
165#1491C2×C3112yes—
166#1467C2×C3111yescharacteristic
167C22×C31—21no—
168C22×C31—21no—
169C22×C31#37911yescharacteristic
170C22×C31C2×#10411yescharacteristic
171C22×C31#42111yescharacteristic
172C4×C31—22no—
173C4×C31—24no—
174C4×C31—21no—
175C4×C31—22no—
176C4×C31—22no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31—42no—
180C4×C31—41no—
181C4×C31—42no—
182C4×C31—42no—
183C4×C31C2×#10112yes—
184#557—24no—
185#557—24no—
186C2×C4⋊Q8—21no—
187C2×C4⋊Q8C4×C3111yescharacteristic
188C2×#125—21no—
189C2×#125—21no—
190C2×#125C4×C3111yescharacteristic
191C2×#125C22×C3111yescharacteristic
192C2×C4×Q8—21no—
193C2×C4×Q8C4×C3111yescharacteristic
194C2×C4×Q8C4×C3111yescharacteristic
195C2×C4×Q8C22×C3111yescharacteristic
196C2×C4×Q8C22×C3111yescharacteristic
197#432C22×C3112yes—
198C2×#101—21no—
199C4×M16C22×C3112yes—
200#343—21no—
201#330—24no—
202Q8⋊C8—24no—
203#324—21no—
204#324—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31#178411yescharacteristic
208C2×C31#178911yescharacteristic
209C2×C31#179611yescharacteristic
210C22×Q8—21no—
211C22×Q8C2×C4×C3111yescharacteristic
212C22×Q8D4×C3111yescharacteristic
213C2×M16—22no—
214C4⋊Q8—28no—
215C4⋊Q8—22no—
216C4⋊Q8—22no—
217#125—28no—
218#125—28no—
219#125—22no—
220#125—22no—
221#125—22no—
222#125D4×C3114yes—
223C4×Q8—28no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8D4×C3114yes—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C3111yescharacteristic
241C2×C4⋊C4C2×C4×C3111yescharacteristic
242C2×C4⋊C4C2×C4×C3111yescharacteristic
243C2×C4⋊C4D4×C3111yescharacteristic
244C2×C4⋊C4D4×C3111yescharacteristic
245C2×C4⋊C4D4×C3111yescharacteristic
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C2×C4×C3111yescharacteristic
250C2×C42C2×C4×C3111yescharacteristic
251C2×C42C23×C3111yescharacteristic
252C4⋊C8—22no—
253#101—24no—
254C22⋊C8—22no—
255#97—22no—
256#97—22no—
257C4×C8—22no—
258C31#837411yescharacteristic, direct product factor, Sylow
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8C22⋊C4×C3112yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4C22⋊C4×C3111yescharacteristic
276C22×C4C22×C4×C3111yescharacteristic
277C22×C4C2×D4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279M16—24no—
280M16—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4C22⋊C4×C3112yes—
298C4⋊C4C22⋊C4×C3112yes—
299C4⋊C4C22⋊C4×C3112yes—
300C42—24no—
301C42—24no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—24no—
307C42C2×D4×C3112yes—
308C42C2×D4×C3112yes—
309C23C2×C22⋊C4×C3111yescharacteristic
310Q8—24no—
311Q8—22no—
312Q8—44no—
313Q8—48no—
314Q8C31×#10114yescomplemented
315C2×C4—24no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C31×#10412yes—
339C2×C4C2×C22⋊C4×C3111yescharacteristic
340C2×C4C2×C22⋊C4×C3111yescharacteristic
341C2×C4C31×#12012yes—
342C2×C4C31×#12012yes—
343C8—44no—
344C8—82no—
345C22—21no—
346C22—21no—
347C22C31×#37911yescharacteristic
348C22C2×C31×#10411yescharacteristic
349C22C31×#42111yescharacteristic
350C4—22no—
351C4—24no—
352C4—21no—
353C4—22no—
354C4—22no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—42no—
360C4—42no—
361C4C2×C31×#10112yes—
362C2—21no—
363C2—21no—
364C2C31×#178411yescharacteristic
365C2C31×#178911yescharacteristic
366C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
125. #8374C31direct (N × H)
131. Q8×C31#101semidirect
258. C31#8374direct (N × H)
314. Q8C31×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5572
C4×C31×#1012
C31×#15282
C31×#14912
C31×#14672
#837431