Finite Group Databasebeta

← C31×#8610 #21465369

Subgroups — C31×#8610 #21465369

Order 7936.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#435C211yesmaximal, characteristic
2C31×#1808C211yesmaximal, characteristic, complemented
3C31×#1807C211yesmaximal, characteristic, complemented
4C31×#1799C212yesmaximal
5C31×#1289C212yesmaximal, complemented
6C22×M16×C31C411yescharacteristic, complemented
7C23×C8×C31C2211yescharacteristic
8C2×C4×D4×C31C2211yescharacteristic
9C31×#435—21no—
10C31×#435—21no—
11C31×#435—21no—
12C31×#435—21no—
13C2×C31×#107—21no—
14C2×C31×#106—21no—
15C2×C31×C4⋊C8C411yescharacteristic, complemented
16C2×C31×#99—22no—
17C2×C31×C22⋊C8C411yescharacteristic, complemented
18C2×C31×C22⋊C8C2211yescharacteristic
19C2×C31×#97C411yescharacteristic, complemented
20C31×#380C2212yes—
21C31×#380C2212yes—
22C31×#342—22no—
23C31×#340—21no—
24C31×#340—21no—
25C22×D4×C31D411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2311yescharacteristic
28C2×M16×C31—21no—
29C2×M16×C31—21no—
30C2×M16×C31—42no—
31C22×C8×C31—42no—
32C22×C8×C31C2×C411yescharacteristic
33C22×C8×C31C2×C411yescharacteristic
34C22×C8×C31C2×C411yescharacteristic
35C22×C8×C31C2×C411yescharacteristic
36C22×C8×C31D411yescharacteristic
37C22×C8×C31D411yescharacteristic
38C22×C8×C31D411yescharacteristic
39C22×C8×C31D411yescharacteristic
40C4×D4×C31—21no—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C4×D4×C31—21no—
44C2×C4⋊C4×C31—22no—
45C2×C4⋊C4×C31—22no—
46C2×C4⋊C4×C31Q811yescharacteristic
47C2×C22⋊C4×C31—22no—
48C2×C22⋊C4×C31—22no—
49C2×C22⋊C4×C31D411yescharacteristic
50C2×C22⋊C4×C31Q811yescharacteristic
51C2×C42×C31C2×C411yescharacteristic
52C31×#107—42no—
53C31×#106—42no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×#99—44no—
57C31×C22⋊C8—21no—
58C31×C22⋊C8—21no—
59C31×C22⋊C8—21no—
60C31×C22⋊C8—21no—
61C31×#97—21no—
62C31×#97—21no—
63C31×#95—22no—
64C31×#95—22no—
65C24×C31C4⋊C411yescharacteristic
66C24×C31C2×D411yescharacteristic
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31—22no—
70C2×D4×C31—22no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31C4⋊C411yescharacteristic
80C22×C4×C31C4⋊C411yescharacteristic
81C22×C4×C31C4⋊C411yescharacteristic
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×Q811yescharacteristic
86C22×C4×C31#4111yescharacteristic
87C22×C4×C31#4111yescharacteristic
88M16×C31—42no—
89M16×C31—42no—
90C2×C8×C31—22no—
91C2×C8×C31—22no—
92C2×C8×C31—22no—
93C2×C8×C31—21no—
94C2×C8×C31—21no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31C22⋊C411yescharacteristic
101C2×C8×C31C22⋊C411yescharacteristic
102C2×C8×C31C22⋊C411yescharacteristic
103C2×C8×C31C22⋊C411yescharacteristic
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—42no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—42no—
110C22⋊C4×C31—21no—
111C22⋊C4×C31—21no—
112C22⋊C4×C31—21no—
113C22⋊C4×C31—21no—
114C22⋊C4×C31—42no—
115C22⋊C4×C31—42no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—42no—
118C42×C31—21no—
119C42×C31—21no—
120#8610C3111yesmaximal, characteristic, direct product factor, Sylow
121C23×C31—21no—
122C23×C31—22no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31C2×C4⋊C411yescharacteristic
128C23×C31#12111yescharacteristic
129C23×C31#12111yescharacteristic
130C23×C31AGL(1,ℤ/8)12yes—
131C23×C31#13712yes—
132D4×C31—42no—
133D4×C31—41no—
134D4×C31—41no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—22no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
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—82no—
154C2×C4×C31—82no—
155C2×C4×C31—82no—
156C2×C4×C31—82no—
157C2×C4×C31—82no—
158C2×C4×C31—82no—
159C2×C4×C31C2×C22⋊C411yescharacteristic
160C2×C4×C31#11711yescharacteristic
161C2×C4×C31C22⋊Q811yescharacteristic
162C2×C4×C31C22⋊Q811yescharacteristic
163C8×C31—21no—
164C8×C31—21no—
165C8×C31—21no—
166C8×C31—41no—
167C8×C31—41no—
168C8×C31#9912yescomplemented
169C2×#435C2×C3111yescharacteristic
170#1808C2×C3111yescharacteristic, complemented
171#1807C2×C3111yescharacteristic, complemented
172#1799C2×C3112yes—
173#1289C2×C3112yescomplemented
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—41no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31—82no—
186C22×C31#38011yescharacteristic
187C22×C31#42812yes—
188C22×C31#46812yes—
189C22×C31#46911yescharacteristic
190C22×C31#47011yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—41no—
195C4×C31—41no—
196C4×C31—41no—
197C4×C31—162no—
198C4×C31—162no—
199C4×C31C2×#9911yescharacteristic
200C4×C31#41011yescharacteristic
201C22×M16C4×C3111yescharacteristic, complemented
202C23×C8C22×C3111yescharacteristic
203C2×C4×D4C22×C3111yescharacteristic
204#435—21no—
205#435—21no—
206#435—21no—
207#435—21no—
208C2×#107—21no—
209C2×#106—21no—
210C2×C4⋊C8C4×C3111yescharacteristic, complemented
211C2×#99—22no—
212C2×C22⋊C8C4×C3111yescharacteristic, complemented
213C2×C22⋊C8C22×C3111yescharacteristic
214C2×#97C4×C3111yescharacteristic, complemented
215#380C22×C3112yes—
216#380C22×C3112yes—
217#342—22no—
218#340—21no—
219#340—21no—
220C2×C31—21no—
221C2×C31—22no—
222C2×C31—22no—
223C2×C31—21no—
224C2×C31—81no—
225C2×C31#179911yescharacteristic
226C2×C31#180911yescharacteristic
227C2×C31#181211yescharacteristic
228C22×D4D4×C3111yescharacteristic
229C23×C4C2×C4×C3111yescharacteristic
230C23×C4C23×C3111yescharacteristic
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—42no—
234C22×C8—42no—
235C22×C8C2×C4×C3111yescharacteristic
236C22×C8C2×C4×C3111yescharacteristic
237C22×C8C2×C4×C3111yescharacteristic
238C22×C8C2×C4×C3111yescharacteristic
239C22×C8D4×C3111yescharacteristic
240C22×C8D4×C3111yescharacteristic
241C22×C8D4×C3111yescharacteristic
242C22×C8D4×C3111yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4Q8×C3111yescharacteristic
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4D4×C3111yescharacteristic
253C2×C22⋊C4Q8×C3111yescharacteristic
254C2×C42C2×C4×C3111yescharacteristic
255#107—42no—
256#106—42no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259#99—44no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#97—21no—
265#97—21no—
266#95—22no—
267#95—22no—
268C31#861011yescharacteristic, direct product factor, Sylow
269C24C4⋊C4×C3111yescharacteristic
270C24C2×D4×C3111yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4C4⋊C4×C3111yescharacteristic
284C22×C4C4⋊C4×C3111yescharacteristic
285C22×C4C4⋊C4×C3111yescharacteristic
286C22×C4C22×C4×C3111yescharacteristic
287C22×C4C2×D4×C3111yescharacteristic
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×Q8×C3111yescharacteristic
290C22×C4#41×C3111yescharacteristic
291C22×C4#41×C3111yescharacteristic
292M16—42no—
293M16—42no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8C22⋊C4×C3111yescharacteristic
305C2×C8C22⋊C4×C3111yescharacteristic
306C2×C8C22⋊C4×C3111yescharacteristic
307C2×C8C22⋊C4×C3111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C42—21no—
323C42—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C2×C4⋊C4×C3111yescharacteristic
331C23C31×#12111yescharacteristic
332C23C31×#12111yescharacteristic
333C23C31×AGL(1,ℤ/8)12yes—
334C23C31×#13712yes—
335D4—42no—
336D4—41no—
337D4—41no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4C2×C22⋊C4×C3111yescharacteristic
363C2×C4C31×#11711yescharacteristic
364C2×C4C31×C22⋊Q811yescharacteristic
365C2×C4C31×C22⋊Q811yescharacteristic
366C8—21no—
367C8—21no—
368C8—21no—
369C8—41no—
370C8—41no—
371C8C31×#9912yescomplemented
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—82no—
384C22C31×#38011yescharacteristic
385C22C31×#42812yes—
386C22C31×#46812yes—
387C22C31×#46911yescharacteristic
388C22C31×#47011yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—162no—
396C4—162no—
397C4C2×C31×#9911yescharacteristic
398C4C31×#41011yescharacteristic
399C2—21no—
400C2—22no—
401C2—22no—
402C2—21no—
403C2—81no—
404C2C31×#179911yescharacteristic
405C2C31×#180911yescharacteristic
406C2C31×#181211yescharacteristic
subgroupG/H
center, socleC22×C31#380
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1808C2semidirect
3. C31×#1807C2semidirect
5. C31×#1289C2semidirect
6. C22×M16×C31C4semidirect
15. C2×C31×C4⋊C8C4semidirect
17. C2×C31×C22⋊C8C4semidirect
19. C2×C31×#97C4semidirect
120. #8610C31direct (N × H)
168. C8×C31#99semidirect
170. #1808C2×C31semidirect
171. #1807C2×C31semidirect
173. #1289C2×C31semidirect
201. C22×M16C4×C31semidirect
210. C2×C4⋊C8C4×C31semidirect
212. C2×C22⋊C8C4×C31semidirect
214. C2×#97C4×C31semidirect
268. C31#8610direct (N × H)
371. C8C31×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4352
C31×#18082
C31×#18072
C31×#17992
C31×#12892
#861031