Finite Group Databasebeta

← C31×#8365 #21465124

Subgroups — C31×#8365 #21465124

Order 7936.

782 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic
2C31×#1826C212yesmaximal, complemented
3C4×C31×#99C211yesmaximal, characteristic
4C31×#1508C212yesmaximal, complemented
5C31×#1465C211yesmaximal, characteristic
6C31×#556—24no—
7C31×#556—24no—
8C2×C31×C4⋊Q8C411yescharacteristic, complemented
9C2×C31×#126—21no—
10C2×C31×#126—21no—
11C2×C31×#124—21no—
12C2×C31×C22⋊Q8C411yescharacteristic, complemented
13C2×C31×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C31—21no—
15C2×C4×Q8×C31C411yescharacteristic, complemented
16C2×C4×D4×C31C2211yescharacteristic
17C2×C31×#117C411yescharacteristic, complemented
18C2×C31×#117C2211yescharacteristic
19C2×C31×#99—21no—
20C31×#407C2212yes—
21C4×C22⋊C4×C31C2212yes—
22C31×#342—21no—
23C31×#339—24no—
24C31×#328—24no—
25C31×#324—21no—
26C31×#323—21no—
27C22×Q8×C31—21no—
28C22×Q8×C31C2×C411yescharacteristic
29C22×D4×C31D411yescharacteristic
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31C2311yescharacteristic
32C2×M16×C31—22no—
33C31×C4⋊Q8—22no—
34C31×C4⋊Q8—22no—
35C31×#126—28no—
36C31×#126—28no—
37C31×#124—28no—
38C31×C22⋊Q8—22no—
39C31×C22⋊Q8—22no—
40C31×C22⋊Q8—22no—
41C31×C22⋊Q8D414yes—
42C4×Q8×C31—28no—
43C4×Q8×C31—22no—
44C4×Q8×C31—22no—
45C4×D4×C31—22no—
46C4×D4×C31—22no—
47C31×#117—22no—
48C31×#117—22no—
49C31×#117—22no—
50C31×#117D414yes—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31C2×C411yescharacteristic
56C2×C4⋊C4×C31C2×C411yescharacteristic
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31D411yescharacteristic
65C2×C22⋊C4×C31D411yescharacteristic
66C2×C42×C31—21no—
67C2×C42×C31—21no—
68C2×C42×C31—21no—
69C2×C42×C31—22no—
70C2×C42×C31C2×C411yescharacteristic
71C31×#99—24no—
72C31×C22⋊C8—22no—
73C31×C22⋊C8—22no—
74C31×#95—22no—
75C24×C31C22⋊C411yescharacteristic
76C24×C31C2×D411yescharacteristic
77C2×Q8×C31—24no—
78C2×Q8×C31—21no—
79C2×Q8×C31—42no—
80C2×Q8×C31—42no—
81C2×Q8×C31—42no—
82C2×Q8×C31C22⋊C412yes—
83C2×D4×C31—22no—
84C2×D4×C31—22no—
85C2×D4×C31—41no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31C22×C411yescharacteristic
99C22×C4×C31C2×D412yes—
100C22×C4×C31C2×D412yes—
101C22×C4×C31C2×D411yescharacteristic
102M16×C31—44no—
103C2×C8×C31—42no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—24no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—24no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31C22⋊C412yes—
113C4⋊C4×C31C22⋊C412yes—
114C4⋊C4×C31C22⋊C412yes—
115C22⋊C4×C31—24no—
116C22⋊C4×C31—24no—
117C22⋊C4×C31—24no—
118C22⋊C4×C31—24no—
119C22⋊C4×C31—22no—
120C22⋊C4×C31—22no—
121C22⋊C4×C31—24no—
122C22⋊C4×C31—42no—
123C42×C31—24no—
124C42×C31—24no—
125C42×C31—21no—
126C42×C31—21no—
127C42×C31—24no—
128C42×C31—44no—
129#8365C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—21no—
131C23×C31—21no—
132C23×C31—21no—
133C23×C31—21no—
134C23×C31—21no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31C2×C22⋊C411yescharacteristic
140C23×C31#12012yes—
141Q8×C31—42no—
142Q8×C31—48no—
143Q8×C31—42no—
144D4×C31—44no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—24no—
148C2×C4×C31—22no—
149C2×C4×C31—22no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—44no—
168C2×C4×C31—82no—
169C2×C4×C31—82no—
170C2×C4×C31#10412yes—
171C2×C4×C31C2×C22⋊C411yescharacteristic
172C2×C4×C31C2×C22⋊C411yescharacteristic
173C2×C4×C31#12012yes—
174C8×C31—82no—
175C2×#556C2×C3111yescharacteristic
176#1826C2×C3112yescomplemented
177C4×#99C2×C3111yescharacteristic
178#1508C2×C3112yescomplemented
179#1465C2×C3111yescharacteristic
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—22no—
183C22×C31—22no—
184C22×C31—22no—
185C22×C31—41no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31—81no—
192C22×C31#37911yescharacteristic
193C22×C31C2×#10411yescharacteristic
194C22×C31#42111yescharacteristic
195C4×C31—22no—
196C4×C31—21no—
197C4×C31—22no—
198C4×C31—41no—
199C4×C31—42no—
200C4×C31—41no—
201C4×C31—42no—
202C4×C31—42no—
203C4×C31—42no—
204C4×C31—84no—
205C4×C31#41012yes—
206#556—24no—
207#556—24no—
208C2×C4⋊Q8C4×C3111yescharacteristic, complemented
209C2×#126—21no—
210C2×#126—21no—
211C2×#124—21no—
212C2×C22⋊Q8C4×C3111yescharacteristic, complemented
213C2×C22⋊Q8C22×C3111yescharacteristic
214C2×C4×Q8—21no—
215C2×C4×Q8C4×C3111yescharacteristic, complemented
216C2×C4×D4C22×C3111yescharacteristic
217C2×#117C4×C3111yescharacteristic, complemented
218C2×#117C22×C3111yescharacteristic
219C2×#99—21no—
220#407C22×C3112yes—
221C4×C22⋊C4C22×C3112yes—
222#342—21no—
223#339—24no—
224#328—24no—
225#324—21no—
226#323—21no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—42no—
230C2×C31—81no—
231C2×C31#178211yescharacteristic
232C2×C31#178911yescharacteristic
233C2×C31#179611yescharacteristic
234C22×Q8—21no—
235C22×Q8C2×C4×C3111yescharacteristic
236C22×D4D4×C3111yescharacteristic
237C23×C4C2×C4×C3111yescharacteristic
238C23×C4C23×C3111yescharacteristic
239C2×M16—22no—
240C4⋊Q8—22no—
241C4⋊Q8—22no—
242#126—28no—
243#126—28no—
244#124—28no—
245C22⋊Q8—22no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8D4×C3114yes—
249C4×Q8—28no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×D4—22no—
253C4×D4—22no—
254#117—22no—
255#117—22no—
256#117—22no—
257#117D4×C3114yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C2×C4×C3111yescharacteristic
263C2×C4⋊C4C2×C4×C3111yescharacteristic
264C2×C4⋊C4C2×C4×C3111yescharacteristic
265C2×C4⋊C4D4×C3111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4D4×C3111yescharacteristic
272C2×C22⋊C4D4×C3111yescharacteristic
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—22no—
277C2×C42C2×C4×C3111yescharacteristic
278#99—24no—
279C22⋊C8—22no—
280C22⋊C8—22no—
281#95—22no—
282C31#836511yescharacteristic, direct product factor, Sylow
283C24C22⋊C4×C3111yescharacteristic
284C24C2×D4×C3111yescharacteristic
285C2×Q8—24no—
286C2×Q8—21no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8—42no—
290C2×Q8C22⋊C4×C3112yes—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4C22⋊C4×C3111yescharacteristic
304C22×C4C22⋊C4×C3111yescharacteristic
305C22×C4C22⋊C4×C3111yescharacteristic
306C22×C4C22×C4×C3111yescharacteristic
307C22×C4C2×D4×C3112yes—
308C22×C4C2×D4×C3112yes—
309C22×C4C2×D4×C3111yescharacteristic
310M16—44no—
311C2×C8—42no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4C22⋊C4×C3112yes—
321C4⋊C4C22⋊C4×C3112yes—
322C4⋊C4C22⋊C4×C3112yes—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—24no—
330C22⋊C4—42no—
331C42—24no—
332C42—24no—
333C42—21no—
334C42—21no—
335C42—24no—
336C42—44no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23C2×C22⋊C4×C3111yescharacteristic
347C23C31×#12012yes—
348Q8—42no—
349Q8—48no—
350Q8—42no—
351D4—44no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—44no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4C31×#10412yes—
378C2×C4C2×C22⋊C4×C3111yescharacteristic
379C2×C4C2×C22⋊C4×C3111yescharacteristic
380C2×C4C31×#12012yes—
381C8—82no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22C31×#37911yescharacteristic
395C22C2×C31×#10411yescharacteristic
396C22C31×#42111yescharacteristic
397C4—22no—
398C4—21no—
399C4—22no—
400C4—42no—
401C4—41no—
402C4—41no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—84no—
407C4C31×#41012yes—
408C2—21no—
409C2—21no—
410C2—42no—
411C2—81no—
412C2C31×#178211yescharacteristic
413C2C31×#178911yescharacteristic
414C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
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×#1826C2semidirect
4. C31×#1508C2semidirect
8. C2×C31×C4⋊Q8C4semidirect
12. C2×C31×C22⋊Q8C4semidirect
15. C2×C4×Q8×C31C4semidirect
17. C2×C31×#117C4semidirect
129. #8365C31direct (N × H)
176. #1826C2×C31semidirect
178. #1508C2×C31semidirect
208. C2×C4⋊Q8C4×C31semidirect
212. C2×C22⋊Q8C4×C31semidirect
215. C2×C4×Q8C4×C31semidirect
217. C2×#117C4×C31semidirect
282. C31#8365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C31×#18262
C4×C31×#992
C31×#15082
C31×#14652
#836531