Finite Group Databasebeta

← C31×#10736 #21467495

Subgroups — C31×#10736 #21467495

Order 7936.

1510 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C31×#381C211yesmaximal, characteristic
3C2×C31×#381C211yesmaximal, characteristic
4C2×C31×#342C214yesmaximal
5C24×C4×C31C2211yescharacteristic
6C2×C31×#117—22no—
7C2×C31×#117—28no—
8C2×C31×#117C414yescomplemented
9C22×C4⋊C4×C31—21no—
10C22×C22⋊C4×C31C2212yes—
11C22×C22⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2212yes—
13C22×C42×C31—21no—
14C31×#381—22no—
15C31×#381—21no—
16C31×#381—21no—
17C31×#381—22no—
18C31×#381C414yescomplemented
19C2×C31×#95—22no—
20C2×C31×#95C414yescomplemented
21C31×#342—28no—
22C25×C31C2311yescharacteristic
23C23×C4×C31—24no—
24C23×C4×C31—24no—
25C23×C4×C31—22no—
26C23×C4×C31—22no—
27C23×C4×C31C2×C412yes—
28C23×C4×C31C2×C412yes—
29C23×C4×C31C2×C412yes—
30C23×C4×C31C2×C414yes—
31C23×C4×C31D411yescharacteristic
32C23×C4×C31D411yescharacteristic
33C23×C4×C31D412yes—
34C23×C4×C31D412yes—
35C23×C4×C31Q812yes—
36C31×#117—216no—
37C31×#117—216no—
38C2×C4⋊C4×C31—28no—
39C2×C4⋊C4×C31—24no—
40C2×C22⋊C4×C31—24no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—24no—
43C2×C22⋊C4×C31—24no—
44C2×C22⋊C4×C31—24no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31—22no—
48C2×C22⋊C4×C31—24no—
49C2×C22⋊C4×C31C2×C414yes—
50C2×C22⋊C4×C31C2×C414yes—
51C2×C22⋊C4×C31D418yes—
52C2×C42×C31—28no—
53C2×C42×C31—24no—
54C31×#95—28no—
55C31×#95—24no—
56C31×#95—24no—
57C24×C31—44no—
58C24×C31C22×C411yescharacteristic
59C24×C31C22×C411yescharacteristic
60C24×C31C22×C411yescharacteristic
61C24×C31C2×D411yescharacteristic
62C24×C31C2×D411yescharacteristic
63C24×C31C2×D411yescharacteristic
64C24×C31C2×D414yes—
65C24×C31C2×Q811yescharacteristic
66C24×C31#4114yes—
67C22×C4×C31—24no—
68C22×C4×C31—24no—
69C22×C4×C31—28no—
70C22×C4×C31—28no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—24no—
74C22×C4×C31—28no—
75C22×C4×C31—28no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—24no—
79C22×C4×C31—24no—
80C22×C4×C31—28no—
81C22×C4×C31—24no—
82C22×C4×C31—24no—
83C22×C4×C31—28no—
84C22×C4×C31—48no—
85C22×C4×C31—48no—
86C22×C4×C31—44no—
87C22×C4×C31—48no—
88C22×C4×C31C4214yes—
89C22×C4×C31C22⋊C414yes—
90C22×C4×C31C22⋊C412yes—
91C22×C4×C31C22⋊C412yes—
92C22×C4×C31C22⋊C412yes—
93C22×C4×C31C22⋊C412yes—
94C22×C4×C31C4⋊C414yes—
95C22×C4×C31C4⋊C414yes—
96C22×C4×C31C4⋊C412yes—
97C22×C4×C31C4⋊C412yes—
98C4⋊C4×C31—216no—
99C22⋊C4×C31—24no—
100C22⋊C4×C31—28no—
101C22⋊C4×C31—28no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—44no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31C22⋊C418yes—
108C42×C31—216no—
109#10736C3111yesmaximal, characteristic, direct product factor, Sylow
110C23×C31—24no—
111C23×C31—24no—
112C23×C31—24no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—48no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—48no—
119C23×C31C2×C4211yescharacteristic
120C23×C31C2×C22⋊C411yescharacteristic
121C23×C31C2×C22⋊C411yescharacteristic
122C23×C31C2×C22⋊C412yes—
123C23×C31C2×C22⋊C411yescharacteristic
124C23×C31C2×C4⋊C411yescharacteristic
125C23×C31C2×C4⋊C411yescharacteristic
126C23×C31C2×C4⋊C411yescharacteristic
127C23×C31#11712yes—
128C23×C31C4×D414yes—
129C23×C31C4×D414yes—
130C23×C31#12012yes—
131C23×C31#12012yes—
132C23×C31#12114yes—
133C23×C31C22⋊Q814yes—
134C23×C31#12312yes—
135C23×C31#12312yes—
136C2×C4×C31—28no—
137C2×C4×C31—22no—
138C2×C4×C31—22no—
139C2×C4×C31—28no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—24no—
143C2×C4×C31—24no—
144C2×C4×C31—28no—
145C2×C4×C31—28no—
146C2×C4×C31—24no—
147C2×C4×C31—24no—
148C2×C4×C31—28no—
149C2×C4×C31—416no—
150C2×C4×C31—48no—
151C2×C4×C31—48no—
152C2×C4×C31—44no—
153C2×C4×C31—44no—
154C2×C4×C31—48no—
155C2×C4×C31—88no—
156C2×C4×C31—88no—
157C2×C4×C31#9514yes—
158C2×C4×C31#9514yes—
159C22×#117C2×C3111yescharacteristic
160C2×#381C2×C3111yescharacteristic
161C2×#381C2×C3111yescharacteristic
162C2×#342C2×C3114yes—
163C22×C31—24no—
164C22×C31—28no—
165C22×C31—28no—
166C22×C31—24no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—42no—
174C22×C31—42no—
175C22×C31—44no—
176C22×C31—42no—
177C22×C31—44no—
178C22×C31—42no—
179C22×C31C2×#9511yescharacteristic
180C22×C31C4×C22⋊C412yes—
181C22×C31#37911yescharacteristic
182C22×C31#38012yes—
183C22×C31#38111yescharacteristic
184C22×C31#38512yes—
185C22×C31#38512yes—
186C22×C31#38612yes—
187C22×C31#38612yes—
188C22×C31#41014yes—
189C4×C31—24no—
190C4×C31—24no—
191C4×C31—48no—
192C4×C31—84no—
193C4×C31—84no—
194C24×C4C22×C3111yescharacteristic
195C2×#117—22no—
196C2×#117—28no—
197C2×#117C4×C3114yescomplemented
198C22×C4⋊C4—21no—
199C22×C22⋊C4C22×C3112yes—
200C22×C22⋊C4C22×C3112yes—
201C22×C22⋊C4C22×C3112yes—
202C22×C42—21no—
203#381—22no—
204#381—21no—
205#381—22no—
206#381—21no—
207#381C4×C3114yescomplemented
208C2×#95—22no—
209C2×#95C4×C3114yescomplemented
210#342—28no—
211C2×C31—21no—
212C2×C31—22no—
213C2×C31—22no—
214C2×C31—22no—
215C2×C31—21no—
216C2×C31—22no—
217C2×C31—22no—
218C2×C31C22⋊#9511yescharacteristic
219C2×C31#174012yes—
220C2×C31#189914yes—
221C25C23×C3111yescharacteristic
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C2×C4×C3112yes—
227C23×C4C2×C4×C3112yes—
228C23×C4C2×C4×C3112yes—
229C23×C4C2×C4×C3114yes—
230C23×C4D4×C3111yescharacteristic
231C23×C4D4×C3112yes—
232C23×C4D4×C3112yes—
233C23×C4D4×C3111yescharacteristic
234C23×C4Q8×C3112yes—
235#117—216no—
236#117—216no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—24no—
248C2×C22⋊C4C2×C4×C3114yes—
249C2×C22⋊C4C2×C4×C3114yes—
250C2×C22⋊C4D4×C3118yes—
251C2×C42—28no—
252C2×C42—24no—
253#95—28no—
254#95—24no—
255#95—24no—
256C31#1073611yescharacteristic, direct product factor, Sylow
257C24—44no—
258C24C22×C4×C3111yescharacteristic
259C24C22×C4×C3111yescharacteristic
260C24C22×C4×C3111yescharacteristic
261C24C2×D4×C3111yescharacteristic
262C24C2×D4×C3111yescharacteristic
263C24C2×D4×C3111yescharacteristic
264C24C2×D4×C3114yes—
265C24C2×Q8×C3111yescharacteristic
266C24#41×C3114yes—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—28no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—28no—
284C22×C4—48no—
285C22×C4—48no—
286C22×C4—44no—
287C22×C4—48no—
288C22×C4C42×C3114yes—
289C22×C4C22⋊C4×C3114yes—
290C22×C4C22⋊C4×C3112yes—
291C22×C4C22⋊C4×C3112yes—
292C22×C4C22⋊C4×C3112yes—
293C22×C4C22⋊C4×C3112yes—
294C22×C4C4⋊C4×C3114yes—
295C22×C4C4⋊C4×C3114yes—
296C22×C4C4⋊C4×C3112yes—
297C22×C4C4⋊C4×C3112yes—
298C4⋊C4—216no—
299C22⋊C4—24no—
300C22⋊C4—28no—
301C22⋊C4—28no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4C22⋊C4×C3118yes—
308C42—216no—
309C23—24no—
310C23—24no—
311C23—24no—
312C23—42no—
313C23—42no—
314C23—48no—
315C23—42no—
316C23—42no—
317C23—48no—
318C23C2×C42×C3111yescharacteristic
319C23C2×C22⋊C4×C3111yescharacteristic
320C23C2×C22⋊C4×C3111yescharacteristic
321C23C2×C22⋊C4×C3112yes—
322C23C2×C22⋊C4×C3111yescharacteristic
323C23C2×C4⋊C4×C3111yescharacteristic
324C23C2×C4⋊C4×C3111yescharacteristic
325C23C2×C4⋊C4×C3111yescharacteristic
326C23C31×#11712yes—
327C23C4×D4×C3114yes—
328C23C4×D4×C3114yes—
329C23C31×#12012yes—
330C23C31×#12012yes—
331C23C31×#12114yes—
332C23C31×C22⋊Q814yes—
333C23C31×#12312yes—
334C23C31×#12312yes—
335C2×C4—28no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—28no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—28no—
348C2×C4—416no—
349C2×C4—48no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—88no—
355C2×C4—88no—
356C2×C4C31×#9514yes—
357C2×C4C31×#9514yes—
358C22—24no—
359C22—28no—
360C22—28no—
361C22—24no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—42no—
370C22—44no—
371C22—42no—
372C22—44no—
373C22—42no—
374C22C2×C31×#9511yescharacteristic
375C22C4×C22⋊C4×C3112yes—
376C22C31×#37911yescharacteristic
377C22C31×#38012yes—
378C22C31×#38111yescharacteristic
379C22C31×#38512yes—
380C22C31×#38512yes—
381C22C31×#38612yes—
382C22C31×#38612yes—
383C22C31×#41014yes—
384C4—24no—
385C4—24no—
386C4—48no—
387C4—84no—
388C4—84no—
389C2—21no—
390C2—22no—
391C2—22no—
392C2—22no—
393C2—21no—
394C2—22no—
395C2—22no—
396C2C31×C22⋊#9511yescharacteristic
397C2C31×#174012yes—
398C2C31×#189914yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
8. C2×C31×#117C4semidirect
18. C31×#381C4semidirect
20. C2×C31×#95C4semidirect
109. #10736C31direct (N × H)
197. C2×#117C4×C31semidirect
207. #381C4×C31semidirect
209. C2×#95C4×C31semidirect
256. C31#10736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C31×#3812
C2×C31×#3422
#1073631