Finite Group Databasebeta

← C31×#10382 #21467141

Subgroups — C31×#10382 #21467141

Order 7936.

446 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2665C211yesmaximal, characteristic, complemented
2C31×#1964C211yesmaximal, characteristic
3C31×#1510C211yesmaximal, characteristic
4C31×#1507C211yesmaximal, characteristic
5C31×#1305C211yesmaximal, characteristic, complemented
6C31×#1297C211yesmaximal, characteristic, complemented
7C31×#1284C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#99—21no—
10C2×C31×#99—21no—
11C31×#407C2211yescharacteristic
12C31×#407C2211yescharacteristic
13C31×#400—21no—
14C31×#396—21no—
15C31×#395—21no—
16C31×#393—21no—
17C31×#391—21no—
18C31×#387—21no—
19C31×#381C2211yescharacteristic
20C31×#380C2211yescharacteristic
21C4×C22⋊C4×C31C2211yescharacteristic
22C4×C22⋊C4×C31C2211yescharacteristic
23C31×#327—21no—
24C31×#327—21no—
25C31×#327—21no—
26C31×#327—21no—
27C22×Q8×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31Q811yescharacteristic, complemented
30C23×C4×C31C2311yescharacteristic
31C2×M16×C31—21no—
32C2×M16×C31—21no—
33C31×#121—21no—
34C31×#121—21no—
35C31×#121—21no—
36C31×#121—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31Q811yescharacteristic, complemented
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C22⋊C4×C31D411yescharacteristic
48C2×C42×C31—21no—
49C2×C42×C31—21no—
50C31×#99—42no—
51C31×#99—42no—
52C31×C22⋊C8—21no—
53C31×C22⋊C8—21no—
54C31×C22⋊C8—21no—
55C31×C22⋊C8—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95D411yescharacteristic
64C31×#95D411yescharacteristic
65C31×#95D411yescharacteristic
66C31×#95D411yescharacteristic
67C24×C31—21no—
68C24×C31C2×D411yescharacteristic
69C2×Q8×C31—42no—
70C2×Q8×C31—81no—
71C2×Q8×C31—81no—
72C2×D4×C31—21no—
73C2×D4×C31—21no—
74C2×D4×C31—41no—
75C2×D4×C31—41no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—81no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—41no—
89C22×C4×C31—81no—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×Q811yescharacteristic
93C22×C4×C31#4111yescharacteristic
94C22×C4×C31#4111yescharacteristic
95C22×C4×C31#4111yescharacteristic
96M16×C31—81no—
97M16×C31—81no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—81no—
104C4⋊C4×C31—81no—
105C4⋊C4×C31—81no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—41no—
110C22⋊C4×C31—41no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—81no—
114C42×C31—81no—
115C42×C31—81no—
116#10382C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—81no—
125C23×C31—81no—
126C23×C31#12011yescharacteristic
127C23×C31C22⋊Q811yescharacteristic
128C23×C31#12411yescharacteristic
129Q8×C31—84no—
130D4×C31—81no—
131D4×C31—81no—
132D4×C31—81no—
133D4×C31—81no—
134D4×C31—81no—
135D4×C31—81no—
136C2×C4×C31—22no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—42no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
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—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31C22⋊Q811yescharacteristic
167C2×C4×C31C22⋊Q811yescharacteristic
168C2×C4×C31#12411yescharacteristic
169C2×C4×C31#12411yescharacteristic
170C8×C31—81no—
171C8×C31—81no—
172#2665C2×C3111yescharacteristic, complemented
173#1964C2×C3111yescharacteristic
174#1510C2×C3111yescharacteristic
175#1507C2×C3111yescharacteristic
176#1305C2×C3111yescharacteristic, complemented
177#1297C2×C3111yescharacteristic, complemented
178#1284C2×C3111yescharacteristic, complemented
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31—81no—
192C22×C31—161no—
193C22×C31—161no—
194C22×C31#39311yescharacteristic
195C22×C31#45311yescharacteristic
196C22×C31#45411yescharacteristic
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—21no—
201C4×C31—42no—
202C4×C31—81no—
203C4×C31—81no—
204C4×C31—81no—
205C4×C31—81no—
206C4×C31—81no—
207C4×C31—82no—
208C4×C31—81no—
209C2×#121C22×C3111yescharacteristic
210C2×#99—21no—
211C2×#99—21no—
212#407C22×C3111yescharacteristic
213#407C22×C3111yescharacteristic
214#400—21no—
215#396—21no—
216#395—21no—
217#393—21no—
218#391—21no—
219#387—21no—
220#381C22×C3111yescharacteristic
221#380C22×C3111yescharacteristic
222C4×C22⋊C4C22×C3111yescharacteristic
223C4×C22⋊C4C22×C3111yescharacteristic
224#327—21no—
225#327—21no—
226#327—21no—
227#327—21no—
228C2×C31—21no—
229C2×C31—21no—
230C2×C31—41no—
231C2×C31—41no—
232C2×C31—161no—
233C2×C31#202711yescharacteristic
234C2×C31#203111yescharacteristic
235C2×C31#203211yescharacteristic
236C22×Q8—21no—
237C22×D4—21no—
238C22×D4Q8×C3111yescharacteristic, complemented
239C23×C4C23×C3111yescharacteristic
240C2×M16—21no—
241C2×M16—21no—
242#121—21no—
243#121—21no—
244#121—21no—
245#121—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4Q8×C3111yescharacteristic, complemented
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4D4×C3111yescharacteristic
256C2×C22⋊C4D4×C3111yescharacteristic
257C2×C42—21no—
258C2×C42—21no—
259#99—42no—
260#99—42no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95D4×C3111yescharacteristic
273#95D4×C3111yescharacteristic
274#95D4×C3111yescharacteristic
275#95D4×C3111yescharacteristic
276C31#1038211yescharacteristic, direct product factor, Sylow
277C24—21no—
278C24C2×D4×C3111yescharacteristic
279C2×Q8—42no—
280C2×Q8—81no—
281C2×Q8—81no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—81no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—81no—
300C22×C4C2×D4×C3111yescharacteristic
301C22×C4C2×D4×C3111yescharacteristic
302C22×C4C2×Q8×C3111yescharacteristic
303C22×C4#41×C3111yescharacteristic
304C22×C4#41×C3111yescharacteristic
305C22×C4#41×C3111yescharacteristic
306M16—81no—
307M16—81no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C4⋊C4—81no—
315C4⋊C4—81no—
316C22⋊C4—22no—
317C22⋊C4—42no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C42—81no—
325C42—81no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—81no—
335C23C31×#12011yescharacteristic
336C23C31×C22⋊Q811yescharacteristic
337C23C31×#12411yescharacteristic
338Q8—84no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343D4—81no—
344D4—81no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C31×C22⋊Q811yescharacteristic
376C2×C4C31×C22⋊Q811yescharacteristic
377C2×C4C31×#12411yescharacteristic
378C2×C4C31×#12411yescharacteristic
379C8—81no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—161no—
395C22—161no—
396C22C31×#39311yescharacteristic
397C22C31×#45311yescharacteristic
398C22C31×#45411yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—82no—
410C4—81no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—161no—
416C2C31×#202711yescharacteristic
417C2C31×#203111yescharacteristic
418C2C31×#203211yescharacteristic
subgroupG/H
center, socleC22×C31#393
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2665C2semidirect
5. C31×#1305C2semidirect
6. C31×#1297C2semidirect
7. C31×#1284C2semidirect
29. C22×D4×C31Q8semidirect
41. C2×C4⋊C4×C31Q8semidirect
116. #10382C31direct (N × H)
172. #2665C2×C31semidirect
176. #1305C2×C31semidirect
177. #1297C2×C31semidirect
178. #1284C2×C31semidirect
238. C22×D4Q8×C31semidirect
250. C2×C4⋊C4Q8×C31semidirect
276. C31#10382direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26652
C31×#19642
C31×#15102
C31×#15072
C31×#13052
C31×#12972
C31×#12842
#1038231