Finite Group Databasebeta

← C31×#9170 #21465929

Subgroups — C31×#9170 #21465929

Order 7936.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3079C211yesmaximal, characteristic
2C31×#2925C211yesmaximal, characteristic
3C31×#1549C211yesmaximal, characteristic, complemented
4C2×C31×#333C211yesmaximal, characteristic, complemented
5C31×#1477C211yesmaximal, characteristic
6C31×#1301C211yesmaximal, characteristic, complemented
7C31×#1292C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#477—21no—
11C31×#476—21no—
12C31×#475C412yes—
13C31×#474C412yes—
14C31×#433—22no—
15C31×#432—21no—
16C31×#431—21no—
17C31×#431C2211yescharacteristic
18C31×#428—21no—
19C31×#423C2211yescharacteristic
20C31×#423C2211yescharacteristic
21C2×C31×C4⋊C8C2211yescharacteristic
22C2×C31×C4⋊C8C2211yescharacteristic
23C31×#417—21no—
24C31×#408—21no—
25C31×#405—21no—
26C31×#333—21no—
27C31×#333—21no—
28C31×#332—22no—
29C31×Q8⋊C8—21no—
30C31×D4⋊C8—21no—
31C2×#41×C31D411yescharacteristic
32C22×Q8×C31—21no—
33C2×M16×C31—21no—
34C2×M16×C31—21no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8C2×C412yes—
41C4×Q8×C31C2×C411yescharacteristic
42C4×Q8×C31D411yescharacteristic
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C4×D4×C31C2×C411yescharacteristic
46C4×D4×C31D411yescharacteristic
47C31×#117—21no—
48C31×#117D411yescharacteristic
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31C2311yescharacteristic
53C31×#107—22no—
54C31×#106—22no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8C2×C412yes—
62C31×C4⋊C8D411yescharacteristic
63C31×C4⋊C8D411yescharacteristic
64C31×C4⋊C8D412yes—
65C31×#103—22no—
66C31×#102—22no—
67C31×C22⋊C8—22no—
68C31×C22⋊C8—22no—
69C31×C22⋊C8—21no—
70C31×#97—22no—
71C4×C8×C31—22no—
72C4×C8×C31—21no—
73#41×C31—21no—
74#41×C31—21no—
75#41×C31—21no—
76#41×C31—21no—
77C2×Q8×C31—22no—
78C2×Q8×C31—41no—
79C2×Q8×C31—82no—
80C2×Q8×C31C22⋊C411yescharacteristic
81C2×D4×C31—21no—
82C2×D4×C31C22⋊C411yescharacteristic
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—41no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4111yescharacteristic
89C22×C4×C31#4111yescharacteristic
90M16×C31—41no—
91M16×C31—41no—
92M16×C31—41no—
93M16×C31—41no—
94C2×C8×C31—22no—
95C2×C8×C31—21no—
96C2×C8×C31—22no—
97C2×C8×C31—21no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31—81no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—22no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31C22⋊C411yescharacteristic
110C4⋊C4×C31C22⋊C411yescharacteristic
111C22⋊C4×C31—21no—
112C22⋊C4×C31—21no—
113C22⋊C4×C31—21no—
114C42×C31—21no—
115C42×C31—21no—
116C42×C31—21no—
117C42×C31C22×C411yescharacteristic
118C42×C31C2×D411yescharacteristic
119C42×C31C2×D411yescharacteristic
120C42×C31C2×D411yescharacteristic
121#9170C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—21no—
123C23×C31#12311yescharacteristic
124Q8×C31—21no—
125Q8×C31—21no—
126Q8×C31—82no—
127Q8×C31—82no—
128D4×C31—21no—
129D4×C31—21no—
130D4×C31—41no—
131D4×C31—41no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—81no—
144C2×C4×C31—82no—
145C2×C4×C31C2×C22⋊C411yescharacteristic
146C2×C4×C31C4×D411yescharacteristic
147C2×C4×C31C4×D411yescharacteristic
148C2×C4×C31#12011yescharacteristic
149C2×C4×C31#12111yescharacteristic
150C2×C4×C31#12111yescharacteristic
151C2×C4×C31#13511yescharacteristic
152C2×C4×C31#13511yescharacteristic
153C2×C4×C31#13711yescharacteristic
154C2×C4×C31#13711yescharacteristic
155C8×C31—42no—
156C8×C31—41no—
157C8×C31—41no—
158C8×C31—42no—
159C8×C31—81no—
160C8×C31—81no—
161#3079C2×C3111yescharacteristic
162#2925C2×C3111yescharacteristic
163#1549C2×C3111yescharacteristic, complemented
164C2×#333C2×C3111yescharacteristic, complemented
165#1477C2×C3111yescharacteristic
166#1301C2×C3111yescharacteristic, complemented
167#1292C2×C3111yescharacteristic, complemented
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31#38611yescharacteristic
174C22×C31#48511yescharacteristic
175C22×C31#48511yescharacteristic
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—82no—
183C4×C31#41611yescharacteristic
184C4×C31#41911yescharacteristic
185C4×C31#45211yescharacteristic
186C4×C31#45211yescharacteristic
187C4×C31#47111yescharacteristic
188C4×C31#47311yescharacteristic
189C2×C4⋊Q8C22×C3111yescharacteristic
190C4×#41C22×C3111yescharacteristic
191#477—21no—
192#476—21no—
193#475C4×C3112yes—
194#474C4×C3112yes—
195#433—22no—
196#432—21no—
197#431—21no—
198#431C22×C3111yescharacteristic
199#428—21no—
200#423C22×C3111yescharacteristic
201#423C22×C3111yescharacteristic
202C2×C4⋊C8C22×C3111yescharacteristic
203C2×C4⋊C8C22×C3111yescharacteristic
204#417—21no—
205#408—21no—
206#405—21no—
207#333—21no—
208#333—21no—
209#332—22no—
210Q8⋊C8—21no—
211D4⋊C8—21no—
212C2×C31—21no—
213C2×C31—21no—
214C2×C31—81no—
215C2×C31#187311yescharacteristic
216C2×C31#190311yescharacteristic
217C2×C31#190811yescharacteristic
218C2×#41D4×C3111yescharacteristic
219C22×Q8—21no—
220C2×M16—21no—
221C2×M16—21no—
222C22×C8—21no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C2×C4×C3112yes—
228C4×Q8C2×C4×C3111yescharacteristic
229C4×Q8D4×C3111yescharacteristic
230C4×D4—21no—
231C4×D4—21no—
232C4×D4C2×C4×C3111yescharacteristic
233C4×D4D4×C3111yescharacteristic
234#117—21no—
235#117D4×C3111yescharacteristic
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42C23×C3111yescharacteristic
240#107—22no—
241#106—22no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8C2×C4×C3112yes—
249C4⋊C8D4×C3112yes—
250C4⋊C8D4×C3111yescharacteristic
251C4⋊C8D4×C3111yescharacteristic
252#103—22no—
253#102—22no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—21no—
257#97—22no—
258C4×C8—22no—
259C4×C8—21no—
260C31#917011yescharacteristic, direct product factor, Sylow
261#41—21no—
262#41—21no—
263#41—21no—
264#41—21no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8C22⋊C4×C3111yescharacteristic
269C2×D4—21no—
270C2×D4C22⋊C4×C3111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4C2×D4×C3111yescharacteristic
276C22×C4#41×C3111yescharacteristic
277C22×C4#41×C3111yescharacteristic
278M16—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—81no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4C22⋊C4×C3111yescharacteristic
298C4⋊C4C22⋊C4×C3111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42C22×C4×C3111yescharacteristic
306C42C2×D4×C3111yescharacteristic
307C42C2×D4×C3111yescharacteristic
308C42C2×D4×C3111yescharacteristic
309C23—21no—
310C23C31×#12311yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—82no—
314Q8—82no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—82no—
332C2×C4C2×C22⋊C4×C3111yescharacteristic
333C2×C4C4×D4×C3111yescharacteristic
334C2×C4C4×D4×C3111yescharacteristic
335C2×C4C31×#12011yescharacteristic
336C2×C4C31×#12111yescharacteristic
337C2×C4C31×#12111yescharacteristic
338C2×C4C31×#13511yescharacteristic
339C2×C4C31×#13511yescharacteristic
340C2×C4C31×#13711yescharacteristic
341C2×C4C31×#13711yescharacteristic
342C8—42no—
343C8—41no—
344C8—41no—
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C31×#38611yescharacteristic
354C22C31×#48511yescharacteristic
355C22C31×#48511yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—82no—
363C4C31×#41611yescharacteristic
364C4C31×#41911yescharacteristic
365C4C31×#45211yescharacteristic
366C4C31×#45211yescharacteristic
367C4C31×#47111yescharacteristic
368C4C31×#47311yescharacteristic
369C2—21no—
370C2—21no—
371C2—81no—
372C2C31×#187311yescharacteristic
373C2C31×#190311yescharacteristic
374C2C31×#190811yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1549C2semidirect
4. C2×C31×#333C2semidirect
6. C31×#1301C2semidirect
7. C31×#1292C2semidirect
121. #9170C31direct (N × H)
163. #1549C2×C31semidirect
164. C2×#333C2×C31semidirect
166. #1301C2×C31semidirect
167. #1292C2×C31semidirect
260. C31#9170direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30792
C31×#29252
C31×#15492
C2×C31×#3332
C31×#14772
C31×#13012
C31×#12922
#917031