Finite Group Databasebeta

← C31×#9338 #21466097

Subgroups — C31×#9338 #21466097

Order 7936.

400 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3238C211yesmaximal, characteristic
2C31×#2995C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1556C211yesmaximal, characteristic, complemented
5C31×#1529C211yesmaximal, characteristic
6C31×#1307C211yesmaximal, characteristic, complemented
7C31×#1291C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C31×#529C2211yescharacteristic
10C31×#501—21no—
11C31×#489—21no—
12C31×#483C412yes—
13C31×#480C412yes—
14C31×#477—21no—
15C31×#476—21no—
16C31×#446—21no—
17C31×#436—21no—
18C31×#435—21no—
19C31×#435—21no—
20C31×#433—21no—
21C31×#432C2211yescharacteristic
22C31×#432C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C31×#424—21no—
25C31×#423C2211yescharacteristic
26C4×M16×C31C2211yescharacteristic
27C31×#343—21no—
28C31×#343—21no—
29C31×#332—21no—
30C31×#332—21no—
31C31×#330—21no—
32C31×#329—21no—
33C22×Q8×C31—21no—
34C2×M16×C31—21no—
35C2×M16×C31—21no—
36C2×M16×C31D411yescharacteristic
37C2×M16×C31D411yescharacteristic
38C22×C8×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×#126—21no—
44C31×#125D411yescharacteristic
45C31×#124D411yescharacteristic
46C31×#123—21no—
47C31×C22⋊Q8C2×C411yescharacteristic
48C31×#121C2×C411yescharacteristic
49C4×Q8×C31D411yescharacteristic
50C4×D4×C31—21no—
51C4×D4×C31D411yescharacteristic
52C31×#117—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31C2×C412yes—
55C2×C42×C31C2311yescharacteristic
56C31×#107—22no—
57C31×#106—22no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8D411yescharacteristic
65C31×C4⋊C8D411yescharacteristic
66C31×#103—22no—
67C31×#102—22no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8C2×C412yes—
73C31×#97—21no—
74C31×#97—21no—
75C31×#97—21no—
76C31×#97—21no—
77C31×#97—21no—
78C4×C8×C31—21no—
79C4×C8×C31—21no—
80C2×Q8×C31—41no—
81C2×Q8×C31—41no—
82C2×Q8×C31—82no—
83C2×Q8×C31C22⋊C411yescharacteristic
84C2×D4×C31—21no—
85C2×D4×C31C22⋊C411yescharacteristic
86C22×C4×C31—21no—
87C22×C4×C31—22no—
88C22×C4×C31C22×C411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31#4111yescharacteristic
91M16×C31—22no—
92M16×C31—41no—
93M16×C31—41no—
94M16×C31—41no—
95M16×C31—81no—
96C2×C8×C31—22no—
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C2×C8×C31—81no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31C22⋊C411yescharacteristic
113C4⋊C4×C31C22⋊C411yescharacteristic
114C22⋊C4×C31—21no—
115C22⋊C4×C31—21no—
116C22⋊C4×C31—21no—
117C22⋊C4×C31—21no—
118C22⋊C4×C31—21no—
119C42×C31—21no—
120C42×C31C2×D411yescharacteristic
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123C42×C31#4111yescharacteristic
124#9338C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—21no—
126C23×C31C4×D411yescharacteristic
127Q8×C31—41no—
128Q8×C31—82no—
129Q8×C31—82no—
130D4×C31—41no—
131D4×C31—81no—
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—42no—
142C2×C4×C31—82no—
143C2×C4×C31C2×C22⋊C411yescharacteristic
144C2×C4×C31C4×D411yescharacteristic
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31#12111yescharacteristic
147C2×C4×C31#12111yescharacteristic
148C2×C4×C31#12311yescharacteristic
149C8×C31—42no—
150C8×C31—42no—
151C8×C31—41no—
152C8×C31—41no—
153C8×C31—41no—
154C8×C31—41no—
155C8×C31—81no—
156#3238C2×C3111yescharacteristic
157#2995C2×C3111yescharacteristic
158#1997C2×C3111yescharacteristic, complemented
159#1556C2×C3111yescharacteristic, complemented
160#1529C2×C3111yescharacteristic
161#1307C2×C3111yescharacteristic, complemented
162#1291C2×C3111yescharacteristic, complemented
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—41no—
169C22×C31#38611yescharacteristic
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—82no—
179C4×C31#45511yescharacteristic
180C4×C31#45611yescharacteristic
181C2×C4⋊Q8C22×C3111yescharacteristic
182#529C22×C3111yescharacteristic
183#501—21no—
184#489—21no—
185#483C4×C3112yes—
186#480C4×C3112yes—
187#477—21no—
188#476—21no—
189#446—21no—
190#436—21no—
191#435—21no—
192#435—21no—
193#433—21no—
194#432C22×C3111yescharacteristic
195#432C22×C3111yescharacteristic
196#432C22×C3111yescharacteristic
197#424—21no—
198#423C22×C3111yescharacteristic
199C4×M16C22×C3111yescharacteristic
200#343—21no—
201#343—21no—
202#332—21no—
203#332—21no—
204#330—21no—
205#329—21no—
206C2×C31—41no—
207C2×C31—81no—
208C2×C31#188211yescharacteristic
209C2×C31#190311yescharacteristic
210C2×C31#191511yescharacteristic
211C22×Q8—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16D4×C3111yescharacteristic
215C2×M16D4×C3111yescharacteristic
216C22×C8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221#126—21no—
222#125D4×C3111yescharacteristic
223#124D4×C3111yescharacteristic
224#123—21no—
225C22⋊Q8C2×C4×C3111yescharacteristic
226#121C2×C4×C3111yescharacteristic
227C4×Q8D4×C3111yescharacteristic
228C4×D4—21no—
229C4×D4D4×C3111yescharacteristic
230#117—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C2×C4×C3112yes—
233C2×C42C23×C3111yescharacteristic
234#107—22no—
235#106—22no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8D4×C3111yescharacteristic
243C4⋊C8D4×C3111yescharacteristic
244#103—22no—
245#102—22no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8C2×C4×C3112yes—
251#97—21no—
252#97—21no—
253#97—21no—
254#97—21no—
255#97—21no—
256C4×C8—21no—
257C4×C8—21no—
258C31#933811yescharacteristic, direct product factor, Sylow
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×Q8C22⋊C4×C3111yescharacteristic
263C2×D4—21no—
264C2×D4C22⋊C4×C3111yescharacteristic
265C22×C4—21no—
266C22×C4—22no—
267C22×C4C22×C4×C3111yescharacteristic
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4#41×C3111yescharacteristic
270M16—22no—
271M16—41no—
272M16—41no—
273M16—41no—
274M16—81no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—81no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C3111yescharacteristic
292C4⋊C4C22⋊C4×C3111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C42—21no—
299C42C2×D4×C3111yescharacteristic
300C42C2×D4×C3111yescharacteristic
301C42C2×D4×C3111yescharacteristic
302C42#41×C3111yescharacteristic
303C23—21no—
304C23C4×D4×C3111yescharacteristic
305Q8—41no—
306Q8—82no—
307Q8—82no—
308D4—41no—
309D4—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—82no—
321C2×C4C2×C22⋊C4×C3111yescharacteristic
322C2×C4C4×D4×C3111yescharacteristic
323C2×C4C31×#12011yescharacteristic
324C2×C4C31×#12111yescharacteristic
325C2×C4C31×#12111yescharacteristic
326C2×C4C31×#12311yescharacteristic
327C8—42no—
328C8—42no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—41no—
333C8—81no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C31×#38611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—82no—
350C4C31×#45511yescharacteristic
351C4C31×#45611yescharacteristic
352C2—41no—
353C2—81no—
354C2C31×#188211yescharacteristic
355C2C31×#190311yescharacteristic
356C2C31×#191511yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#121C2×C4
LCSG ▷ C22×C4 ▷ 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×#1997C2semidirect
4. C31×#1556C2semidirect
6. C31×#1307C2semidirect
7. C31×#1291C2semidirect
124. #9338C31direct (N × H)
158. #1997C2×C31semidirect
159. #1556C2×C31semidirect
161. #1307C2×C31semidirect
162. #1291C2×C31semidirect
258. C31#9338direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32382
C31×#29952
C31×#19972
C31×#15562
C31×#15292
C31×#13072
C31×#12912
#933831