Finite Group Databasebeta

← C31×#9356 #21466115

Subgroups — C31×#9356 #21466115

Order 7936.

438 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3079C211yesmaximal, characteristic
2C31×#2991C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1546C211yesmaximal, characteristic, complemented
5C31×#1489C211yesmaximal, characteristic
6C31×#1309C211yesmaximal, characteristic, complemented
7C31×#1299C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#477—21no—
11C31×#476—21no—
12C31×#475—21no—
13C31×#474—21no—
14C8×Q8×C31—21no—
15C31×#436—22no—
16C31×#436—21no—
17C31×#431—21no—
18C31×#431C2211yescharacteristic
19C31×#428C412yes—
20C31×#423—21no—
21C31×#423C2211yescharacteristic
22C31×#423C2211yescharacteristic
23C31×#423C2211yescharacteristic
24C31×#417C412yes—
25C4×M16×C31C2211yescharacteristic
26C31×#343—22no—
27C31×#332—21no—
28C31×#332—21no—
29C31×Q8⋊C8—21no—
30C31×D4⋊C8—21no—
31C2×#41×C31C2×C411yescharacteristic
32C22×Q8×C31—21no—
33C2×M16×C31—22no—
34C2×M16×C31—21no—
35C2×M16×C31—21no—
36C2×M16×C31C2×C412yes—
37C2×M16×C31D412yes—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C4×Q8×C31D411yescharacteristic
43C4×Q8×C31D411yescharacteristic
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C4×D4×C31D411yescharacteristic
47C4×D4×C31D411yescharacteristic
48C31×#117—21no—
49C31×#117C2×C411yescharacteristic
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31C2×C412yes—
52C2×C42×C31—21no—
53C2×C42×C31C2311yescharacteristic
54C31×#107—22no—
55C31×#106—22no—
56C31×C4⋊C8—22no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8D411yescharacteristic
64C31×C4⋊C8D411yescharacteristic
65C31×#103—22no—
66C31×#102—22no—
67C31×C22⋊C8—22no—
68C31×C22⋊C8—21no—
69C31×#97—21no—
70C4×C8×C31—22no—
71C4×C8×C31—21no—
72C4×C8×C31—21no—
73#41×C31—22no—
74#41×C31—41no—
75C2×Q8×C31—41no—
76C2×Q8×C31—41no—
77C2×Q8×C31—81no—
78C2×Q8×C31—81no—
79C2×Q8×C31C22⋊C411yescharacteristic
80C2×D4×C31—21no—
81C2×D4×C31C22⋊C411yescharacteristic
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—22no—
86C22×C4×C31C22×C411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4111yescharacteristic
89M16×C31—22no—
90M16×C31—41no—
91M16×C31—42no—
92M16×C31—42no—
93M16×C31—82no—
94M16×C31—81no—
95C2×C8×C31—22no—
96C2×C8×C31—21no—
97C2×C8×C31—22no—
98C2×C8×C31—21no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31C22⋊C411yescharacteristic
108C4⋊C4×C31C22⋊C411yescharacteristic
109C22⋊C4×C31—21no—
110C22⋊C4×C31—21no—
111C22⋊C4×C31—21no—
112C42×C31—21no—
113C42×C31—21no—
114C42×C31—21no—
115C42×C31C2×D411yescharacteristic
116C42×C31C2×D411yescharacteristic
117C42×C31C2×D411yescharacteristic
118C42×C31#4111yescharacteristic
119#9356C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—21no—
121C23×C31C4×D411yescharacteristic
122Q8×C31—21no—
123Q8×C31—82no—
124Q8×C31—81no—
125Q8×C31—81no—
126Q8×C31#10112yes—
127D4×C31—21no—
128D4×C31—21no—
129D4×C31—42no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—82no—
146C2×C4×C31C2×C22⋊C411yescharacteristic
147C2×C4×C31C4×D411yescharacteristic
148C2×C4×C31#12011yescharacteristic
149C2×C4×C31#12111yescharacteristic
150C2×C4×C31#12111yescharacteristic
151C2×C4×C31#12311yescharacteristic
152C8×C31—42no—
153C8×C31—42no—
154C8×C31—42no—
155C8×C31—41no—
156C8×C31—41no—
157C8×C31—81no—
158#3079C2×C3111yescharacteristic
159#2991C2×C3111yescharacteristic
160#1997C2×C3111yescharacteristic, complemented
161#1546C2×C3111yescharacteristic, complemented
162#1489C2×C3111yescharacteristic
163#1309C2×C3111yescharacteristic, complemented
164#1299C2×C3111yescharacteristic, complemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31#38611yescharacteristic
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—21no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—82no—
179C4×C31C2×#10111yescharacteristic
180C4×C31#41311yescharacteristic
181C4×C31#45511yescharacteristic
182C4×C31#45611yescharacteristic
183C4×C31#47111yescharacteristic
184C4×C31#47211yescharacteristic
185C2×C4⋊Q8C22×C3111yescharacteristic
186C4×#41C22×C3111yescharacteristic
187#477—21no—
188#476—21no—
189#475—21no—
190#474—21no—
191C8×Q8—21no—
192#436—22no—
193#436—21no—
194#431—21no—
195#431C22×C3111yescharacteristic
196#428C4×C3112yes—
197#423—21no—
198#423C22×C3111yescharacteristic
199#423C22×C3111yescharacteristic
200#423C22×C3111yescharacteristic
201#417C4×C3112yes—
202C4×M16C22×C3111yescharacteristic
203#343—22no—
204#332—21no—
205#332—21no—
206Q8⋊C8—21no—
207D4⋊C8—21no—
208C2×C31—41no—
209C2×C31—81no—
210C2×C31#188211yescharacteristic
211C2×C31#190111yescharacteristic
212C2×C31#190711yescharacteristic
213C2×#41C2×C4×C3111yescharacteristic
214C22×Q8—21no—
215C2×M16—22no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16C2×C4×C3112yes—
219C2×M16D4×C3112yes—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4×Q8D4×C3111yescharacteristic
225C4×Q8D4×C3111yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4D4×C3111yescharacteristic
229C4×D4D4×C3111yescharacteristic
230#117—21no—
231#117C2×C4×C3111yescharacteristic
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C3112yes—
234C2×C42—21no—
235C2×C42C23×C3111yescharacteristic
236#107—22no—
237#106—22no—
238C4⋊C8—22no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C3111yescharacteristic
246C4⋊C8D4×C3111yescharacteristic
247#103—22no—
248#102—22no—
249C22⋊C8—22no—
250C22⋊C8—21no—
251#97—21no—
252C4×C8—22no—
253C4×C8—21no—
254C4×C8—21no—
255C31#935611yescharacteristic, direct product factor, Sylow
256#41—22no—
257#41—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—81no—
261C2×Q8—81no—
262C2×Q8C22⋊C4×C3111yescharacteristic
263C2×D4—21no—
264C2×D4C22⋊C4×C3111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4C22×C4×C3111yescharacteristic
270C22×C4C2×D4×C3111yescharacteristic
271C22×C4#41×C3111yescharacteristic
272M16—22no—
273M16—41no—
274M16—42no—
275M16—42no—
276M16—82no—
277M16—81no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C3111yescharacteristic
291C4⋊C4C22⋊C4×C3111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42C2×D4×C3111yescharacteristic
299C42C2×D4×C3111yescharacteristic
300C42C2×D4×C3111yescharacteristic
301C42#41×C3111yescharacteristic
302C23—21no—
303C23C4×D4×C3111yescharacteristic
304Q8—21no—
305Q8—82no—
306Q8—81no—
307Q8—81no—
308Q8C31×#10112yes—
309D4—21no—
310D4—21no—
311D4—42no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4C2×C22⋊C4×C3111yescharacteristic
329C2×C4C4×D4×C3111yescharacteristic
330C2×C4C31×#12011yescharacteristic
331C2×C4C31×#12111yescharacteristic
332C2×C4C31×#12111yescharacteristic
333C2×C4C31×#12311yescharacteristic
334C8—42no—
335C8—42no—
336C8—42no—
337C8—41no—
338C8—41no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C31×#38611yescharacteristic
347C4—21no—
348C4—21no—
349C4—22no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—82no—
354C4C2×C31×#10111yescharacteristic
355C4C31×#41311yescharacteristic
356C4C31×#45511yescharacteristic
357C4C31×#45611yescharacteristic
358C4C31×#47111yescharacteristic
359C4C31×#47211yescharacteristic
360C2—41no—
361C2—81no—
362C2C31×#188211yescharacteristic
363C2C31×#190111yescharacteristic
364C2C31×#190711yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×#41×C31C2×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×#1546C2semidirect
6. C31×#1309C2semidirect
7. C31×#1299C2semidirect
119. #9356C31direct (N × H)
160. #1997C2×C31semidirect
161. #1546C2×C31semidirect
163. #1309C2×C31semidirect
164. #1299C2×C31semidirect
255. C31#9356direct (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×#29912
C31×#19972
C31×#15462
C31×#14892
C31×#13092
C31×#12992
#935631