Finite Group Databasebeta

← C31×#9353 #21466112

Subgroups — C31×#9353 #21466112

Order 7936.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3039C211yesmaximal, characteristic
2C31×#2990C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1548C211yesmaximal, characteristic, complemented
5C31×#1489C211yesmaximal, characteristic
6C31×#1309C211yesmaximal, characteristic, complemented
7C31×#1299C211yesmaximal, characteristic, complemented
8C2×C31×#137C412yes—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C4×#41×C31C2211yescharacteristic
11C31×#462—21no—
12C31×#462—21no—
13C31×#461—21no—
14C31×#461—21no—
15C31×#446—21no—
16C31×#435—22no—
17C8×D4×C31—21no—
18C31×#432—21no—
19C31×#431C2211yescharacteristic
20C31×#423C2211yescharacteristic
21C31×#423C2211yescharacteristic
22C31×#423C2211yescharacteristic
23C2×C31×C4⋊C8—21no—
24C31×#419C412yes—
25C4×M16×C31C2211yescharacteristic
26C31×#343—22no—
27C31×#333—21no—
28C31×#333—21no—
29C31×Q8⋊C8—21no—
30C31×D4⋊C8—21no—
31C2×#41×C31C2×C411yescharacteristic
32C22×Q8×C31C2×C412yes—
33C31×#137—44no—
34C2×Q16×C31—22no—
35C2×SD16×C31—22no—
36C2×M16×C31—21no—
37C2×M16×C31—21no—
38C2×M16×C31C2×C412yes—
39C2×M16×C31D412yes—
40C22×C8×C31—22no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C4×Q8×C31D411yescharacteristic
46C4×Q8×C31D411yescharacteristic
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31D411yescharacteristic
50C4×D4×C31D411yescharacteristic
51C31×#117—21no—
52C31×#117C2×C411yescharacteristic
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C42×C31—21no—
56C2×C42×C31C2311yescharacteristic
57C31×C4⋊C8—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×#103—22no—
68C31×C22⋊C8—22no—
69C31×C22⋊C8—21no—
70C31×#97—22no—
71C31×#97—21no—
72C4×C8×C31—21no—
73C4×C8×C31—21no—
74#41×C31—22no—
75#41×C31—41no—
76C2×Q8×C31—22no—
77C2×Q8×C31—22no—
78C2×Q8×C31—42no—
79C2×Q8×C31—42no—
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—22no—
87C22×C4×C31C22×C411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31#4111yescharacteristic
90Q16×C31—44no—
91SD16×C31—44no—
92M16×C31—22no—
93M16×C31—41no—
94M16×C31—42no—
95M16×C31—42no—
96M16×C31—81no—
97C2×C8×C31—22no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—22no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C2×C8×C31—82no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31C22⋊C411yescharacteristic
111C4⋊C4×C31C22⋊C411yescharacteristic
112C22⋊C4×C31—21no—
113C22⋊C4×C31—21no—
114C22⋊C4×C31—21no—
115C42×C31—21no—
116C42×C31—21no—
117C42×C31—21no—
118C42×C31C2×D411yescharacteristic
119C42×C31C2×D411yescharacteristic
120C42×C31C2×D411yescharacteristic
121C42×C31#4111yescharacteristic
122#9353C3111yesmaximal, characteristic, direct product factor, Sylow
123C23×C31—21no—
124C23×C31C4×D411yescharacteristic
125Q8×C31—21no—
126Q8×C31—21no—
127Q8×C31—42no—
128Q8×C31—42no—
129Q8×C31—82no—
130D4×C31—21no—
131D4×C31—42no—
132D4×C31#10012yes—
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—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31—82no—
149C2×C4×C31C2×C22⋊C411yescharacteristic
150C2×C4×C31C4×D411yescharacteristic
151C2×C4×C31#12011yescharacteristic
152C2×C4×C31#12111yescharacteristic
153C2×C4×C31#12111yescharacteristic
154C2×C4×C31#12311yescharacteristic
155C8×C31—42no—
156C8×C31—42no—
157C8×C31—41no—
158C8×C31—42no—
159C8×C31—41no—
160C8×C31—81no—
161#3039C2×C3111yescharacteristic
162#2990C2×C3111yescharacteristic
163#1997C2×C3111yescharacteristic, complemented
164#1548C2×C3111yescharacteristic, complemented
165#1489C2×C3111yescharacteristic
166#1309C2×C3111yescharacteristic, complemented
167#1299C2×C3111yescharacteristic, complemented
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—22no—
171C22×C31—21no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31#38611yescharacteristic
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—41no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—82no—
182C4×C31C2×#10011yescharacteristic
183C4×C31#41311yescharacteristic
184C4×C31#45511yescharacteristic
185C4×C31#45611yescharacteristic
186C4×C31#47111yescharacteristic
187C4×C31#47311yescharacteristic
188C2×#137C4×C3112yes—
189C2×C4⋊Q8C22×C3111yescharacteristic
190C4×#41C22×C3111yescharacteristic
191#462—21no—
192#462—21no—
193#461—21no—
194#461—21no—
195#446—21no—
196#435—22no—
197C8×D4—21no—
198#432—21no—
199#431C22×C3111yescharacteristic
200#423C22×C3111yescharacteristic
201#423C22×C3111yescharacteristic
202#423C22×C3111yescharacteristic
203C2×C4⋊C8—21no—
204#419C4×C3112yes—
205C4×M16C22×C3111yescharacteristic
206#343—22no—
207#333—21no—
208#333—21no—
209Q8⋊C8—21no—
210D4⋊C8—21no—
211C2×C31—41no—
212C2×C31—42no—
213C2×C31#188211yescharacteristic
214C2×C31#190011yescharacteristic
215C2×C31#190811yescharacteristic
216C2×#41C2×C4×C3111yescharacteristic
217C22×Q8C2×C4×C3112yes—
218#137—44no—
219C2×Q16—22no—
220C2×SD16—22no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16C2×C4×C3112yes—
224C2×M16D4×C3112yes—
225C22×C8—22no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4×Q8D4×C3111yescharacteristic
231C4×Q8D4×C3111yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4D4×C3111yescharacteristic
235C4×D4D4×C3111yescharacteristic
236#117—21no—
237#117C2×C4×C3111yescharacteristic
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C3111yescharacteristic
242C4⋊C8—22no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8D4×C3111yescharacteristic
250C4⋊C8D4×C3111yescharacteristic
251#103—22no—
252#103—22no—
253C22⋊C8—22no—
254C22⋊C8—21no—
255#97—22no—
256#97—21no—
257C4×C8—21no—
258C4×C8—21no—
259C31#935311yescharacteristic, direct product factor, Sylow
260#41—22no—
261#41—41no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8C22⋊C4×C3111yescharacteristic
267C2×D4—21no—
268C2×D4C22⋊C4×C3111yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4C22×C4×C3111yescharacteristic
274C22×C4C2×D4×C3111yescharacteristic
275C22×C4#41×C3111yescharacteristic
276Q16—44no—
277SD16—44no—
278M16—22no—
279M16—41no—
280M16—42no—
281M16—42no—
282M16—81no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—82no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4C22⋊C4×C3111yescharacteristic
297C4⋊C4C22⋊C4×C3111yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42C2×D4×C3111yescharacteristic
305C42C2×D4×C3111yescharacteristic
306C42C2×D4×C3111yescharacteristic
307C42#41×C3111yescharacteristic
308C23—21no—
309C23C4×D4×C3111yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315D4—21no—
316D4—42no—
317D4C31×#10012yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4C2×C22⋊C4×C3111yescharacteristic
335C2×C4C4×D4×C3111yescharacteristic
336C2×C4C31×#12011yescharacteristic
337C2×C4C31×#12111yescharacteristic
338C2×C4C31×#12111yescharacteristic
339C2×C4C31×#12311yescharacteristic
340C8—42no—
341C8—42no—
342C8—41no—
343C8—42no—
344C8—41no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22C31×#38611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—82no—
360C4C2×C31×#10011yescharacteristic
361C4C31×#41311yescharacteristic
362C4C31×#45511yescharacteristic
363C4C31×#45611yescharacteristic
364C4C31×#47111yescharacteristic
365C4C31×#47311yescharacteristic
366C2—41no—
367C2—42no—
368C2C31×#188211yescharacteristic
369C2C31×#190011yescharacteristic
370C2C31×#190811yescharacteristic
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×#1548C2semidirect
6. C31×#1309C2semidirect
7. C31×#1299C2semidirect
122. #9353C31direct (N × H)
163. #1997C2×C31semidirect
164. #1548C2×C31semidirect
166. #1309C2×C31semidirect
167. #1299C2×C31semidirect
259. C31#9353direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30392
C31×#29902
C31×#19972
C31×#15482
C31×#14892
C31×#13092
C31×#12992
#935331