Finite Group Databasebeta

← C31×#9337 #21466096

Subgroups — C31×#9337 #21466096

Order 7936.

412 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3218C211yesmaximal, characteristic
2C31×#2995C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1558C211yesmaximal, characteristic, complemented
5C31×#1529C211yesmaximal, characteristic
6C31×#1307C211yesmaximal, characteristic, complemented
7C31×#1291C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C31×#529C2211yescharacteristic
10C31×#497—21no—
11C31×#491—21no—
12C31×#462—21no—
13C31×#461—21no—
14C31×#451C412yes—
15C31×#448C412yes—
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×#333—21no—
30C31×#333—21no—
31C31×#330—21no—
32C31×#329—21no—
33C22×Q8×C31C2×C412yes—
34C2×Q16×C31—22no—
35C2×SD16×C31—22no—
36C2×M16×C31—21no—
37C2×M16×C31—21no—
38C2×M16×C31D411yescharacteristic
39C2×M16×C31D411yescharacteristic
40C22×C8×C31—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×#126—21no—
46C31×#125D411yescharacteristic
47C31×#124D411yescharacteristic
48C31×#123—21no—
49C31×C22⋊Q8C2×C411yescharacteristic
50C31×#121C2×C411yescharacteristic
51C4×Q8×C31D411yescharacteristic
52C4×D4×C31—21no—
53C4×D4×C31D411yescharacteristic
54C31×#117—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C42×C31C2311yescharacteristic
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—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—22no—
81C2×Q8×C31—22no—
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
91Q16×C31—82no—
92SD16×C31—82no—
93M16×C31—22no—
94M16×C31—41no—
95M16×C31—41no—
96M16×C31—41no—
97M16×C31—81no—
98C2×C8×C31—22no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—21no—
102C2×C8×C31—21no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C2×C8×C31—81no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31C22⋊C411yescharacteristic
115C4⋊C4×C31C22⋊C411yescharacteristic
116C22⋊C4×C31—21no—
117C22⋊C4×C31—21no—
118C22⋊C4×C31—21no—
119C22⋊C4×C31—21no—
120C22⋊C4×C31—21no—
121C42×C31—21no—
122C42×C31C2×D411yescharacteristic
123C42×C31C2×D411yescharacteristic
124C42×C31C2×D411yescharacteristic
125C42×C31#4111yescharacteristic
126#9337C3111yesmaximal, characteristic, direct product factor, Sylow
127C23×C31—21no—
128C23×C31C4×D411yescharacteristic
129Q8×C31—41no—
130Q8×C31—42no—
131Q8×C31—42no—
132Q8×C31—82no—
133D4×C31—41no—
134D4×C31—81no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
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—41no—
155C8×C31—41no—
156C8×C31—41no—
157C8×C31—41no—
158C8×C31—81no—
159#3218C2×C3111yescharacteristic
160#2995C2×C3111yescharacteristic
161#1997C2×C3111yescharacteristic, complemented
162#1558C2×C3111yescharacteristic, complemented
163#1529C2×C3111yescharacteristic
164#1307C2×C3111yescharacteristic, complemented
165#1291C2×C3111yescharacteristic, complemented
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31#38611yescharacteristic
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—41no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—82no—
182C4×C31#45511yescharacteristic
183C4×C31#45611yescharacteristic
184C2×C4⋊Q8C22×C3111yescharacteristic
185#529C22×C3111yescharacteristic
186#497—21no—
187#491—21no—
188#462—21no—
189#461—21no—
190#451C4×C3112yes—
191#448C4×C3112yes—
192#446—21no—
193#436—21no—
194#435—21no—
195#435—21no—
196#433—21no—
197#432C22×C3111yescharacteristic
198#432C22×C3111yescharacteristic
199#432C22×C3111yescharacteristic
200#424—21no—
201#423C22×C3111yescharacteristic
202C4×M16C22×C3111yescharacteristic
203#343—21no—
204#343—21no—
205#333—21no—
206#333—21no—
207#330—21no—
208#329—21no—
209C2×C31—41no—
210C2×C31—81no—
211C2×C31#188211yescharacteristic
212C2×C31#190211yescharacteristic
213C2×C31#191411yescharacteristic
214C22×Q8C2×C4×C3112yes—
215C2×Q16—22no—
216C2×SD16—22no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16D4×C3111yescharacteristic
220C2×M16D4×C3111yescharacteristic
221C22×C8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226#126—21no—
227#125D4×C3111yescharacteristic
228#124D4×C3111yescharacteristic
229#123—21no—
230C22⋊Q8C2×C4×C3111yescharacteristic
231#121C2×C4×C3111yescharacteristic
232C4×Q8D4×C3111yescharacteristic
233C4×D4—21no—
234C4×D4D4×C3111yescharacteristic
235#117—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42C23×C3111yescharacteristic
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#103—22no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8C2×C4×C3112yes—
254#97—21no—
255#97—21no—
256#97—21no—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C31#933711yescharacteristic, direct product factor, Sylow
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—82no—
265C2×Q8C22⋊C4×C3111yescharacteristic
266C2×D4—21no—
267C2×D4C22⋊C4×C3111yescharacteristic
268C22×C4—21no—
269C22×C4—22no—
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3111yescharacteristic
272C22×C4#41×C3111yescharacteristic
273Q16—82no—
274SD16—82no—
275M16—22no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—81no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—81no—
288C4⋊C4—21no—
289C4⋊C4—21no—
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—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C42—21no—
304C42C2×D4×C3111yescharacteristic
305C42C2×D4×C3111yescharacteristic
306C42C2×D4×C3111yescharacteristic
307C42#41×C3111yescharacteristic
308C23—21no—
309C23C4×D4×C3111yescharacteristic
310Q8—41no—
311Q8—42no—
312Q8—42no—
313Q8—82no—
314D4—41no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4C2×C22⋊C4×C3111yescharacteristic
328C2×C4C4×D4×C3111yescharacteristic
329C2×C4C31×#12011yescharacteristic
330C2×C4C31×#12111yescharacteristic
331C2×C4C31×#12111yescharacteristic
332C2×C4C31×#12311yescharacteristic
333C8—42no—
334C8—42no—
335C8—41no—
336C8—41no—
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—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—82no—
356C4C31×#45511yescharacteristic
357C4C31×#45611yescharacteristic
358C2—41no—
359C2—81no—
360C2C31×#188211yescharacteristic
361C2C31×#190211yescharacteristic
362C2C31×#191411yescharacteristic
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×#1558C2semidirect
6. C31×#1307C2semidirect
7. C31×#1291C2semidirect
126. #9337C31direct (N × H)
161. #1997C2×C31semidirect
162. #1558C2×C31semidirect
164. #1307C2×C31semidirect
165. #1291C2×C31semidirect
261. C31#9337direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32182
C31×#29952
C31×#19972
C31×#15582
C31×#15292
C31×#13072
C31×#12912
#933731