Finite Group Databasebeta

← C31×#8876 #21465635

Subgroups — C31×#8876 #21465635

Order 7936.

380 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2992C211yesmaximal, characteristic
2C31×#1843C211yesmaximal, characteristic, complemented
3C31×#1573C211yesmaximal, characteristic, complemented
4C31×#1500C211yesmaximal, characteristic
5C31×#1483C211yesmaximal, characteristic
6C31×#1300C211yesmaximal, characteristic, complemented
7C31×#1283C211yesmaximal, characteristic, complemented
8C31×#529C2211yescharacteristic
9C31×#446—21no—
10C31×#435—21no—
11C31×#435—21no—
12C8×D4×C31—21no—
13C31×#433—21no—
14C31×#432C2211yescharacteristic
15C31×#431C2211yescharacteristic
16C31×#424—21no—
17C2×C31×C4⋊C8—21no—
18C2×C31×C4⋊C8—21no—
19C2×C31×C4⋊C8C2211yescharacteristic
20C2×C31×C4⋊C8C2211yescharacteristic
21C4×M16×C31C2211yescharacteristic
22C31×#376C2211yescharacteristic
23C31×#335—21no—
24C31×#334—21no—
25C31×#328C411yescharacteristic
26C31×#328C411yescharacteristic
27C31×#327C411yescharacteristic
28C31×#327C411yescharacteristic
29C31×Q8⋊C8—21no—
30C31×D4⋊C8—21no—
31C2×M16×C31—21no—
32C2×M16×C31—21no—
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C22×C8×C31D411yescharacteristic
36C22×C8×C31D411yescharacteristic
37C31×#126—21no—
38C31×#125Q811yescharacteristic
39C31×#124Q811yescharacteristic
40C31×#123—21no—
41C31×C22⋊Q8C2×C411yescharacteristic
42C31×#121C2×C411yescharacteristic
43C4×Q8×C31D411yescharacteristic
44C4×D4×C31—21no—
45C4×D4×C31D411yescharacteristic
46C31×#117—21no—
47C2×C42×C31—21no—
48C2×C42×C31C2311yescharacteristic
49C31×C4⋊C8—21no—
50C31×C4⋊C8—21no—
51C31×C4⋊C8—21no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—42no—
57C31×C4⋊C8—42no—
58C31×C4⋊C8D411yescharacteristic
59C31×C4⋊C8D411yescharacteristic
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8—21no—
63C31×C22⋊C8C2×C411yescharacteristic
64C31×C22⋊C8C2×C411yescharacteristic
65C31×#97—21no—
66C31×#97—21no—
67C31×#97—21no—
68C4×C8×C31—21no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71C31×#95—21no—
72C31×#95C2×C411yescharacteristic
73C31×#95C2×C411yescharacteristic
74C2×Q8×C31C4⋊C411yescharacteristic
75C2×D4×C31—21no—
76C2×D4×C31C4⋊C411yescharacteristic
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31#4111yescharacteristic
83M16×C31—22no—
84M16×C31—41no—
85M16×C31—81no—
86C2×C8×C31—21no—
87C2×C8×C31—21no—
88C2×C8×C31—21no—
89C2×C8×C31—21no—
90C2×C8×C31—21no—
91C2×C8×C31—21no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C2×C8×C31—81no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31C4⋊C411yescharacteristic
104C4⋊C4×C31C4⋊C411yescharacteristic
105C22⋊C4×C31—21no—
106C22⋊C4×C31—21no—
107C22⋊C4×C31—21no—
108C22⋊C4×C31—21no—
109C22⋊C4×C31—21no—
110C42×C31—22no—
111C42×C31—22no—
112C42×C31—21no—
113C42×C31C2×D411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31C2×Q811yescharacteristic
116C42×C31#4111yescharacteristic
117#8876C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—21no—
119C23×C31C4×D411yescharacteristic
120Q8×C31—41no—
121D4×C31—41no—
122D4×C31—41no—
123D4×C31—41no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—22no—
129C2×C4×C31—22no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31C2×C4⋊C411yescharacteristic
141C2×C4×C31C4×D411yescharacteristic
142C2×C4×C31#12011yescharacteristic
143C2×C4×C31C22⋊Q811yescharacteristic
144C2×C4×C31C22⋊Q811yescharacteristic
145C2×C4×C31#12311yescharacteristic
146C8×C31—41no—
147C8×C31—41no—
148C8×C31—42no—
149C8×C31—41no—
150C8×C31—41no—
151C8×C31—41no—
152C8×C31—41no—
153C8×C31—81no—
154#2992C2×C3111yescharacteristic
155#1843C2×C3111yescharacteristic, complemented
156#1573C2×C3111yescharacteristic, complemented
157#1500C2×C3111yescharacteristic
158#1483C2×C3111yescharacteristic
159#1300C2×C3111yescharacteristic, complemented
160#1283C2×C3111yescharacteristic, complemented
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31#38511yescharacteristic
167C22×C31#44311yescharacteristic
168C22×C31#44411yescharacteristic
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—42no—
175C4×C31—42no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31#45311yescharacteristic
180C4×C31#45611yescharacteristic
181#529C22×C3111yescharacteristic
182#446—21no—
183#435—21no—
184#435—21no—
185C8×D4—21no—
186#433—21no—
187#432C22×C3111yescharacteristic
188#431C22×C3111yescharacteristic
189#424—21no—
190C2×C4⋊C8—21no—
191C2×C4⋊C8—21no—
192C2×C4⋊C8C22×C3111yescharacteristic
193C2×C4⋊C8C22×C3111yescharacteristic
194C4×M16C22×C3111yescharacteristic
195#376C22×C3111yescharacteristic
196#335—21no—
197#334—21no—
198#328C4×C3111yescharacteristic
199#328C4×C3111yescharacteristic
200#327C4×C3111yescharacteristic
201#327C4×C3111yescharacteristic
202Q8⋊C8—21no—
203D4⋊C8—21no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—81no—
207C2×C31#185911yescharacteristic
208C2×C31#186611yescharacteristic
209C2×C31#186811yescharacteristic
210C2×M16—21no—
211C2×M16—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8D4×C3111yescharacteristic
215C22×C8D4×C3111yescharacteristic
216#126—21no—
217#125Q8×C3111yescharacteristic
218#124Q8×C3111yescharacteristic
219#123—21no—
220C22⋊Q8C2×C4×C3111yescharacteristic
221#121C2×C4×C3111yescharacteristic
222C4×Q8D4×C3111yescharacteristic
223C4×D4—21no—
224C4×D4D4×C3111yescharacteristic
225#117—21no—
226C2×C42—21no—
227C2×C42C23×C3111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—42no—
236C4⋊C8—42no—
237C4⋊C8D4×C3111yescharacteristic
238C4⋊C8D4×C3111yescharacteristic
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8C2×C4×C3111yescharacteristic
243C22⋊C8C2×C4×C3111yescharacteristic
244#97—21no—
245#97—21no—
246#97—21no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250#95—21no—
251#95C2×C4×C3111yescharacteristic
252#95C2×C4×C3111yescharacteristic
253C31#887611yescharacteristic, direct product factor, Sylow
254C2×Q8C4⋊C4×C3111yescharacteristic
255C2×D4—21no—
256C2×D4C4⋊C4×C3111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C22×C4×C3111yescharacteristic
261C22×C4C2×D4×C3111yescharacteristic
262C22×C4#41×C3111yescharacteristic
263M16—22no—
264M16—41no—
265M16—81no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—81no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4C4⋊C4×C3111yescharacteristic
284C4⋊C4C4⋊C4×C3111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C42—22no—
291C42—22no—
292C42—21no—
293C42C2×D4×C3111yescharacteristic
294C42C2×D4×C3111yescharacteristic
295C42C2×Q8×C3111yescharacteristic
296C42#41×C3111yescharacteristic
297C23—21no—
298C23C4×D4×C3111yescharacteristic
299Q8—41no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4C2×C4⋊C4×C3111yescharacteristic
320C2×C4C4×D4×C3111yescharacteristic
321C2×C4C31×#12011yescharacteristic
322C2×C4C31×C22⋊Q811yescharacteristic
323C2×C4C31×C22⋊Q811yescharacteristic
324C2×C4C31×#12311yescharacteristic
325C8—41no—
326C8—41no—
327C8—42no—
328C8—41no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22C31×#38511yescharacteristic
339C22C31×#44311yescharacteristic
340C22C31×#44411yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4C31×#45311yescharacteristic
352C4C31×#45611yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2C31×#185911yescharacteristic
357C2C31×#186611yescharacteristic
358C2C31×#186811yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#385
prime radicalC31×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1843C2semidirect
3. C31×#1573C2semidirect
6. C31×#1300C2semidirect
7. C31×#1283C2semidirect
117. #8876C31direct (N × H)
155. #1843C2×C31semidirect
156. #1573C2×C31semidirect
159. #1300C2×C31semidirect
160. #1283C2×C31semidirect
253. C31#8876direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29922
C31×#18432
C31×#15732
C31×#15002
C31×#14832
C31×#13002
C31×#12832
#887631