Finite Group Databasebeta

← C31×#11844 #21468603

Subgroups — C31×#11844 #21468603

Order 7936.

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2610C211yesmaximal, characteristic
2C31×#1820C211yesmaximal, characteristic, complemented
3C31×#1458C211yesmaximal, characteristic, complemented
4C31×#1351C212yesmaximal, complemented
5C31×#1343C212yesmaximal
6C2×C31×#124C411yescharacteristic, complemented
7C2×C31×#117C2211yescharacteristic
8C31×#431—21no—
9C31×#395C411yescharacteristic, complemented
10C31×#394C411yescharacteristic, complemented
11C31×#393C2211yescharacteristic
12C31×#392C2211yescharacteristic
13C31×#390—21no—
14C31×#388—21no—
15C31×#388—21no—
16C31×#386—21no—
17C31×#381—21no—
18C31×#376C411yescharacteristic, complemented
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#324—21no—
22C31×#323C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C31×#124—41no—
28C31×#124—41no—
29C31×#117—41no—
30C31×#117—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31C2311yescharacteristic
43C2×C42×C31—21no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C31×C4⋊C8—41no—
47C31×C22⋊C8—22no—
48C4×C8×C31—41no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—41no—
53C31×#95—41no—
54C31×#95C2×C411yescharacteristic
55C31×#95C2×C411yescharacteristic
56C24×C31—21no—
57C24×C31C2×D411yescharacteristic
58C2×Q8×C31—41no—
59C2×Q8×C31—81no—
60C2×D4×C31—42no—
61C2×D4×C31—41no—
62C2×D4×C31—42no—
63C2×D4×C31—81no—
64C2×D4×C31—81no—
65C22×C4×C31—21no—
66C22×C4×C31—22no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—41no—
72C22×C4×C31—42no—
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D411yescharacteristic
79C2×C8×C31—42no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—81no—
83C22⋊C4×C31—41no—
84C22⋊C4×C31—41no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—81no—
93C22⋊C4×C31—81no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—42no—
99#11844C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31C2×C22⋊C411yescharacteristic
112C23×C31#13512yes—
113Q8×C31—82no—
114D4×C31—84no—
115D4×C31—82no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—22no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
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×C31—82no—
141C2×C4×C31—82no—
142C2×C4×C31—82no—
143C2×C4×C31#9911yescharacteristic
144C2×C4×C31#9911yescharacteristic
145C8×C31—82no—
146#2610C2×C3111yescharacteristic
147#1820C2×C3111yescharacteristic, complemented
148#1458C2×C3111yescharacteristic, complemented
149#1351C2×C3112yescomplemented
150#1343C2×C3112yes—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—22no—
154C22×C31—42no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31—81no—
161C22×C31—81no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31—81no—
165C22×C31C2×#9911yescharacteristic
166C22×C31#41611yescharacteristic
167C22×C31#42111yescharacteristic
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—42no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—81no—
177C4×C31—81no—
178C4×C31—162no—
179C2×#124C4×C3111yescharacteristic, complemented
180C2×#117C22×C3111yescharacteristic
181#431—21no—
182#395C4×C3111yescharacteristic, complemented
183#394C4×C3111yescharacteristic, complemented
184#393C22×C3111yescharacteristic
185#392C22×C3111yescharacteristic
186#390—21no—
187#388—21no—
188#388—21no—
189#386—21no—
190#381—21no—
191#376C4×C3111yescharacteristic, complemented
192#342—21no—
193#342C22×C3112yes—
194#324—21no—
195#323C22×C3112yes—
196C2×C31—21no—
197C2×C31—21no—
198C2×C31—42no—
199C2×C31—161no—
200C2×C31#151611yescharacteristic
201C2×C31#212211yescharacteristic
202C2×C31#212611yescharacteristic
203C22×Q8C2×C4×C3111yescharacteristic
204C22×D4—21no—
205C22×D4C2×C4×C3111yescharacteristic
206C23×C4D4×C3111yescharacteristic
207#124—41no—
208#124—41no—
209#117—41no—
210#117—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×C4×C3111yescharacteristic
213C2×C4⋊C4D4×C3111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4D4×C3111yescharacteristic
222C2×C22⋊C4C23×C3111yescharacteristic
223C2×C42—21no—
224C2×C42C2×C4×C3111yescharacteristic
225C2×C42D4×C3111yescharacteristic
226C4⋊C8—41no—
227C22⋊C8—22no—
228C4×C8—41no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—41no—
233#95—41no—
234#95C2×C4×C3111yescharacteristic
235#95C2×C4×C3111yescharacteristic
236C31#1184411yescharacteristic, direct product factor, Sylow
237C24—21no—
238C24C2×D4×C3111yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—81no—
245C2×D4—81no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22⋊C4×C3111yescharacteristic
257C22×C4C22⋊C4×C3111yescharacteristic
258C22×C4C22×C4×C3111yescharacteristic
259C22×C4C2×D4×C3111yescharacteristic
260C2×C8—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—42no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊C4×C3111yescharacteristic
292C23C31×#13512yes—
293Q8—82no—
294D4—84no—
295D4—82no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4C31×#9911yescharacteristic
324C2×C4C31×#9911yescharacteristic
325C8—82no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C2×C31×#9911yescharacteristic
341C22C31×#41611yescharacteristic
342C22C31×#42111yescharacteristic
343C4—21no—
344C4—21no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—162no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—161no—
358C2C31×#151611yescharacteristic
359C2C31×#212211yescharacteristic
360C2C31×#212611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1820C2semidirect
3. C31×#1458C2semidirect
4. C31×#1351C2semidirect
6. C2×C31×#124C4semidirect
9. C31×#395C4semidirect
10. C31×#394C4semidirect
18. C31×#376C4semidirect
99. #11844C31direct (N × H)
147. #1820C2×C31semidirect
148. #1458C2×C31semidirect
149. #1351C2×C31semidirect
179. C2×#124C4×C31semidirect
182. #395C4×C31semidirect
183. #394C4×C31semidirect
191. #376C4×C31semidirect
236. C31#11844direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26102
C31×#18202
C31×#14582
C31×#13512
C31×#13432
#1184431