Finite Group Databasebeta

← C31×#9502 #21466261

Subgroups — C31×#9502 #21466261

Order 7936.

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2483C211yesmaximal, characteristic
2C31×#2312C211yesmaximal, characteristic
3C31×#1819C212yesmaximal
4C31×#1819C211yesmaximal, characteristic
5C31×#1304C212yesmaximal
6C22×C22⋊C4×C31C2211yescharacteristic
7C22×C22⋊C4×C31C2211yescharacteristic
8C31×#397—22no—
9C31×#388—24no—
10C31×#385—21no—
11C31×#385C412yescomplemented
12C31×#381—21no—
13C31×#381C412yescomplemented
14C31×#380—21no—
15C31×#379C2212yes—
16C31×#379C2211yescharacteristic
17C31×#379C2212yes—
18C4×C22⋊C4×C31—21no—
19C31×#342—24no—
20C31×#342—22no—
21C25×C31C2311yescharacteristic
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C22⋊C4×C31—22no—
29C2×C22⋊C4×C31—22no—
30C2×C22⋊C4×C31—21no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—21no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31C2×C412yes—
42C2×C22⋊C4×C31C2×C412yes—
43C2×C22⋊C4×C31D412yes—
44C2×C22⋊C4×C31D414yes—
45C2×C42×C31—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95—22no—
50C31×#95—22no—
51C24×C31—42no—
52C24×C31—42no—
53C24×C31—81no—
54C24×C31C22×C411yescharacteristic
55C24×C31C2×D411yescharacteristic
56C24×C31C2×D411yescharacteristic
57C24×C31C2×D412yes—
58C24×C31#4112yes—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—22no—
65C22×C4×C31—21no—
66C22×C4×C31—24no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
71C22×C4×C31—42no—
72C22×C4×C31—81no—
73C22×C4×C31—81no—
74C22×C4×C31C22⋊C412yes—
75C22×C4×C31C22⋊C412yes—
76C4⋊C4×C31—82no—
77C4⋊C4×C31—82no—
78C22⋊C4×C31—24no—
79C22⋊C4×C31—24no—
80C22⋊C4×C31—44no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—41no—
83C22⋊C4×C31—42no—
84C22⋊C4×C31—41no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—44no—
87C22⋊C4×C31—44no—
88C22⋊C4×C31—44no—
89C22⋊C4×C31—82no—
90C22⋊C4×C31—81no—
91C22⋊C4×C31—82no—
92C42×C31—82no—
93#9502C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31—22no—
95C23×C31—22no—
96C23×C31—22no—
97C23×C31—22no—
98C23×C31—24no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—42no—
104C23×C31—42no—
105C23×C31—41no—
106C23×C31—42no—
107C23×C31—42no—
108C23×C31—42no—
109C23×C31—88no—
110C23×C31C2×C22⋊C411yescharacteristic
111C23×C31C4×D412yes—
112C23×C31#12011yescharacteristic
113C23×C31#12112yes—
114C23×C31#12311yescharacteristic
115C2×C4×C31—22no—
116C2×C4×C31—22no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—44no—
122C2×C4×C31—42no—
123C2×C4×C31—44no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—44no—
131C2×C4×C31—81no—
132C2×C4×C31—81no—
133C2×C4×C31—82no—
134C2×C4×C31—82no—
135C2×C4×C31—82no—
136C2×C4×C31—82no—
137C2×C4×C31—82no—
138#2483C2×C3111yescharacteristic
139#2312C2×C3111yescharacteristic
140#1819C2×C3112yes—
141#1819C2×C3111yescharacteristic
142#1304C2×C3112yes—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—22no—
148C22×C31—21no—
149C22×C31—22no—
150C22×C31—22no—
151C22×C31—22no—
152C22×C31—21no—
153C22×C31—22no—
154C22×C31—22no—
155C22×C31—21no—
156C22×C31—44no—
157C22×C31—44no—
158C22×C31—84no—
159C22×C31—82no—
160C22×C31—84no—
161C22×C31#38611yescharacteristic
162C22×C31#41012yes—
163C22×C31#45812yes—
164C4×C31—42no—
165C4×C31—42no—
166C4×C31—84no—
167C4×C31—82no—
168C4×C31—81no—
169C4×C31—81no—
170C4×C31—162no—
171C22×C22⋊C4C22×C3111yescharacteristic
172C22×C22⋊C4C22×C3111yescharacteristic
173#397—22no—
174#388—24no—
175#385—21no—
176#385C4×C3112yescomplemented
177#381—21no—
178#381C4×C3112yescomplemented
179#380—21no—
180#379C22×C3112yes—
181#379C22×C3111yescharacteristic
182#379C22×C3112yes—
183C4×C22⋊C4—21no—
184#342—24no—
185#342—22no—
186C2×C31—22no—
187C2×C31—22no—
188C2×C31—42no—
189C2×C31—41no—
190C2×C31—42no—
191C2×C31#189011yescharacteristic
192C2×C31#189911yescharacteristic
193C2×C31#191311yescharacteristic
194C25C23×C3111yescharacteristic
195C23×C4C2×C4×C3111yescharacteristic
196C23×C4C2×C4×C3111yescharacteristic
197C23×C4D4×C3111yescharacteristic
198C23×C4D4×C3111yescharacteristic
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4C2×C4×C3112yes—
215C2×C22⋊C4C2×C4×C3112yes—
216C2×C22⋊C4D4×C3112yes—
217C2×C22⋊C4D4×C3114yes—
218C2×C42—22no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224C31#950211yescharacteristic, direct product factor, Sylow
225C24—42no—
226C24—42no—
227C24—81no—
228C24C22×C4×C3111yescharacteristic
229C24C2×D4×C3111yescharacteristic
230C24C2×D4×C3111yescharacteristic
231C24C2×D4×C3112yes—
232C24#41×C3112yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊C4×C3112yes—
249C22×C4C22⋊C4×C3112yes—
250C4⋊C4—82no—
251C4⋊C4—82no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—44no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C22⋊C4—44no—
262C22⋊C4—44no—
263C22⋊C4—82no—
264C22⋊C4—81no—
265C22⋊C4—82no—
266C42—82no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—22no—
271C23—24no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—88no—
283C23C2×C22⋊C4×C3111yescharacteristic
284C23C4×D4×C3112yes—
285C23C31×#12011yescharacteristic
286C23C31×#12112yes—
287C23C31×#12311yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22C31×#38611yescharacteristic
330C22C31×#41012yes—
331C22C31×#45812yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—162no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2C31×#189011yescharacteristic
345C2C31×#189911yescharacteristic
346C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
11. C31×#385C4semidirect
13. C31×#381C4semidirect
93. #9502C31direct (N × H)
176. #385C4×C31semidirect
178. #381C4×C31semidirect
224. C31#9502direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24832
C31×#23122
C31×#18192
C31×#13042
#950231