Finite Group Databasebeta

← C31×#19058 #21475817

Subgroups — C31×#19058 #21475817

Order 7936.

840 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 222 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×#3550C211yesmaximal, characteristic
2C31×#3237C212yesmaximal, complemented
3C31×#3135C211yesmaximal, characteristic
4C31×#1664C218yesmaximal, complemented
5C31×#1536C211yesmaximal, characteristic
6C31×#1531C212yesmaximal, complemented
7C31×#563C2214yes—
8C31×#559—21no—
9Q82×C31—21no—
10C31×#556—22no—
11D4×Q8×C31—22no—
12C31×#542—24no—
13C31×#536—22no—
14C31×#533C2211yescharacteristic
15C31×#533C2212yes—
16C31×#532C2211yescharacteristic
17C31×#501C2214yes—
18C31×#491—21no—
19C31×#491C2214yes—
20C31×#490—21no—
21C31×#489C2214yes—
22C31×#485—24no—
23C31×#477—22no—
24C31×#475—22no—
25C31×#432C2212yes—
26C31×#416—22no—
27C2×C31×#97C2211yescharacteristic
28C31×#330C2218yes—
29C31×#329C2214yes—
30C2×#41×C31D412yes—
31C22×Q8×C31—22no—
32C22×C8×C31—21no—
33C31×C4⋊Q8—24no—
34C31×C4⋊Q8—24no—
35C31×C4⋊Q8D411yescharacteristic
36C31×C4⋊Q8D412yes—
37C31×C4⋊Q8D412yes—
38C31×C4⋊Q8C2312yes—
39C31×#127D411yescharacteristic
40C31×#126—28no—
41C31×#125—21no—
42C31×#125C2314yes—
43C31×#124—24no—
44C31×#124—24no—
45C31×#124C2312yes—
46C31×#123—24no—
47C31×#123—24no—
48C31×C22⋊Q8—24no—
49C31×C22⋊Q8—22no—
50C31×C22⋊Q8—22no—
51C31×C22⋊Q8—28no—
52C31×C22⋊Q8—22no—
53C31×#121—22no—
54C4×Q8×C31—24no—
55C4×Q8×C31—22no—
56C4×Q8×C31—22no—
57C4×Q8×C31—22no—
58C4×D4×C31—24no—
59C4×D4×C31—22no—
60C31×#117—22no—
61C31×#117—21no—
62C31×#117D414yes—
63C2×C42×C31C2311yescharacteristic
64C31×#107—24no—
65C31×#106—24no—
66C31×C4⋊C8—22no—
67C31×#103—24no—
68C31×#103—24no—
69C31×#103—24no—
70C31×#102—24no—
71C31×C22⋊C8—22no—
72C31×#97—21no—
73C31×#97C2312yes—
74C31×#97C2314yes—
75#41×C31—44no—
76C2×Q8×C31—24no—
77C2×Q8×C31—22no—
78C2×Q8×C31—22no—
79C2×Q8×C31—22no—
80C2×Q8×C31—84no—
81C2×Q8×C31C2×D412yes—
82C2×D4×C31—22no—
83C2×D4×C31—22no—
84C2×D4×C31C2×D412yes—
85C22×C4×C31—24no—
86C22×C4×C31—22no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D412yes—
89C2×C8×C31—22no—
90C2×C8×C31—24no—
91C2×C8×C31—42no—
92C4⋊C4×C31—28no—
93C4⋊C4×C31—22no—
94C4⋊C4×C31—22no—
95C4⋊C4×C31—22no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—24no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—42no—
101C4⋊C4×C31C2×D414yes—
102C4⋊C4×C31C2×D414yes—
103C22⋊C4×C31—24no—
104C22⋊C4×C31—28no—
105C22⋊C4×C31—24no—
106C22⋊C4×C31—24no—
107C22⋊C4×C31—41no—
108C42×C31—24no—
109C42×C31—24no—
110C42×C31—41no—
111C42×C31C2×D411yescharacteristic
112C42×C31C2×D412yes—
113C42×C31C2411yescharacteristic
114#19058C3111yesmaximal, characteristic, direct product factor, Sylow
115C23×C31—22no—
116C23×C31#12011yescharacteristic
117Q8×C31—42no—
118Q8×C31—44no—
119Q8×C31—44no—
120Q8×C31—44no—
121Q8×C31—84no—
122D4×C31—42no—
123D4×C31—44no—
124D4×C31—82no—
125C2×C4×C31—22no—
126C2×C4×C31—24no—
127C2×C4×C31—22no—
128C2×C4×C31—24no—
129C2×C4×C31—42no—
130C2×C4×C31—44no—
131C2×C4×C31—42no—
132C2×C4×C31—84no—
133C2×C4×C31#12012yes—
134C2×C4×C31#12011yescharacteristic
135C2×C4×C31C22×D412yes—
136C2×C4×C31C22×D411yescharacteristic
137C8×C31—44no—
138C8×C31—42no—
139#3550C2×C3111yescharacteristic
140#3237C2×C3112yescomplemented
141#3135C2×C3111yescharacteristic
142#1664C2×C3118yescomplemented
143#1536C2×C3111yescharacteristic
144#1531C2×C3112yescomplemented
145C22×C31—21no—
146C22×C31—22no—
147C22×C31—42no—
148C22×C31—44no—
149C22×C31C2×#12011yescharacteristic
150C4×C31—21no—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—42no—
154C4×C31—44no—
155C4×C31—44no—
156C4×C31—82no—
157C4×C31#45512yes—
158#563C22×C3114yes—
159#559—21no—
160Q82—21no—
161#556—22no—
162D4×Q8—22no—
163#542—24no—
164#536—22no—
165#533C22×C3111yescharacteristic
166#533C22×C3112yes—
167#532C22×C3111yescharacteristic
168#501C22×C3114yes—
169#491—21no—
170#491C22×C3114yes—
171#490—21no—
172#489C22×C3114yes—
173#485—24no—
174#477—22no—
175#475—22no—
176#432C22×C3112yes—
177#416—22no—
178C2×#97C22×C3111yescharacteristic
179#330C22×C3118yes—
180#329C22×C3114yes—
181C2×C31—41no—
182C2×C31—82no—
183C2×C31C2×#45511yescharacteristic
184C2×C31#302012yes—
185C2×#41D4×C3112yes—
186C22×Q8—22no—
187C22×C8—21no—
188C4⋊Q8—24no—
189C4⋊Q8—24no—
190C4⋊Q8D4×C3111yescharacteristic
191C4⋊Q8D4×C3112yes—
192C4⋊Q8D4×C3112yes—
193C4⋊Q8C23×C3112yes—
194#127D4×C3111yescharacteristic
195#126—28no—
196#125—21no—
197#125C23×C3114yes—
198#124—24no—
199#124—24no—
200#124C23×C3112yes—
201#123—24no—
202#123—24no—
203C22⋊Q8—24no—
204C22⋊Q8—22no—
205C22⋊Q8—22no—
206C22⋊Q8—28no—
207C22⋊Q8—22no—
208#121—22no—
209C4×Q8—24no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×D4—24no—
214C4×D4—22no—
215#117—22no—
216#117—21no—
217#117D4×C3114yes—
218C2×C42C23×C3111yescharacteristic
219#107—24no—
220#106—24no—
221C4⋊C8—22no—
222#103—24no—
223#103—24no—
224#103—24no—
225#102—24no—
226C22⋊C8—22no—
227#97—21no—
228#97C23×C3114yes—
229#97C23×C3112yes—
230C31#1905811yescharacteristic, direct product factor, Sylow
231#41—44no—
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—84no—
237C2×Q8C2×D4×C3112yes—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4C2×D4×C3112yes—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4C2×D4×C3111yescharacteristic
244C22×C4C2×D4×C3112yes—
245C2×C8—22no—
246C2×C8—24no—
247C2×C8—42no—
248C4⋊C4—28no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4C2×D4×C3114yes—
258C4⋊C4C2×D4×C3114yes—
259C22⋊C4—24no—
260C22⋊C4—28no—
261C22⋊C4—24no—
262C22⋊C4—24no—
263C22⋊C4—41no—
264C42—24no—
265C42—24no—
266C42—41no—
267C42C2×D4×C3111yescharacteristic
268C42C2×D4×C3112yes—
269C42C24×C3111yescharacteristic
270C23—22no—
271C23C31×#12011yescharacteristic
272Q8—42no—
273Q8—44no—
274Q8—44no—
275Q8—44no—
276Q8—84no—
277D4—42no—
278D4—44no—
279D4—82no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—84no—
288C2×C4C31×#12012yes—
289C2×C4C31×#12011yescharacteristic
290C2×C4C22×D4×C3112yes—
291C2×C4C22×D4×C3111yescharacteristic
292C8—44no—
293C8—42no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—44no—
298C22C2×C31×#12011yescharacteristic
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—44no—
304C4—44no—
305C4—82no—
306C4C31×#45512yes—
307C2—41no—
308C2—82no—
309C2C2×C31×#45511yescharacteristic
310C2C31×#302012yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3237C2semidirect
4. C31×#1664C2semidirect
6. C31×#1531C2semidirect
114. #19058C31direct (N × H)
140. #3237C2×C31semidirect
142. #1664C2×C31semidirect
144. #1531C2×C31semidirect
230. C31#19058direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35502
C31×#32372
C31×#31352
C31×#16642
C31×#15362
C31×#15312
#1905831