Finite Group Databasebeta

← C31×#10143 #21466902

Subgroups — C31×#10143 #21466902

Order 7936.

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3236C211yesmaximal, characteristic
2C31×#3229C211yesmaximal, characteristic
3C2×C31×#501C211yesmaximal, characteristic
4C31×#1558C211yesmaximal, characteristic
5C31×#1531C211yesmaximal, characteristic
6C31×#1470C211yesmaximal, characteristic
7C31×#1302C211yesmaximal, characteristic
8C31×#533C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×#125C2211yescharacteristic
11C31×#501—22no—
12C31×#501—21no—
13C31×#501—22no—
14C31×#498—21no—
15C31×#491—21no—
16C31×#487—21no—
17C31×#484—21no—
18C31×#483—21no—
19C31×#483—22no—
20C31×#479—22no—
21C31×#475—22no—
22C31×#432C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C31×#431C2211yescharacteristic
25C2×C31×#107—21no—
26C2×C31×#106—21no—
27C2×C31×#97C2211yescharacteristic
28C31×#333—22no—
29C31×#330—22no—
30C31×#324—22no—
31C22×Q8×C31—21no—
32C22×C8×C31—21no—
33C31×C4⋊Q8—21no—
34C31×C4⋊Q8—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8D412yes—
37C31×C4⋊Q8D411yescharacteristic
38C31×C4⋊Q8D411yescharacteristic
39C31×#125—21no—
40C31×#125—21no—
41C31×#125—21no—
42C31×#125—21no—
43C31×#125—21no—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C4×Q8×C31—21no—
47C4×Q8×C31—21no—
48C31×#117—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C42×C31C2311yescharacteristic
56C31×#107—24no—
57C31×#107—22no—
58C31×#106—24no—
59C31×#106—24no—
60C31×#106—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8D412yes—
64C31×#103—24no—
65C31×#103—22no—
66C31×#103—22no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8D412yes—
70C31×#97—21no—
71C31×#97—21no—
72C31×#97—21no—
73C31×#97D412yes—
74C4×C8×C31—21no—
75C2×Q8×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—22no—
78C2×Q8×C31—41no—
79C2×Q8×C31—82no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—41no—
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31#4111yescharacteristic
86C2×C8×C31—24no—
87C2×C8×C31—22no—
88C2×C8×C31—22no—
89C2×C8×C31—22no—
90C2×C8×C31—41no—
91C4⋊C4×C31—22no—
92C4⋊C4×C31—21no—
93C4⋊C4×C31—21no—
94C4⋊C4×C31—21no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—22no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C22⋊C4×C31—41no—
110C42×C31—41no—
111C42×C31C2×D411yescharacteristic
112C42×C31C2×D411yescharacteristic
113C42×C31C2×D411yescharacteristic
114C42×C31C2×D411yescharacteristic
115#10143C3111yesmaximal, characteristic, direct product factor, Sylow
116C23×C31#12111yescharacteristic
117Q8×C31—42no—
118Q8×C31—42no—
119Q8×C31—82no—
120Q8×C31—82no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—82no—
131C2×C4×C31—81no—
132C2×C4×C31#12011yescharacteristic
133C2×C4×C31#12011yescharacteristic
134C2×C4×C31#12011yescharacteristic
135C2×C4×C31#12111yescharacteristic
136C2×C4×C31#12111yescharacteristic
137C2×C4×C31#12711yescharacteristic
138C8×C31—24no—
139C8×C31—42no—
140C8×C31—42no—
141C8×C31—81no—
142#3236C2×C3111yescharacteristic
143#3229C2×C3111yescharacteristic
144C2×#501C2×C3111yescharacteristic
145#1558C2×C3111yescharacteristic
146#1531C2×C3111yescharacteristic
147#1470C2×C3111yescharacteristic
148#1302C2×C3111yescharacteristic
149C22×C31—21no—
150C22×C31—21no—
151C22×C31#39211yescharacteristic
152C22×C31#47112yes—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—81no—
159C4×C31—81no—
160C4×C31—81no—
161C4×C31—81no—
162C4×C31—82no—
163C4×C31#45612yes—
164#533C22×C3111yescharacteristic
165C2×C4⋊Q8C22×C3111yescharacteristic
166C2×#125C22×C3111yescharacteristic
167#501—22no—
168#501—21no—
169#501—22no—
170#498—21no—
171#491—21no—
172#487—21no—
173#484—21no—
174#483—21no—
175#483—22no—
176#479—22no—
177#475—22no—
178#432C22×C3111yescharacteristic
179#432C22×C3111yescharacteristic
180#431C22×C3111yescharacteristic
181C2×#107—21no—
182C2×#106—21no—
183C2×#97C22×C3111yescharacteristic
184#333—22no—
185#330—22no—
186#324—22no—
187C2×C31—22no—
188C2×C31#200511yescharacteristic
189C2×C31#200911yescharacteristic
190C2×C31#201911yescharacteristic
191C22×Q8—21no—
192C22×C8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8D4×C3112yes—
197C4⋊Q8D4×C3111yescharacteristic
198C4⋊Q8D4×C3111yescharacteristic
199#125—21no—
200#125—21no—
201#125—21no—
202#125—21no—
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208#117—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C3111yescharacteristic
214C2×C4⋊C4D4×C3111yescharacteristic
215C2×C42C23×C3111yescharacteristic
216#107—24no—
217#107—22no—
218#106—24no—
219#106—24no—
220#106—22no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8D4×C3112yes—
224#103—24no—
225#103—22no—
226#103—22no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8D4×C3112yes—
230#97—21no—
231#97—21no—
232#97—21no—
233#97D4×C3112yes—
234C4×C8—21no—
235C31#1014311yescharacteristic, direct product factor, Sylow
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—82no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4C2×D4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246C22×C4#41×C3111yescharacteristic
247C2×C8—24no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—41no—
271C42—41no—
272C42C2×D4×C3111yescharacteristic
273C42C2×D4×C3111yescharacteristic
274C42C2×D4×C3111yescharacteristic
275C42C2×D4×C3111yescharacteristic
276C23C31×#12111yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—82no—
280Q8—82no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—82no—
291C2×C4—81no—
292C2×C4C31×#12011yescharacteristic
293C2×C4C31×#12011yescharacteristic
294C2×C4C31×#12011yescharacteristic
295C2×C4C31×#12111yescharacteristic
296C2×C4C31×#12111yescharacteristic
297C2×C4C31×#12711yescharacteristic
298C8—24no—
299C8—42no—
300C8—42no—
301C8—81no—
302C22—21no—
303C22—21no—
304C22C31×#39211yescharacteristic
305C22C31×#47112yes—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—82no—
316C4C31×#45612yes—
317C2—22no—
318C2C31×#200511yescharacteristic
319C2C31×#200911yescharacteristic
320C2C31×#201911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
115. #10143C31direct (N × H)
235. C31#10143direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32362
C31×#32292
C2×C31×#5012
C31×#15582
C31×#15312
C31×#14702
C31×#13022
#1014331