Finite Group Databasebeta

← C31×#10115 #21466874

Subgroups — C31×#10115 #21466874

Order 7936.

466 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3255C211yesmaximal, characteristic
2C31×#3209C211yesmaximal, characteristic
3C31×#3139C211yesmaximal, characteristic
4C31×#1997C211yesmaximal, characteristic
5C31×#1526C211yesmaximal, characteristic
6C31×#1485C211yesmaximal, characteristic
7C31×#1299C211yesmaximal, characteristic
8C31×#533C2211yescharacteristic
9C31×#533C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C31×#494—21no—
12C31×#491—22no—
13C31×#487—21no—
14C31×#487—21no—
15C31×#487—21no—
16C31×#475—21no—
17C31×#475—21no—
18C31×#470—22no—
19C31×#462—21no—
20C31×#462—21no—
21C31×#462—22no—
22C31×#451—22no—
23C31×#431C2211yescharacteristic
24C31×#423C2211yescharacteristic
25C31×#419—22no—
26C4×M16×C31C2211yescharacteristic
27C4×M16×C31C2211yescharacteristic
28C31×#343—22no—
29C31×#330—22no—
30C31×Q8⋊C8—22no—
31C22×Q8×C31D412yes—
32C2×Q16×C31—24no—
33C2×Q16×C31—22no—
34C2×M16×C31—21no—
35C2×M16×C31—21no—
36C2×M16×C31D412yes—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8D411yescharacteristic
42C31×C4⋊Q8D411yescharacteristic
43C31×C4⋊Q8D411yescharacteristic
44C31×C4⋊Q8D411yescharacteristic
45C31×#125—21no—
46C31×#125—21no—
47C31×C22⋊Q8—21no—
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C31×C22⋊Q8—21no—
51C4×Q8×C31—21no—
52C4×Q8×C31—21no—
53C4×Q8×C31—21no—
54C4×Q8×C31—21no—
55C31×#117—21no—
56C31×#117—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C42×C31C2311yescharacteristic
60C31×#106—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8D412yes—
64C31×#103—24no—
65C31×#103—24no—
66C31×#103—24no—
67C31×#103—22no—
68C31×#103—22no—
69C31×C22⋊C8—21no—
70C31×#97—21no—
71C31×#97D412yes—
72C4×C8×C31—21no—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C2×Q8×C31—22no—
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—22no—
79C2×Q8×C31—21no—
80C2×Q8×C31—21no—
81C2×Q8×C31—44no—
82C22×C4×C31—22no—
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31#4111yescharacteristic
86Q16×C31—82no—
87Q16×C31—84no—
88M16×C31—22no—
89M16×C31—42no—
90M16×C31—41no—
91M16×C31—42no—
92C2×C8×C31—22no—
93C2×C8×C31—22no—
94C2×C8×C31—22no—
95C2×C8×C31—41no—
96C4⋊C4×C31—21no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—41no—
114C42×C31—41no—
115C42×C31—41no—
116C42×C31C2×D411yescharacteristic
117C42×C31C2×D411yescharacteristic
118C42×C31C2×D411yescharacteristic
119C42×C31C2×D411yescharacteristic
120#10115C3111yesmaximal, characteristic, direct product factor, Sylow
121C23×C31#12111yescharacteristic
122Q8×C31—44no—
123Q8×C31—42no—
124Q8×C31—41no—
125Q8×C31—41no—
126Q8×C31—44no—
127Q8×C31—41no—
128Q8×C31—41no—
129Q8×C31—42no—
130C2×C4×C31—21no—
131C2×C4×C31—22no—
132C2×C4×C31—21no—
133C2×C4×C31—22no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—82no—
140C2×C4×C31#12011yescharacteristic
141C2×C4×C31#12011yescharacteristic
142C2×C4×C31#12011yescharacteristic
143C2×C4×C31#12111yescharacteristic
144C2×C4×C31#12111yescharacteristic
145C2×C4×C31#12711yescharacteristic
146C8×C31—42no—
147C8×C31—42no—
148C8×C31—42no—
149C8×C31—42no—
150#3255C2×C3111yescharacteristic
151#3209C2×C3111yescharacteristic
152#3139C2×C3111yescharacteristic
153#1997C2×C3111yescharacteristic
154#1526C2×C3111yescharacteristic
155#1485C2×C3111yescharacteristic
156#1299C2×C3111yescharacteristic
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31#39211yescharacteristic
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—82no—
165C4×C31—81no—
166C4×C31—81no—
167C4×C31—81no—
168C4×C31—81no—
169C4×C31#45512yes—
170C4×C31#45511yescharacteristic
171C4×C31#45611yescharacteristic
172C4×C31#47312yes—
173#533C22×C3111yescharacteristic
174#533C22×C3111yescharacteristic
175C2×C4⋊Q8C22×C3111yescharacteristic
176#494—21no—
177#491—22no—
178#487—21no—
179#487—21no—
180#487—21no—
181#475—21no—
182#475—21no—
183#470—22no—
184#462—21no—
185#462—21no—
186#462—22no—
187#451—22no—
188#431C22×C3111yescharacteristic
189#423C22×C3111yescharacteristic
190#419—22no—
191C4×M16C22×C3111yescharacteristic
192C4×M16C22×C3111yescharacteristic
193#343—22no—
194#330—22no—
195Q8⋊C8—22no—
196C2×C31—41no—
197C2×C31#200411yescharacteristic
198C2×C31#200711yescharacteristic
199C2×C31#202011yescharacteristic
200C22×Q8D4×C3112yes—
201C2×Q16—24no—
202C2×Q16—22no—
203C2×M16—21no—
204C2×M16—21no—
205C2×M16D4×C3112yes—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8D4×C3111yescharacteristic
211C4⋊Q8D4×C3111yescharacteristic
212C4⋊Q8D4×C3111yescharacteristic
213C4⋊Q8D4×C3111yescharacteristic
214#125—21no—
215#125—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224#117—21no—
225#117—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C42C23×C3111yescharacteristic
229#106—22no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8D4×C3112yes—
233#103—24no—
234#103—24no—
235#103—24no—
236#103—22no—
237#103—22no—
238C22⋊C8—21no—
239#97—21no—
240#97D4×C3112yes—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8—21no—
244C31#1011511yescharacteristic, direct product factor, Sylow
245C2×Q8—22no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—44no—
252C22×C4—22no—
253C22×C4C2×D4×C3111yescharacteristic
254C22×C4C2×D4×C3111yescharacteristic
255C22×C4#41×C3111yescharacteristic
256Q16—82no—
257Q16—84no—
258M16—22no—
259M16—42no—
260M16—41no—
261M16—42no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42—41no—
286C42C2×D4×C3111yescharacteristic
287C42C2×D4×C3111yescharacteristic
288C42C2×D4×C3111yescharacteristic
289C42C2×D4×C3111yescharacteristic
290C23C31×#12111yescharacteristic
291Q8—44no—
292Q8—42no—
293Q8—41no—
294Q8—41no—
295Q8—44no—
296Q8—41no—
297Q8—41no—
298Q8—42no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—82no—
309C2×C4C31×#12011yescharacteristic
310C2×C4C31×#12011yescharacteristic
311C2×C4C31×#12011yescharacteristic
312C2×C4C31×#12111yescharacteristic
313C2×C4C31×#12111yescharacteristic
314C2×C4C31×#12711yescharacteristic
315C8—42no—
316C8—42no—
317C8—42no—
318C8—42no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22C31×#39211yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4C31×#45512yes—
332C4C31×#45511yescharacteristic
333C4C31×#45611yescharacteristic
334C4C31×#47312yes—
335C2—41no—
336C2C31×#200411yescharacteristic
337C2C31×#200711yescharacteristic
338C2C31×#202011yescharacteristic
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
120. #10115C31direct (N × H)
244. C31#10115direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32552
C31×#32092
C31×#31392
C31×#19972
C31×#15262
C31×#14852
C31×#12992
#1011531