Finite Group Databasebeta

← C31×#10228 #21466987

Subgroups — C31×#10228 #21466987

Order 7936.

828 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C2×C31×#459C212yesmaximal, complemented
2C31×#2537C211yesmaximal, characteristic, complemented
3C31×#1957C211yesmaximal, characteristic, complemented
4C2×C31×D4⋊C8C212yesmaximal, complemented
5C31×#1296C211yesmaximal, characteristic, complemented
6C22×D8×C31—22no—
7C2×C31×#127C2211yescharacteristic
8C2×C31×#121—22no—
9C2×C4×D4×C31C2212yes—
10C31×#459—24no—
11C31×#459—24no—
12C2×C31×C4⋊C8C2212yes—
13C2×C31×#102—22no—
14C2×C31×#102—22no—
15C2×C4×C8×C31C2211yescharacteristic
16C31×#394—22no—
17C31×#384C2211yescharacteristic
18C31×#380—22no—
19C31×D4⋊C8—24no—
20C22×D4×C31—22no—
21C22×D4×C31—21no—
22C22×D4×C31—22no—
23C22×D4×C31D412yes—
24C23×C4×C31—22no—
25C2×D8×C31—28no—
26C2×D8×C31—44no—
27C2×D8×C31—44no—
28C22×C8×C31—21no—
29C22×C8×C31—22no—
30C31×#127—22no—
31C31×#127—21no—
32C31×#127D412yescomplemented
33C31×#121—44no—
34C31×#121—44no—
35C4×D4×C31—22no—
36C4×D4×C31—22no—
37C4×D4×C31—22no—
38C4×D4×C31—22no—
39C2×C4⋊C4×C31—22no—
40C2×C4⋊C4×C31D412yes—
41C2×C4⋊C4×C31D412yes—
42C2×C22⋊C4×C31—24no—
43C2×C22⋊C4×C31—22no—
44C2×C42×C31C2311yescharacteristic
45C31×C4⋊C8—22no—
46C31×C4⋊C8D414yescomplemented
47C31×#102—28no—
48C31×#102—44no—
49C4×C8×C31—22no—
50C31×#95—22no—
51C24×C31—22no—
52C24×C31—41no—
53C2×D4×C31—22no—
54C2×D4×C31—24no—
55C2×D4×C31—22no—
56C2×D4×C31—22no—
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—22no—
60C2×D4×C31—42no—
61C2×D4×C31—42no—
62C2×D4×C31—48no—
63C2×D4×C31—42no—
64C2×D4×C31—41no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31—82no—
70C2×D4×C31D814yescomplemented
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31C2×D412yes—
81D8×C31—416no—
82C2×C8×C31—22no—
83C2×C8×C31—24no—
84C2×C8×C31—41no—
85C2×C8×C31—41no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—22no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—42no—
92C4⋊C4×C31—42no—
93C22⋊C4×C31—48no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C42×C31C2×D411yescharacteristic
97C42×C31C2×D412yes—
98C42×C31#4111yescharacteristic
99#10228C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—24no—
101C23×C31—42no—
102C23×C31—42no—
103C23×C31—42no—
104C23×C31—42no—
105C23×C31—42no—
106C23×C31—42no—
107C23×C31—42no—
108C23×C31—82no—
109C23×C31—82no—
110C23×C31—81no—
111C23×C31—81no—
112C23×C31#12011yescharacteristic
113D4×C31—24no—
114D4×C31—24no—
115D4×C31—44no—
116D4×C31—44no—
117D4×C31—42no—
118D4×C31—44no—
119D4×C31—42no—
120D4×C31—82no—
121D4×C31—88no—
122D4×C31—82no—
123D4×C31—82no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—44no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—82no—
132C2×C4×C31—82no—
133C2×C4×C31—82no—
134C2×C4×C31—82no—
135C2×C4×C31#12012yes—
136C2×C4×C31#12111yescharacteristic
137C2×C4×C31#12112yes—
138C2×C4×C31#12711yescharacteristic
139C2×C4×C31C2×D812yes—
140C2×C4×C31#13512yes—
141C2×C4×C31AGL(1,ℤ/8)12yes—
142C2×C4×C31AGL(1,ℤ/8)12yes—
143C8×C31—42no—
144C8×C31—44no—
145C2×#459C2×C3112yescomplemented
146#2537C2×C3111yescharacteristic, complemented
147#1957C2×C3111yescharacteristic, complemented
148C2×D4⋊C8C2×C3112yescomplemented
149#1296C2×C3111yescharacteristic, complemented
150C22×C31—44no—
151C22×C31—44no—
152C22×C31—44no—
153C22×C31—82no—
154C22×C31—82no—
155C22×C31—82no—
156C22×C31—82no—
157C22×C31—84no—
158C22×C31—82no—
159C22×C31—161no—
160C22×C31—161no—
161C22×C31—162no—
162C22×C31#39211yescharacteristic
163C22×C31#44712yes—
164C22×C31#44912yes—
165C22×C31#45311yescharacteristic
166C22×C31#45411yescharacteristic
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—82no—
170C4×C31—82no—
171C4×C31#44712yes—
172C4×C31#44912yes—
173C4×C31#46612yes—
174C4×C31#46912yes—
175C22×D8—22no—
176C2×#127C22×C3111yescharacteristic
177C2×#121—22no—
178C2×C4×D4C22×C3112yes—
179#459—24no—
180#459—24no—
181C2×C4⋊C8C22×C3112yes—
182C2×#102—22no—
183C2×#102—22no—
184C2×C4×C8C22×C3111yescharacteristic
185#394—22no—
186#384C22×C3111yescharacteristic
187#380—22no—
188D4⋊C8—24no—
189C2×C31—84no—
190C2×C31—162no—
191C2×C31#161911yescharacteristic
192C2×C31#162411yescharacteristic
193C2×C31#162512yes—
194C2×C31#199912yes—
195C2×C31#200611yescharacteristic
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—21no—
199C22×D4D4×C3112yes—
200C23×C4—22no—
201C2×D8—28no—
202C2×D8—44no—
203C2×D8—44no—
204C22×C8—22no—
205C22×C8—21no—
206#127—22no—
207#127—21no—
208#127D4×C3112yescomplemented
209#121—44no—
210#121—44no—
211C4×D4—22no—
212C4×D4—22no—
213C4×D4—22no—
214C4×D4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4D4×C3112yes—
217C2×C4⋊C4D4×C3112yes—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—22no—
220C2×C42C23×C3111yescharacteristic
221C4⋊C8—22no—
222C4⋊C8D4×C3114yescomplemented
223#102—28no—
224#102—44no—
225C4×C8—22no—
226#95—22no—
227C31#1022811yescharacteristic, direct product factor, Sylow
228C24—22no—
229C24—41no—
230C2×D4—22no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—48no—
240C2×D4—42no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—82no—
247C2×D4D8×C3114yescomplemented
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4C2×D4×C3111yescharacteristic
257C22×C4C2×D4×C3112yes—
258D8—416no—
259C2×C8—22no—
260C2×C8—24no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—48no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42C2×D4×C3111yescharacteristic
274C42C2×D4×C3112yes—
275C42#41×C3111yescharacteristic
276C23—24no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—82no—
285C23—82no—
286C23—81no—
287C23—81no—
288C23C31×#12011yescharacteristic
289D4—24no—
290D4—24no—
291D4—44no—
292D4—44no—
293D4—42no—
294D4—44no—
295D4—42no—
296D4—82no—
297D4—88no—
298D4—82no—
299D4—82no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4C31×#12012yes—
312C2×C4C31×#12111yescharacteristic
313C2×C4C31×#12112yes—
314C2×C4C31×#12711yescharacteristic
315C2×C4C2×D8×C3112yes—
316C2×C4C31×#13512yes—
317C2×C4C31×AGL(1,ℤ/8)12yes—
318C2×C4C31×AGL(1,ℤ/8)12yes—
319C8—42no—
320C8—44no—
321C22—44no—
322C22—44no—
323C22—44no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—82no—
328C22—84no—
329C22—82no—
330C22—161no—
331C22—161no—
332C22—162no—
333C22C31×#39211yescharacteristic
334C22C31×#44712yes—
335C22C31×#44912yes—
336C22C31×#45311yescharacteristic
337C22C31×#45411yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4C31×#44712yes—
343C4C31×#44912yes—
344C4C31×#46612yes—
345C4C31×#46912yes—
346C2—84no—
347C2—162no—
348C2C31×#161911yescharacteristic
349C2C31×#162411yescharacteristic
350C2C31×#162512yes—
351C2C31×#199912yes—
352C2C31×#200611yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#459C2semidirect
2. C31×#2537C2semidirect
3. C31×#1957C2semidirect
4. C2×C31×D4⋊C8C2semidirect
5. C31×#1296C2semidirect
32. C31×#127D4semidirect
46. C31×C4⋊C8D4semidirect
70. C2×D4×C31D8semidirect
99. #10228C31direct (N × H)
145. C2×#459C2×C31semidirect
146. #2537C2×C31semidirect
147. #1957C2×C31semidirect
148. C2×D4⋊C8C2×C31semidirect
149. #1296C2×C31semidirect
208. #127D4×C31semidirect
222. C4⋊C8D4×C31semidirect
227. C31#10228direct (N × H)
247. C2×D4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C31×#25372
C31×#19572
C2×C31×D4⋊C82
C31×#12962
#1022831