Finite Group Databasebeta

← C31×#9457 #21466216

Subgroups — C31×#9457 #21466216

Order 7936.

690 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973C211yesmaximal, characteristic, complemented
2C31×#2541C211yesmaximal, characteristic
3C31×#1555C212yesmaximal, complemented
4C31×#1466C211yesmaximal, characteristic, complemented
5C31×#1285C212yesmaximal, complemented
6C2×C31×#127C412yes—
7C2×C31×#127C2211yescharacteristic
8C2×C31×#121—21no—
9C2×C31×#121—21no—
10C2×C4×D4×C31C2211yescharacteristic
11C31×#435—24no—
12C31×#432C2212yes—
13C31×#432C2212yes—
14C31×#407—21no—
15C2×C31×C22⋊C8—21no—
16C31×#392—21no—
17C31×#392—21no—
18C31×#390C412yes—
19C4×C4⋊C4×C31C2211yescharacteristic
20C31×#331—24no—
21C31×#323—21no—
22C31×#323—21no—
23C22×D4×C31—22no—
24C22×D4×C31—22no—
25C22×D4×C31—21no—
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C22×D4×C31C2×C412yes—
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C2×M16×C31—22no—
32C22×C8×C31—22no—
33C31×#127—22no—
34C31×#127—22no—
35C31×#127—44no—
36C31×#121—44no—
37C31×#121—44no—
38C4×D4×C31—22no—
39C4×D4×C31—22no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31D411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C42×C31C2×C412yes—
47C2×C42×C31C2311yescharacteristic
48C31×C4⋊C8—22no—
49C31×C4⋊C8D414yescomplemented
50C31×C22⋊C8—22no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×C22⋊C8—22no—
54C31×#97—22no—
55C31×#97—22no—
56C31×#95—21no—
57C24×C31—22no—
58C24×C31C22⋊C411yescharacteristic
59C24×C31C22⋊C411yescharacteristic
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—24no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—42no—
66C2×D4×C31—44no—
67C2×D4×C31—44no—
68C2×D4×C31—42no—
69C2×D4×C31—42no—
70C2×D4×C31—44no—
71C2×D4×C31—44no—
72C2×D4×C31—41no—
73C2×D4×C31—42no—
74C2×D4×C31—41no—
75C2×D4×C31—82no—
76C2×D4×C31—82no—
77C2×D4×C31—82no—
78C22×C4×C31—22no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31C22⋊C411yescharacteristic
86C22×C4×C31C22⋊C411yescharacteristic
87C22×C4×C31C22×C411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90M16×C31—82no—
91C2×C8×C31—24no—
92C2×C8×C31—42no—
93C2×C8×C31—82no—
94C4⋊C4×C31—24no—
95C4⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—22no—
98C22⋊C4×C31—44no—
99C22⋊C4×C31—44no—
100C42×C31—42no—
101C42×C31C2×D412yes—
102C42×C31#4112yes—
103#9457C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31#10012yes—
121C23×C31C2×C22⋊C411yescharacteristic
122D4×C31—44no—
123D4×C31—84no—
124D4×C31—82no—
125D4×C31—84no—
126D4×C31—88no—
127D4×C31—88no—
128D4×C31—82no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—22no—
132C2×C4×C31—24no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—41no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—81no—
143C2×C4×C31—81no—
144C2×C4×C31C4×D412yes—
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31#12112yes—
147C2×C4×C31#12311yescharacteristic
148C8×C31—44no—
149C8×C31—82no—
150#2973C2×C3111yescharacteristic, complemented
151#2541C2×C3111yescharacteristic
152#1555C2×C3112yescomplemented
153#1466C2×C3111yescharacteristic, complemented
154#1285C2×C3112yescomplemented
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—22no—
158C22×C31—42no—
159C22×C31—42no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—82no—
168C22×C31—82no—
169C22×C31—82no—
170C22×C31—82no—
171C22×C31—82no—
172C22×C31—82no—
173C22×C31—82no—
174C22×C31#38611yescharacteristic
175C22×C31C2×#10011yescharacteristic
176C22×C31#41311yescharacteristic
177C4×C31—21no—
178C4×C31—22no—
179C4×C31—22no—
180C4×C31—44no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31#45312yes—
184C2×#127C4×C3112yes—
185C2×#127C22×C3111yescharacteristic
186C2×#121—21no—
187C2×#121—21no—
188C2×C4×D4C22×C3111yescharacteristic
189#435—24no—
190#432C22×C3112yes—
191#432C22×C3112yes—
192#407—21no—
193C2×C22⋊C8—21no—
194#392—21no—
195#392—21no—
196#390C4×C3112yes—
197C4×C4⋊C4C22×C3111yescharacteristic
198#331—24no—
199#323—21no—
200#323—21no—
201C2×C31—21no—
202C2×C31—21no—
203C2×C31—42no—
204C2×C31—81no—
205C2×C31—162no—
206C2×C31#188711yescharacteristic
207C2×C31#190011yescharacteristic
208C2×C31#191011yescharacteristic
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4C2×C4×C3111yescharacteristic
214C22×D4C2×C4×C3112yes—
215C23×C4D4×C3111yescharacteristic
216C23×C4D4×C3111yescharacteristic
217C2×M16—22no—
218C22×C8—22no—
219#127—22no—
220#127—22no—
221#127—44no—
222#121—44no—
223#121—44no—
224C4×D4—22no—
225C4×D4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C3111yescharacteristic
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4D4×C3111yescharacteristic
231C2×C22⋊C4D4×C3111yescharacteristic
232C2×C42C2×C4×C3112yes—
233C2×C42C23×C3111yescharacteristic
234C4⋊C8—22no—
235C4⋊C8D4×C3114yescomplemented
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240#97—22no—
241#97—22no—
242#95—21no—
243C31#945711yescharacteristic, direct product factor, Sylow
244C24—22no—
245C24C22⋊C4×C3111yescharacteristic
246C24C22⋊C4×C3111yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—24no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—44no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—41no—
262C2×D4—82no—
263C2×D4—82no—
264C2×D4—82no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22×C4×C3111yescharacteristic
275C22×C4C2×D4×C3111yescharacteristic
276C22×C4C2×D4×C3111yescharacteristic
277M16—82no—
278C2×C8—24no—
279C2×C8—42no—
280C2×C8—82no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C42—42no—
288C42C2×D4×C3112yes—
289C42#41×C3112yes—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23C31×#10012yes—
307C23C2×C22⋊C4×C3111yescharacteristic
308D4—44no—
309D4—84no—
310D4—82no—
311D4—84no—
312D4—88no—
313D4—88no—
314D4—82no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4C4×D4×C3112yes—
331C2×C4C31×#12011yescharacteristic
332C2×C4C31×#12112yes—
333C2×C4C31×#12311yescharacteristic
334C8—44no—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22—82no—
352C22—82no—
353C22—82no—
354C22—82no—
355C22C31×#38611yescharacteristic
356C22C2×C31×#10011yescharacteristic
357C22C31×#41311yescharacteristic
358C4—21no—
359C4—22no—
360C4—22no—
361C4—44no—
362C4—41no—
363C4—41no—
364C4C31×#45312yes—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—81no—
369C2—162no—
370C2C31×#188711yescharacteristic
371C2C31×#190011yescharacteristic
372C2C31×#191011yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2541C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2973C2semidirect
3. C31×#1555C2semidirect
4. C31×#1466C2semidirect
5. C31×#1285C2semidirect
49. C31×C4⋊C8D4semidirect
103. #9457C31direct (N × H)
150. #2973C2×C31semidirect
152. #1555C2×C31semidirect
153. #1466C2×C31semidirect
154. #1285C2×C31semidirect
235. C4⋊C8D4×C31semidirect
243. C31#9457direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29732
C31×#25412
C31×#15552
C31×#14662
C31×#12852
#945731