Finite Group Databasebeta

← C31×#9494 #21466253

Subgroups — C31×#9494 #21466253

Order 7936.

514 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic, complemented
2C31×#2598C211yesmaximal, characteristic
3C31×#1490C212yesmaximal, complemented
4C31×#1464C211yesmaximal, characteristic, complemented
5C31×#1288C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C2×C31×#117C2211yescharacteristic
8C31×#433—24no—
9C31×#432C2212yes—
10C31×#423—21no—
11C31×#407—21no—
12C4×M16×C31C2212yes—
13C31×#400C411yescharacteristic
14C31×#399C411yescharacteristic
15C31×#394C411yescharacteristic
16C31×#392C411yescharacteristic
17C31×#388—21no—
18C31×#386—21no—
19C31×#386—21no—
20C31×#385—21no—
21C31×#383C2211yescharacteristic
22C31×D4⋊C8—24no—
23C31×#324—21no—
24C31×#323—21no—
25C22×D4×C31—21no—
26C22×D4×C31C2×C411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C2×M16×C31—22no—
30C4×D4×C31—22no—
31C4×D4×C31—22no—
32C31×#117—22no—
33C31×#117—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31C2×C411yescharacteristic
44C2×C22⋊C4×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31C2311yescharacteristic
47C31×C4⋊C8—24no—
48C31×C4⋊C8—22no—
49C31×C22⋊C8—24no—
50C31×C22⋊C8—22no—
51C31×#97—22no—
52C31×#97—22no—
53C4×C8×C31D414yescomplemented
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95C2×C411yescharacteristic
59C31×#95C2×C411yescharacteristic
60C24×C31—21no—
61C24×C31C22⋊C411yescharacteristic
62C2×D4×C31—22no—
63C2×D4×C31—42no—
64C2×D4×C31—42no—
65C2×D4×C31—42no—
66C2×D4×C31—81no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—42no—
75C22×C4×C31—81no—
76C22×C4×C31—81no—
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83M16×C31—42no—
84M16×C31—42no—
85C2×C8×C31—24no—
86C2×C8×C31—42no—
87C4⋊C4×C31—22no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—22no—
90C4⋊C4×C31—81no—
91C22⋊C4×C31—22no—
92C22⋊C4×C31—22no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—81no—
98C22⋊C4×C31—81no—
99C42×C31—21no—
100C42×C31—21no—
101C42×C31C2×D412yes—
102C42×C31#4112yes—
103#9494C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—22no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31C2×C22⋊C411yescharacteristic
117D4×C31—24no—
118D4×C31—42no—
119D4×C31—84no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—84no—
143C2×C4×C31C4×D412yes—
144C2×C4×C31#12011yescharacteristic
145C2×C4×C31#12112yes—
146C2×C4×C31#12311yescharacteristic
147C8×C31—44no—
148C8×C31—82no—
149#2921C2×C3111yescharacteristic, complemented
150#2598C2×C3111yescharacteristic
151#1490C2×C3112yescomplemented
152#1464C2×C3111yescharacteristic, complemented
153#1288C2×C3112yescomplemented
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—42no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—42no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—81no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31#38611yescharacteristic
169C22×C31#42111yescharacteristic
170C22×C31#42111yescharacteristic
171C4×C31—22no—
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—81no—
179C4×C31—81no—
180C4×C31—81no—
181C2×C4×D4C22×C3111yescharacteristic
182C2×#117C22×C3111yescharacteristic
183#433—24no—
184#432C22×C3112yes—
185#423—21no—
186#407—21no—
187C4×M16C22×C3112yes—
188#400C4×C3111yescharacteristic
189#399C4×C3111yescharacteristic
190#394C4×C3111yescharacteristic
191#392C4×C3111yescharacteristic
192#388—21no—
193#386—21no—
194#386—21no—
195#385—21no—
196#383C22×C3111yescharacteristic
197D4⋊C8—24no—
198#324—21no—
199#323—21no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—81no—
203C2×C31—82no—
204C2×C31#189111yescharacteristic
205C2×C31#189711yescharacteristic
206C2×C31#191011yescharacteristic
207C22×D4—21no—
208C22×D4C2×C4×C3111yescharacteristic
209C23×C4—21no—
210C23×C4D4×C3111yescharacteristic
211C2×M16—22no—
212C4×D4—22no—
213C4×D4—22no—
214#117—22no—
215#117—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×C4×C3111yescharacteristic
218C2×C4⋊C4C2×C4×C3111yescharacteristic
219C2×C4⋊C4D4×C3111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C2×C4×C3111yescharacteristic
226C2×C22⋊C4D4×C3111yescharacteristic
227C2×C42D4×C3111yescharacteristic
228C2×C42C23×C3111yescharacteristic
229C4⋊C8—24no—
230C4⋊C8—22no—
231C22⋊C8—24no—
232C22⋊C8—22no—
233#97—22no—
234#97—22no—
235C4×C8D4×C3114yescomplemented
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95C2×C4×C3111yescharacteristic
241#95C2×C4×C3111yescharacteristic
242C31#949411yescharacteristic, direct product factor, Sylow
243C24—21no—
244C24C22⋊C4×C3111yescharacteristic
245C2×D4—22no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—81no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4C22⋊C4×C3111yescharacteristic
261C22×C4C22⋊C4×C3111yescharacteristic
262C22×C4C22⋊C4×C3111yescharacteristic
263C22×C4C22×C4×C3111yescharacteristic
264C22×C4C2×D4×C3111yescharacteristic
265C22×C4C2×D4×C3111yescharacteristic
266M16—42no—
267M16—42no—
268C2×C8—24no—
269C2×C8—42no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—81no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C42—21no—
283C42—21no—
284C42C2×D4×C3112yes—
285C42#41×C3112yes—
286C23—22no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23C2×C22⋊C4×C3111yescharacteristic
299D4—24no—
300D4—42no—
301D4—84no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—84no—
325C2×C4C4×D4×C3112yes—
326C2×C4C31×#12011yescharacteristic
327C2×C4C31×#12112yes—
328C2×C4C31×#12311yescharacteristic
329C8—44no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C31×#38611yescharacteristic
346C22C31×#42111yescharacteristic
347C22C31×#42111yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—82no—
362C2C31×#189111yescharacteristic
363C2C31×#189711yescharacteristic
364C2C31×#191011yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#392C4
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×#2921C2semidirect
3. C31×#1490C2semidirect
4. C31×#1464C2semidirect
5. C31×#1288C2semidirect
53. C4×C8×C31D4semidirect
103. #9494C31direct (N × H)
149. #2921C2×C31semidirect
151. #1490C2×C31semidirect
152. #1464C2×C31semidirect
153. #1288C2×C31semidirect
235. C4×C8D4×C31semidirect
242. C31#9494direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29212
C31×#25982
C31×#14902
C31×#14642
C31×#12882
#949431