Finite Group Databasebeta

← C31×#9307 #21466066

Subgroups — C31×#9307 #21466066

Order 7936.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3077C211yesmaximal, characteristic
2C31×#2975C211yesmaximal, characteristic
3C31×#1804C211yesmaximal, characteristic
4C31×#1518C211yesmaximal, characteristic, complemented
5C31×#1481C211yesmaximal, characteristic, complemented
6C31×#1301C211yesmaximal, characteristic, complemented
7C31×#1286C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C4×D4×C31C2211yescharacteristic
10C31×#478—22no—
11C31×#476C412yescomplemented
12C31×#474C412yescomplemented
13C31×#436—22no—
14C31×#436—22no—
15C31×#431C2211yescharacteristic
16C31×#431C2211yescharacteristic
17C31×#428—21no—
18C31×#423C2211yescharacteristic
19C2×C31×C4⋊C8C2211yescharacteristic
20C31×#418—21no—
21C2×C31×#102—21no—
22C31×#407—22no—
23C31×#382C2211yescharacteristic
24C31×#340—21no—
25C31×#328—22no—
26C31×Q8⋊C8—22no—
27C22×D4×C31D411yescharacteristic
28C23×C4×C31—21no—
29C2×M16×C31—21no—
30C2×M16×C31—24no—
31C22×C8×C31—21no—
32C31×C4⋊Q8C2×C411yescharacteristic
33C31×C4⋊Q8C2×C411yescharacteristic
34C31×#125—21no—
35C31×C22⋊Q8—21no—
36C31×C22⋊Q8—21no—
37C4×Q8×C31—21no—
38C4×Q8×C31—21no—
39C4×D4×C31—21no—
40C4×D4×C31—21no—
41C4×D4×C31C2×C412yes—
42C4×D4×C31D412yes—
43C31×#117—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C22⋊C4×C31—21no—
47C2×C42×C31C2311yescharacteristic
48C31×#107—22no—
49C31×#106—22no—
50C31×C4⋊C8—21no—
51C31×C4⋊C8—21no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8C2×C412yes—
56C31×#102—22no—
57C31×#102—22no—
58C31×#102—42no—
59C31×C22⋊C8—24no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8D412yes—
62C4×C8×C31—21no—
63C4×C8×C31D412yes—
64C31×#95—21no—
65C31×#95—21no—
66C24×C31—21no—
67C2×Q8×C31—21no—
68C2×Q8×C31—21no—
69C2×D4×C31—21no—
70C2×D4×C31—21no—
71C2×D4×C31—21no—
72C2×D4×C31—21no—
73C2×D4×C31—21no—
74C2×D4×C31C22⋊C412yes—
75C22×C4×C31—21no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—41no—
79C22×C4×C31—82no—
80C22×C4×C31C2×D411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31#4111yescharacteristic
83M16×C31—41no—
84M16×C31—41no—
85M16×C31—84no—
86C2×C8×C31—22no—
87C2×C8×C31—22no—
88C2×C8×C31—22no—
89C2×C8×C31—41no—
90C2×C8×C31—41no—
91C2×C8×C31—41no—
92C4⋊C4×C31—21no—
93C4⋊C4×C31—21no—
94C4⋊C4×C31—21no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—21no—
97C4⋊C4×C31—41no—
98C4⋊C4×C31—41no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31C22⋊C412yes—
102C22⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—41no—
105C42×C31—41no—
106C42×C31C22×C411yescharacteristic
107C42×C31C2×D411yescharacteristic
108C42×C31C2×D411yescharacteristic
109C42×C31#4111yescharacteristic
110#9307C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—22no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—81no—
115C23×C31—81no—
116C23×C31#12111yescharacteristic
117Q8×C31—42no—
118Q8×C31—81no—
119D4×C31—22no—
120D4×C31—22no—
121D4×C31—41no—
122D4×C31—41no—
123C2×C4×C31—22no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—44no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—82no—
130C2×C4×C31—81no—
131C2×C4×C31—81no—
132C2×C4×C31—81no—
133C2×C4×C31—81no—
134C2×C4×C31C2×C22⋊C411yescharacteristic
135C2×C4×C31C4×D411yescharacteristic
136C2×C4×C31C4×D411yescharacteristic
137C2×C4×C31#12011yescharacteristic
138C2×C4×C31#12111yescharacteristic
139C2×C4×C31#12311yescharacteristic
140C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C31#13711yescharacteristic
142C2×C4×C31#13711yescharacteristic
143C2×C4×C31#13711yescharacteristic
144C8×C31—42no—
145C8×C31—42no—
146C8×C31—42no—
147C8×C31—81no—
148#3077C2×C3111yescharacteristic
149#2975C2×C3111yescharacteristic
150#1804C2×C3111yescharacteristic
151#1518C2×C3111yescharacteristic, complemented
152#1481C2×C3111yescharacteristic, complemented
153#1301C2×C3111yescharacteristic, complemented
154#1286C2×C3111yescharacteristic, complemented
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—42no—
160C22×C31—82no—
161C22×C31—82no—
162C22×C31#38611yescharacteristic
163C22×C31#46811yescharacteristic
164C22×C31#47011yescharacteristic
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—42no—
170C4×C31—81no—
171C4×C31—81no—
172C4×C31—161no—
173C4×C31#41711yescharacteristic
174C4×C31#41911yescharacteristic
175C4×C31#46811yescharacteristic
176C4×C31#47011yescharacteristic
177#533C22×C3111yescharacteristic
178C2×C4×D4C22×C3111yescharacteristic
179#478—22no—
180#476C4×C3112yescomplemented
181#474C4×C3112yescomplemented
182#436—22no—
183#436—22no—
184#431C22×C3111yescharacteristic
185#431C22×C3111yescharacteristic
186#428—21no—
187#423C22×C3111yescharacteristic
188C2×C4⋊C8C22×C3111yescharacteristic
189#418—21no—
190C2×#102—21no—
191#407—22no—
192#382C22×C3111yescharacteristic
193#340—21no—
194#328—22no—
195Q8⋊C8—22no—
196C2×C31—21no—
197C2×C31—21no—
198C2×C31—82no—
199C2×C31#188111yescharacteristic
200C2×C31#189411yescharacteristic
201C2×C31#190411yescharacteristic
202C22×D4D4×C3111yescharacteristic
203C23×C4—21no—
204C2×M16—21no—
205C2×M16—24no—
206C22×C8—21no—
207C4⋊Q8C2×C4×C3111yescharacteristic
208C4⋊Q8C2×C4×C3111yescharacteristic
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4C2×C4×C3112yes—
217C4×D4D4×C3112yes—
218#117—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4D4×C3111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C23×C3111yescharacteristic
223#107—22no—
224#106—22no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8C2×C4×C3112yes—
231#102—22no—
232#102—22no—
233#102—42no—
234C22⋊C8—24no—
235C22⋊C8—21no—
236C22⋊C8D4×C3112yes—
237C4×C8—21no—
238C4×C8D4×C3112yes—
239#95—21no—
240#95—21no—
241C31#930711yescharacteristic, direct product factor, Sylow
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4C22⋊C4×C3112yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—82no—
256C22×C4C2×D4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4#41×C3111yescharacteristic
259M16—41no—
260M16—41no—
261M16—84no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4C22⋊C4×C3112yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C42—41no—
282C42C22×C4×C3111yescharacteristic
283C42C2×D4×C3111yescharacteristic
284C42C2×D4×C3111yescharacteristic
285C42#41×C3111yescharacteristic
286C23—22no—
287C23—41no—
288C23—41no—
289C23—81no—
290C23—81no—
291C23C31×#12111yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—22no—
295D4—22no—
296D4—41no—
297D4—41no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×C22⋊C4×C3111yescharacteristic
310C2×C4C4×D4×C3111yescharacteristic
311C2×C4C4×D4×C3111yescharacteristic
312C2×C4C31×#12011yescharacteristic
313C2×C4C31×#12111yescharacteristic
314C2×C4C31×#12311yescharacteristic
315C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
316C2×C4C31×#13711yescharacteristic
317C2×C4C31×#13711yescharacteristic
318C2×C4C31×#13711yescharacteristic
319C8—42no—
320C8—42no—
321C8—42no—
322C8—81no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22C31×#38611yescharacteristic
331C22C31×#46811yescharacteristic
332C22C31×#47011yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4C31×#41711yescharacteristic
342C4C31×#41911yescharacteristic
343C4C31×#46811yescharacteristic
344C4C31×#47011yescharacteristic
345C2—21no—
346C2—21no—
347C2—82no—
348C2C31×#188111yescharacteristic
349C2C31×#189411yescharacteristic
350C2C31×#190411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1518C2semidirect
5. C31×#1481C2semidirect
6. C31×#1301C2semidirect
7. C31×#1286C2semidirect
11. C31×#476C4semidirect
12. C31×#474C4semidirect
110. #9307C31direct (N × H)
151. #1518C2×C31semidirect
152. #1481C2×C31semidirect
153. #1301C2×C31semidirect
154. #1286C2×C31semidirect
180. #476C4×C31semidirect
181. #474C4×C31semidirect
241. C31#9307direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30772
C31×#29752
C31×#18042
C31×#15182
C31×#14812
C31×#13012
C31×#12862
#930731