Finite Group Databasebeta

← C31×#18397 #21475156

Subgroups — C31×#18397 #21475156

Order 7936.

1010 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#3230C212yesmaximal, complemented
3C31×#2542C211yesmaximal, characteristic
4C31×#1614C218yesmaximal, complemented
5C31×#1503C212yesmaximal, complemented
6C31×#1460C211yesmaximal, characteristic
7C31×#554—22no—
8C31×#554—24no—
9D4×Q8×C31—22no—
10C31×#544—21no—
11C31×#543C2214yes—
12C31×#533C2212yes—
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C31×C22⋊Q8—22no—
15C2×C31×C22⋊Q8—22no—
16C31×#518—21no—
17C2×C4×D4×C31C2211yescharacteristic
18C31×#500—22no—
19C31×#487—22no—
20C31×#484C2218yes—
21C31×#477—24no—
22C31×#431C2212yes—
23C31×#399C2214yes—
24C31×#390—21no—
25C31×#384—21no—
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×#328C2218yes—
28C31×#323C2214yes—
29C22×Q8×C31—22no—
30C22×Q8×C31—21no—
31C22×D4×C31D411yescharacteristic
32C23×C4×C31D412yes—
33C31×C4⋊Q8—24no—
34C31×C4⋊Q8—22no—
35C31×C4⋊Q8—22no—
36C31×C4⋊Q8D412yes—
37C31×C4⋊Q8D412yes—
38C31×#125—24no—
39C31×#125—22no—
40C31×C22⋊Q8—24no—
41C31×C22⋊Q8—24no—
42C31×C22⋊Q8—28no—
43C31×C22⋊Q8—22no—
44C31×C22⋊Q8—24no—
45C31×C22⋊Q8—28no—
46C31×C22⋊Q8—48no—
47C31×C22⋊Q8C2314yes—
48C4×Q8×C31—22no—
49C4×Q8×C31D414yes—
50C4×D4×C31—24no—
51C4×D4×C31—24no—
52C4×D4×C31—22no—
53C4×D4×C31—22no—
54C31×#117—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C4⋊C4×C31C2312yes—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31C2312yes—
65C2×C42×C31—21no—
66C2×C42×C31C2311yescharacteristic
67C31×#107—28no—
68C31×C4⋊C8—22no—
69C31×#103—28no—
70C31×C22⋊C8C2314yes—
71C4×C8×C31—22no—
72C31×#95C2312yes—
73C24×C31C2×D412yes—
74C2×Q8×C31—24no—
75C2×Q8×C31—22no—
76C2×Q8×C31—44no—
77C2×Q8×C31—41no—
78C2×Q8×C31—41no—
79C2×Q8×C31—84no—
80C2×Q8×C31C2×D414yes—
81C2×D4×C31—22no—
82C2×D4×C31—22no—
83C2×D4×C31Q1614yes—
84C22×C4×C31—22no—
85C22×C4×C31—24no—
86C22×C4×C31—24no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—44no—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D412yes—
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2411yescharacteristic
95C2×C8×C31—24no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—28no—
98C4⋊C4×C31—24no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—24no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—48no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31C2×D414yes—
109C22⋊C4×C31—28no—
110C22⋊C4×C31—24no—
111C22⋊C4×C31—24no—
112C22⋊C4×C31—48no—
113C42×C31—24no—
114C42×C31—42no—
115C42×C31C2×D412yes—
116C42×C31C2×D412yes—
117#18397C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—22no—
119C23×C31—22no—
120C23×C31—42no—
121C23×C31—42no—
122C23×C31C2×Q1614yes—
123C23×C31C22×D411yescharacteristic
124Q8×C31—44no—
125Q8×C31—44no—
126Q8×C31—82no—
127Q8×C31—84no—
128Q8×C31—82no—
129D4×C31—28no—
130C2×C4×C31—22no—
131C2×C4×C31—24no—
132C2×C4×C31—24no—
133C2×C4×C31—24no—
134C2×C4×C31—22no—
135C2×C4×C31—41no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—44no—
139C2×C4×C31—42no—
140C2×C4×C31—44no—
141C2×C4×C31—42no—
142C2×C4×C31—82no—
143C2×C4×C31—84no—
144C2×C4×C31—84no—
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31#12012yes—
147C2×C4×C31#12011yescharacteristic
148C2×C4×C31C2×Q1612yes—
149C2×C4×C31#13712yes—
150C2×C4×C31C22×D412yes—
151C8×C31—44no—
152#3501C2×C3111yescharacteristic
153#3230C2×C3112yescomplemented
154#2542C2×C3111yescharacteristic
155#1614C2×C3118yescomplemented
156#1503C2×C3112yescomplemented
157#1460C2×C3111yescharacteristic
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—24no—
161C22×C31—44no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—82no—
165C22×C31C2×#12011yescharacteristic
166C22×C31C22×Q1611yescharacteristic
167C22×C31C2×#13711yescharacteristic
168C4×C31—21no—
169C4×C31—22no—
170C4×C31—44no—
171C4×C31—42no—
172C4×C31—44no—
173C4×C31—44no—
174C4×C31—82no—
175C4×C31#45114yes—
176C4×C31#45312yes—
177#554—22no—
178#554—24no—
179D4×Q8—22no—
180#544—21no—
181#543C22×C3114yes—
182#533C22×C3112yes—
183C2×C4⋊Q8C22×C3111yescharacteristic
184C2×C22⋊Q8—22no—
185C2×C22⋊Q8—22no—
186#518—21no—
187C2×C4×D4C22×C3111yescharacteristic
188#500—22no—
189#487—22no—
190#484C22×C3118yes—
191#477—24no—
192#431C22×C3112yes—
193#399C22×C3114yes—
194#390—21no—
195#384—21no—
196C4×C4⋊C4C22×C3111yescharacteristic
197#328C22×C3118yes—
198#323C22×C3114yes—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—44no—
202C2×C31C2×#45111yescharacteristic
203C2×C31C2×#45311yescharacteristic
204C2×C31#302811yescharacteristic
205C22×Q8—22no—
206C22×Q8—21no—
207C22×D4D4×C3111yescharacteristic
208C23×C4D4×C3112yes—
209C4⋊Q8—24no—
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212C4⋊Q8D4×C3112yes—
213C4⋊Q8D4×C3112yes—
214#125—24no—
215#125—22no—
216C22⋊Q8—24no—
217C22⋊Q8—24no—
218C22⋊Q8—28no—
219C22⋊Q8—22no—
220C22⋊Q8—24no—
221C22⋊Q8—28no—
222C22⋊Q8—48no—
223C22⋊Q8C23×C3114yes—
224C4×Q8—22no—
225C4×Q8D4×C3114yes—
226C4×D4—24no—
227C4×D4—24no—
228C4×D4—22no—
229C4×D4—22no—
230#117—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C3111yescharacteristic
237C2×C4⋊C4C23×C3112yes—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4C23×C3112yes—
241C2×C42—21no—
242C2×C42C23×C3111yescharacteristic
243#107—28no—
244C4⋊C8—22no—
245#103—28no—
246C22⋊C8C23×C3114yes—
247C4×C8—22no—
248#95C23×C3112yes—
249C31#1839711yescharacteristic, direct product factor, Sylow
250C24C2×D4×C3112yes—
251C2×Q8—24no—
252C2×Q8—22no—
253C2×Q8—44no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—84no—
257C2×Q8C2×D4×C3114yes—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4Q16×C3114yes—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—44no—
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4C2×D4×C3112yes—
270C22×C4C2×D4×C3111yescharacteristic
271C22×C4C24×C3111yescharacteristic
272C2×C8—24no—
273C4⋊C4—24no—
274C4⋊C4—28no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—48no—
284C4⋊C4—42no—
285C4⋊C4C2×D4×C3114yes—
286C22⋊C4—28no—
287C22⋊C4—24no—
288C22⋊C4—24no—
289C22⋊C4—48no—
290C42—24no—
291C42—42no—
292C42C2×D4×C3112yes—
293C42C2×D4×C3112yes—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23C2×Q16×C3114yes—
299C23C22×D4×C3111yescharacteristic
300Q8—44no—
301Q8—44no—
302Q8—82no—
303Q8—84no—
304Q8—82no—
305D4—28no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—84no—
320C2×C4—84no—
321C2×C4C31×#12011yescharacteristic
322C2×C4C31×#12012yes—
323C2×C4C31×#12011yescharacteristic
324C2×C4C2×Q16×C3112yes—
325C2×C4C31×#13712yes—
326C2×C4C22×D4×C3112yes—
327C8—44no—
328C22—21no—
329C22—21no—
330C22—24no—
331C22—44no—
332C22—42no—
333C22—42no—
334C22—82no—
335C22C2×C31×#12011yescharacteristic
336C22C22×Q16×C3111yescharacteristic
337C22C2×C31×#13711yescharacteristic
338C4—21no—
339C4—22no—
340C4—44no—
341C4—42no—
342C4—44no—
343C4—44no—
344C4—82no—
345C4C31×#45114yes—
346C4C31×#45312yes—
347C2—21no—
348C2—21no—
349C2—44no—
350C2C2×C31×#45111yescharacteristic
351C2C2×C31×#45311yescharacteristic
352C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
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
2. C31×#3230C2semidirect
4. C31×#1614C2semidirect
5. C31×#1503C2semidirect
117. #18397C31direct (N × H)
153. #3230C2×C31semidirect
155. #1614C2×C31semidirect
156. #1503C2×C31semidirect
249. C31#18397direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#32302
C31×#25422
C31×#16142
C31×#15032
C31×#14602
#1839731