Finite Group Databasebeta

← C31×#18189 #21474948

Subgroups — C31×#18189 #21474948

Order 7936.

902 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3502C211yesmaximal, characteristic
2C31×#3113C212yesmaximal
3C31×#2399C211yesmaximal, characteristic
4C31×#1611C214yesmaximal
5C31×#1605C214yesmaximal
6C31×#1506C212yesmaximal
7C31×#1467C211yesmaximal, characteristic
8Q82×C31—22no—
9C31×#557—22no—
10C31×#557—24no—
11C31×#544—21no—
12C31×#544C2214yes—
13C31×#533—22no—
14C31×#533C2212yes—
15C31×#519—21no—
16C2×C4×Q8×C31C2211yescharacteristic
17C2×C4×Q8×C31C2211yescharacteristic
18C31×#483C2214yes—
19C31×#475—22no—
20C31×#462—22no—
21C31×#451C2214yes—
22C31×#441—24no—
23C31×#432C2212yes—
24C31×#398—21no—
25C31×#398C2212yes—
26C31×#395—21no—
27C31×#395C2212yes—
28C4×C4⋊C4×C31—22no—
29C31×#376C2211yescharacteristic
30C31×#328C2218yes—
31C31×#324C2214yes—
32C22×Q8×C31D411yescharacteristic
33C22×Q8×C31C2311yescharacteristic
34C2×Q16×C31—24no—
35C31×C4⋊Q8—22no—
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8—24no—
38C31×C4⋊Q8—28no—
39C31×C4⋊Q8D412yes—
40C31×C4⋊Q8D412yes—
41C31×#125—24no—
42C31×#125—24no—
43C31×#125—28no—
44C31×#125—22no—
45C31×C22⋊Q8—22no—
46C31×C22⋊Q8—24no—
47C31×C22⋊Q8C2314yes—
48C4×Q8×C31—24no—
49C4×Q8×C31—24no—
50C4×Q8×C31—24no—
51C4×Q8×C31—24no—
52C4×Q8×C31—22no—
53C4×Q8×C31—22no—
54C4×Q8×C31—22no—
55C4×Q8×C31—22no—
56C4×Q8×C31—22no—
57C4×Q8×C31D414yes—
58C31×#117—24no—
59C31×#117—22no—
60C2×C4⋊C4×C31—21no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31D411yescharacteristic
64C2×C4⋊C4×C31C2311yescharacteristic
65C2×C4⋊C4×C31C2312yes—
66C2×C42×C31—21no—
67C2×C42×C31—21no—
68C2×C42×C31D412yes—
69C2×C42×C31C2311yescharacteristic
70C31×#106—24no—
71C31×C4⋊C8—22no—
72C31×#103—24no—
73C31×#103—24no—
74C31×C22⋊C8C2314yes—
75C31×#97—22no—
76C31×#95—22no—
77C31×#95—21no—
78C31×#95—22no—
79C31×#95C2312yes—
80C2×Q8×C31—24no—
81C2×Q8×C31—22no—
82C2×Q8×C31—22no—
83C2×Q8×C31—24no—
84C2×Q8×C31—22no—
85C2×Q8×C31—42no—
86C2×Q8×C31C2×D414yes—
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D412yes—
93C22×C4×C31C2×D412yes—
94C22×C4×C31C2411yescharacteristic
95Q16×C31—48no—
96C2×C8×C31—24no—
97C4⋊C4×C31—24no—
98C4⋊C4×C31—24no—
99C4⋊C4×C31—24no—
100C4⋊C4×C31—28no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—24no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—44no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31—44no—
112C4⋊C4×C31C2×D414yes—
113C22⋊C4×C31—24no—
114C42×C31—24no—
115C42×C31—28no—
116C42×C31—22no—
117C42×C31—22no—
118C42×C31—24no—
119C42×C31—41no—
120C42×C31—41no—
121C42×C31C2×D412yes—
122C42×C31C2×D412yes—
123#18189C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31C22×D411yescharacteristic
125Q8×C31—28no—
126Q8×C31—24no—
127Q8×C31—44no—
128Q8×C31—42no—
129Q8×C31—44no—
130Q8×C31—84no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
133C2×C4×C31—22no—
134C2×C4×C31—22no—
135C2×C4×C31—24no—
136C2×C4×C31—22no—
137C2×C4×C31—24no—
138C2×C4×C31—24no—
139C2×C4×C31—22no—
140C2×C4×C31—41no—
141C2×C4×C31—42no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31#12011yescharacteristic
149C2×C4×C31#12012yes—
150C2×C4×C31#12011yescharacteristic
151C2×C4×C31#13714yes—
152C2×C4×C31C22×D412yes—
153C8×C31—44no—
154#3502C2×C3111yescharacteristic
155#3113C2×C3112yes—
156#2399C2×C3111yescharacteristic
157#1611C2×C3114yes—
158#1605C2×C3114yes—
159#1506C2×C3112yes—
160#1467C2×C3111yescharacteristic
161C22×C31—21no—
162C22×C31—21no—
163C22×C31C2×#12011yescharacteristic
164C22×C31C2×#13712yes—
165C4×C31—22no—
166C4×C31—24no—
167C4×C31—21no—
168C4×C31—22no—
169C4×C31—44no—
170C4×C31—44no—
171C4×C31—42no—
172C4×C31—42no—
173C4×C31—44no—
174C4×C31—81no—
175C4×C31#45612yes—
176Q82—22no—
177#557—22no—
178#557—24no—
179#544—21no—
180#544C22×C3114yes—
181#533—22no—
182#533C22×C3112yes—
183#519—21no—
184C2×C4×Q8C22×C3111yescharacteristic
185C2×C4×Q8C22×C3111yescharacteristic
186#483C22×C3114yes—
187#475—22no—
188#462—22no—
189#451C22×C3114yes—
190#441—24no—
191#432C22×C3112yes—
192#398—21no—
193#398C22×C3112yes—
194#395—21no—
195#395C22×C3112yes—
196C4×C4⋊C4—22no—
197#376C22×C3111yescharacteristic
198#328C22×C3118yes—
199#324C22×C3114yes—
200C2×C31—22no—
201C2×C31#300411yescharacteristic
202C2×C31C2×#45611yescharacteristic
203C2×C31#302511yescharacteristic
204C22×Q8D4×C3111yescharacteristic
205C22×Q8C23×C3111yescharacteristic
206C2×Q16—24no—
207C4⋊Q8—22no—
208C4⋊Q8—22no—
209C4⋊Q8—24no—
210C4⋊Q8—28no—
211C4⋊Q8D4×C3112yes—
212C4⋊Q8D4×C3112yes—
213#125—24no—
214#125—24no—
215#125—28no—
216#125—22no—
217C22⋊Q8—22no—
218C22⋊Q8—24no—
219C22⋊Q8C23×C3114yes—
220C4×Q8—24no—
221C4×Q8—24no—
222C4×Q8—24no—
223C4×Q8—24no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×Q8D4×C3114yes—
230#117—24no—
231#117—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4D4×C3111yescharacteristic
236C2×C4⋊C4C23×C3111yescharacteristic
237C2×C4⋊C4C23×C3112yes—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42D4×C3112yes—
241C2×C42C23×C3111yescharacteristic
242#106—24no—
243C4⋊C8—22no—
244#103—24no—
245#103—24no—
246C22⋊C8C23×C3114yes—
247#97—22no—
248#95—21no—
249#95—22no—
250#95—22no—
251#95C23×C3112yes—
252C31#1818911yescharacteristic, direct product factor, Sylow
253C2×Q8—24no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—42no—
259C2×Q8C2×D4×C3114yes—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4C2×D4×C3111yescharacteristic
264C22×C4C2×D4×C3111yescharacteristic
265C22×C4C2×D4×C3112yes—
266C22×C4C2×D4×C3112yes—
267C22×C4C24×C3111yescharacteristic
268Q16—48no—
269C2×C8—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—28no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—22no—
282C4⋊C4—44no—
283C4⋊C4—42no—
284C4⋊C4—44no—
285C4⋊C4C2×D4×C3114yes—
286C22⋊C4—24no—
287C42—24no—
288C42—28no—
289C42—22no—
290C42—22no—
291C42—24no—
292C42—41no—
293C42—41no—
294C42C2×D4×C3112yes—
295C42C2×D4×C3112yes—
296C23C22×D4×C3111yescharacteristic
297Q8—28no—
298Q8—24no—
299Q8—44no—
300Q8—42no—
301Q8—44no—
302Q8—84no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4C31×#12011yescharacteristic
321C2×C4C31×#12012yes—
322C2×C4C31×#12011yescharacteristic
323C2×C4C31×#13714yes—
324C2×C4C22×D4×C3112yes—
325C8—44no—
326C22—21no—
327C22—21no—
328C22C2×C31×#12011yescharacteristic
329C22C2×C31×#13712yes—
330C4—22no—
331C4—24no—
332C4—21no—
333C4—22no—
334C4—44no—
335C4—44no—
336C4—42no—
337C4—42no—
338C4—44no—
339C4—81no—
340C4C31×#45612yes—
341C2—22no—
342C2C31×#300411yescharacteristic
343C2C2×C31×#45611yescharacteristic
344C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×C31C22×D4
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
123. #18189C31direct (N × H)
252. C31#18189direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35022
C31×#31132
C31×#23992
C31×#16112
C31×#16052
C31×#15062
C31×#14672
#1818931