Finite Group Databasebeta

← C31×#32994 #21489753

Subgroups — C31×#32994 #21489753

Order 7936.

1212 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
1C2×C31×#519C211yesmaximal, characteristic
2C31×#3095C212yesmaximal
3C31×#2434C211yesmaximal, characteristic
4C31×#1886C214yesmaximal, complemented
5C31×#1857C214yesmaximal, complemented
6C31×#1826C212yesmaximal
7C31×#1784C211yesmaximal, characteristic
8C23×Q8×C31C2211yescharacteristic
9C2×C31×C4⋊Q8C2212yes—
10C2×C31×C22⋊Q8C2211yescharacteristic
11C31×#519—22no—
12C31×#519—24no—
13C31×#519C2214yes—
14C2×C4×Q8×C31—22no—
15C2×C4×Q8×C31—22no—
16C2×C31×#117—22no—
17C2×C31×#117C2212yes—
18C31×#485—24no—
19C31×#484—22no—
20C31×#483—22no—
21C31×#428C2214yes—
22C31×#419C2214yes—
23C2×C31×#101C2214yes—
24C31×#407C2212yes—
25C31×#395—22no—
26C31×#391C2212yes—
27C31×#385—22no—
28C4×C22⋊C4×C31C2211yescharacteristic
29C31×#339C2218yes—
30C22×Q8×C31—28no—
31C22×Q8×C31—22no—
32C22×Q8×C31—22no—
33C22×Q8×C31D412yes—
34C22×Q8×C31C2311yescharacteristic
35C22×Q8×C31C2312yes—
36C23×C4×C31D412yes—
37C23×C4×C31C2311yescharacteristic
38C2×M16×C31C2314yes—
39C31×C4⋊Q8—28no—
40C31×C22⋊Q8—22no—
41C31×C22⋊Q8—22no—
42C4×Q8×C31—28no—
43C4×Q8×C31—28no—
44C4×Q8×C31—28no—
45C4×Q8×C31—28no—
46C31×#117—28no—
47C31×#117—28no—
48C31×#117—22no—
49C31×#117—22no—
50C31×#117D414yes—
51C31×#117C2314yes—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31D412yes—
57C2×C4⋊C4×C31D412yes—
58C2×C4⋊C4×C31C2311yescharacteristic
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C42×C31—24no—
63C2×C42×C31—22no—
64C2×C42×C31C2312yes—
65C31×#107—24no—
66C31×#106—24no—
67C31×#103—24no—
68C31×#103—24no—
69C31×#101—28no—
70C31×C22⋊C8—22no—
71C31×C22⋊C8—22no—
72C31×#95—21no—
73C31×#95—24no—
74C24×C31C2×D411yescharacteristic
75C2×Q8×C31—216no—
76C2×Q8×C31—216no—
77C2×Q8×C31—24no—
78C2×Q8×C31—28no—
79C2×Q8×C31—24no—
80C2×Q8×C31—24no—
81C2×Q8×C31—22no—
82C2×Q8×C31—24no—
83C2×Q8×C31#4118yes—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31—28no—
87C22×C4×C31—24no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D412yes—
95C22×C4×C31C2×D412yes—
96C22×C4×C31C2×D414yes—
97C22×C4×C31C2411yescharacteristic
98M16×C31—28no—
99C2×C8×C31—24no—
100C4⋊C4×C31—28no—
101C4⋊C4×C31—28no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—42no—
106C4⋊C4×C31—48no—
107C4⋊C4×C31C2×D414yes—
108C4⋊C4×C31C2×D414yes—
109C22⋊C4×C31—24no—
110C22⋊C4×C31—24no—
111C22⋊C4×C31—24no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—41no—
114C42×C31—216no—
115C42×C31—24no—
116C42×C31—24no—
117C42×C31—24no—
118#32994C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—22no—
120C23×C31—22no—
121C23×C31—41no—
122C23×C31#12011yescharacteristic
123C23×C31#12011yescharacteristic
124C23×C31C22×D411yescharacteristic
125Q8×C31—216no—
126Q8×C31—216no—
127Q8×C31—44no—
128C2×C4×C31—28no—
129C2×C4×C31—28no—
130C2×C4×C31—24no—
131C2×C4×C31—22no—
132C2×C4×C31—24no—
133C2×C4×C31—24no—
134C2×C4×C31—24no—
135C2×C4×C31—24no—
136C2×C4×C31—24no—
137C2×C4×C31—24no—
138C2×C4×C31—42no—
139C2×C4×C31—44no—
140C2×C4×C31—42no—
141C2×C4×C31—44no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—42no—
146C2×C4×C31#12012yes—
147C2×C4×C31#12318yes—
148C2×C4×C31C22×D412yes—
149C2×C4×C31C2×#4114yes—
150C8×C31—44no—
151C2×#519C2×C3111yescharacteristic
152#3095C2×C3112yes—
153#2434C2×C3111yescharacteristic
154#1886C2×C3114yescomplemented
155#1857C2×C3114yescomplemented
156#1826C2×C3112yes—
157#1784C2×C3111yescharacteristic
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—44no—
166C22×C31#45612yes—
167C22×C31C2×#12011yescharacteristic
168C22×C31C2×#12312yes—
169C4×C31—22no—
170C4×C31—28no—
171C4×C31—44no—
172C4×C31—44no—
173C4×C31—44no—
174C4×C31—81no—
175C4×C31—81no—
176C4×C31#52514yes—
177C23×Q8C22×C3111yescharacteristic
178C2×C4⋊Q8C22×C3112yes—
179C2×C22⋊Q8C22×C3111yescharacteristic
180#519—22no—
181#519—24no—
182#519C22×C3114yes—
183C2×C4×Q8—22no—
184C2×C4×Q8—22no—
185C2×#117—22no—
186C2×#117C22×C3112yes—
187#485—24no—
188#484—22no—
189#483—22no—
190#428C22×C3114yes—
191#419C22×C3114yes—
192C2×#101C22×C3114yes—
193#407C22×C3112yes—
194#395—22no—
195#391C22×C3112yes—
196#385—22no—
197C4×C22⋊C4C22×C3111yescharacteristic
198#339C22×C3118yes—
199C2×C31—22no—
200C2×C31—22no—
201C2×C31—41no—
202C2×C31#284911yescharacteristic
203C2×C31C2×#45611yescharacteristic
204C2×C31#302011yescharacteristic
205C22×Q8—28no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8D4×C3112yes—
209C22×Q8C23×C3111yescharacteristic
210C22×Q8C23×C3112yes—
211C23×C4D4×C3112yes—
212C23×C4C23×C3111yescharacteristic
213C2×M16C23×C3114yes—
214C4⋊Q8—28no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C4×Q8—28no—
218C4×Q8—28no—
219C4×Q8—28no—
220C4×Q8—28no—
221#117—28no—
222#117—28no—
223#117—22no—
224#117—22no—
225#117D4×C3114yes—
226#117C23×C3114yes—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4D4×C3112yes—
232C2×C4⋊C4D4×C3112yes—
233C2×C4⋊C4C23×C3111yescharacteristic
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—24no—
238C2×C42—22no—
239C2×C42C23×C3112yes—
240#107—24no—
241#106—24no—
242#103—24no—
243#103—24no—
244#101—28no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247#95—21no—
248#95—24no—
249C31#3299411yescharacteristic, direct product factor, Sylow
250C24C2×D4×C3111yescharacteristic
251C2×Q8—216no—
252C2×Q8—216no—
253C2×Q8—24no—
254C2×Q8—28no—
255C2×Q8—24no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—24no—
259C2×Q8#41×C3118yes—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—28no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C2×D4×C3111yescharacteristic
270C22×C4C2×D4×C3112yes—
271C22×C4C2×D4×C3112yes—
272C22×C4C2×D4×C3114yes—
273C22×C4C24×C3111yescharacteristic
274M16—28no—
275C2×C8—24no—
276C4⋊C4—28no—
277C4⋊C4—28no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—48no—
283C4⋊C4C2×D4×C3114yes—
284C4⋊C4C2×D4×C3114yes—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C22⋊C4—24no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—216no—
291C42—24no—
292C42—24no—
293C42—24no—
294C23—22no—
295C23—22no—
296C23—41no—
297C23C31×#12011yescharacteristic
298C23C31×#12011yescharacteristic
299C23C22×D4×C3111yescharacteristic
300Q8—216no—
301Q8—216no—
302Q8—44no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4C31×#12012yes—
322C2×C4C31×#12318yes—
323C2×C4C22×D4×C3112yes—
324C2×C4C2×#41×C3114yes—
325C8—44no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—44no—
334C22C31×#45612yes—
335C22C2×C31×#12011yescharacteristic
336C22C2×C31×#12312yes—
337C4—22no—
338C4—28no—
339C4—44no—
340C4—44no—
341C4—44no—
342C4—81no—
343C4—81no—
344C4C31×#52514yes—
345C2—22no—
346C2—22no—
347C2—41no—
348C2C31×#284911yescharacteristic
349C2C2×C31×#45611yescharacteristic
350C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1886C2semidirect
5. C31×#1857C2semidirect
118. #32994C31direct (N × H)
154. #1886C2×C31semidirect
155. #1857C2×C31semidirect
249. C31#32994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5192
C31×#30952
C31×#24342
C31×#18862
C31×#18572
C31×#18262
C31×#17842
#3299431