Finite Group Databasebeta

← C31×#18148 #21474907

Subgroups — C31×#18148 #21474907

Order 7936.

930 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C31×#3095C212yesmaximal
3C31×#2484C211yesmaximal, characteristic
4C31×#1617C214yesmaximal, complemented
5C31×#1611C214yesmaximal, complemented
6C31×#1511C212yesmaximal
7C31×#1463C211yesmaximal, characteristic
8C31×#544—24no—
9C31×#544—22no—
10C31×#544C2214yes—
11C2×C31×C4⋊Q8—22no—
12C2×C31×#125—22no—
13C2×C31×C22⋊Q8—21no—
14C2×C31×C22⋊Q8C2212yes—
15C2×C31×#117—21no—
16C2×C31×#117C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C31×#485—24no—
19C31×#484C2214yes—
20C31×#483C2214yes—
21C31×#428—22no—
22C31×#419—22no—
23C31×#407C2212yes—
24C31×#400C2212yes—
25C31×#398C2212yes—
26C31×#387—22no—
27C31×#385—21no—
28C31×#381—21no—
29C31×#381C2211yescharacteristic
30C31×#328C2218yes—
31C31×#324C2214yes—
32C22×Q8×C31—21no—
33C22×Q8×C31D412yes—
34C23×C4×C31D411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C2×M16×C31—22no—
38C31×C4⋊Q8—28no—
39C31×C4⋊Q8—28no—
40C31×#125—28no—
41C31×#125—28no—
42C31×C22⋊Q8—24no—
43C31×C22⋊Q8—24no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8—22no—
46C31×C22⋊Q8D414yes—
47C31×C22⋊Q8C2314yes—
48C31×#117—24no—
49C31×#117—24no—
50C31×#117—22no—
51C31×#117—22no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31D412yes—
61C2×C4⋊C4×C31D412yes—
62C2×C4⋊C4×C31C2311yescharacteristic
63C2×C4⋊C4×C31C2311yescharacteristic
64C2×C4⋊C4×C31C2312yes—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—21no—
67C2×C22⋊C4×C31—21no—
68C2×C42×C31—22no—
69C2×C42×C31—21no—
70C31×#107—24no—
71C31×#106—24no—
72C31×#103—24no—
73C31×#103—24no—
74C31×C22⋊C8—22no—
75C31×C22⋊C8C2314yes—
76C31×#95—22no—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—21no—
80C31×#95C2312yes—
81C24×C31C2×D411yescharacteristic
82C2×Q8×C31—24no—
83C2×Q8×C31—22no—
84C2×Q8×C31—44no—
85C2×Q8×C31—82no—
86C2×Q8×C31C2×D414yes—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—24no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—42no—
98C22×C4×C31—42no—
99C22×C4×C31C2×D412yes—
100C22×C4×C31C2×D412yes—
101C22×C4×C31C2×D412yes—
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31C2×D412yes—
104C22×C4×C31C2411yescharacteristic
105M16×C31—44no—
106C2×C8×C31—24no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—24no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—28no—
111C4⋊C4×C31—24no—
112C4⋊C4×C31—24no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—24no—
115C4⋊C4×C31—24no—
116C4⋊C4×C31—22no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—44no—
119C4⋊C4×C31C2×D414yes—
120C22⋊C4×C31—24no—
121C22⋊C4×C31—24no—
122C22⋊C4×C31—42no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C42×C31—28no—
126C42×C31—42no—
127#18148C3111yesmaximal, characteristic, direct product factor, Sylow
128C23×C31—22no—
129C23×C31—22no—
130C23×C31—41no—
131C23×C31#12011yescharacteristic
132C23×C31#12011yescharacteristic
133C23×C31C22×D411yescharacteristic
134Q8×C31—44no—
135Q8×C31—82no—
136Q8×C31—84no—
137C2×C4×C31—24no—
138C2×C4×C31—24no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—24no—
142C2×C4×C31—24no—
143C2×C4×C31—24no—
144C2×C4×C31—22no—
145C2×C4×C31—42no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—44no—
149C2×C4×C31—42no—
150C2×C4×C31—44no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—81no—
160C2×C4×C31#12012yes—
161C2×C4×C31#13714yes—
162C2×C4×C31C22×D412yes—
163C8×C31—44no—
164C2×#544C2×C3111yescharacteristic
165#3095C2×C3112yes—
166#2484C2×C3111yescharacteristic
167#1617C2×C3114yescomplemented
168#1611C2×C3114yescomplemented
169#1511C2×C3112yes—
170#1463C2×C3111yescharacteristic
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—44no—
179C22×C31#45812yes—
180C22×C31C2×#12011yescharacteristic
181C22×C31C2×#13712yes—
182C4×C31—24no—
183C4×C31—22no—
184C4×C31—22no—
185C4×C31—44no—
186C4×C31—42no—
187C4×C31—44no—
188C4×C31—82no—
189C4×C31—81no—
190C4×C31—81no—
191#544—24no—
192#544—22no—
193#544C22×C3114yes—
194C2×C4⋊Q8—22no—
195C2×#125—22no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8C22×C3112yes—
198C2×#117—21no—
199C2×#117C22×C3111yescharacteristic
200C22×C4⋊C4C22×C3111yescharacteristic
201#485—24no—
202#484C22×C3114yes—
203#483C22×C3114yes—
204#428—22no—
205#419—22no—
206#407C22×C3112yes—
207#400C22×C3112yes—
208#398C22×C3112yes—
209#387—22no—
210#385—21no—
211#381—21no—
212#381C22×C3111yescharacteristic
213#328C22×C3118yes—
214#324C22×C3114yes—
215C2×C31—22no—
216C2×C31—22no—
217C2×C31—41no—
218C2×C31#300411yescharacteristic
219C2×C31#302011yescharacteristic
220C2×C31C2×#45811yescharacteristic
221C22×Q8—21no—
222C22×Q8D4×C3112yes—
223C23×C4D4×C3111yescharacteristic
224C23×C4D4×C3111yescharacteristic
225C23×C4C23×C3111yescharacteristic
226C2×M16—22no—
227C4⋊Q8—28no—
228C4⋊Q8—28no—
229#125—28no—
230#125—28no—
231C22⋊Q8—24no—
232C22⋊Q8—24no—
233C22⋊Q8—22no—
234C22⋊Q8—22no—
235C22⋊Q8D4×C3114yes—
236C22⋊Q8C23×C3114yes—
237#117—24no—
238#117—24no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4D4×C3112yes—
250C2×C4⋊C4D4×C3112yes—
251C2×C4⋊C4C23×C3111yescharacteristic
252C2×C4⋊C4C23×C3111yescharacteristic
253C2×C4⋊C4C23×C3112yes—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C42—22no—
258C2×C42—21no—
259#107—24no—
260#106—24no—
261#103—24no—
262#103—24no—
263C22⋊C8—22no—
264C22⋊C8C23×C3114yes—
265#95—22no—
266#95—22no—
267#95—21no—
268#95—22no—
269#95C23×C3112yes—
270C31#1814811yescharacteristic, direct product factor, Sylow
271C24C2×D4×C3111yescharacteristic
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—44no—
275C2×Q8—82no—
276C2×Q8C2×D4×C3114yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×D4×C3112yes—
290C22×C4C2×D4×C3112yes—
291C22×C4C2×D4×C3112yes—
292C22×C4C2×D4×C3111yescharacteristic
293C22×C4C2×D4×C3112yes—
294C22×C4C24×C3111yescharacteristic
295M16—44no—
296C2×C8—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—44no—
309C4⋊C4C2×D4×C3114yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—28no—
316C42—42no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23C31×#12011yescharacteristic
321C23C31×#12011yescharacteristic
322C23C22×D4×C3111yescharacteristic
323Q8—44no—
324Q8—82no—
325Q8—84no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4C31×#12012yes—
350C2×C4C31×#13714yes—
351C2×C4C22×D4×C3112yes—
352C8—44no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22C31×#45812yes—
362C22C2×C31×#12011yescharacteristic
363C22C2×C31×#13712yes—
364C4—24no—
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4—81no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C31×#300411yescharacteristic
377C2C31×#302011yescharacteristic
378C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1617C2semidirect
5. C31×#1611C2semidirect
127. #18148C31direct (N × H)
167. #1617C2×C31semidirect
168. #1611C2×C31semidirect
270. C31#18148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C31×#30952
C31×#24842
C31×#16172
C31×#16112
C31×#15112
C31×#14632
#1814831