Finite Group Databasebeta

← C31×#10966 #21467725

Subgroups — C31×#10966 #21467725

Order 7936.

1634 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C22×C31×#99C212yesmaximal
3C2×C31×#381C212yesmaximal, complemented
4C2×C31×#342C212yesmaximal, complemented
5C23×D4×C31C2211yescharacteristic
6C24×C4×C31C2211yescharacteristic
7C2×C31×#123—24no—
8C2×C31×#123—24no—
9C2×C31×#123—24no—
10C22×C4⋊C4×C31C412yescomplemented
11C22×C22⋊C4×C31C412yescomplemented
12C22×C22⋊C4×C31C2214yes—
13C22×C22⋊C4×C31C2211yescharacteristic
14C2×C31×#99—24no—
15C2×C31×#99—28no—
16C31×#381—28no—
17C2×C31×#95—24no—
18C31×#342—24no—
19C25×C31C2×C411yescharacteristic
20C25×C31C2311yescharacteristic
21C22×D4×C31—24no—
22C22×D4×C31—22no—
23C22×D4×C31—22no—
24C22×D4×C31—24no—
25C22×D4×C31D414yes—
26C23×C4×C31—22no—
27C23×C4×C31—22no—
28C23×C4×C31—24no—
29C23×C4×C31—24no—
30C23×C4×C31—24no—
31C23×C4×C31C2×C412yes—
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C412yes—
34C23×C4×C31D414yes—
35C31×#123—232no—
36C2×C4⋊C4×C31—24no—
37C2×C4⋊C4×C31—24no—
38C2×C4⋊C4×C31—24no—
39C2×C22⋊C4×C31—24no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—24no—
43C2×C22⋊C4×C31—24no—
44C2×C22⋊C4×C31—24no—
45C2×C22⋊C4×C31—24no—
46C2×C22⋊C4×C31—24no—
47C2×C22⋊C4×C31—24no—
48C2×C22⋊C4×C31—24no—
49C2×C22⋊C4×C31D418yes—
50C2×C22⋊C4×C31D414yes—
51C31×#99—216no—
52C31×#95—216no—
53C24×C31—21no—
54C24×C31—21no—
55C24×C31—24no—
56C24×C31—44no—
57C24×C31—44no—
58C24×C31C22⋊C412yes—
59C24×C31C22×C411yescharacteristic
60C24×C31C2×D412yes—
61C24×C31C2×D412yes—
62C24×C31C2×D412yes—
63C24×C31C2×D414yes—
64C24×C31#4114yes—
65C2×D4×C31—24no—
66C2×D4×C31—28no—
67C2×D4×C31—28no—
68C2×D4×C31—24no—
69C2×D4×C31—42no—
70C2×D4×C31—44no—
71C2×D4×C31—44no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C2×D4×C31—42no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—21no—
81C22×C4×C31—28no—
82C22×C4×C31—24no—
83C22×C4×C31—24no—
84C22×C4×C31—28no—
85C22×C4×C31—28no—
86C22×C4×C31—24no—
87C22×C4×C31—28no—
88C22×C4×C31—42no—
89C22×C4×C31—44no—
90C22×C4×C31—44no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—44no—
95C22×C4×C31—416no—
96C22×C4×C31—44no—
97C22×C4×C31—44no—
98C22×C4×C31C22⋊C412yes—
99C22×C4×C31C22⋊C414yes—
100C22×C4×C31C22⋊C414yes—
101C4⋊C4×C31—216no—
102C22⋊C4×C31—216no—
103C22⋊C4×C31—28no—
104C22⋊C4×C31—28no—
105C22⋊C4×C31—28no—
106C22⋊C4×C31—44no—
107C22⋊C4×C31—44no—
108#10966C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—28no—
110C23×C31—24no—
111C23×C31—22no—
112C23×C31—24no—
113C23×C31—48no—
114C23×C31—44no—
115C23×C31—44no—
116C23×C31—48no—
117C23×C31—44no—
118C23×C31—44no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—44no—
122C23×C31—88no—
123C23×C31C2×C22⋊C411yescharacteristic
124C23×C31C2×C22⋊C411yescharacteristic
125C23×C31C2×C22⋊C411yescharacteristic
126C23×C31C4×D414yes—
127C23×C31#12014yes—
128C23×C31#12012yes—
129C23×C31#12012yes—
130C23×C31#12114yes—
131C23×C31#12114yes—
132C23×C31#12114yes—
133C23×C31#12312yes—
134C23×C31#12312yes—
135C23×C31#12412yes—
136C23×C31#12712yes—
137D4×C31—48no—
138D4×C31—48no—
139C2×C4×C31—24no—
140C2×C4×C31—24no—
141C2×C4×C31—22no—
142C2×C4×C31—28no—
143C2×C4×C31—24no—
144C2×C4×C31—44no—
145C2×C4×C31—44no—
146C2×C4×C31—42no—
147C2×C4×C31—44no—
148C2×C4×C31—42no—
149C2×C4×C31—48no—
150C2×C4×C31—48no—
151C2×C4×C31—44no—
152C2×C4×C31—44no—
153C2×C4×C31—416no—
154C2×C4×C31—48no—
155C2×C4×C31—88no—
156C2×C4×C31—88no—
157C22×#123C2×C3111yescharacteristic
158C22×#99C2×C3112yes—
159C2×#381C2×C3112yescomplemented
160C2×#342C2×C3112yescomplemented
161C22×C31—24no—
162C22×C31—28no—
163C22×C31—28no—
164C22×C31—24no—
165C22×C31—22no—
166C22×C31—22no—
167C22×C31—28no—
168C22×C31—42no—
169C22×C31—44no—
170C22×C31—44no—
171C22×C31—42no—
172C22×C31—42no—
173C22×C31—42no—
174C22×C31—42no—
175C22×C31—44no—
176C22×C31—84no—
177C22×C31—84no—
178C22×C31—84no—
179C22×C31#37911yescharacteristic
180C22×C31#38612yes—
181C22×C31#38612yes—
182C22×C31#39012yes—
183C22×C31#39214yes—
184C22×C31#39414yes—
185C22×C31#41014yes—
186C4×C31—44no—
187C4×C31—42no—
188C4×C31—44no—
189C4×C31—88no—
190C23×D4C22×C3111yescharacteristic
191C24×C4C22×C3111yescharacteristic
192C2×#123—24no—
193C2×#123—24no—
194C2×#123—24no—
195C22×C4⋊C4C4×C3112yescomplemented
196C22×C22⋊C4C4×C3112yescomplemented
197C22×C22⋊C4C22×C3114yes—
198C22×C22⋊C4C22×C3111yescharacteristic
199C2×#99—24no—
200C2×#99—28no—
201#381—28no—
202C2×#95—24no—
203#342—24no—
204C2×C31—24no—
205C2×C31—22no—
206C2×C31—22no—
207C2×C31—24no—
208C2×C31—82no—
209C2×C31#143811yescharacteristic
210C2×C31#178212yes—
211C2×C31#189914yes—
212C25C2×C4×C3111yescharacteristic
213C25C23×C3111yescharacteristic
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4D4×C3114yes—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4C2×C4×C3112yes—
225C23×C4C2×C4×C3111yescharacteristic
226C23×C4C2×C4×C3112yes—
227C23×C4D4×C3114yes—
228#123—232no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—24no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4D4×C3118yes—
243C2×C22⋊C4D4×C3114yes—
244#99—216no—
245#95—216no—
246C31#1096611yescharacteristic, direct product factor, Sylow
247C24—21no—
248C24—21no—
249C24—24no—
250C24—44no—
251C24—44no—
252C24C22⋊C4×C3112yes—
253C24C22×C4×C3111yescharacteristic
254C24C2×D4×C3112yes—
255C24C2×D4×C3112yes—
256C24C2×D4×C3112yes—
257C24C2×D4×C3114yes—
258C24#41×C3114yes—
259C2×D4—24no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—24no—
263C2×D4—42no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—24no—
281C22×C4—28no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—44no—
289C22×C4—416no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4C22⋊C4×C3114yes—
293C22×C4C22⋊C4×C3112yes—
294C22×C4C22⋊C4×C3114yes—
295C4⋊C4—216no—
296C22⋊C4—216no—
297C22⋊C4—28no—
298C22⋊C4—28no—
299C22⋊C4—28no—
300C22⋊C4—44no—
301C22⋊C4—44no—
302C23—28no—
303C23—24no—
304C23—22no—
305C23—24no—
306C23—48no—
307C23—44no—
308C23—44no—
309C23—48no—
310C23—44no—
311C23—44no—
312C23—44no—
313C23—42no—
314C23—42no—
315C23—88no—
316C23C2×C22⋊C4×C3111yescharacteristic
317C23C2×C22⋊C4×C3111yescharacteristic
318C23C2×C22⋊C4×C3111yescharacteristic
319C23C4×D4×C3114yes—
320C23C31×#12014yes—
321C23C31×#12012yes—
322C23C31×#12012yes—
323C23C31×#12114yes—
324C23C31×#12114yes—
325C23C31×#12114yes—
326C23C31×#12312yes—
327C23C31×#12312yes—
328C23C31×#12412yes—
329C23C31×#12712yes—
330D4—48no—
331D4—48no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—48no—
344C2×C4—48no—
345C2×C4—44no—
346C2×C4—416no—
347C2×C4—48no—
348C2×C4—88no—
349C2×C4—88no—
350C22—24no—
351C22—28no—
352C22—28no—
353C22—24no—
354C22—22no—
355C22—22no—
356C22—28no—
357C22—42no—
358C22—44no—
359C22—44no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—44no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22C31×#37911yescharacteristic
369C22C31×#38612yes—
370C22C31×#38612yes—
371C22C31×#39012yes—
372C22C31×#39214yes—
373C22C31×#39414yes—
374C22C31×#41014yes—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—88no—
379C2—24no—
380C2—22no—
381C2—22no—
382C2—24no—
383C2—82no—
384C2C31×#143811yescharacteristic
385C2C31×#178212yes—
386C2C31×#189914yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#381C2semidirect
4. C2×C31×#342C2semidirect
10. C22×C4⋊C4×C31C4semidirect
11. C22×C22⋊C4×C31C4semidirect
108. #10966C31direct (N × H)
159. C2×#381C2×C31semidirect
160. C2×#342C2×C31semidirect
195. C22×C4⋊C4C4×C31semidirect
196. C22×C22⋊C4C4×C31semidirect
246. C31#10966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#992
C2×C31×#3812
C2×C31×#3422
#1096631