Finite Group Databasebeta

← C31×#12090 #21468849

Subgroups — C31×#12090 #21468849

Order 7936.

1062 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2403C211yesmaximal, characteristic, complemented
2C31×#2021C211yesmaximal, characteristic, complemented
3C31×#1595C212yesmaximal, complemented
4C31×#1343C212yesmaximal, complemented
5C31×#1316C211yesmaximal, characteristic, complemented
6C23×D4×C31—21no—
7C31×#534C2211yescharacteristic, complemented
8C2×C31×#120—22no—
9C2×C31×#120—21no—
10C31×#447—22no—
11C2×C31×#99—21no—
12C31×#392—21no—
13C31×#392C2212yes—
14C31×#386—22no—
15C31×#379C2211yescharacteristic
16C31×#342C2211yescharacteristic, complemented
17C31×#327—22no—
18C31×#323C2212yescomplemented
19C25×C31—21no—
20C25×C31D411yescharacteristic
21C22×D4×C31—22no—
22C22×D4×C31—21no—
23C22×D4×C31—22no—
24C22×D4×C31—21no—
25C22×D4×C31—48no—
26C22×D4×C31—42no—
27C22×D4×C31—42no—
28C22×D4×C31—41no—
29C22×D4×C31D412yescomplemented
30C23×C4×C31—21no—
31C2×D8×C31—42no—
32C31×#123—41no—
33C31×#121—22no—
34C31×#120—42no—
35C31×#120—41no—
36C31×#120—48no—
37C31×#120—42no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—41no—
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C22⋊C4×C31C2311yescharacteristic
45C31×#102—42no—
46C31×#99—42no—
47C31×C22⋊C8—22no—
48C31×#95—21no—
49C31×#95D412yescomplemented
50C24×C31—21no—
51C24×C31—22no—
52C24×C31—21no—
53C24×C31—21no—
54C24×C31—41no—
55C24×C31—44no—
56C24×C31—42no—
57C24×C31—44no—
58C24×C31—41no—
59C24×C31—44no—
60C24×C31—81no—
61C24×C31—81no—
62C24×C31D812yescomplemented
63C24×C31C2×D411yescharacteristic
64C2×D4×C31—28no—
65C2×D4×C31—22no—
66C2×D4×C31—44no—
67C2×D4×C31—42no—
68C2×D4×C31—44no—
69C2×D4×C31—44no—
70C2×D4×C31—44no—
71C2×D4×C31—416no—
72C2×D4×C31—416no—
73C2×D4×C31—42no—
74C2×D4×C31—42no—
75C2×D4×C31—44no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C2×D4×C31—44no—
79C2×D4×C31—41no—
80C2×D4×C31—44no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—81no—
85C2×D4×C31—84no—
86C22×C4×C31—22no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—44no—
90C22×C4×C31—42no—
91C22×C4×C31—41no—
92C22×C4×C31C2×D412yes—
93D8×C31—84no—
94C2×C8×C31—42no—
95C4⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—44no—
99C22⋊C4×C31—44no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—44no—
102C22⋊C4×C31—44no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105#12090C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—24no—
107C23×C31—22no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—24no—
111C23×C31—42no—
112C23×C31—42no—
113C23×C31—44no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—44no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—44no—
124C23×C31—48no—
125C23×C31—42no—
126C23×C31—42no—
127C23×C31—42no—
128C23×C31—41no—
129C23×C31—81no—
130C23×C31—84no—
131C23×C31—84no—
132C23×C31—82no—
133C23×C31—88no—
134C23×C31—88no—
135C23×C31—84no—
136C23×C31—82no—
137C23×C31#12011yescharacteristic
138C23×C31C2×D811yescharacteristic
139C23×C31AGL(1,ℤ/8)11yescharacteristic
140D4×C31—416no—
141D4×C31—44no—
142D4×C31—48no—
143D4×C31—48no—
144D4×C31—82no—
145D4×C31—82no—
146D4×C31—81no—
147D4×C31—81no—
148D4×C31—84no—
149D4×C31—88no—
150D4×C31—81no—
151D4×C31—81no—
152C2×C4×C31—24no—
153C2×C4×C31—22no—
154C2×C4×C31—42no—
155C2×C4×C31—48no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—82no—
165C8×C31—82no—
166#2403C2×C3111yescharacteristic, complemented
167#2021C2×C3111yescharacteristic, complemented
168#1595C2×C3112yescomplemented
169#1343C2×C3112yescomplemented
170#1316C2×C3111yescharacteristic, complemented
171C22×C31—22no—
172C22×C31—24no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—42no—
178C22×C31—44no—
179C22×C31—44no—
180C22×C31—44no—
181C22×C31—44no—
182C22×C31—42no—
183C22×C31—42no—
184C22×C31—44no—
185C22×C31—44no—
186C22×C31—81no—
187C22×C31—82no—
188C22×C31—82no—
189C22×C31—82no—
190C22×C31—84no—
191C22×C31—816no—
192C22×C31—82no—
193C22×C31—82no—
194C22×C31—82no—
195C22×C31—81no—
196C22×C31—82no—
197C22×C31—161no—
198C22×C31#44711yescharacteristic
199C22×C31#45311yescharacteristic
200C22×C31B(4,𝔽2)11yescharacteristic
201C4×C31—44no—
202C4×C31—42no—
203C4×C31—81no—
204C4×C31—82no—
205C4×C31—81no—
206C23×D4—21no—
207#534C22×C3111yescharacteristic, complemented
208C2×#120—22no—
209C2×#120—21no—
210#447—22no—
211C2×#99—21no—
212#392—21no—
213#392C22×C3112yes—
214#386—22no—
215#379C22×C3111yescharacteristic
216#342C22×C3111yescharacteristic, complemented
217#327—22no—
218#323C22×C3112yescomplemented
219C2×C31—21no—
220C2×C31—21no—
221C2×C31—41no—
222C2×C31—44no—
223C2×C31—41no—
224C2×C31—84no—
225C2×C31—161no—
226C2×C31#159511yescharacteristic
227C2×C31#219612yes—
228C25—21no—
229C25D4×C3111yescharacteristic
230C22×D4—22no—
231C22×D4—21no—
232C22×D4—22no—
233C22×D4—21no—
234C22×D4—48no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—41no—
238C22×D4D4×C3112yescomplemented
239C23×C4—21no—
240C2×D8—42no—
241#123—41no—
242#121—22no—
243#120—42no—
244#120—41no—
245#120—48no—
246#120—42no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—41no—
252C2×C22⋊C4D4×C3111yescharacteristic
253C2×C22⋊C4C23×C3111yescharacteristic
254#102—42no—
255#99—42no—
256C22⋊C8—22no—
257#95—21no—
258#95D4×C3112yescomplemented
259C31#1209011yescharacteristic, direct product factor, Sylow
260C24—21no—
261C24—22no—
262C24—21no—
263C24—21no—
264C24—41no—
265C24—44no—
266C24—42no—
267C24—44no—
268C24—41no—
269C24—44no—
270C24—81no—
271C24—81no—
272C24D8×C3112yescomplemented
273C24C2×D4×C3111yescharacteristic
274C2×D4—28no—
275C2×D4—22no—
276C2×D4—44no—
277C2×D4—42no—
278C2×D4—44no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4—416no—
282C2×D4—416no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—44no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—44no—
289C2×D4—41no—
290C2×D4—44no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—81no—
295C2×D4—84no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—44no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4C2×D4×C3112yes—
303D8—84no—
304C2×C8—42no—
305C4⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—41no—
308C22⋊C4—44no—
309C22⋊C4—44no—
310C22⋊C4—42no—
311C22⋊C4—44no—
312C22⋊C4—44no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C23—24no—
316C23—22no—
317C23—21no—
318C23—21no—
319C23—24no—
320C23—42no—
321C23—42no—
322C23—44no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—44no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—44no—
333C23—48no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—41no—
338C23—81no—
339C23—84no—
340C23—84no—
341C23—82no—
342C23—88no—
343C23—88no—
344C23—84no—
345C23—82no—
346C23C31×#12011yescharacteristic
347C23C2×D8×C3111yescharacteristic
348C23C31×AGL(1,ℤ/8)11yescharacteristic
349D4—416no—
350D4—44no—
351D4—48no—
352D4—48no—
353D4—82no—
354D4—82no—
355D4—81no—
356D4—81no—
357D4—84no—
358D4—88no—
359D4—81no—
360D4—81no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—48no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C8—82no—
375C22—22no—
376C22—24no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—44no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—42no—
387C22—42no—
388C22—44no—
389C22—44no—
390C22—81no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—84no—
395C22—816no—
396C22—82no—
397C22—82no—
398C22—82no—
399C22—81no—
400C22—82no—
401C22—161no—
402C22C31×#44711yescharacteristic
403C22C31×#45311yescharacteristic
404C22C31×B(4,𝔽2)11yescharacteristic
405C4—44no—
406C4—42no—
407C4—81no—
408C4—82no—
409C4—81no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—44no—
414C2—41no—
415C2—84no—
416C2—161no—
417C2C31×#159511yescharacteristic
418C2C31×#219612yes—
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C31
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2403C2semidirect
2. C31×#2021C2semidirect
3. C31×#1595C2semidirect
4. C31×#1343C2semidirect
5. C31×#1316C2semidirect
7. C31×#534C22semidirect
16. C31×#342C22semidirect
18. C31×#323C22semidirect
29. C22×D4×C31D4semidirect
49. C31×#95D4semidirect
62. C24×C31D8semidirect
105. #12090C31direct (N × H)
166. #2403C2×C31semidirect
167. #2021C2×C31semidirect
168. #1595C2×C31semidirect
169. #1343C2×C31semidirect
170. #1316C2×C31semidirect
207. #534C22×C31semidirect
216. #342C22×C31semidirect
218. #323C22×C31semidirect
238. C22×D4D4×C31semidirect
258. #95D4×C31semidirect
259. C31#12090direct (N × H)
272. C24D8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#24032
C31×#20212
C31×#15952
C31×#13432
C31×#13162
#1209031