Finite Group Databasebeta

← C31×#11808 #21468567

Subgroups — C31×#11808 #21468567

Order 7936.

680 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C31×#393C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic
3C31×#1462C211yesmaximal, characteristic
4C31×#1351C214yesmaximal, complemented
5C23×Q8×C31C411yescharacteristic, complemented
6C22×C22⋊C4×C31—21no—
7C22×C22⋊C4×C31C2211yescharacteristic
8C31×#407—21no—
9C31×#393—21no—
10C31×#393—21no—
11C31×#393C412yescomplemented
12C31×#393C2212yes—
13C31×#379—21no—
14C2×C31×#95—21no—
15C2×C31×#95C411yescharacteristic, complemented
16C31×#342—21no—
17C31×#342C2212yes—
18C31×#323—21no—
19C31×#323C2212yes—
20C25×C31D411yescharacteristic
21C22×Q8×C31—21no—
22C22×Q8×C31—44no—
23C22×Q8×C31—41no—
24C22×Q8×C31—41no—
25C22×Q8×C31C2×C412yes—
26C23×C4×C31—21no—
27C23×C4×C31—21no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C2×M16×C31—41no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—41no—
35C2×C22⋊C4×C31—41no—
36C2×C22⋊C4×C31—44no—
37C2×C22⋊C4×C31—41no—
38C2×C22⋊C4×C31—41no—
39C2×C22⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31D411yescharacteristic
41C2×C22⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31C2311yescharacteristic
43C31×C22⋊C8—22no—
44C31×C22⋊C8—41no—
45C31×#95—22no—
46C31×#95—21no—
47C31×#95—22no—
48C31×#95C2×C412yes—
49C24×C31—22no—
50C24×C31—21no—
51C24×C31—21no—
52C24×C31—41no—
53C24×C31—42no—
54C24×C31—42no—
55C24×C31C22⋊C411yescharacteristic
56C24×C31C22⋊C411yescharacteristic
57C24×C31C2×D411yescharacteristic
58C2×Q8×C31—44no—
59C2×Q8×C31—42no—
60C2×Q8×C31—44no—
61C2×Q8×C31—42no—
62C2×Q8×C31—48no—
63C2×Q8×C31—44no—
64C2×Q8×C31—44no—
65C22×C4×C31—24no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—22no—
70C22×C4×C31—21no—
71C22×C4×C31—22no—
72C22×C4×C31—42no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22×C411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85M16×C31—82no—
86C2×C8×C31—42no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—44no—
92C22⋊C4×C31—44no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—82no—
96C22⋊C4×C31—82no—
97#11808C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—22no—
99C23×C31—22no—
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—42no—
108C23×C31—42no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—48no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—81no—
117C23×C31—81no—
118C23×C31—84no—
119C23×C31#9911yescharacteristic
120C23×C31#9911yescharacteristic
121C23×C31C2×C22⋊C411yescharacteristic
122C23×C31#13712yes—
123Q8×C31—44no—
124Q8×C31—48no—
125Q8×C31—44no—
126C2×C4×C31—24no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—42no—
132C2×C4×C31—44no—
133C2×C4×C31—42no—
134C2×C4×C31—44no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—81no—
146C2×C4×C31—84no—
147C2×C4×C31—82no—
148C2×C4×C31—82no—
149C2×C4×C31—82no—
150C8×C31—82no—
151C2×#393C2×C3111yescharacteristic
152#1819C2×C3111yescharacteristic
153#1462C2×C3111yescharacteristic
154#1351C2×C3114yescomplemented
155C22×C31—24no—
156C22×C31—24no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—22no—
164C22×C31—42no—
165C22×C31—42no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—81no—
172C22×C31—84no—
173C22×C31—84no—
174C22×C31—81no—
175C22×C31AΣL(1,𝔽16)12yes—
176C22×C31#35412yes—
177C22×C31C2×#9911yescharacteristic
178C22×C31#41911yescharacteristic
179C22×C31#42111yescharacteristic
180C4×C31—44no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31—41no—
184C4×C31—41no—
185C4×C31—82no—
186C4×C31—162no—
187C23×Q8C4×C3111yescharacteristic, complemented
188C22×C22⋊C4—21no—
189C22×C22⋊C4C22×C3111yescharacteristic
190#407—21no—
191#393—21no—
192#393—21no—
193#393C4×C3112yescomplemented
194#393C22×C3112yes—
195#379—21no—
196C2×#95—21no—
197C2×#95C4×C3111yescharacteristic, complemented
198#342—21no—
199#342C22×C3112yes—
200#323—21no—
201#323C22×C3112yes—
202C2×C31—21no—
203C2×C31—21no—
204C2×C31—22no—
205C2×C31—22no—
206C2×C31—42no—
207C2×C31—81no—
208C2×C31#151111yescharacteristic
209C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
210C2×C31C2×#35411yescharacteristic
211C25D4×C3111yescharacteristic
212C22×Q8—21no—
213C22×Q8—44no—
214C22×Q8—41no—
215C22×Q8—41no—
216C22×Q8C2×C4×C3112yes—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4C2×C4×C3111yescharacteristic
220C23×C4D4×C3111yescharacteristic
221C2×M16—41no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4—44no—
228C2×C22⋊C4—41no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4C2×C4×C3111yescharacteristic
231C2×C22⋊C4D4×C3111yescharacteristic
232C2×C22⋊C4D4×C3111yescharacteristic
233C2×C22⋊C4C23×C3111yescharacteristic
234C22⋊C8—22no—
235C22⋊C8—41no—
236#95—22no—
237#95—21no—
238#95—22no—
239#95C2×C4×C3112yes—
240C31#1180811yescharacteristic, direct product factor, Sylow
241C24—22no—
242C24—21no—
243C24—21no—
244C24—41no—
245C24—42no—
246C24—42no—
247C24C22⋊C4×C3111yescharacteristic
248C24C22⋊C4×C3111yescharacteristic
249C24C2×D4×C3111yescharacteristic
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—48no—
255C2×Q8—44no—
256C2×Q8—44no—
257C22×C4—24no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4C22×C4×C3111yescharacteristic
276C22×C4C2×D4×C3111yescharacteristic
277M16—82no—
278C2×C8—42no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—44no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—82no—
288C22⋊C4—82no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—84no—
310C23C31×#9911yescharacteristic
311C23C31×#9911yescharacteristic
312C23C2×C22⋊C4×C3111yescharacteristic
313C23C31×#13712yes—
314Q8—44no—
315Q8—44no—
316Q8—48no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—84no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C8—82no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—84no—
360C22—84no—
361C22—81no—
362C22C31×AΣL(1,𝔽16)12yes—
363C22C31×#35412yes—
364C22C2×C31×#9911yescharacteristic
365C22C31×#41911yescharacteristic
366C22C31×#42111yescharacteristic
367C4—44no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—82no—
373C4—162no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—42no—
379C2—81no—
380C2C31×#151111yescharacteristic
381C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
382C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1351C2semidirect
5. C23×Q8×C31C4semidirect
11. C31×#393C4semidirect
15. C2×C31×#95C4semidirect
97. #11808C31direct (N × H)
154. #1351C2×C31semidirect
187. C23×Q8C4×C31semidirect
193. #393C4×C31semidirect
197. C2×#95C4×C31semidirect
240. C31#11808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3932
C31×#18192
C31×#14622
C31×#13512
#1180831