Finite Group Databasebeta

← C31×#11754 #21468513

Subgroups — C31×#11754 #21468513

Order 7936.

500 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2598C211yesmaximal, characteristic
2C31×#1740C211yesmaximal, characteristic, complemented
3C31×#1464C211yesmaximal, characteristic, complemented
4C31×#1352C212yesmaximal, complemented
5C31×#1343C212yesmaximal
6C2×C4×D4×C31C411yescharacteristic, complemented
7C2×C31×#117—21no—
8C2×C31×#117C2211yescharacteristic
9C31×#432—21no—
10C31×#400C411yescharacteristic, complemented
11C31×#399C2211yescharacteristic
12C31×#394C411yescharacteristic, complemented
13C31×#392C2211yescharacteristic
14C31×#388—21no—
15C31×#386—21no—
16C31×#386—21no—
17C31×#385—21no—
18C31×#383C411yescharacteristic, complemented
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#324—21no—
22C31×#323C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31D411yescharacteristic
27C4×D4×C31—41no—
28C4×D4×C31—41no—
29C31×#117—24no—
30C31×#117—41no—
31C31×#117—41no—
32C31×#117—42no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—41no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31D411yescharacteristic
45C2×C22⋊C4×C31C2311yescharacteristic
46C2×C42×C31—41no—
47C2×C42×C31C2×C411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C31×C4⋊C8—41no—
50C31×C22⋊C8—22no—
51C31×#97—41no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31C2×D411yescharacteristic
60C2×D4×C31—41no—
61C2×D4×C31—42no—
62C2×D4×C31—42no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
65C2×D4×C31—81no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—22no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—42no—
75C22×C4×C31—42no—
76C22×C4×C31—81no—
77C22×C4×C31—81no—
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C2×C8×C31—42no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—44no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—81no—
90C22⋊C4×C31—24no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—81no—
99C22⋊C4×C31—81no—
100C42×C31—21no—
101C42×C31—21no—
102C42×C31—21no—
103C42×C31—21no—
104C42×C31—44no—
105#11754C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—22no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31C2×C22⋊C411yescharacteristic
118C23×C31AGL(1,ℤ/8)11yescharacteristic
119C23×C31#13711yescharacteristic
120D4×C31—42no—
121D4×C31—42no—
122D4×C31—82no—
123D4×C31—82no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—44no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—84no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31#9911yescharacteristic
154C2×C4×C31#9911yescharacteristic
155C2×C4×C31#10412yes—
156C8×C31—82no—
157#2598C2×C3111yescharacteristic
158#1740C2×C3111yescharacteristic, complemented
159#1464C2×C3111yescharacteristic, complemented
160#1352C2×C3112yescomplemented
161#1343C2×C3112yes—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—42no—
169C22×C31—42no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—42no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31C2×#9911yescharacteristic
179C22×C31#41711yescharacteristic
180C22×C31C2×#10411yescharacteristic
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—22no—
184C4×C31—41no—
185C4×C31—41no—
186C4×C31—41no—
187C4×C31—41no—
188C4×C31—81no—
189C4×C31—81no—
190C4×C31—84no—
191C4×C31—81no—
192C2×C4×D4C4×C3111yescharacteristic, complemented
193C2×#117—21no—
194C2×#117C22×C3111yescharacteristic
195#432—21no—
196#400C4×C3111yescharacteristic, complemented
197#399C22×C3111yescharacteristic
198#394C4×C3111yescharacteristic, complemented
199#392C22×C3111yescharacteristic
200#388—21no—
201#386—21no—
202#386—21no—
203#385—21no—
204#383C4×C3111yescharacteristic, complemented
205#342—21no—
206#342C22×C3112yes—
207#324—21no—
208#323C22×C3112yes—
209C2×C31—21no—
210C2×C31—21no—
211C2×C31—41no—
212C2×C31—41no—
213C2×C31—82no—
214C2×C31#150411yescharacteristic
215C2×C31#212011yescharacteristic
216C2×C31#212811yescharacteristic
217C22×D4—21no—
218C22×D4C2×C4×C3111yescharacteristic
219C23×C4—21no—
220C23×C4D4×C3111yescharacteristic
221C4×D4—41no—
222C4×D4—41no—
223#117—24no—
224#117—41no—
225#117—41no—
226#117—42no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4C2×C4×C3111yescharacteristic
230C2×C4⋊C4C2×C4×C3111yescharacteristic
231C2×C4⋊C4D4×C3111yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4D4×C3111yescharacteristic
239C2×C22⋊C4C23×C3111yescharacteristic
240C2×C42—41no—
241C2×C42C2×C4×C3111yescharacteristic
242C2×C42D4×C3111yescharacteristic
243C4⋊C8—41no—
244C22⋊C8—22no—
245#97—41no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95C2×C4×C3111yescharacteristic
251#95C2×C4×C3111yescharacteristic
252C31#1175411yescharacteristic, direct product factor, Sylow
253C24—21no—
254C24C2×D4×C3111yescharacteristic
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—81no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4C22⋊C4×C3111yescharacteristic
276C22×C4C22⋊C4×C3111yescharacteristic
277C22×C4C22×C4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279C2×C8—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—44no—
284C4⋊C4—81no—
285C22⋊C4—24no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—44no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C22⋊C4×C3111yescharacteristic
312C23C31×AGL(1,ℤ/8)11yescharacteristic
313C23C31×#13711yescharacteristic
314D4—42no—
315D4—42no—
316D4—82no—
317D4—82no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—84no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4C31×#9911yescharacteristic
348C2×C4C31×#9911yescharacteristic
349C2×C4C31×#10412yes—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—42no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22C2×C31×#9911yescharacteristic
368C22C31×#41711yescharacteristic
369C22C2×C31×#10411yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—84no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—41no—
384C2—41no—
385C2—82no—
386C2C31×#150411yescharacteristic
387C2C31×#212011yescharacteristic
388C2C31×#212811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1740C2semidirect
3. C31×#1464C2semidirect
4. C31×#1352C2semidirect
6. C2×C4×D4×C31C4semidirect
10. C31×#400C4semidirect
12. C31×#394C4semidirect
18. C31×#383C4semidirect
105. #11754C31direct (N × H)
158. #1740C2×C31semidirect
159. #1464C2×C31semidirect
160. #1352C2×C31semidirect
192. C2×C4×D4C4×C31semidirect
196. #400C4×C31semidirect
198. #394C4×C31semidirect
204. #383C4×C31semidirect
252. C31#11754direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25982
C31×#17402
C31×#14642
C31×#13522
C31×#13432
#1175431