Finite Group Databasebeta

← C31×#11876 #21468635

Subgroups — C31×#11876 #21468635

Order 7936.

522 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2543C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic, complemented
3C31×#1460C211yesmaximal, characteristic, complemented
4C31×#1344C212yesmaximal, complemented
5C31×#1343C212yesmaximal, complemented
6C2×C31×#121—21no—
7C2×C31×#121C411yescharacteristic, complemented
8C2×C4×D4×C31C2211yescharacteristic
9C31×#431—21no—
10C2×C31×#99—21no—
11C31×#398C411yescharacteristic, complemented
12C31×#397C2211yescharacteristic
13C31×#394C411yescharacteristic, complemented
14C31×#392C2211yescharacteristic
15C31×#388—21no—
16C31×#386—21no—
17C31×#386—21no—
18C31×#380—21no—
19C2×C31×#95C411yescharacteristic, complemented
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C22×D4×C31D411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C31×#121—42no—
31C31×#121—42no—
32C31×#121—41no—
33C31×#121—41no—
34C4×D4×C31—41no—
35C4×D4×C31—41no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—41no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C22⋊C4×C31C2311yescharacteristic
48C2×C42×C31D411yescharacteristic
49C31×C4⋊C8—41no—
50C31×#99—42no—
51C31×C22⋊C8—22no—
52C4×C8×C31—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—41no—
57C31×#95C2×C411yescharacteristic
58C31×#95C2×C411yescharacteristic
59C24×C31—21no—
60C24×C31C22⋊C411yescharacteristic
61C24×C31C2×D411yescharacteristic
62C2×D4×C31—41no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—41no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—81no—
72C2×D4×C31—81no—
73C2×D4×C31D812yes—
74C2×D4×C31SD1612yes—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—81no—
86C22×C4×C31—81no—
87C22×C4×C31—81no—
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22×C411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C2×C8×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—42no—
97C4⋊C4×C31—82no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—81no—
109C42×C31—21no—
110C42×C31—21no—
111#11876C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31#10212yes—
128C23×C31C2×C22⋊C411yescharacteristic
129C23×C31C2×D811yescharacteristic
130C23×C31C2×SD1611yescharacteristic
131D4×C31—42no—
132D4×C31—42no—
133D4×C31—82no—
134D4×C31—82no—
135D4×C31—82no—
136D4×C31—84no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—22no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31—84no—
160C2×C4×C31—82no—
161C2×C4×C31—82no—
162C2×C4×C31—82no—
163C2×C4×C31#9911yescharacteristic
164C2×C4×C31#9911yescharacteristic
165C2×C4×C31#10212yes—
166C8×C31—82no—
167#2543C2×C3111yescharacteristic
168#1799C2×C3111yescharacteristic, complemented
169#1460C2×C3111yescharacteristic, complemented
170#1344C2×C3112yescomplemented
171#1343C2×C3112yescomplemented
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—22no—
176C22×C31—21no—
177C22×C31—42no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—42no—
181C22×C31—41no—
182C22×C31—41no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31—81no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31—81no—
192C22×C31—81no—
193C22×C31C2×#9911yescharacteristic
194C22×C31C2×#10211yescharacteristic
195C22×C31#42111yescharacteristic
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—22no—
199C4×C31—42no—
200C4×C31—41no—
201C4×C31—41no—
202C4×C31—41no—
203C4×C31—81no—
204C4×C31—81no—
205C4×C31—162no—
206C2×#121—21no—
207C2×#121C4×C3111yescharacteristic, complemented
208C2×C4×D4C22×C3111yescharacteristic
209#431—21no—
210C2×#99—21no—
211#398C4×C3111yescharacteristic, complemented
212#397C22×C3111yescharacteristic
213#394C4×C3111yescharacteristic, complemented
214#392C22×C3111yescharacteristic
215#388—21no—
216#386—21no—
217#386—21no—
218#380—21no—
219C2×#95C4×C3111yescharacteristic, complemented
220#342C22×C3112yes—
221#323—21no—
222#323C22×C3112yes—
223C2×C31—21no—
224C2×C31—21no—
225C2×C31—41no—
226C2×C31—42no—
227C2×C31—41no—
228C2×C31—161no—
229C2×C31#151911yescharacteristic
230C2×C31#212111yescharacteristic
231C2×C31#212611yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4C2×C4×C3111yescharacteristic
235C22×D4D4×C3111yescharacteristic
236C23×C4—21no—
237C23×C4C2×C4×C3111yescharacteristic
238C23×C4D4×C3111yescharacteristic
239#121—42no—
240#121—42no—
241#121—41no—
242#121—41no—
243C4×D4—41no—
244C4×D4—41no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4C2×C4×C3111yescharacteristic
248C2×C4⋊C4C2×C4×C3111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4D4×C3111yescharacteristic
256C2×C22⋊C4C23×C3111yescharacteristic
257C2×C42D4×C3111yescharacteristic
258C4⋊C8—41no—
259#99—42no—
260C22⋊C8—22no—
261C4×C8—41no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—41no—
266#95C2×C4×C3111yescharacteristic
267#95C2×C4×C3111yescharacteristic
268C31#1187611yescharacteristic, direct product factor, Sylow
269C24—21no—
270C24C22⋊C4×C3111yescharacteristic
271C24C2×D4×C3111yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—81no—
283C2×D4D8×C3112yes—
284C2×D4SD16×C3112yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—81no—
298C22×C4C22⋊C4×C3111yescharacteristic
299C22×C4C22⋊C4×C3111yescharacteristic
300C22×C4C22⋊C4×C3111yescharacteristic
301C22×C4C22×C4×C3111yescharacteristic
302C22×C4C2×D4×C3111yescharacteristic
303C2×C8—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—82no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—81no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C31×#10212yes—
337C23C2×C22⋊C4×C3111yescharacteristic
338C23C2×D8×C3111yescharacteristic
339C23C2×SD16×C3111yescharacteristic
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—84no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—84no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4C31×#9911yescharacteristic
373C2×C4C31×#9911yescharacteristic
374C2×C4C31×#10212yes—
375C8—82no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×C31×#9911yescharacteristic
398C22C2×C31×#10211yescharacteristic
399C22C31×#42111yescharacteristic
400C4—21no—
401C4—21no—
402C4—22no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—81no—
409C4—162no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—161no—
416C2C31×#151911yescharacteristic
417C2C31×#212111yescharacteristic
418C2C31×#212611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1799C2semidirect
3. C31×#1460C2semidirect
4. C31×#1344C2semidirect
5. C31×#1343C2semidirect
7. C2×C31×#121C4semidirect
11. C31×#398C4semidirect
13. C31×#394C4semidirect
19. C2×C31×#95C4semidirect
111. #11876C31direct (N × H)
168. #1799C2×C31semidirect
169. #1460C2×C31semidirect
170. #1344C2×C31semidirect
171. #1343C2×C31semidirect
207. C2×#121C4×C31semidirect
211. #398C4×C31semidirect
213. #394C4×C31semidirect
219. C2×#95C4×C31semidirect
268. C31#11876direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25432
C31×#17992
C31×#14602
C31×#13442
C31×#13432
#1187631