Finite Group Databasebeta

← C31×#11906 #21468665

Subgroups — C31×#11906 #21468665

Order 7936.

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

normal subgroups only

This group has 440 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×#2564C211yesmaximal, characteristic
2C31×#1800C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C31×#1354C212yesmaximal, complemented
5C31×#1353C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#423—21no—
9C2×C31×#100—21no—
10C2×C31×C22⋊C8—21no—
11C31×#400C2211yescharacteristic
12C31×#399C411yescharacteristic
13C31×#395C2211yescharacteristic
14C31×#393C411yescharacteristic
15C31×#387—21no—
16C31×#386—21no—
17C31×#385—21no—
18C31×#380—21no—
19C2×C31×#95C411yescharacteristic
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31D411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C2×M16×C31—22no—
29C22×C8×C31—41no—
30C31×C22⋊Q8—41no—
31C31×C22⋊Q8—41no—
32C4×D4×C31—41no—
33C4×D4×C31—41no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2311yescharacteristic
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—41no—
46C31×C4⋊C8—41no—
47C31×#100—42no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—41no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31C22⋊C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C2×Q8×C31—41no—
60C2×Q8×C31—81no—
61C2×D4×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31SD1612yes—
64C2×D4×C31Q1612yes—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—81no—
76C22×C4×C31—81no—
77C22×C4×C31—81no—
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83M16×C31—42no—
84M16×C31—42no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C2×C8×C31—82no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—81no—
94C22⋊C4×C31—41no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—81no—
99C42×C31—21no—
100C42×C31—21no—
101#11906C3111yesmaximal, characteristic, direct product factor, Sylow
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31#10312yes—
111C23×C31#10312yes—
112C23×C31C2×C22⋊C411yescharacteristic
113Q8×C31—82no—
114D4×C31—42no—
115D4×C31—42no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—22no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31—84no—
142C2×C4×C31#9911yescharacteristic
143C2×C4×C31#9911yescharacteristic
144C2×C4×C31C2×SD1611yescharacteristic
145C2×C4×C31C2×Q1611yescharacteristic
146C8×C31—82no—
147C8×C31—82no—
148#2564C2×C3111yescharacteristic
149#1800C2×C3111yescharacteristic
150#1459C2×C3111yescharacteristic
151#1354C2×C3112yescomplemented
152#1353C2×C3112yescomplemented
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—22no—
156C22×C31—22no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—42no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—81no—
165C22×C31C2×#9911yescharacteristic
166C22×C31C2×#10311yescharacteristic
167C22×C31#42111yescharacteristic
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—42no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—81no—
177C4×C31—81no—
178C4×C31—81no—
179C2×C22⋊Q8C4×C3111yescharacteristic
180C2×C4×D4C22×C3111yescharacteristic
181#423—21no—
182C2×#100—21no—
183C2×C22⋊C8—21no—
184#400C22×C3111yescharacteristic
185#399C4×C3111yescharacteristic
186#395C22×C3111yescharacteristic
187#393C4×C3111yescharacteristic
188#387—21no—
189#386—21no—
190#385—21no—
191#380—21no—
192C2×#95C4×C3111yescharacteristic
193#343C22×C3112yes—
194#324C22×C3112yes—
195#323—21no—
196C2×C31—21no—
197C2×C31—21no—
198C2×C31—42no—
199C2×C31—42no—
200C2×C31#152011yescharacteristic
201C2×C31#212111yescharacteristic
202C2×C31#213211yescharacteristic
203C22×Q8C2×C4×C3111yescharacteristic
204C22×D4D4×C3111yescharacteristic
205C23×C4—21no—
206C23×C4C2×C4×C3111yescharacteristic
207C23×C4D4×C3111yescharacteristic
208C2×M16—22no—
209C22×C8—41no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×C4×C3111yescharacteristic
218C2×C4⋊C4C23×C3111yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4C2×C4×C3111yescharacteristic
223C2×C22⋊C4D4×C3111yescharacteristic
224C2×C42D4×C3111yescharacteristic
225C4⋊C8—41no—
226C4⋊C8—41no—
227#100—42no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C2×C4×C3111yescharacteristic
236#95C2×C4×C3111yescharacteristic
237C31#1190611yescharacteristic, direct product factor, Sylow
238C24C22⋊C4×C3111yescharacteristic
239C24C22⋊C4×C3111yescharacteristic
240C2×Q8—41no—
241C2×Q8—81no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4SD16×C3112yes—
245C2×D4Q16×C3112yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4C22⋊C4×C3111yescharacteristic
260C22×C4C22⋊C4×C3111yescharacteristic
261C22×C4C22×C4×C3111yescharacteristic
262C22×C4C2×D4×C3111yescharacteristic
263C22×C4C2×D4×C3111yescharacteristic
264M16—42no—
265M16—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—81no—
280C42—21no—
281C42—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C31×#10312yes—
291C23C31×#10312yes—
292C23C2×C22⋊C4×C3111yescharacteristic
293Q8—82no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—84no—
322C2×C4C31×#9911yescharacteristic
323C2×C4C31×#9911yescharacteristic
324C2×C4C2×SD16×C3111yescharacteristic
325C2×C4C2×Q16×C3111yescharacteristic
326C8—82no—
327C8—82no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×C31×#9911yescharacteristic
341C22C2×C31×#10311yescharacteristic
342C22C31×#42111yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2C31×#152011yescharacteristic
359C2C31×#212111yescharacteristic
360C2C31×#213211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×D4×C31D4
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
4. C31×#1354C2semidirect
5. C31×#1353C2semidirect
101. #11906C31direct (N × H)
151. #1354C2×C31semidirect
152. #1353C2×C31semidirect
237. C31#11906direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25642
C31×#18002
C31×#14592
C31×#13542
C31×#13532
#1190631