Finite Group Databasebeta

← C31×#11693 #21468452

Subgroups — C31×#11693 #21468452

Order 7936.

568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2619C211yesmaximal, characteristic
2C31×#1740C211yesmaximal, characteristic, complemented
3C31×#1458C211yesmaximal, characteristic, complemented
4C31×#1343C214yesmaximal, complemented
5C2×C31×#127C411yescharacteristic, complemented
6C2×C31×#121—21no—
7C2×C31×#117—21no—
8C2×C31×#117C2211yescharacteristic
9C31×#431—21no—
10C31×#394—21no—
11C31×#394C412yescomplemented
12C31×#392—21no—
13C31×#392C2212yes—
14C31×#390—21no—
15C31×#382C411yescharacteristic, complemented
16C31×#342—21no—
17C31×#342C2212yes—
18C31×#324—21no—
19C31×#323C2212yes—
20C22×D4×C31—22no—
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31C2×C412yes—
24C23×C4×C31D411yescharacteristic
25C31×#127—41no—
26C31×#127—41no—
27C31×#121—42no—
28C31×#121—42no—
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×C31D411yescharacteristic
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31C2311yescharacteristic
43C2×C42×C31—41no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C31×C4⋊C8—41no—
47C31×C22⋊C8—22no—
48C4×C8×C31—41no—
49C31×#95—21no—
50C31×#95C2×C412yes—
51C24×C31—22no—
52C24×C31C2×D411yescharacteristic
53C2×D4×C31—42no—
54C2×D4×C31—42no—
55C2×D4×C31—42no—
56C2×D4×C31—42no—
57C2×D4×C31—41no—
58C2×D4×C31—41no—
59C2×D4×C31—42no—
60C2×D4×C31—42no—
61C2×D4×C31—82no—
62C2×D4×C31—82no—
63C2×D4×C31—82no—
64C2×D4×C31—82no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—42no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31D812yes—
75C22×C4×C31SD1612yes—
76C22×C4×C31C22×C411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78C2×C8×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—44no—
82C4⋊C4×C31—42no—
83C22⋊C4×C31—24no—
84C22⋊C4×C31—41no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—44no—
88C22⋊C4×C31—82no—
89C22⋊C4×C31—82no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31—21no—
94C42×C31—44no—
95#11693C3111yesmaximal, characteristic, direct product factor, Sylow
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—41no—
99C23×C31—41no—
100C23×C31—42no—
101C23×C31—42no—
102C23×C31—42no—
103C23×C31—42no—
104C23×C31—42no—
105C23×C31—42no—
106C23×C31—42no—
107C23×C31C2×C22⋊C411yescharacteristic
108C23×C31C2×D811yescharacteristic
109C23×C31C2×SD1611yescharacteristic
110D4×C31—84no—
111D4×C31—84no—
112D4×C31—84no—
113D4×C31—84no—
114D4×C31—82no—
115D4×C31—82no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—22no—
119C2×C4×C31—22no—
120C2×C4×C31—22no—
121C2×C4×C31—22no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—44no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—82no—
135C2×C4×C31—82no—
136C2×C4×C31#9911yescharacteristic
137C2×C4×C31#9911yescharacteristic
138C2×C4×C31#10212yes—
139C2×C4×C31#10212yes—
140C2×C4×C31#10412yes—
141C8×C31—82no—
142#2619C2×C3111yescharacteristic
143#1740C2×C3111yescharacteristic, complemented
144#1458C2×C3111yescharacteristic, complemented
145#1343C2×C3114yescomplemented
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—81no—
155C22×C31—82no—
156C22×C31—82no—
157C22×C31—82no—
158C22×C31—82no—
159C22×C31—82no—
160C22×C31—82no—
161C22×C31—82no—
162C22×C31C2×#9911yescharacteristic
163C22×C31C2×#10211yescharacteristic
164C22×C31C2×#10411yescharacteristic
165C4×C31—22no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—82no—
171C4×C31—84no—
172C4×C31#32712yes—
173C4×C31#32712yes—
174C2×#127C4×C3111yescharacteristic, complemented
175C2×#121—21no—
176C2×#117—21no—
177C2×#117C22×C3111yescharacteristic
178#431—21no—
179#394—21no—
180#394C4×C3112yescomplemented
181#392—21no—
182#392C22×C3112yes—
183#390—21no—
184#382C4×C3111yescharacteristic, complemented
185#342—21no—
186#342C22×C3112yes—
187#324—21no—
188#323C22×C3112yes—
189C2×C31—21no—
190C2×C31—21no—
191C2×C31—41no—
192C2×C31—41no—
193C2×C31—162no—
194C2×C31C2×#32711yescharacteristic
195C2×C31#212211yescharacteristic
196C2×C31#212811yescharacteristic
197C22×D4—22no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4C2×C4×C3112yes—
201C23×C4D4×C3111yescharacteristic
202#127—41no—
203#127—41no—
204#121—42no—
205#121—42no—
206#117—24no—
207#117—41no—
208#117—41no—
209#117—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4C2×C4×C3111yescharacteristic
213C2×C4⋊C4D4×C3111yescharacteristic
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4D4×C3111yescharacteristic
219C2×C22⋊C4C23×C3111yescharacteristic
220C2×C42—41no—
221C2×C42C2×C4×C3111yescharacteristic
222C2×C42D4×C3111yescharacteristic
223C4⋊C8—41no—
224C22⋊C8—22no—
225C4×C8—41no—
226#95—21no—
227#95C2×C4×C3112yes—
228C31#1169311yescharacteristic, direct product factor, Sylow
229C24—22no—
230C24C2×D4×C3111yescharacteristic
231C2×D4—42no—
232C2×D4—42no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—82no—
240C2×D4—82no—
241C2×D4—82no—
242C2×D4—82no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4C22⋊C4×C3111yescharacteristic
249C22×C4C22⋊C4×C3111yescharacteristic
250C22×C4C22⋊C4×C3111yescharacteristic
251C22×C4C22⋊C4×C3111yescharacteristic
252C22×C4D8×C3112yes—
253C22×C4SD16×C3112yes—
254C22×C4C22×C4×C3111yescharacteristic
255C22×C4C2×D4×C3111yescharacteristic
256C2×C8—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—44no—
260C4⋊C4—42no—
261C22⋊C4—24no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—44no—
266C22⋊C4—82no—
267C22⋊C4—82no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—44no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23C2×C22⋊C4×C3111yescharacteristic
285C23C2×D8×C3111yescharacteristic
286C23C2×SD16×C3111yescharacteristic
287D4—84no—
288D4—84no—
289D4—84no—
290D4—84no—
291D4—82no—
292D4—82no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4C31×#9911yescharacteristic
314C2×C4C31×#9911yescharacteristic
315C2×C4C31×#10212yes—
316C2×C4C31×#10212yes—
317C2×C4C31×#10412yes—
318C8—82no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22C2×C31×#9911yescharacteristic
336C22C2×C31×#10211yescharacteristic
337C22C2×C31×#10411yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—82no—
344C4—84no—
345C4C31×#32712yes—
346C4C31×#32712yes—
347C2—21no—
348C2—21no—
349C2—41no—
350C2—41no—
351C2—162no—
352C2C2×C31×#32711yescharacteristic
353C2C31×#212211yescharacteristic
354C2C31×#212811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2619C2
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×#1458C2semidirect
4. C31×#1343C2semidirect
5. C2×C31×#127C4semidirect
11. C31×#394C4semidirect
15. C31×#382C4semidirect
95. #11693C31direct (N × H)
143. #1740C2×C31semidirect
144. #1458C2×C31semidirect
145. #1343C2×C31semidirect
174. C2×#127C4×C31semidirect
180. #394C4×C31semidirect
184. #382C4×C31semidirect
228. C31#11693direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26192
C31×#17402
C31×#14582
C31×#13432
#1169331