Finite Group Databasebeta

← C31×#12091 #21468850

Subgroups — C31×#12091 #21468850

Order 7936.

618 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2483C211yesmaximal, characteristic, complemented
2C31×#2021C211yesmaximal, characteristic
3C31×#1607C212yesmaximal, complemented
4C31×#1344C212yesmaximal, complemented
5C31×#1316C211yesmaximal, characteristic, complemented
6C31×#534C2211yescharacteristic
7C2×C31×#120—21no—
8C22×C22⋊C4×C31—21no—
9C31×#480—22no—
10C2×C31×#99—21no—
11C31×#397—21no—
12C31×#397C2212yes—
13C31×#385—22no—
14C31×#381—22no—
15C31×#379C2211yescharacteristic
16C31×#342C2211yescharacteristic
17C31×#327—22no—
18C31×#323C2212yes—
19C25×C31D411yescharacteristic
20C22×D4×C31—21no—
21C22×D4×C31—41no—
22C23×C4×C31—21no—
23C23×C4×C31—21no—
24C31×#123—41no—
25C31×#121—22no—
26C31×#120—42no—
27C31×#120—41no—
28C31×#120—42no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31D412yescomplemented
31C2×C22⋊C4×C31—21no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—41no—
36C2×C22⋊C4×C31—42no—
37C2×C22⋊C4×C31—42no—
38C2×C22⋊C4×C31D411yescharacteristic
39C2×C22⋊C4×C31C2311yescharacteristic
40C31×#107—42no—
41C31×#102—42no—
42C31×#99—42no—
43C31×C22⋊C8—22no—
44C31×#95—21no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95D412yescomplemented
48C24×C31—21no—
49C24×C31—21no—
50C24×C31—21no—
51C24×C31—41no—
52C24×C31—44no—
53C24×C31—41no—
54C24×C31D812yes—
55C24×C31C2×D411yescharacteristic
56C2×D4×C31—22no—
57C2×D4×C31—41no—
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31—44no—
61C2×D4×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31—41no—
64C2×D4×C31—84no—
65C22×C4×C31—21no—
66C22×C4×C31—22no—
67C22×C4×C31—21no—
68C22×C4×C31—22no—
69C22×C4×C31—41no—
70C22×C4×C31—42no—
71C22×C4×C31—42no—
72C22×C4×C31—44no—
73C22×C4×C31—81no—
74C22×C4×C31—81no—
75C22×C4×C31C2×D412yes—
76C2×C8×C31—42no—
77C4⋊C4×C31—22no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—81no—
80C22⋊C4×C31—22no—
81C22⋊C4×C31—41no—
82C22⋊C4×C31—42no—
83C22⋊C4×C31—44no—
84C22⋊C4×C31—44no—
85C22⋊C4×C31—44no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—41no—
90#12091C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—24no—
92C23×C31—22no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31—44no—
98C23×C31—42no—
99C23×C31—44no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—44no—
105C23×C31—41no—
106C23×C31—81no—
107C23×C31—84no—
108C23×C31—82no—
109C23×C31—82no—
110C23×C31#12011yescharacteristic
111C23×C31C2×D811yescharacteristic
112C23×C31AGL(1,ℤ/8)11yescharacteristic
113D4×C31—82no—
114D4×C31—81no—
115D4×C31—81no—
116D4×C31—88no—
117D4×C31—81no—
118D4×C31—81no—
119C2×C4×C31—22no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31—44no—
125C2×C4×C31—41no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—41no—
131C2×C4×C31—42no—
132C2×C4×C31—84no—
133C2×C4×C31—84no—
134C2×C4×C31—82no—
135C8×C31—82no—
136#2483C2×C3111yescharacteristic, complemented
137#2021C2×C3111yescharacteristic
138#1607C2×C3112yescomplemented
139#1344C2×C3112yescomplemented
140#1316C2×C3111yescharacteristic, complemented
141C22×C31—22no—
142C22×C31—24no—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—41no—
146C22×C31—41no—
147C22×C31—42no—
148C22×C31—44no—
149C22×C31—44no—
150C22×C31—42no—
151C22×C31—42no—
152C22×C31—44no—
153C22×C31—81no—
154C22×C31—82no—
155C22×C31—84no—
156C22×C31—82no—
157C22×C31—81no—
158C22×C31—82no—
159C22×C31—161no—
160C22×C31#44711yescharacteristic
161C22×C31#45311yescharacteristic
162C22×C31B(4,𝔽2)11yescharacteristic
163C4×C31—42no—
164C4×C31—81no—
165C4×C31—82no—
166C4×C31—82no—
167C4×C31—82no—
168C4×C31—81no—
169#534C22×C3111yescharacteristic
170C2×#120—21no—
171C22×C22⋊C4—21no—
172#480—22no—
173C2×#99—21no—
174#397—21no—
175#397C22×C3112yes—
176#385—22no—
177#381—22no—
178#379C22×C3111yescharacteristic
179#342C22×C3111yescharacteristic
180#327—22no—
181#323C22×C3112yes—
182C2×C31—21no—
183C2×C31—21no—
184C2×C31—41no—
185C2×C31—44no—
186C2×C31—41no—
187C2×C31—161no—
188C2×C31#159511yescharacteristic
189C2×C31#219712yes—
190C25D4×C3111yescharacteristic
191C22×D4—21no—
192C22×D4—41no—
193C23×C4—21no—
194C23×C4—21no—
195#123—41no—
196#121—22no—
197#120—42no—
198#120—41no—
199#120—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4D4×C3112yescomplemented
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—42no—
208C2×C22⋊C4—42no—
209C2×C22⋊C4D4×C3111yescharacteristic
210C2×C22⋊C4C23×C3111yescharacteristic
211#107—42no—
212#102—42no—
213#99—42no—
214C22⋊C8—22no—
215#95—21no—
216#95—22no—
217#95—22no—
218#95D4×C3112yescomplemented
219C31#1209111yescharacteristic, direct product factor, Sylow
220C24—21no—
221C24—21no—
222C24—21no—
223C24—41no—
224C24—44no—
225C24—41no—
226C24D8×C3112yes—
227C24C2×D4×C3111yescharacteristic
228C2×D4—22no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—44no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—84no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—44no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4C2×D4×C3112yes—
248C2×C8—42no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—81no—
252C22⋊C4—22no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—44no—
256C22⋊C4—44no—
257C22⋊C4—44no—
258C22⋊C4—42no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C23—24no—
263C23—22no—
264C23—21no—
265C23—21no—
266C23—42no—
267C23—42no—
268C23—44no—
269C23—42no—
270C23—44no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—44no—
276C23—41no—
277C23—81no—
278C23—84no—
279C23—82no—
280C23—82no—
281C23C31×#12011yescharacteristic
282C23C2×D8×C3111yescharacteristic
283C23C31×AGL(1,ℤ/8)11yescharacteristic
284D4—82no—
285D4—81no—
286D4—81no—
287D4—88no—
288D4—81no—
289D4—81no—
290C2×C4—22no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—84no—
304C2×C4—84no—
305C2×C4—82no—
306C8—82no—
307C22—22no—
308C22—24no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—44no—
315C22—44no—
316C22—42no—
317C22—42no—
318C22—44no—
319C22—81no—
320C22—82no—
321C22—84no—
322C22—82no—
323C22—81no—
324C22—82no—
325C22—161no—
326C22C31×#44711yescharacteristic
327C22C31×#45311yescharacteristic
328C22C31×B(4,𝔽2)11yescharacteristic
329C4—42no—
330C4—82no—
331C4—81no—
332C4—82no—
333C4—82no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—41no—
338C2—44no—
339C2—41no—
340C2—161no—
341C2C31×#159511yescharacteristic
342C2C31×#219712yes—
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2021C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2483C2semidirect
3. C31×#1607C2semidirect
4. C31×#1344C2semidirect
5. C31×#1316C2semidirect
30. C2×C4⋊C4×C31D4semidirect
47. C31×#95D4semidirect
90. #12091C31direct (N × H)
136. #2483C2×C31semidirect
138. #1607C2×C31semidirect
139. #1344C2×C31semidirect
140. #1316C2×C31semidirect
201. C2×C4⋊C4D4×C31semidirect
218. #95D4×C31semidirect
219. C31#12091direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24832
C31×#20212
C31×#16072
C31×#13442
C31×#13162
#1209131