Finite Group Databasebeta

← C31×#9879 #21466638

Subgroups — C31×#9879 #21466638

Order 7936.

616 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C4×C31×C22⋊C8C211yesmaximal, characteristic
4C31×#1280C214yesmaximal
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C4⋊C4×C31C412yes—
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8C2212yes—
11C2×C31×C22⋊C8C2212yes—
12C2×C4×C8×C31—21no—
13C31×#389—21no—
14C31×#389—21no—
15C31×#389—21no—
16C31×#389—21no—
17C2×C31×#95C2212yes—
18C31×#336—21no—
19C31×#336—21no—
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C412yes—
23C23×C4×C31C2×C412yes—
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31—44no—
36C2×C4⋊C4×C31C814yescomplemented
37C2×C42×C31—42no—
38C2×C42×C31D411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C31×C4⋊C8—42no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—24no—
45C31×C22⋊C8Q814yes—
46C4×C8×C31—42no—
47C31×#95—22no—
48C31×#95—22no—
49C24×C31C22×C411yescharacteristic
50C22×C4×C31—22no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—24no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31—41no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—42no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C2×C812yes—
70C22×C4×C31C2×C814yes—
71C22×C4×C31M1612yes—
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74C22×C4×C31C2×Q812yes—
75C22×C4×C31#4112yes—
76C2×C8×C31—24no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C4⋊C4×C31—24no—
83C4⋊C4×C31—24no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—44no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—44no—
88C42×C31—22no—
89C42×C31—22no—
90C42×C31—41no—
91C42×C31—41no—
92#9879C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31C2×C22⋊C411yescharacteristic
98C23×C31C4×Q812yes—
99C23×C31C22×C811yescharacteristic
100C23×C31C2×M1611yescharacteristic
101C23×C31#13112yes—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—24no—
111C2×C4×C31—24no—
112C2×C4×C31—24no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—44no—
119C2×C4×C31—44no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—44no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—84no—
127C2×C4×C31C22⋊C812yes—
128C2×C4×C31C22⋊C812yes—
129C2×C4×C31#9912yes—
130C2×C4×C31#10012yes—
131C2×C4×C31#10112yes—
132C2×C4×C31C22⋊Q812yes—
133C2×C4×C31#12411yescharacteristic
134C2×C4×C31C4⋊Q811yescharacteristic
135C8×C31—44no—
136C8×C31—82no—
137C2×#389C2×C3111yescharacteristic
138#1797C2×C3111yescharacteristic
139C4×C22⋊C8C2×C3111yescharacteristic
140#1280C2×C3114yes—
141C22×C31—21no—
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—22no—
148C22×C31—22no—
149C22×C31#39111yescharacteristic
150C22×C31C2×C22⋊C811yescharacteristic
151C22×C31#40811yescharacteristic
152C22×C31C2×#9911yescharacteristic
153C22×C31#41011yescharacteristic
154C22×C31C2×#10011yescharacteristic
155C22×C31C2×#10111yescharacteristic
156C22×C31C8×Q812yes—
157C22×C31#44612yes—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—22no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—44no—
164C4×C31—41no—
165C4×C31—82no—
166C4×C31#32414yes—
167C22×C4⋊C4C4×C3111yescharacteristic
168C22×C4⋊C4C4×C3112yes—
169C22×C4⋊C4C4×C3111yescharacteristic
170C22×C42C22×C3111yescharacteristic
171C2×C4⋊C8—21no—
172C2×C22⋊C8C22×C3112yes—
173C2×C22⋊C8C22×C3112yes—
174C2×C4×C8—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179C2×#95C22×C3112yes—
180#336—21no—
181#336—21no—
182C2×C31—22no—
183C2×C31—22no—
184C2×C31C2×#32411yescharacteristic
185C2×C31#146011yescharacteristic
186C2×C31#147011yescharacteristic
187C2×C31#147111yescharacteristic
188C2×C31#198411yescharacteristic
189C2×C31#199611yescharacteristic
190C2×C31#199711yescharacteristic
191C23×C4C2×C4×C3111yescharacteristic
192C23×C4C2×C4×C3111yescharacteristic
193C23×C4C2×C4×C3112yes—
194C23×C4C2×C4×C3112yes—
195C23×C4C23×C3111yescharacteristic
196C22×C8—22no—
197C22×C8—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4C8×C3114yescomplemented
208C2×C42—42no—
209C2×C42D4×C3111yescharacteristic
210C2×C42D4×C3111yescharacteristic
211C2×C42D4×C3111yescharacteristic
212C2×C42D4×C3111yescharacteristic
213C4⋊C8—42no—
214C22⋊C8—22no—
215C22⋊C8—24no—
216C22⋊C8Q8×C3114yes—
217C4×C8—42no—
218#95—22no—
219#95—22no—
220C31#987911yescharacteristic, direct product factor, Sylow
221C24C22×C4×C3111yescharacteristic
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22⋊C4×C3111yescharacteristic
240C22×C4C22⋊C4×C3111yescharacteristic
241C22×C4C2×C8×C3112yes—
242C22×C4C2×C8×C3114yes—
243C22×C4M16×C3112yes—
244C22×C4C2×D4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246C22×C4C2×Q8×C3112yes—
247C22×C4#41×C3112yes—
248C2×C8—24no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—42no—
257C4⋊C4—44no—
258C4⋊C4—42no—
259C4⋊C4—44no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×C22⋊C4×C3111yescharacteristic
269C23C4×Q8×C3112yes—
270C23C22×C8×C3111yescharacteristic
271C23C2×M16×C3111yescharacteristic
272C23C31×#13112yes—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—84no—
298C2×C4C31×C22⋊C812yes—
299C2×C4C31×C22⋊C812yes—
300C2×C4C31×#9912yes—
301C2×C4C31×#10012yes—
302C2×C4C31×#10112yes—
303C2×C4C31×C22⋊Q812yes—
304C2×C4C31×#12411yescharacteristic
305C2×C4C31×C4⋊Q811yescharacteristic
306C8—44no—
307C8—82no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22C31×#39111yescharacteristic
317C22C2×C31×C22⋊C811yescharacteristic
318C22C31×#40811yescharacteristic
319C22C2×C31×#9911yescharacteristic
320C22C31×#41011yescharacteristic
321C22C2×C31×#10011yescharacteristic
322C22C2×C31×#10111yescharacteristic
323C22C8×Q8×C3112yes—
324C22C31×#44612yes—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—44no—
331C4—41no—
332C4—82no—
333C4C31×#32414yes—
334C2—22no—
335C2—22no—
336C2C2×C31×#32411yescharacteristic
337C2C31×#146011yescharacteristic
338C2C31×#147011yescharacteristic
339C2C31×#147111yescharacteristic
340C2C31×#198411yescharacteristic
341C2C31×#199611yescharacteristic
342C2C31×#199711yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊C4×C31C8semidirect
92. #9879C31direct (N × H)
207. C2×C4⋊C4C8×C31semidirect
220. C31#9879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#17972
C4×C31×C22⋊C82
C31×#12802
#987931