Finite Group Databasebeta

← C31×#7618 #21464377

Subgroups — C31×#7618 #21464377

Order 7936.

494 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#124C211yesmaximal, characteristic
2C31×#1831C211yesmaximal, characteristic, complemented
3C31×#1745C211yesmaximal, characteristic, complemented
4C31×#1272C212yesmaximal, complemented
5C31×#1270C212yesmaximal
6C2×C31×#124C411yescharacteristic
7C2×C4×Q8×C31C411yescharacteristic
8C2×C4×D4×C31C411yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×#97—21no—
11C31×#391C2211yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#388—21no—
14C31×#388—21no—
15C31×#382C411yescharacteristic
16C4×C22⋊C4×C31—21no—
17C4×C22⋊C4×C31—21no—
18C43×C31C2211yescharacteristic
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C22×C8×C31—22no—
27C22×C8×C31—22no—
28C31×#124—22no—
29C31×#124—22no—
30C4×Q8×C31—42no—
31C4×D4×C31—42no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C42×C31—21no—
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31C2×C411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31C2311yescharacteristic
48C31×C4⋊C8—42no—
49C31×#97—24no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C24×C31—21no—
55C2×Q8×C31—21no—
56C2×Q8×C31—41no—
57C2×Q8×C31—41no—
58C2×Q8×C31M1612yes—
59C2×D4×C31—21no—
60C2×D4×C31—41no—
61C2×D4×C31—41no—
62C2×D4×C31M1612yes—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22×C411yescharacteristic
74C22×C4×C31C2×D411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
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—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—42no—
85C22⋊C4×C31—24no—
86C22⋊C4×C31—24no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C42×C31—22no—
92C42×C31—22no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—22no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—41no—
99C42×C31—41no—
100C42×C31—42no—
101#7618C3111yesmaximal, characteristic, direct product factor, Sylow
102C23×C31—22no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31C2×C22⋊C411yescharacteristic
110Q8×C31—42no—
111Q8×C31—42no—
112D4×C31—42no—
113D4×C31—42no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—22no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
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—41no—
139C2×C4×C31—84no—
140C2×C4×C31#10012yes—
141C2×C4×C31#10412yes—
142C2×C4×C31C2×M1611yescharacteristic
143C2×C4×C31C2×M1611yescharacteristic
144C2×C4×C31#13512yes—
145C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C31#13711yescharacteristic
147C8×C31—44no—
148C8×C31—82no—
149C4×#124C2×C3111yescharacteristic
150#1831C2×C3111yescharacteristic, complemented
151#1745C2×C3111yescharacteristic, complemented
152#1272C2×C3112yescomplemented
153#1270C2×C3112yes—
154C22×C31—42no—
155C22×C31—42no—
156C22×C31—42no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31—81no—
161C22×C31#40711yescharacteristic
162C22×C31#41011yescharacteristic
163C22×C31C2×#10011yescharacteristic
164C22×C31#41611yescharacteristic
165C22×C31#41711yescharacteristic
166C22×C31C2×#10411yescharacteristic
167C22×C31#42111yescharacteristic
168C4×C31—22no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—22no—
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—42no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31—81no—
179C4×C31—81no—
180C2×#124C4×C3111yescharacteristic
181C2×C4×Q8C4×C3111yescharacteristic
182C2×C4×D4C4×C3111yescharacteristic
183C2×C4⋊C8—21no—
184C2×#97—21no—
185#391C22×C3111yescharacteristic
186#390C22×C3111yescharacteristic
187#388—21no—
188#388—21no—
189#382C4×C3111yescharacteristic
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C43C22×C3111yescharacteristic
193#336—21no—
194#336—21no—
195#336C22×C3112yes—
196#336C22×C3112yes—
197C2×C31—82no—
198C2×C31#146611yescharacteristic
199C2×C31#148811yescharacteristic
200C2×C31#148911yescharacteristic
201C2×C31#150011yescharacteristic
202C2×C31#151211yescharacteristic
203C2×C31#152711yescharacteristic
204C2×C31#155111yescharacteristic
205C22×Q8C2×C4×C3111yescharacteristic
206C22×D4C2×C4×C3111yescharacteristic
207C23×C4—21no—
208C22×C8—22no—
209C22×C8—22no—
210#124—22no—
211#124—22no—
212C4×Q8—42no—
213C4×D4—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C3111yescharacteristic
216C2×C4⋊C4C2×C4×C3111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C2×C42C2×C4×C3111yescharacteristic
224C2×C42C2×C4×C3111yescharacteristic
225C2×C42D4×C3111yescharacteristic
226C2×C42D4×C3111yescharacteristic
227C2×C42D4×C3111yescharacteristic
228C2×C42D4×C3111yescharacteristic
229C2×C42C23×C3111yescharacteristic
230C4⋊C8—42no—
231#97—24no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236C31#761811yescharacteristic, direct product factor, Sylow
237C24—21no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8M16×C3112yes—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4M16×C3112yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C22⋊C4×C3111yescharacteristic
253C22×C4C22⋊C4×C3111yescharacteristic
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22×C4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4C2×D4×C3111yescharacteristic
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—22no—
275C42—22no—
276C42—21no—
277C42—21no—
278C42—22no—
279C42—21no—
280C42—21no—
281C42—41no—
282C42—41no—
283C42—42no—
284C23—22no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊C4×C3111yescharacteristic
292Q8—42no—
293Q8—42no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—84no—
322C2×C4C31×#10012yes—
323C2×C4C31×#10412yes—
324C2×C4C2×M16×C3111yescharacteristic
325C2×C4C2×M16×C3111yescharacteristic
326C2×C4C31×#13512yes—
327C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
328C2×C4C31×#13711yescharacteristic
329C8—44no—
330C8—82no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22C31×#40711yescharacteristic
339C22C31×#41011yescharacteristic
340C22C2×C31×#10011yescharacteristic
341C22C31×#41611yescharacteristic
342C22C31×#41711yescharacteristic
343C22C2×C31×#10411yescharacteristic
344C22C31×#42111yescharacteristic
345C4—22no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—42no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C2—82no—
358C2C31×#146611yescharacteristic
359C2C31×#148811yescharacteristic
360C2C31×#148911yescharacteristic
361C2C31×#150011yescharacteristic
362C2C31×#151211yescharacteristic
363C2C31×#152711yescharacteristic
364C2C31×#155111yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1831C2semidirect
3. C31×#1745C2semidirect
4. C31×#1272C2semidirect
101. #7618C31direct (N × H)
150. #1831C2×C31semidirect
151. #1745C2×C31semidirect
152. #1272C2×C31semidirect
236. C31#7618direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1242
C31×#18312
C31×#17452
C31×#12722
C31×#12702
#761831