Finite Group Databasebeta

← C31×#7718 #21464477

Subgroups — C31×#7718 #21464477

Order 7936.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2854C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic, complemented
3C31×#1817C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C31×#390C411yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#389C411yescharacteristic
14C31×#389C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#386—21no—
18C31×#380C411yescharacteristic
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C22×C8×C31—22no—
29C22×C8×C31—22no—
30C31×#123—44no—
31C31×#121—42no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C42×C31—42no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31C2311yescharacteristic
48C31×C22⋊C8—42no—
49C31×C22⋊C8—42no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C24×C31—21no—
54C24×C31C22⋊C411yescharacteristic
55C2×D4×C31—22no—
56C2×D4×C31—41no—
57C2×D4×C31—41no—
58C2×D4×C31—42no—
59C2×D4×C31—42no—
60C2×D4×C31—42no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—41no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22×C411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78C22×C4×C31C2×D411yescharacteristic
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C2×C8×C31—42no—
83C2×C8×C31—42no—
84C2×C8×C31—42no—
85C4⋊C4×C31—22no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C42×C31—41no—
97C42×C31—41no—
98C42×C31—41no—
99C42×C31—41no—
100#7718C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31#9912yes—
115C23×C31C2×C22⋊C411yescharacteristic
116D4×C31—82no—
117D4×C31—84no—
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—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—44no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31#13112yes—
146C2×C4×C31#13512yes—
147C2×C4×C31AGL(1,ℤ/8)12yes—
148C8×C31—82no—
149C8×C31—82no—
150#2854C2×C3111yescharacteristic
151#1817C2×C3111yescharacteristic, complemented
152#1817C2×C3111yescharacteristic, complemented
153#1271C2×C3112yescomplemented
154#1270C2×C3112yescomplemented
155C22×C31—22no—
156C22×C31—22no—
157C22×C31—22no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31#40811yescharacteristic
170C22×C31C2×#9911yescharacteristic
171C22×C31#41311yescharacteristic
172C22×C31#41611yescharacteristic
173C22×C31#41811yescharacteristic
174C22×C31#42111yescharacteristic
175C22×C31#42111yescharacteristic
176C4×C31—22no—
177C4×C31—22no—
178C4×C31—22no—
179C4×C31—41no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—81no—
183C4×C31—81no—
184C4×C31—81no—
185C2×#123—21no—
186C2×#121C4×C3111yescharacteristic
187C22×C42C22×C3111yescharacteristic
188C2×C22⋊C8—21no—
189C2×C22⋊C8—21no—
190#390C4×C3111yescharacteristic
191#390C22×C3111yescharacteristic
192#389C4×C3111yescharacteristic
193#389C22×C3111yescharacteristic
194#388—21no—
195#388—21no—
196#386—21no—
197#380C4×C3111yescharacteristic
198#336—21no—
199#336—21no—
200#336C22×C3112yes—
201#336C22×C3112yes—
202C2×C31—42no—
203C2×C31—161no—
204C2×C31#146811yescharacteristic
205C2×C31#148211yescharacteristic
206C2×C31#149611yescharacteristic
207C2×C31#151011yescharacteristic
208C2×C31#151611yescharacteristic
209C2×C31#153511yescharacteristic
210C2×C31#155311yescharacteristic
211C22×D4—21no—
212C22×D4C2×C4×C3111yescharacteristic
213C23×C4C2×C4×C3111yescharacteristic
214C23×C4D4×C3111yescharacteristic
215C23×C4D4×C3111yescharacteristic
216C22×C8—22no—
217C22×C8—22no—
218#123—44no—
219#121—42no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C2×C4×C3111yescharacteristic
223C2×C4⋊C4C2×C4×C3111yescharacteristic
224C2×C4⋊C4C2×C4×C3111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C42—42no—
232C2×C42C2×C4×C3111yescharacteristic
233C2×C42D4×C3111yescharacteristic
234C2×C42D4×C3111yescharacteristic
235C2×C42C23×C3111yescharacteristic
236C22⋊C8—42no—
237C22⋊C8—42no—
238#95—21no—
239#95—21no—
240#95—21no—
241C31#771811yescharacteristic, direct product factor, Sylow
242C24—21no—
243C24C22⋊C4×C3111yescharacteristic
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C22⋊C4×C3111yescharacteristic
263C22×C4C22⋊C4×C3111yescharacteristic
264C22×C4C22⋊C4×C3111yescharacteristic
265C22×C4C22×C4×C3111yescharacteristic
266C22×C4C2×D4×C3111yescharacteristic
267C22×C4C2×D4×C3111yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23C31×#9912yes—
303C23C2×C22⋊C4×C3111yescharacteristic
304D4—82no—
305D4—84no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4C31×#13112yes—
334C2×C4C31×#13512yes—
335C2×C4C31×AGL(1,ℤ/8)12yes—
336C8—82no—
337C8—82no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C31×#40811yescharacteristic
353C22C2×C31×#9911yescharacteristic
354C22C31×#41311yescharacteristic
355C22C31×#41611yescharacteristic
356C22C31×#41811yescharacteristic
357C22C31×#42111yescharacteristic
358C22C31×#42111yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—81no—
368C2—42no—
369C2—161no—
370C2C31×#146811yescharacteristic
371C2C31×#148211yescharacteristic
372C2C31×#149611yescharacteristic
373C2C31×#151011yescharacteristic
374C2C31×#151611yescharacteristic
375C2C31×#153511yescharacteristic
376C2C31×#155311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1817C2semidirect
3. C31×#1817C2semidirect
4. C31×#1271C2semidirect
5. C31×#1270C2semidirect
100. #7718C31direct (N × H)
151. #1817C2×C31semidirect
152. #1817C2×C31semidirect
153. #1271C2×C31semidirect
154. #1270C2×C31semidirect
241. C31#7718direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28542
C31×#18172
C31×#12712
C31×#12702
#771831