Finite Group Databasebeta

← C31×#13297 #21470056

Subgroups — C31×#13297 #21470056

Order 7936.

488 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2579C211yesmaximal, characteristic
2C31×#1800C211yesmaximal, characteristic
3C4×C31×#99C211yesmaximal, characteristic
4C31×#1390C212yesmaximal
5C31×#1390C212yesmaximal
6C2×C4×D4×C31C2211yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic, complemented
8C31×#423—21no—
9C2×C31×#100C2212yes—
10C2×C31×#99C2212yes—
11C31×#398—21no—
12C31×#396—21no—
13C31×#387—21no—
14C31×#386C2211yescharacteristic
15C31×#386C2211yescharacteristic
16C31×#385—21no—
17C31×#385C411yescharacteristic, complemented
18C31×#385C411yescharacteristic, complemented
19C31×#380C411yescharacteristic, complemented
20C4×C22⋊C4×C31—21no—
21C31×#343—21no—
22C31×#342—21no—
23C22×D4×C31C2311yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C2×M16×C31—22no—
29C4×D4×C31—41no—
30C4×D4×C31—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—41no—
37C2×C4⋊C4×C31—41no—
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31C2×C411yescharacteristic
44C2×C22⋊C4×C31C2×C411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C42×C31—41no—
47C2×C42×C31D411yescharacteristic
48C31×C4⋊C8—41no—
49C31×C4⋊C8—41no—
50C31×#100—24no—
51C31×#99—22no—
52C31×#99Q814yes—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—41no—
59C24×C31C22×C411yescharacteristic
60C24×C31C2×D411yescharacteristic
61C2×D4×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31C2×Q812yes—
64C2×D4×C31#4112yes—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—42no—
74C22×C4×C31—41no—
75C22×C4×C31—42no—
76C22×C4×C31—41no—
77C22×C4×C31—81no—
78C22×C4×C31—81no—
79C22×C4×C31—81no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85M16×C31—42no—
86M16×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—81no—
94C4⋊C4×C31—81no—
95C22⋊C4×C31—24no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—81no—
103C42×C31—21no—
104C42×C31—21no—
105C42×C31—82no—
106#13297C3111yesmaximal, characteristic, direct product factor, Sylow
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31C2×C22⋊C411yescharacteristic
116C23×C31C4×Q812yes—
117C23×C31C22⋊Q812yes—
118D4×C31—42no—
119D4×C31—42no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—22no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—41no—
127C2×C4×C31—42no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—42no—
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—81no—
146C2×C4×C31—81no—
147C2×C4×C31—81no—
148C2×C4×C31—82no—
149C2×C4×C31—82no—
150C2×C4×C31—82no—
151C2×C4×C31#9911yescharacteristic
152C2×C4×C31#9911yescharacteristic
153C2×C4×C31#12411yescharacteristic
154C2×C4×C31C4⋊Q811yescharacteristic
155C8×C31—82no—
156#2579C2×C3111yescharacteristic
157#1800C2×C3111yescharacteristic
158C4×#99C2×C3111yescharacteristic
159#1390C2×C3112yes—
160#1390C2×C3112yes—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—22no—
164C22×C31—22no—
165C22×C31—42no—
166C22×C31—42no—
167C22×C31—42no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—81no—
173C22×C31#39111yescharacteristic
174C22×C31C2×#9911yescharacteristic
175C22×C31#41011yescharacteristic
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—41no—
181C4×C31—42no—
182C4×C31—41no—
183C4×C31—41no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—84no—
187C4×C31—81no—
188C2×C4×D4C22×C3111yescharacteristic
189C22×C4⋊C4C4×C3111yescharacteristic, complemented
190#423—21no—
191C2×#100C22×C3112yes—
192C2×#99C22×C3112yes—
193#398—21no—
194#396—21no—
195#387—21no—
196#386C22×C3111yescharacteristic
197#386C22×C3111yescharacteristic
198#385—21no—
199#385C4×C3111yescharacteristic, complemented
200#385C4×C3111yescharacteristic, complemented
201#380C4×C3111yescharacteristic, complemented
202C4×C22⋊C4—21no—
203#343—21no—
204#342—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31—42no—
208C2×C31—42no—
209C2×C31#199611yescharacteristic
210C2×C31#212011yescharacteristic
211C2×C31#212111yescharacteristic
212C22×D4C23×C3111yescharacteristic
213C23×C4C2×C4×C3111yescharacteristic
214C23×C4C2×C4×C3111yescharacteristic
215C23×C4C2×C4×C3111yescharacteristic
216C23×C4D4×C3111yescharacteristic
217C2×M16—22no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4D4×C3111yescharacteristic
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4C2×C4×C3111yescharacteristic
232C2×C22⋊C4C2×C4×C3111yescharacteristic
233C2×C22⋊C4C2×C4×C3111yescharacteristic
234C2×C22⋊C4D4×C3111yescharacteristic
235C2×C42—41no—
236C2×C42D4×C3111yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#100—24no—
240#99—22no—
241#99Q8×C3114yes—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—41no—
248C31#1329711yescharacteristic, direct product factor, Sylow
249C24C22×C4×C3111yescharacteristic
250C24C2×D4×C3111yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4C2×Q8×C3112yes—
254C2×D4#41×C3112yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4C22⋊C4×C3111yescharacteristic
271C22×C4C22⋊C4×C3111yescharacteristic
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C2×D4×C3111yescharacteristic
275M16—42no—
276M16—42no—
277C2×C8—42no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C22⋊C4—24no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—82no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C2×C22⋊C4×C3111yescharacteristic
305C23C4×Q8×C3112yes—
306C23C31×C22⋊Q812yes—
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—44no—
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×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4C31×#9911yescharacteristic
341C2×C4C31×#9911yescharacteristic
342C2×C4C31×#12411yescharacteristic
343C2×C4C31×C4⋊Q811yescharacteristic
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22C31×#39111yescharacteristic
358C22C2×C31×#9911yescharacteristic
359C22C31×#41011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—84no—
371C4—81no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2C31×#199611yescharacteristic
377C2C31×#212011yescharacteristic
378C2C31×#212111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
7. C22×C4⋊C4×C31C4semidirect
17. C31×#385C4semidirect
18. C31×#385C4semidirect
19. C31×#380C4semidirect
106. #13297C31direct (N × H)
189. C22×C4⋊C4C4×C31semidirect
199. #385C4×C31semidirect
200. #385C4×C31semidirect
201. #380C4×C31semidirect
248. C31#13297direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25792
C31×#18002
C4×C31×#992
C31×#13902
#1329731