Finite Group Databasebeta

← C31×#8560 #21465319

Subgroups — C31×#8560 #21465319

Order 7936.

682 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
2C31×#1797C212yesmaximal
3C2×C31×#324C212yesmaximal
4C31×#1280C212yesmaximal
5C22×C4⋊C4×C31C411yescharacteristic
6C22×C4⋊C4×C31C2211yescharacteristic
7C22×C42×C31C411yescharacteristic
8C22×C42×C31C411yescharacteristic
9C22×C42×C31C2211yescharacteristic
10C2×C31×C4⋊C8—22no—
11C2×C31×C22⋊C8C2214yes—
12C4×C4⋊C4×C31—22no—
13C4×C4⋊C4×C31—22no—
14C2×C31×#95C411yescharacteristic
15C2×C31×#95C2211yescharacteristic
16C31×#336—22no—
17C31×#324—24no—
18C23×C4×C31C2×C411yescharacteristic
19C23×C4×C31C2×C411yescharacteristic
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—24no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31C814yescomplemented
31C2×C4⋊C4×C31D412yes—
32C2×C4⋊C4×C31Q812yes—
33C2×C42×C31—21no—
34C2×C42×C31—21no—
35C2×C42×C31—22no—
36C2×C42×C31—22no—
37C2×C42×C31—21no—
38C2×C42×C31—21no—
39C2×C42×C31—42no—
40C2×C42×C31—42no—
41C2×C42×C31D412yes—
42C2×C42×C31D412yes—
43C31×C4⋊C8—44no—
44C31×C22⋊C8—24no—
45C31×C22⋊C8—24no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31C22×C411yescharacteristic
49C22×C4×C31—21no—
50C22×C4×C31—21no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—41no—
64C22×C4×C31—41no—
65C22×C4×C31—41no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31C22⋊C412yes—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C4⋊C412yes—
77C22×C4×C31C4⋊C412yes—
78C22×C4×C31C2×C812yes—
79C22×C4×C31C2×C812yes—
80C22×C4×C31C2×C812yes—
81C22×C4×C31M1612yes—
82C22×C4×C31M1612yes—
83C22×C4×C31M1612yes—
84C22×C4×C31C2×D412yes—
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31C2×Q811yescharacteristic
87C22×C4×C31#4112yes—
88C2×C8×C31—44no—
89C2×C8×C31—44no—
90C2×C8×C31—44no—
91C4⋊C4×C31—28no—
92C4⋊C4×C31—24no—
93C4⋊C4×C31—24no—
94C42×C31—24no—
95C42×C31—24no—
96C42×C31—24no—
97C42×C31—42no—
98C42×C31—42no—
99C42×C31—42no—
100#8560C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31C2×C22⋊C411yescharacteristic
106C23×C31C2×C4⋊C411yescharacteristic
107C23×C31#11711yescharacteristic
108C23×C31C22×C811yescharacteristic
109C23×C31C2×M1611yescharacteristic
110C23×C31C2×M1611yescharacteristic
111C23×C31C2×M1611yescharacteristic
112C2×C4×C31—24no—
113C2×C4×C31—24no—
114C2×C4×C31—22no—
115C2×C4×C31—22no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—22no—
119C2×C4×C31—22no—
120C2×C4×C31—22no—
121C2×C4×C31—21no—
122C2×C4×C31—22no—
123C2×C4×C31—21no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—22no—
129C2×C4×C31—22no—
130C2×C4×C31—22no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
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—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31C22⋊C814yes—
149C2×C4×C31#9912yes—
150C2×C4×C31#10112yes—
151C2×C4×C31C4⋊C814yescomplemented
152C2×C4×C31#12112yes—
153C2×C4×C31C22⋊Q812yes—
154C8×C31—84no—
155C2×C4×C4⋊C4C2×C3111yescharacteristic
156#1797C2×C3112yes—
157C2×#324C2×C3112yes—
158#1280C2×C3112yes—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31#38011yescharacteristic
172C22×C31C2×C22⋊C811yescharacteristic
173C22×C31#40711yescharacteristic
174C22×C31C2×#9911yescharacteristic
175C22×C31#41011yescharacteristic
176C22×C31C2×#10111yescharacteristic
177C22×C31#41311yescharacteristic
178C22×C31C2×C4⋊C811yescharacteristic
179C22×C31#42311yescharacteristic
180C22×C31#43111yescharacteristic
181C22×C31#43211yescharacteristic
182C4×C31—24no—
183C4×C31—22no—
184C4×C31—22no—
185C4×C31—24no—
186C4×C31—22no—
187C4×C31—22no—
188C4×C31—42no—
189C4×C31—42no—
190C4×C31—42no—
191C22×C4⋊C4C4×C3111yescharacteristic
192C22×C4⋊C4C22×C3111yescharacteristic
193C22×C42C4×C3111yescharacteristic
194C22×C42C4×C3111yescharacteristic
195C22×C42C22×C3111yescharacteristic
196C2×C4⋊C8—22no—
197C2×C22⋊C8C22×C3114yes—
198C4×C4⋊C4—22no—
199C4×C4⋊C4—22no—
200C2×#95C4×C3111yescharacteristic
201C2×#95C22×C3111yescharacteristic
202#336—22no—
203#324—24no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31—21no—
208C2×C31#145911yescharacteristic
209C2×C31#146111yescharacteristic
210C2×C31#146311yescharacteristic
211C2×C31#146411yescharacteristic
212C2×C31#179711yescharacteristic
213C2×C31#179911yescharacteristic
214C2×C31#180111yescharacteristic
215C23×C4C2×C4×C3111yescharacteristic
216C23×C4C2×C4×C3111yescharacteristic
217C23×C4C2×C4×C3111yescharacteristic
218C23×C4C2×C4×C3111yescharacteristic
219C23×C4C2×C4×C3111yescharacteristic
220C23×C4C2×C4×C3111yescharacteristic
221C23×C4C23×C3111yescharacteristic
222C22×C8—24no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C8×C3114yescomplemented
228C2×C4⋊C4D4×C3112yes—
229C2×C4⋊C4Q8×C3112yes—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—42no—
237C2×C42—42no—
238C2×C42D4×C3112yes—
239C2×C42D4×C3112yes—
240C4⋊C8—44no—
241C22⋊C8—24no—
242C22⋊C8—24no—
243#95—22no—
244#95—22no—
245C31#856011yescharacteristic, direct product factor, Sylow
246C24C22×C4×C3111yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C22⋊C4×C3112yes—
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C4⋊C4×C3112yes—
275C22×C4C4⋊C4×C3112yes—
276C22×C4C2×C8×C3112yes—
277C22×C4C2×C8×C3112yes—
278C22×C4C2×C8×C3112yes—
279C22×C4M16×C3112yes—
280C22×C4M16×C3112yes—
281C22×C4M16×C3112yes—
282C22×C4C2×D4×C3112yes—
283C22×C4C2×D4×C3111yescharacteristic
284C22×C4C2×Q8×C3111yescharacteristic
285C22×C4#41×C3112yes—
286C2×C8—44no—
287C2×C8—44no—
288C2×C8—44no—
289C4⋊C4—28no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C42—24no—
293C42—24no—
294C42—24no—
295C42—42no—
296C42—42no—
297C42—42no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊C4×C3111yescharacteristic
303C23C2×C4⋊C4×C3111yescharacteristic
304C23C31×#11711yescharacteristic
305C23C22×C8×C3111yescharacteristic
306C23C2×M16×C3111yescharacteristic
307C23C2×M16×C3111yescharacteristic
308C23C2×M16×C3111yescharacteristic
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4C31×C22⋊C814yes—
346C2×C4C31×#9912yes—
347C2×C4C31×#10112yes—
348C2×C4C31×C4⋊C814yescomplemented
349C2×C4C31×#12112yes—
350C2×C4C31×C22⋊Q812yes—
351C8—84no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22C31×#38011yescharacteristic
365C22C2×C31×C22⋊C811yescharacteristic
366C22C31×#40711yescharacteristic
367C22C2×C31×#9911yescharacteristic
368C22C31×#41011yescharacteristic
369C22C2×C31×#10111yescharacteristic
370C22C31×#41311yescharacteristic
371C22C2×C31×C4⋊C811yescharacteristic
372C22C31×#42311yescharacteristic
373C22C31×#43111yescharacteristic
374C22C31×#43211yescharacteristic
375C4—24no—
376C4—22no—
377C4—22no—
378C4—24no—
379C4—22no—
380C4—22no—
381C4—42no—
382C4—42no—
383C4—42no—
384C2—21no—
385C2—21no—
386C2—21no—
387C2—21no—
388C2C31×#145911yescharacteristic
389C2C31×#146111yescharacteristic
390C2C31×#146311yescharacteristic
391C2C31×#146411yescharacteristic
392C2C31×#179711yescharacteristic
393C2C31×#179911yescharacteristic
394C2C31×#180111yescharacteristic
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
30. C2×C4⋊C4×C31C8semidirect
100. #8560C31direct (N × H)
151. C2×C4×C31C4⋊C8semidirect
227. C2×C4⋊C4C8×C31semidirect
245. C31#8560direct (N × H)
348. C2×C4C31×C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊C4×C312
C31×#17972
C2×C31×#3242
C31×#12802
#856031