Finite Group Databasebeta

← C31×#9880 #21466639

Subgroups — C31×#9880 #21466639

Order 7936.

572 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×C31×#387C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C4×C31×C22⋊C8C211yesmaximal, characteristic
4C31×#1280C212yesmaximal
5C31×#1280C212yesmaximal
6C22×C4⋊C4×C31C411yescharacteristic
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×#387—21no—
14C31×#387—21no—
15C31×#387—21no—
16C31×#387—21no—
17C2×C31×#95C411yescharacteristic
18C2×C31×#95C411yescharacteristic
19C2×C31×#95C2211yescharacteristic
20C2×C31×#95C2211yescharacteristic
21C31×#336—21no—
22C31×#336—21no—
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31C2311yescharacteristic
30C22×C8×C31—22no—
31C22×C8×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—42no—
38C2×C4⋊C4×C31C814yescomplemented
39C2×C42×C31—42no—
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C31×C4⋊C8—42no—
45C31×C22⋊C8—22no—
46C31×C22⋊C8—24no—
47C31×C22⋊C8Q814yes—
48C4×C8×C31—42no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C24×C31C22×C411yescharacteristic
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22⋊C411yescharacteristic
85C22×C4×C31C2×C812yes—
86C22×C4×C31C2×C812yes—
87C22×C4×C31C2×C812yes—
88C22×C4×C31M1612yes—
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×Q812yes—
92C22×C4×C31#4112yes—
93C2×C8×C31—24no—
94C2×C8×C31—42no—
95C2×C8×C31—42no—
96C2×C8×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—42no—
99C4⋊C4×C31—24no—
100C4⋊C4×C31—24no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—42no—
103C42×C31—22no—
104C42×C31—22no—
105C42×C31—41no—
106C42×C31—41no—
107#9880C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31C2×C22⋊C411yescharacteristic
113C23×C31C4×Q812yes—
114C23×C31C22×C811yescharacteristic
115C23×C31C2×M1611yescharacteristic
116C23×C31#13112yes—
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—21no—
127C2×C4×C31—22no—
128C2×C4×C31—22no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—44no—
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—42no—
144C2×C4×C31—42no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31C22⋊C812yes—
154C2×C4×C31C22⋊C812yes—
155C2×C4×C31#9912yes—
156C2×C4×C31C22⋊Q812yes—
157C2×C4×C31#12411yescharacteristic
158C2×C4×C31C4⋊Q811yescharacteristic
159C8×C31—44no—
160C8×C31—82no—
161C2×#387C2×C3111yescharacteristic
162#1797C2×C3111yescharacteristic
163C4×C22⋊C8C2×C3111yescharacteristic
164#1280C2×C3112yes—
165#1280C2×C3112yes—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—22no—
174C22×C31#39111yescharacteristic
175C22×C31C2×C22⋊C811yescharacteristic
176C22×C31#40811yescharacteristic
177C22×C31C2×#9911yescharacteristic
178C22×C31#41011yescharacteristic
179C22×C31#41311yescharacteristic
180C22×C31#41311yescharacteristic
181C22×C31C8×Q812yes—
182C22×C31#44612yes—
183C4×C31—22no—
184C4×C31—22no—
185C4×C31—22no—
186C4×C31—22no—
187C4×C31—21no—
188C4×C31—21no—
189C4×C31—42no—
190C4×C31—42no—
191C4×C31—41no—
192C4×C31—81no—
193C4×C31—81no—
194C22×C4⋊C4C4×C3111yescharacteristic
195C22×C4⋊C4C4×C3111yescharacteristic
196C22×C42C22×C3111yescharacteristic
197C2×C4⋊C8—21no—
198C2×C22⋊C8C22×C3112yes—
199C2×C22⋊C8C22×C3112yes—
200C2×C4×C8—21no—
201#387—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205C2×#95C4×C3111yescharacteristic
206C2×#95C4×C3111yescharacteristic
207C2×#95C22×C3111yescharacteristic
208C2×#95C22×C3111yescharacteristic
209#336—21no—
210#336—21no—
211C2×C31—22no—
212C2×C31—22no—
213C2×C31#145811yescharacteristic
214C2×C31#145911yescharacteristic
215C2×C31#146811yescharacteristic
216C2×C31#147311yescharacteristic
217C2×C31#198411yescharacteristic
218C2×C31#199611yescharacteristic
219C2×C31#199811yescharacteristic
220C23×C4C2×C4×C3111yescharacteristic
221C23×C4C2×C4×C3111yescharacteristic
222C23×C4C2×C4×C3111yescharacteristic
223C23×C4C2×C4×C3111yescharacteristic
224C23×C4C2×C4×C3111yescharacteristic
225C23×C4C2×C4×C3111yescharacteristic
226C23×C4C23×C3111yescharacteristic
227C22×C8—22no—
228C22×C8—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4C8×C3114yescomplemented
236C2×C42—42no—
237C2×C42D4×C3111yescharacteristic
238C2×C42D4×C3111yescharacteristic
239C2×C42D4×C3111yescharacteristic
240C2×C42D4×C3111yescharacteristic
241C4⋊C8—42no—
242C22⋊C8—22no—
243C22⋊C8—24no—
244C22⋊C8Q8×C3114yes—
245C4×C8—42no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C31#988011yescharacteristic, direct product factor, Sylow
255C24C22×C4×C3111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C22⋊C4×C3111yescharacteristic
280C22×C4C22⋊C4×C3111yescharacteristic
281C22×C4C22⋊C4×C3111yescharacteristic
282C22×C4C22⋊C4×C3111yescharacteristic
283C22×C4C2×C8×C3112yes—
284C22×C4C2×C8×C3112yes—
285C22×C4C2×C8×C3112yes—
286C22×C4M16×C3112yes—
287C22×C4C2×D4×C3111yescharacteristic
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×Q8×C3112yes—
290C22×C4#41×C3112yes—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C22⋊C4×C3111yescharacteristic
310C23C4×Q8×C3112yes—
311C23C22×C8×C3111yescharacteristic
312C23C2×M16×C3111yescharacteristic
313C23C31×#13112yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4C31×C22⋊C812yes—
351C2×C4C31×C22⋊C812yes—
352C2×C4C31×#9912yes—
353C2×C4C31×C22⋊Q812yes—
354C2×C4C31×#12411yescharacteristic
355C2×C4C31×C4⋊Q811yescharacteristic
356C8—44no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22C31×#39111yescharacteristic
367C22C2×C31×C22⋊C811yescharacteristic
368C22C31×#40811yescharacteristic
369C22C2×C31×#9911yescharacteristic
370C22C31×#41011yescharacteristic
371C22C31×#41311yescharacteristic
372C22C31×#41311yescharacteristic
373C22C8×Q8×C3112yes—
374C22C31×#44612yes—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2C31×#145811yescharacteristic
389C2C31×#145911yescharacteristic
390C2C31×#146811yescharacteristic
391C2C31×#147311yescharacteristic
392C2C31×#198411yescharacteristic
393C2C31×#199611yescharacteristic
394C2C31×#199811yescharacteristic
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
38. C2×C4⋊C4×C31C8semidirect
107. #9880C31direct (N × H)
235. C2×C4⋊C4C8×C31semidirect
254. C31#9880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C31×#17972
C4×C31×C22⋊C82
C31×#12802
#988031