Finite Group Databasebeta

← C31×#10567 #21467326

Subgroups — C31×#10567 #21467326

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2659C211yesmaximal, characteristic
2C31×#1852C212yesmaximal
3C31×#1444C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1280C211yesmaximal, characteristic
6C2×C31×C22⋊Q8—21no—
7C22×C4⋊C4×C31—21no—
8C22×C4⋊C4×C31C2211yescharacteristic
9C2×C31×#107—22no—
10C2×C31×C22⋊C8C2212yes—
11C31×#398—22no—
12C31×#395—22no—
13C31×#380—21no—
14C31×#380C2212yes—
15C2×C31×#95—21no—
16C2×C31×#95C2211yescharacteristic
17C2×C31×#95C2211yescharacteristic
18C31×#340—22no—
19C22×Q8×C31—21no—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31D411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31C2311yescharacteristic
25C22×C8×C31—22no—
26C31×C22⋊Q8—42no—
27C31×C22⋊Q8—42no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31—42no—
36C2×C4⋊C4×C31—42no—
37C2×C4⋊C4×C31D412yes—
38C2×C4⋊C4×C31D412yes—
39C2×C22⋊C4×C31—22no—
40C31×#107—44no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8Q814yescomplemented
43C31×#95—22no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—21no—
47C31×#95—42no—
48C31×#95Q812yescomplemented
49C24×C31C2×D411yescharacteristic
50C2×Q8×C31—42no—
51C2×Q8×C31—81no—
52C2×Q8×C31—81no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—22no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
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×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31D812yes—
80C22×C4×C31Q1612yes—
81C22×C4×C31C2×D412yes—
82C22×C4×C31C2×Q812yes—
83C22×C4×C31C2×Q811yescharacteristic
84C22×C4×C31#4111yescharacteristic
85C2×C8×C31—24no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—24no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—44no—
92C4⋊C4×C31—42no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—48no—
95C4⋊C4×C31—81no—
96C4⋊C4×C31—81no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99#10567C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—21no—
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31#12011yescharacteristic
105C23×C31C22⋊Q811yescharacteristic
106C23×C31C4⋊Q811yescharacteristic
107C23×C31C2×D811yescharacteristic
108C23×C31C2×Q1611yescharacteristic
109C23×C31AGL(1,ℤ/8)11yescharacteristic
110C23×C31#13711yescharacteristic
111Q8×C31—84no—
112C2×C4×C31—22no—
113C2×C4×C31—22no—
114C2×C4×C31—24no—
115C2×C4×C31—22no—
116C2×C4×C31—22no—
117C2×C4×C31—42no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—81no—
142C2×C4×C31—81no—
143C2×C4×C31—81no—
144C2×C4×C31—81no—
145C2×C4×C31—81no—
146C2×C4×C31—81no—
147C2×C4×C31C22⋊Q812yes—
148C2×C4×C31C4⋊Q812yes—
149C8×C31—44no—
150#2659C2×C3111yescharacteristic
151#1852C2×C3112yes—
152#1444C2×C3111yescharacteristic
153#1294C2×C3112yes—
154#1280C2×C3111yescharacteristic
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
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#39511yescharacteristic
168C22×C31#44711yescharacteristic
169C22×C31#45111yescharacteristic
170C22×C31#45311yescharacteristic
171C22×C31#45611yescharacteristic
172C22×C31B(4,𝔽2)11yescharacteristic
173C22×C31#45811yescharacteristic
174C22×C31#47411yescharacteristic
175C22×C31#47711yescharacteristic
176C22×C31#50011yescharacteristic
177C22×C31#50111yescharacteristic
178C4×C31—22no—
179C4×C31—22no—
180C4×C31—44no—
181C4×C31—42no—
182C4×C31—42no—
183C4×C31—82no—
184C4×C31—82no—
185C4×C31—82no—
186C2×C22⋊Q8—21no—
187C22×C4⋊C4—21no—
188C22×C4⋊C4C22×C3111yescharacteristic
189C2×#107—22no—
190C2×C22⋊C8C22×C3112yes—
191#398—22no—
192#395—22no—
193#380—21no—
194#380C22×C3112yes—
195C2×#95—21no—
196C2×#95C22×C3111yescharacteristic
197C2×#95C22×C3111yescharacteristic
198#340—22no—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—21no—
203C2×C31#159511yescharacteristic
204C2×C31#160511yescharacteristic
205C2×C31#161011yescharacteristic
206C2×C31#161411yescharacteristic
207C2×C31#205711yescharacteristic
208C2×C31#206011yescharacteristic
209C2×C31#206211yescharacteristic
210C22×Q8—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4D4×C3111yescharacteristic
214C23×C4D4×C3111yescharacteristic
215C23×C4C23×C3111yescharacteristic
216C22×C8—22no—
217C22⋊Q8—42no—
218C22⋊Q8—42no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—42no—
227C2×C4⋊C4—42no—
228C2×C4⋊C4D4×C3112yes—
229C2×C4⋊C4D4×C3112yes—
230C2×C22⋊C4—22no—
231#107—44no—
232C22⋊C8—22no—
233C22⋊C8Q8×C3114yescomplemented
234#95—22no—
235#95—22no—
236#95—22no—
237#95—21no—
238#95—42no—
239#95Q8×C3112yescomplemented
240C31#1056711yescharacteristic, direct product factor, Sylow
241C24C2×D4×C3111yescharacteristic
242C2×Q8—42no—
243C2×Q8—81no—
244C2×Q8—81no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
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×C4D8×C3112yes—
272C22×C4Q16×C3112yes—
273C22×C4C2×D4×C3112yes—
274C22×C4C2×Q8×C3112yes—
275C22×C4C2×Q8×C3111yescharacteristic
276C22×C4#41×C3111yescharacteristic
277C2×C8—24no—
278C2×C8—42no—
279C2×C8—42no—
280C4⋊C4—24no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—44no—
286C4⋊C4—48no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C31×#12011yescharacteristic
296C23C31×C22⋊Q811yescharacteristic
297C23C31×C4⋊Q811yescharacteristic
298C23C2×D8×C3111yescharacteristic
299C23C2×Q16×C3111yescharacteristic
300C23C31×AGL(1,ℤ/8)11yescharacteristic
301C23C31×#13711yescharacteristic
302Q8—84no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C31×C22⋊Q812yes—
339C2×C4C31×C4⋊Q812yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22C31×#39511yescharacteristic
354C22C31×#44711yescharacteristic
355C22C31×#45111yescharacteristic
356C22C31×#45311yescharacteristic
357C22C31×#45611yescharacteristic
358C22C31×B(4,𝔽2)11yescharacteristic
359C22C31×#45811yescharacteristic
360C22C31×#47411yescharacteristic
361C22C31×#47711yescharacteristic
362C22C31×#50011yescharacteristic
363C22C31×#50111yescharacteristic
364C4—22no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—82no—
370C4—82no—
371C4—82no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C31×#159511yescharacteristic
377C2C31×#160511yescharacteristic
378C2C31×#161011yescharacteristic
379C2C31×#161411yescharacteristic
380C2C31×#205711yescharacteristic
381C2C31×#206011yescharacteristic
382C2C31×#206211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
42. C31×C22⋊C8Q8semidirect
48. C31×#95Q8semidirect
99. #10567C31direct (N × H)
233. C22⋊C8Q8×C31semidirect
239. #95Q8×C31semidirect
240. C31#10567direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26592
C31×#18522
C31×#14442
C31×#12942
C31×#12802
#1056731