Finite Group Databasebeta

← C31×#9329 #21466088

Subgroups — C31×#9329 #21466088

Order 7936.

530 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3109C211yesmaximal, characteristic
2C31×#2319C211yesmaximal, characteristic, complemented
3C31×#1980C211yesmaximal, characteristic, complemented
4C31×#1505C211yesmaximal, characteristic, complemented
5C31×#1490C211yesmaximal, characteristic, complemented
6C31×#1300C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C4×D4×C31C2211yescharacteristic
10C31×#481—21no—
11C31×#476C412yescomplemented
12C31×#459C412yescomplemented
13C31×#447—21no—
14C31×#442—22no—
15C31×#432C2211yescharacteristic
16C31×#432C2211yescharacteristic
17C2×C31×#104—22no—
18C4×M16×C31C2211yescharacteristic
19C31×#390—21no—
20C31×#389—21no—
21C31×#388—22no—
22C31×#381—21no—
23C31×#380—21no—
24C4×C4⋊C4×C31C2211yescharacteristic
25C31×#376C2211yescharacteristic
26C31×#327—21no—
27C31×#327—21no—
28C31×D4⋊C8—22no—
29C2×#41×C31—21no—
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—21no—
32C2×D8×C31—22no—
33C2×M16×C31—21no—
34C31×C4⋊Q8C2×C411yescharacteristic
35C31×#127C2×C411yescharacteristic
36C31×#124—21no—
37C31×#121—21no—
38C31×#121—21no—
39C4×D4×C31—21no—
40C4×D4×C31—21no—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C4×D4×C31C2×C412yes—
44C4×D4×C31D412yes—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31D411yescharacteristic
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—22no—
51C2×C42×C31—21no—
52C2×C42×C31D412yes—
53C2×C42×C31C2311yescharacteristic
54C31×#106—22no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8C2×C412yes—
57C31×#104—44no—
58C31×#102—22no—
59C31×#102—22no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×#97—21no—
63C31×#97—21no—
64C31×#97—21no—
65C4×C8×C31—21no—
66C31×#95—22no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95D411yescharacteristic
70C31×#95D411yescharacteristic
71C24×C31—21no—
72#41×C31—42no—
73#41×C31—42no—
74C2×Q8×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31—42no—
80C2×D4×C31—41no—
81C2×D4×C31C22⋊C412yes—
82C22×C4×C31—21no—
83C22×C4×C31—22no—
84C22×C4×C31—22no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—21no—
88C22×C4×C31—41no—
89C22×C4×C31—82no—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93D8×C31—44no—
94M16×C31—22no—
95M16×C31—41no—
96C2×C8×C31—22no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—82no—
104C4⋊C4×C31C22⋊C412yes—
105C22⋊C4×C31—22no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—82no—
110C22⋊C4×C31—82no—
111C42×C31—42no—
112C42×C31—42no—
113C42×C31C22×C411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31#4111yescharacteristic
116C42×C31#4111yescharacteristic
117#9329C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—22no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31#12011yescharacteristic
125Q8×C31—42no—
126D4×C31—22no—
127D4×C31—22no—
128D4×C31—42no—
129D4×C31—42no—
130D4×C31—42no—
131D4×C31—81no—
132D4×C31—81no—
133D4×C31—81no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—22no—
137C2×C4×C31—22no—
138C2×C4×C31—41no—
139C2×C4×C31—42no—
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—42no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—82no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31C2×C22⋊C411yescharacteristic
154C2×C4×C31C4×D411yescharacteristic
155C2×C4×C31C4×D411yescharacteristic
156C2×C4×C31#12111yescharacteristic
157C2×C4×C31#12111yescharacteristic
158C2×C4×C31#12311yescharacteristic
159C8×C31—42no—
160C8×C31—42no—
161C8×C31—81no—
162#3109C2×C3111yescharacteristic
163#2319C2×C3111yescharacteristic, complemented
164#1980C2×C3111yescharacteristic, complemented
165#1505C2×C3111yescharacteristic, complemented
166#1490C2×C3111yescharacteristic, complemented
167#1300C2×C3111yescharacteristic, complemented
168#1285C2×C3111yescharacteristic, complemented
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—42no—
172C22×C31—42no—
173C22×C31—42no—
174C22×C31—82no—
175C22×C31—82no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31—81no—
179C22×C31#38611yescharacteristic
180C22×C31#45311yescharacteristic
181C22×C31#45411yescharacteristic
182C4×C31—21no—
183C4×C31—21no—
184C4×C31—21no—
185C4×C31—21no—
186C4×C31—21no—
187C4×C31—42no—
188C4×C31—81no—
189C4×C31—82no—
190C4×C31—81no—
191C4×C31—81no—
192C4×C31#42112yes—
193#532C22×C3111yescharacteristic
194C2×C4×D4C22×C3111yescharacteristic
195#481—21no—
196#476C4×C3112yescomplemented
197#459C4×C3112yescomplemented
198#447—21no—
199#442—22no—
200#432C22×C3111yescharacteristic
201#432C22×C3111yescharacteristic
202C2×#104—22no—
203C4×M16C22×C3111yescharacteristic
204#390—21no—
205#389—21no—
206#388—22no—
207#381—21no—
208#380—21no—
209C4×C4⋊C4C22×C3111yescharacteristic
210#376C22×C3111yescharacteristic
211#327—21no—
212#327—21no—
213D4⋊C8—22no—
214C2×C31—21no—
215C2×C31—21no—
216C2×C31—82no—
217C2×C31—161no—
218C2×C31#188311yescharacteristic
219C2×C31#189711yescharacteristic
220C2×C31#190411yescharacteristic
221C2×#41—21no—
222C22×D4D4×C3111yescharacteristic
223C23×C4—21no—
224C2×D8—22no—
225C2×M16—21no—
226C4⋊Q8C2×C4×C3111yescharacteristic
227#127C2×C4×C3111yescharacteristic
228#124—21no—
229#121—21no—
230#121—21no—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4C2×C4×C3112yes—
236C4×D4D4×C3112yes—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4D4×C3111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C42—21no—
244C2×C42D4×C3112yes—
245C2×C42C23×C3111yescharacteristic
246#106—22no—
247C4⋊C8—21no—
248C4⋊C8C2×C4×C3112yes—
249#104—44no—
250#102—22no—
251#102—22no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254#97—21no—
255#97—21no—
256#97—21no—
257C4×C8—21no—
258#95—22no—
259#95—21no—
260#95—21no—
261#95D4×C3111yescharacteristic
262#95D4×C3111yescharacteristic
263C31#932911yescharacteristic, direct product factor, Sylow
264C24—21no—
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4C22⋊C4×C3112yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4C2×D4×C3111yescharacteristic
284C22×C4C2×D4×C3111yescharacteristic
285C22×C4C2×D4×C3111yescharacteristic
286D8—44no—
287M16—22no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—82no—
297C4⋊C4C22⋊C4×C3112yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—42no—
305C42—42no—
306C42C22×C4×C3111yescharacteristic
307C42C2×D4×C3111yescharacteristic
308C42#41×C3111yescharacteristic
309C42#41×C3111yescharacteristic
310C23—22no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23C31×#12011yescharacteristic
317Q8—42no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—42no—
322D4—42no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4C2×C22⋊C4×C3111yescharacteristic
346C2×C4C4×D4×C3111yescharacteristic
347C2×C4C4×D4×C3111yescharacteristic
348C2×C4C31×#12111yescharacteristic
349C2×C4C31×#12111yescharacteristic
350C2×C4C31×#12311yescharacteristic
351C8—42no—
352C8—42no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C31×#38611yescharacteristic
365C22C31×#45311yescharacteristic
366C22C31×#45411yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4C31×#42112yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C31×#188311yescharacteristic
383C2C31×#189711yescharacteristic
384C2C31×#190411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2319C2semidirect
3. C31×#1980C2semidirect
4. C31×#1505C2semidirect
5. C31×#1490C2semidirect
6. C31×#1300C2semidirect
7. C31×#1285C2semidirect
11. C31×#476C4semidirect
12. C31×#459C4semidirect
117. #9329C31direct (N × H)
163. #2319C2×C31semidirect
164. #1980C2×C31semidirect
165. #1505C2×C31semidirect
166. #1490C2×C31semidirect
167. #1300C2×C31semidirect
168. #1285C2×C31semidirect
196. #476C4×C31semidirect
197. #459C4×C31semidirect
263. C31#9329direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31092
C31×#23192
C31×#19802
C31×#15052
C31×#14902
C31×#13002
C31×#12852
#932931