Finite Group Databasebeta

← C31×#9431 #21466190

Subgroups — C31×#9431 #21466190

Order 7936.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3181C211yesmaximal, characteristic
2C31×#2968C211yesmaximal, characteristic
3C31×#1531C211yesmaximal, characteristic, complemented
4C31×#1518C211yesmaximal, characteristic, complemented
5C31×#1512C211yesmaximal, characteristic
6C31×#1302C211yesmaximal, characteristic, complemented
7C31×#1295C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C31×#529C2211yescharacteristic
10C31×#501C411yescharacteristic, complemented
11C31×#497C411yescharacteristic, complemented
12C31×#491C411yescharacteristic, complemented
13C31×#489C411yescharacteristic, complemented
14C31×#467—21no—
15C31×#465—21no—
16C31×#446—21no—
17C31×#441—21no—
18C31×#440—21no—
19C31×#435—21no—
20C31×#435—21no—
21C8×D4×C31—21no—
22C31×#433—21no—
23C31×#432C2211yescharacteristic
24C31×#431C2211yescharacteristic
25C31×#405—21no—
26C2×C31×#97C2211yescharacteristic
27C2×C31×#97C2211yescharacteristic
28C31×#382C2211yescharacteristic
29C31×#330—21no—
30C31×#330—21no—
31C31×#328—21no—
32C31×#328—21no—
33C31×#328—21no—
34C31×#327—21no—
35C2×Q16×C31—21no—
36C2×SD16×C31—21no—
37C2×M16×C31—21no—
38C22×C8×C31—21no—
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C31×C4⋊Q8C2×C411yescharacteristic
42C31×C4⋊Q8C2×C411yescharacteristic
43C31×#126—21no—
44C31×#125—21no—
45C31×#125C2×C411yescharacteristic
46C31×#124C2×C411yescharacteristic
47C31×#123—21no—
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C31×C22⋊Q8D411yescharacteristic
51C31×#121D411yescharacteristic
52C4×Q8×C31—21no—
53C4×Q8×C31—21no—
54C4×Q8×C31D411yescharacteristic
55C4×D4×C31—21no—
56C4×D4×C31D411yescharacteristic
57C31×#117—21no—
58C31×#117—21no—
59C2×C4⋊C4×C31—21no—
60C2×C42×C31C2311yescharacteristic
61C31×#107—21no—
62C31×#106—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×#103—21no—
68C31×#103—21no—
69C31×#103—21no—
70C31×#102—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D411yescharacteristic
75C31×C22⋊C8D411yescharacteristic
76C31×#97—21no—
77C31×#97—21no—
78C31×#97—21no—
79C31×#97—21no—
80C31×#97C2×C411yescharacteristic
81C31×#97C2×C411yescharacteristic
82C31×#97D411yescharacteristic
83C31×#97D411yescharacteristic
84C4×C8×C31—21no—
85C4×C8×C31—21no—
86C31×#95—21no—
87C31×#95—21no—
88C2×Q8×C31—21no—
89C2×Q8×C31—21no—
90C2×Q8×C31C22⋊C411yescharacteristic
91C2×D4×C31—21no—
92C2×D4×C31C22⋊C411yescharacteristic
93C22×C4×C31—21no—
94C22×C4×C31—41no—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31#4111yescharacteristic
98Q16×C31—42no—
99SD16×C31—42no—
100M16×C31—42no—
101C2×C8×C31—21no—
102C2×C8×C31—21no—
103C2×C8×C31—21no—
104C2×C8×C31—21no—
105C2×C8×C31—21no—
106C2×C8×C31—21no—
107C2×C8×C31—42no—
108C2×C8×C31—42no—
109C2×C8×C31—42no—
110C2×C8×C31—41no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—81no—
122C4⋊C4×C31C22⋊C411yescharacteristic
123C4⋊C4×C31C22⋊C411yescharacteristic
124C22⋊C4×C31—21no—
125C22⋊C4×C31—21no—
126C22⋊C4×C31—21no—
127C22⋊C4×C31—21no—
128C22⋊C4×C31—21no—
129C22⋊C4×C31—41no—
130C42×C31—21no—
131C42×C31—41no—
132C42×C31C22×C411yescharacteristic
133C42×C31C2×D411yescharacteristic
134C42×C31C2×D411yescharacteristic
135C42×C31#4111yescharacteristic
136#9431C3111yesmaximal, characteristic, direct product factor, Sylow
137C23×C31—21no—
138C23×C31#12111yescharacteristic
139Q8×C31—41no—
140Q8×C31—41no—
141Q8×C31—41no—
142Q8×C31—81no—
143D4×C31—41no—
144D4×C31—41no—
145D4×C31—41no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31C2×C22⋊C411yescharacteristic
161C2×C4×C31C4×D411yescharacteristic
162C2×C4×C31C4×D411yescharacteristic
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12311yescharacteristic
166C8×C31—22no—
167C8×C31—22no—
168C8×C31—41no—
169C8×C31—41no—
170C8×C31—41no—
171C8×C31—41no—
172C8×C31—81no—
173#3181C2×C3111yescharacteristic
174#2968C2×C3111yescharacteristic
175#1531C2×C3111yescharacteristic, complemented
176#1518C2×C3111yescharacteristic, complemented
177#1512C2×C3111yescharacteristic
178#1302C2×C3111yescharacteristic, complemented
179#1295C2×C3111yescharacteristic, complemented
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—41no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31#38611yescharacteristic
186C22×C31#47111yescharacteristic
187C22×C31#47311yescharacteristic
188C4×C31—21no—
189C4×C31—21no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—41no—
195C4×C31—41no—
196C4×C31—41no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31—161no—
200#533C22×C3111yescharacteristic
201#529C22×C3111yescharacteristic
202#501C4×C3111yescharacteristic, complemented
203#497C4×C3111yescharacteristic, complemented
204#491C4×C3111yescharacteristic, complemented
205#489C4×C3111yescharacteristic, complemented
206#467—21no—
207#465—21no—
208#446—21no—
209#441—21no—
210#440—21no—
211#435—21no—
212#435—21no—
213C8×D4—21no—
214#433—21no—
215#432C22×C3111yescharacteristic
216#431C22×C3111yescharacteristic
217#405—21no—
218C2×#97C22×C3111yescharacteristic
219C2×#97C22×C3111yescharacteristic
220#382C22×C3111yescharacteristic
221#330—21no—
222#330—21no—
223#328—21no—
224#328—21no—
225#328—21no—
226#327—21no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—81no—
230C2×C31#188411yescharacteristic
231C2×C31#190611yescharacteristic
232C2×C31#190811yescharacteristic
233C2×Q16—21no—
234C2×SD16—21no—
235C2×M16—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8C2×C4×C3111yescharacteristic
240C4⋊Q8C2×C4×C3111yescharacteristic
241#126—21no—
242#125—21no—
243#125C2×C4×C3111yescharacteristic
244#124C2×C4×C3111yescharacteristic
245#123—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8D4×C3111yescharacteristic
249#121D4×C3111yescharacteristic
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D4×C3111yescharacteristic
253C4×D4—21no—
254C4×D4D4×C3111yescharacteristic
255#117—21no—
256#117—21no—
257C2×C4⋊C4—21no—
258C2×C42C23×C3111yescharacteristic
259#107—21no—
260#106—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265#103—21no—
266#103—21no—
267#103—21no—
268#102—21no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8D4×C3111yescharacteristic
273C22⋊C8D4×C3111yescharacteristic
274#97—21no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97C2×C4×C3111yescharacteristic
279#97C2×C4×C3111yescharacteristic
280#97D4×C3111yescharacteristic
281#97D4×C3111yescharacteristic
282C4×C8—21no—
283C4×C8—21no—
284#95—21no—
285#95—21no—
286C31#943111yescharacteristic, direct product factor, Sylow
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C3111yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C3111yescharacteristic
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×D4×C3111yescharacteristic
296C22×C4#41×C3111yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4C22⋊C4×C3111yescharacteristic
322C4⋊C4C22⋊C4×C3111yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—41no—
331C42C22×C4×C3111yescharacteristic
332C42C2×D4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C42#41×C3111yescharacteristic
335C23—21no—
336C23C31×#12111yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4C2×C22⋊C4×C3111yescharacteristic
359C2×C4C4×D4×C3111yescharacteristic
360C2×C4C4×D4×C3111yescharacteristic
361C2×C4C31×#12011yescharacteristic
362C2×C4C31×#12111yescharacteristic
363C2×C4C31×#12311yescharacteristic
364C8—22no—
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22C31×#38611yescharacteristic
377C22C31×#47111yescharacteristic
378C22C31×#47311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2C31×#188411yescharacteristic
395C2C31×#190611yescharacteristic
396C2C31×#190811yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#121D4
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
3. C31×#1531C2semidirect
4. C31×#1518C2semidirect
6. C31×#1302C2semidirect
7. C31×#1295C2semidirect
10. C31×#501C4semidirect
11. C31×#497C4semidirect
12. C31×#491C4semidirect
13. C31×#489C4semidirect
136. #9431C31direct (N × H)
175. #1531C2×C31semidirect
176. #1518C2×C31semidirect
178. #1302C2×C31semidirect
179. #1295C2×C31semidirect
202. #501C4×C31semidirect
203. #497C4×C31semidirect
204. #491C4×C31semidirect
205. #489C4×C31semidirect
286. C31#9431direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31812
C31×#29682
C31×#15312
C31×#15182
C31×#15122
C31×#13022
C31×#12952
#943131