Finite Group Databasebeta

← C31×#9382 #21466141

Subgroups — C31×#9382 #21466141

Order 7936.

462 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
1C31×#3234C211yesmaximal, characteristic
2C31×#2336C211yesmaximal, characteristic, complemented
3C31×#1980C211yesmaximal, characteristic
4C31×#1528C211yesmaximal, characteristic, complemented
5C31×#1514C211yesmaximal, characteristic
6C31×#1288C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×#125C2211yescharacteristic
10C31×#501C412yescomplemented
11C31×#490C412yescomplemented
12C31×#481—21no—
13C31×#480—21no—
14C31×#478—22no—
15C31×#432C2211yescharacteristic
16C31×#432C2211yescharacteristic
17C2×C31×#104—21no—
18C2×C31×#104—21no—
19C4×M16×C31C2211yescharacteristic
20C31×#389—21no—
21C31×#387—21no—
22C31×#387—21no—
23C31×#387—21no—
24C31×#387—21no—
25C31×#383C2211yescharacteristic
26C4×C4⋊C4×C31—21no—
27C4×C4⋊C4×C31C2211yescharacteristic
28C31×#330—22no—
29C31×#327—21no—
30C31×#327—21no—
31C2×#41×C31—21no—
32C2×M16×C31—21no—
33C31×C4⋊Q8C2×C411yescharacteristic
34C31×#127C2×C411yescharacteristic
35C31×#125—21no—
36C31×#125—21no—
37C31×#125C2×C412yes—
38C31×#125D412yes—
39C31×#124—21no—
40C31×#121—21no—
41C31×#121—21no—
42C4×D4×C31—21no—
43C4×D4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31D411yescharacteristic
50C2×C4⋊C4×C31D411yescharacteristic
51C2×C42×C31—21no—
52C2×C42×C31—21no—
53C2×C42×C31D411yescharacteristic
54C2×C42×C31D411yescharacteristic
55C2×C42×C31C2311yescharacteristic
56C31×#107—22no—
57C31×#106—22no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×#104—42no—
61C31×#104—42no—
62C31×#102—22no—
63C31×#102—22no—
64C31×C22⋊C8—21no—
65C31×C22⋊C8—21no—
66C31×#97—21no—
67C31×#97—21no—
68C31×#97C2×C412yes—
69C4×C8×C31—21no—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95—21no—
77C31×#95D411yescharacteristic
78C31×#95D411yescharacteristic
79#41×C31—41no—
80#41×C31—41no—
81#41×C31—41no—
82#41×C31—41no—
83C2×Q8×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31—41no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—41no—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98M16×C31—22no—
99M16×C31—41no—
100C2×C8×C31—22no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—22no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—42no—
112C4⋊C4×C31—42no—
113C4⋊C4×C31—81no—
114C4⋊C4×C31C22⋊C412yes—
115C4⋊C4×C31C22⋊C412yes—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—41no—
118C42×C31—42no—
119C42×C31—41no—
120C42×C31—41no—
121C42×C31—81no—
122C42×C31C22×C411yescharacteristic
123C42×C31C2×D411yescharacteristic
124C42×C31#4111yescharacteristic
125C42×C31#4111yescharacteristic
126#9382C3111yesmaximal, characteristic, direct product factor, Sylow
127C23×C31—41no—
128C23×C31#12011yescharacteristic
129Q8×C31—41no—
130Q8×C31—41no—
131D4×C31—42no—
132D4×C31—41no—
133D4×C31—41no—
134D4×C31—81no—
135D4×C31—81no—
136D4×C31—81no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
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—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31C2×C22⋊C411yescharacteristic
163C2×C4×C31C4×D411yescharacteristic
164C2×C4×C31C4×D411yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12311yescharacteristic
168C8×C31—42no—
169C8×C31—42no—
170C8×C31—81no—
171#3234C2×C3111yescharacteristic
172#2336C2×C3111yescharacteristic, complemented
173#1980C2×C3111yescharacteristic
174#1528C2×C3111yescharacteristic, complemented
175#1514C2×C3111yescharacteristic
176#1288C2×C3111yescharacteristic, complemented
177#1285C2×C3111yescharacteristic, complemented
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31#38611yescharacteristic
184C22×C31#45311yescharacteristic
185C22×C31#45411yescharacteristic
186C4×C31—21no—
187C4×C31—21no—
188C4×C31—21no—
189C4×C31—21no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—42no—
193C4×C31—42no—
194C4×C31—42no—
195C4×C31—81no—
196C4×C31—81no—
197C4×C31—81no—
198C4×C31—81no—
199#532C22×C3111yescharacteristic
200C2×#125C22×C3111yescharacteristic
201#501C4×C3112yescomplemented
202#490C4×C3112yescomplemented
203#481—21no—
204#480—21no—
205#478—22no—
206#432C22×C3111yescharacteristic
207#432C22×C3111yescharacteristic
208C2×#104—21no—
209C2×#104—21no—
210C4×M16C22×C3111yescharacteristic
211#389—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215#387—21no—
216#383C22×C3111yescharacteristic
217C4×C4⋊C4—21no—
218C4×C4⋊C4C22×C3111yescharacteristic
219#330—22no—
220#327—21no—
221#327—21no—
222C2×C31—21no—
223C2×C31—21no—
224C2×C31—161no—
225C2×C31#188311yescharacteristic
226C2×C31#190611yescharacteristic
227C2×C31#191211yescharacteristic
228C2×#41—21no—
229C2×M16—21no—
230C4⋊Q8C2×C4×C3111yescharacteristic
231#127C2×C4×C3111yescharacteristic
232#125—21no—
233#125—21no—
234#125C2×C4×C3112yes—
235#125D4×C3112yes—
236#124—21no—
237#121—21no—
238#121—21no—
239C4×D4—21no—
240C4×D4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C3111yescharacteristic
247C2×C4⋊C4D4×C3111yescharacteristic
248C2×C42—21no—
249C2×C42—21no—
250C2×C42D4×C3111yescharacteristic
251C2×C42D4×C3111yescharacteristic
252C2×C42C23×C3111yescharacteristic
253#107—22no—
254#106—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257#104—42no—
258#104—42no—
259#102—22no—
260#102—22no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263#97—21no—
264#97—21no—
265#97C2×C4×C3112yes—
266C4×C8—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95D4×C3111yescharacteristic
275#95D4×C3111yescharacteristic
276C31#938211yescharacteristic, direct product factor, Sylow
277#41—41no—
278#41—41no—
279#41—41no—
280#41—41no—
281C2×Q8—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C3111yescharacteristic
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×D4×C3111yescharacteristic
296M16—22no—
297M16—41no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—81no—
312C4⋊C4C22⋊C4×C3112yes—
313C4⋊C4C22⋊C4×C3112yes—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42—42no—
319C42—81no—
320C42C22×C4×C3111yescharacteristic
321C42C2×D4×C3111yescharacteristic
322C42#41×C3111yescharacteristic
323C42#41×C3111yescharacteristic
324C23—41no—
325C23C31×#12011yescharacteristic
326Q8—41no—
327Q8—41no—
328D4—42no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C3111yescharacteristic
360C2×C4C4×D4×C3111yescharacteristic
361C2×C4C4×D4×C3111yescharacteristic
362C2×C4C31×#12111yescharacteristic
363C2×C4C31×#12111yescharacteristic
364C2×C4C31×#12311yescharacteristic
365C8—42no—
366C8—42no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C31×#38611yescharacteristic
374C22C31×#45311yescharacteristic
375C22C31×#45411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—42no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—161no—
392C2C31×#188311yescharacteristic
393C2C31×#190611yescharacteristic
394C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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×#2336C2semidirect
4. C31×#1528C2semidirect
6. C31×#1288C2semidirect
7. C31×#1285C2semidirect
10. C31×#501C4semidirect
11. C31×#490C4semidirect
126. #9382C31direct (N × H)
172. #2336C2×C31semidirect
174. #1528C2×C31semidirect
176. #1288C2×C31semidirect
177. #1285C2×C31semidirect
201. #501C4×C31semidirect
202. #490C4×C31semidirect
276. C31#9382direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32342
C31×#23362
C31×#19802
C31×#15282
C31×#15142
C31×#12882
C31×#12852
#938231