Finite Group Databasebeta

← C31×#9283 #21466042

Subgroups — C31×#9283 #21466042

Order 7936.

448 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3207C211yesmaximal, characteristic
2C31×#2981C211yesmaximal, characteristic, complemented
3C31×#1530C211yesmaximal, characteristic, complemented
4C31×#1530C211yesmaximal, characteristic, complemented
5C31×#1496C211yesmaximal, characteristic, complemented
6C31×#1287C211yesmaximal, characteristic, complemented
7C31×#1275C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C31×#532C2211yescharacteristic
10C31×#493C411yescharacteristic
11C31×#492C411yescharacteristic
12C31×#487C411yescharacteristic
13C31×#486C411yescharacteristic
14C31×#463—22no—
15C31×#449—22no—
16C31×#436—21no—
17C31×#435—22no—
18C8×D4×C31—21no—
19C31×#432C2211yescharacteristic
20C31×#432C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C31×#408—22no—
24C2×C31×#97C2211yescharacteristic
25C31×#329—22no—
26C31×#329—22no—
27C31×D4⋊C8—21no—
28C31×D4⋊C8—21no—
29C2×#41×C31—21no—
30C2×#41×C31D412yes—
31C2×SD16×C31—22no—
32C2×D8×C31—22no—
33C2×M16×C31—22no—
34C22×C8×C31—21no—
35C22×C8×C31—22no—
36C31×C4⋊Q8C2×C411yescharacteristic
37C31×C4⋊Q8C2×C411yescharacteristic
38C31×#127C2×C411yescharacteristic
39C31×#127C2×C411yescharacteristic
40C31×#124—21no—
41C31×#124D412yes—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#121—21no—
46C4×D4×C31—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—21no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×#103—22no—
56C31×#102—22no—
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×C22⋊C8—21no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8—21no—
63C31×#97—21no—
64C31×#97—21no—
65C31×#97—21no—
66C31×#97D412yes—
67C4×C8×C31C2×C411yescharacteristic
68C4×C8×C31C2×C411yescharacteristic
69C4×C8×C31D411yescharacteristic
70C4×C8×C31D411yescharacteristic
71#41×C31—82no—
72#41×C31—82no—
73C2×Q8×C31—21no—
74C2×Q8×C31C22⋊C412yes—
75C2×D4×C31—22no—
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—41no—
82C2×D4×C31C22⋊C412yes—
83C22×C4×C31—22no—
84C22×C4×C31—41no—
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31#4111yescharacteristic
87C22×C4×C31#4111yescharacteristic
88SD16×C31—82no—
89D8×C31—82no—
90M16×C31—82no—
91C2×C8×C31—22no—
92C2×C8×C31—21no—
93C2×C8×C31—21no—
94C2×C8×C31—21no—
95C2×C8×C31—21no—
96C2×C8×C31—22no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—82no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C22⋊C4×C31—22no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—41no—
109C42×C31C22×C411yescharacteristic
110C42×C31C2×D411yescharacteristic
111C42×C31C2×D411yescharacteristic
112C42×C31C2×D411yescharacteristic
113#9283C3111yesmaximal, characteristic, direct product factor, Sylow
114C23×C31—22no—
115C23×C31—41no—
116C23×C31#12311yescharacteristic
117Q8×C31—42no—
118Q8×C31—81no—
119D4×C31—42no—
120D4×C31—42no—
121D4×C31—41no—
122D4×C31—41no—
123D4×C31—41no—
124D4×C31—41no—
125D4×C31—81no—
126D4×C31—81no—
127D4×C31—82no—
128D4×C31—82no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—22no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—41no—
137C2×C4×C31—82no—
138C2×C4×C31C2×C22⋊C411yescharacteristic
139C2×C4×C31C4×D411yescharacteristic
140C2×C4×C31C4×D411yescharacteristic
141C2×C4×C31#12011yescharacteristic
142C2×C4×C31#12111yescharacteristic
143C2×C4×C31#12111yescharacteristic
144C8×C31—42no—
145C8×C31—41no—
146C8×C31—42no—
147C8×C31—41no—
148C8×C31—41no—
149C8×C31—41no—
150C8×C31—81no—
151#3207C2×C3111yescharacteristic
152#2981C2×C3111yescharacteristic, complemented
153#1530C2×C3111yescharacteristic, complemented
154#1530C2×C3111yescharacteristic, complemented
155#1496C2×C3111yescharacteristic, complemented
156#1287C2×C3111yescharacteristic, complemented
157#1275C2×C3111yescharacteristic, complemented
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—42no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31#38611yescharacteristic
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—42no—
174C4×C31—81no—
175C4×C31#44311yescharacteristic
176C4×C31#44411yescharacteristic
177#532C22×C3111yescharacteristic
178#532C22×C3111yescharacteristic
179#493C4×C3111yescharacteristic
180#492C4×C3111yescharacteristic
181#487C4×C3111yescharacteristic
182#486C4×C3111yescharacteristic
183#463—22no—
184#449—22no—
185#436—21no—
186#435—22no—
187C8×D4—21no—
188#432C22×C3111yescharacteristic
189#432C22×C3111yescharacteristic
190#431C22×C3111yescharacteristic
191#431C22×C3111yescharacteristic
192#408—22no—
193C2×#97C22×C3111yescharacteristic
194#329—22no—
195#329—22no—
196D4⋊C8—21no—
197D4⋊C8—21no—
198C2×C31—41no—
199C2×C31—82no—
200C2×C31—161no—
201C2×C31#187611yescharacteristic
202C2×C31#190311yescharacteristic
203C2×C31#191111yescharacteristic
204C2×#41—21no—
205C2×#41D4×C3112yes—
206C2×SD16—22no—
207C2×D8—22no—
208C2×M16—22no—
209C22×C8—21no—
210C22×C8—22no—
211C4⋊Q8C2×C4×C3111yescharacteristic
212C4⋊Q8C2×C4×C3111yescharacteristic
213#127C2×C4×C3111yescharacteristic
214#127C2×C4×C3111yescharacteristic
215#124—21no—
216#124D4×C3112yes—
217#121—21no—
218#121—21no—
219#121—21no—
220#121—21no—
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C2×C42C23×C3111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230#103—22no—
231#102—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238#97—21no—
239#97—21no—
240#97—21no—
241#97D4×C3112yes—
242C4×C8C2×C4×C3111yescharacteristic
243C4×C8C2×C4×C3111yescharacteristic
244C4×C8D4×C3111yescharacteristic
245C4×C8D4×C3111yescharacteristic
246C31#928311yescharacteristic, direct product factor, Sylow
247#41—82no—
248#41—82no—
249C2×Q8—21no—
250C2×Q8C22⋊C4×C3112yes—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊C4×C3112yes—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C3111yescharacteristic
262C22×C4#41×C3111yescharacteristic
263C22×C4#41×C3111yescharacteristic
264SD16—82no—
265D8—82no—
266M16—82no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—82no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42C22×C4×C3111yescharacteristic
286C42C2×D4×C3111yescharacteristic
287C42C2×D4×C3111yescharacteristic
288C42C2×D4×C3111yescharacteristic
289C23—22no—
290C23—41no—
291C23C31×#12311yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—41no—
300D4—81no—
301D4—81no—
302D4—82no—
303D4—82no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4C2×C22⋊C4×C3111yescharacteristic
314C2×C4C4×D4×C3111yescharacteristic
315C2×C4C4×D4×C3111yescharacteristic
316C2×C4C31×#12011yescharacteristic
317C2×C4C31×#12111yescharacteristic
318C2×C4C31×#12111yescharacteristic
319C8—42no—
320C8—41no—
321C8—42no—
322C8—41no—
323C8—41no—
324C8—41no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C31×#38611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4C31×#44311yescharacteristic
344C4C31×#44411yescharacteristic
345C2—41no—
346C2—82no—
347C2—161no—
348C2C31×#187611yescharacteristic
349C2C31×#190311yescharacteristic
350C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3207C2
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×#2981C2semidirect
3. C31×#1530C2semidirect
4. C31×#1530C2semidirect
5. C31×#1496C2semidirect
6. C31×#1287C2semidirect
7. C31×#1275C2semidirect
113. #9283C31direct (N × H)
152. #2981C2×C31semidirect
153. #1530C2×C31semidirect
154. #1530C2×C31semidirect
155. #1496C2×C31semidirect
156. #1287C2×C31semidirect
157. #1275C2×C31semidirect
246. C31#9283direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32072
C31×#29812
C31×#15302
C31×#14962
C31×#12872
C31×#12752
#928331