Finite Group Databasebeta

← C31×#10552 #21467311

Subgroups — C31×#10552 #21467311

Order 7936.

386 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3141C211yesmaximal, characteristic
2C31×#1950C211yesmaximal, characteristic, complemented
3C31×#1548C211yesmaximal, characteristic, complemented
4C31×#1547C211yesmaximal, characteristic
5C2×C31×#332C211yesmaximal, characteristic, complemented
6C31×#1480C211yesmaximal, characteristic
7C31×#1283C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C31×#489—22no—
11C31×#487—21no—
12C31×#486—21no—
13C31×#431C2211yescharacteristic
14C2×C31×#108—21no—
15C31×#423C2211yescharacteristic
16C2×C31×C4⋊C8C2211yescharacteristic
17C2×C31×C4⋊C8C2211yescharacteristic
18C31×#417—21no—
19C31×#417—21no—
20C4×M16×C31C2211yescharacteristic
21C31×#341—21no—
22C31×#333—22no—
23C31×#332—21no—
24C31×#332—22no—
25C31×#331—21no—
26C31×D4⋊C8—22no—
27C2×#41×C31—21no—
28C22×Q8×C31—21no—
29C2×M16×C31—21no—
30C2×M16×C31D411yescharacteristic
31C2×M16×C31D411yescharacteristic
32C22×C8×C31—21no—
33C22×C8×C31—21no—
34C31×C4⋊Q8—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8D411yescharacteristic
38C31×C4⋊Q8D412yes—
39C31×#127D411yescharacteristic
40C31×#124—21no—
41C31×#121—21no—
42C31×#121—21no—
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C42×C31C2311yescharacteristic
48C31×#108—42no—
49C31×C4⋊C8—21no—
50C31×C4⋊C8—21no—
51C31×C4⋊C8—21no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8D412yes—
56C31×#103—22no—
57C31×#103—22no—
58C31×#102—22no—
59C31×#102—22no—
60C31×C22⋊C8—21no—
61C31×#97—21no—
62C4×C8×C31—21no—
63C4×C8×C31—21no—
64#41×C31—41no—
65#41×C31—41no—
66#41×C31—41no—
67#41×C31—41no—
68C2×Q8×C31—21no—
69C2×Q8×C31—22no—
70C2×Q8×C31—41no—
71C2×Q8×C31—81no—
72C2×Q8×C31—81no—
73C2×D4×C31—21no—
74C2×D4×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31#4111yescharacteristic
81C22×C4×C31#4111yescharacteristic
82M16×C31—21no—
83M16×C31—21no—
84M16×C31—21no—
85M16×C31—21no—
86M16×C31—41no—
87M16×C31—41no—
88C2×C8×C31—21no—
89C2×C8×C31—21no—
90C2×C8×C31—22no—
91C2×C8×C31—41no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—81no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C42×C31C2×D411yescharacteristic
106C42×C31C2×D411yescharacteristic
107C42×C31C2×D411yescharacteristic
108C42×C31#4111yescharacteristic
109#10552C3111yesmaximal, characteristic, direct product factor, Sylow
110C23×C31—41no—
111C23×C31#12411yescharacteristic
112Q8×C31—41no—
113Q8×C31—41no—
114Q8×C31—82no—
115Q8×C31—81no—
116Q8×C31—81no—
117D4×C31—41no—
118D4×C31—41no—
119D4×C31—41no—
120D4×C31—41no—
121D4×C31—81no—
122D4×C31—81no—
123D4×C31—81no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—42no—
129C2×C4×C31—82no—
130C2×C4×C31—81no—
131C2×C4×C31—81no—
132C2×C4×C31#12011yescharacteristic
133C2×C4×C31#12111yescharacteristic
134C2×C4×C31#12111yescharacteristic
135C2×C4×C31#12111yescharacteristic
136C2×C4×C31#12311yescharacteristic
137C2×C4×C31#12311yescharacteristic
138C2×C4×C31#13511yescharacteristic
139C2×C4×C31#13511yescharacteristic
140C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C31#13711yescharacteristic
142C8×C31—41no—
143C8×C31—41no—
144C8×C31—42no—
145C8×C31—81no—
146C8×C31—81no—
147C8×C31—81no—
148#3141C2×C3111yescharacteristic
149#1950C2×C3111yescharacteristic, complemented
150#1548C2×C3111yescharacteristic, complemented
151#1547C2×C3111yescharacteristic
152C2×#332C2×C3111yescharacteristic, complemented
153#1480C2×C3111yescharacteristic
154#1283C2×C3111yescharacteristic, complemented
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31#39411yescharacteristic
161C22×C31#48811yescharacteristic
162C22×C31#48911yescharacteristic
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—21no—
166C4×C31—82no—
167C4×C31—81no—
168C4×C31#44911yescharacteristic
169C4×C31#45211yescharacteristic
170C4×C31#46311yescharacteristic
171C4×C31#46411yescharacteristic
172C4×C31#47111yescharacteristic
173C4×C31#47211yescharacteristic
174#532C22×C3111yescharacteristic
175C2×C4⋊Q8C22×C3111yescharacteristic
176#489—22no—
177#487—21no—
178#486—21no—
179#431C22×C3111yescharacteristic
180C2×#108—21no—
181#423C22×C3111yescharacteristic
182C2×C4⋊C8C22×C3111yescharacteristic
183C2×C4⋊C8C22×C3111yescharacteristic
184#417—21no—
185#417—21no—
186C4×M16C22×C3111yescharacteristic
187#341—21no—
188#333—22no—
189#332—21no—
190#332—22no—
191#331—21no—
192D4⋊C8—22no—
193C2×C31—21no—
194C2×C31—21no—
195C2×C31—161no—
196C2×C31#204211yescharacteristic
197C2×C31#204911yescharacteristic
198C2×C31#205111yescharacteristic
199C2×#41—21no—
200C22×Q8—21no—
201C2×M16—21no—
202C2×M16D4×C3111yescharacteristic
203C2×M16D4×C3111yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D4×C3112yes—
210C4⋊Q8D4×C3111yescharacteristic
211#127D4×C3111yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C42C23×C3111yescharacteristic
220#108—42no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C3112yes—
228#103—22no—
229#103—22no—
230#102—22no—
231#102—22no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236C31#1055211yescharacteristic, direct product factor, Sylow
237#41—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—81no—
245C2×Q8—81no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C3111yescharacteristic
253C22×C4#41×C3111yescharacteristic
254C22×C4#41×C3111yescharacteristic
255M16—21no—
256M16—21no—
257M16—21no—
258M16—21no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—81no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C42C2×D4×C3111yescharacteristic
279C42C2×D4×C3111yescharacteristic
280C42C2×D4×C3111yescharacteristic
281C42#41×C3111yescharacteristic
282C23—41no—
283C23C31×#12411yescharacteristic
284Q8—41no—
285Q8—41no—
286Q8—82no—
287Q8—81no—
288Q8—81no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4C31×#12011yescharacteristic
305C2×C4C31×#12111yescharacteristic
306C2×C4C31×#12111yescharacteristic
307C2×C4C31×#12111yescharacteristic
308C2×C4C31×#12311yescharacteristic
309C2×C4C31×#12311yescharacteristic
310C2×C4C31×#13511yescharacteristic
311C2×C4C31×#13511yescharacteristic
312C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
313C2×C4C31×#13711yescharacteristic
314C8—41no—
315C8—41no—
316C8—42no—
317C8—81no—
318C8—81no—
319C8—81no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C31×#39411yescharacteristic
326C22C31×#48811yescharacteristic
327C22C31×#48911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—81no—
333C4C31×#44911yescharacteristic
334C4C31×#45211yescharacteristic
335C4C31×#46311yescharacteristic
336C4C31×#46411yescharacteristic
337C4C31×#47111yescharacteristic
338C4C31×#47211yescharacteristic
339C2—21no—
340C2—21no—
341C2—161no—
342C2C31×#204211yescharacteristic
343C2C31×#204911yescharacteristic
344C2C31×#205111yescharacteristic
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C2×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×#1950C2semidirect
3. C31×#1548C2semidirect
5. C2×C31×#332C2semidirect
7. C31×#1283C2semidirect
109. #10552C31direct (N × H)
149. #1950C2×C31semidirect
150. #1548C2×C31semidirect
152. C2×#332C2×C31semidirect
154. #1283C2×C31semidirect
236. C31#10552direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31412
C31×#19502
C31×#15482
C31×#15472
C2×C31×#3322
C31×#14802
C31×#12832
#1055231