Finite Group Databasebeta

← C31×#9433 #21466192

Subgroups — C31×#9433 #21466192

Order 7936.

440 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3141C211yesmaximal, characteristic
2C31×#2979C211yesmaximal, characteristic
3C31×#1560C211yesmaximal, characteristic
4C31×#1548C211yesmaximal, characteristic, complemented
5C31×#1546C211yesmaximal, characteristic, complemented
6C31×#1299C211yesmaximal, characteristic, complemented
7C31×#1299C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C31×#489C414yes—
11C31×#487—21no—
12C31×#486—21no—
13C31×#436—21no—
14C31×#436—21no—
15C8×D4×C31—21no—
16C8×D4×C31—21no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C31×#423C2211yescharacteristic
21C31×#417—22no—
22C31×#408—22no—
23C4×M16×C31C2211yescharacteristic
24C31×#333—21no—
25C31×#333—21no—
26C31×#333—21no—
27C31×#332—21no—
28C31×#332—21no—
29C31×#331—21no—
30C2×#41×C31D412yes—
31C22×Q8×C31—21no—
32C2×M16×C31—21no—
33C2×M16×C31—22no—
34C2×M16×C31—21no—
35C2×M16×C31—21no—
36C22×C8×C31—22no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8C2×C412yes—
41C31×C4⋊Q8D411yescharacteristic
42C31×#127D411yescharacteristic
43C31×#124C2×C412yes—
44C31×#121—21no—
45C31×#121—21no—
46C4×D4×C31—21no—
47C4×D4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—21no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8D411yescharacteristic
56C31×C4⋊C8D411yescharacteristic
57C31×C4⋊C8D411yescharacteristic
58C31×C4⋊C8D411yescharacteristic
59C31×#103—24no—
60C31×#102—24no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—21no—
64C31×C22⋊C8—21no—
65C31×#97C2×C412yes—
66C4×C8×C31—21no—
67C4×C8×C31—21no—
68C4×C8×C31—21no—
69#41×C31—42no—
70#41×C31—42no—
71C2×Q8×C31—22no—
72C2×Q8×C31—41no—
73C2×Q8×C31—81no—
74C2×Q8×C31—81no—
75C2×Q8×C31C22⋊C412yes—
76C2×D4×C31—22no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31C22⋊C412yes—
80C22×C4×C31—22no—
81C22×C4×C31—41no—
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31#4111yescharacteristic
84C22×C4×C31#4111yescharacteristic
85M16×C31—41no—
86M16×C31—41no—
87M16×C31—82no—
88M16×C31—81no—
89M16×C31—81no—
90C2×C8×C31—22no—
91C2×C8×C31—21no—
92C2×C8×C31—21no—
93C2×C8×C31—21no—
94C2×C8×C31—21no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—82no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C22⋊C4×C31—22no—
105C22⋊C4×C31—22no—
106C42×C31C22×C411yescharacteristic
107C42×C31C2×D411yescharacteristic
108C42×C31C2×D411yescharacteristic
109C42×C31C2×D411yescharacteristic
110#9433C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—22no—
112C23×C31#12311yescharacteristic
113Q8×C31—42no—
114Q8×C31—82no—
115Q8×C31—81no—
116Q8×C31—81no—
117D4×C31—42no—
118D4×C31—41no—
119D4×C31—41no—
120D4×C31—41no—
121D4×C31—41no—
122D4×C31—82no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—22no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—82no—
134C2×C4×C31C2×C22⋊C411yescharacteristic
135C2×C4×C31C4×D411yescharacteristic
136C2×C4×C31C4×D411yescharacteristic
137C2×C4×C31#12011yescharacteristic
138C2×C4×C31#12111yescharacteristic
139C2×C4×C31#12111yescharacteristic
140C8×C31—42no—
141C8×C31—41no—
142C8×C31—41no—
143C8×C31—41no—
144C8×C31—41no—
145C8×C31—81no—
146C8×C31—81no—
147#3141C2×C3111yescharacteristic
148#2979C2×C3111yescharacteristic
149#1560C2×C3111yescharacteristic
150#1548C2×C3111yescharacteristic, complemented
151#1546C2×C3111yescharacteristic, complemented
152#1299C2×C3111yescharacteristic, complemented
153#1299C2×C3111yescharacteristic, complemented
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—42no—
160C22×C31#38611yescharacteristic
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—42no—
165C4×C31—82no—
166C4×C31#45511yescharacteristic
167C4×C31#45511yescharacteristic
168C4×C31#47111yescharacteristic
169C4×C31#47111yescharacteristic
170C4×C31#47211yescharacteristic
171C4×C31#47311yescharacteristic
172#532C22×C3111yescharacteristic
173C2×C4⋊Q8C22×C3111yescharacteristic
174#489C4×C3114yes—
175#487—21no—
176#486—21no—
177#436—21no—
178#436—21no—
179C8×D4—21no—
180C8×D4—21no—
181#431C22×C3111yescharacteristic
182#431C22×C3111yescharacteristic
183#423C22×C3111yescharacteristic
184#423C22×C3111yescharacteristic
185#417—22no—
186#408—22no—
187C4×M16C22×C3111yescharacteristic
188#333—21no—
189#333—21no—
190#333—21no—
191#332—21no—
192#332—21no—
193#331—21no—
194C2×C31—41no—
195C2×C31—82no—
196C2×C31#188511yescharacteristic
197C2×C31#190711yescharacteristic
198C2×C31#190811yescharacteristic
199C2×#41D4×C3112yes—
200C22×Q8—21no—
201C2×M16—21no—
202C2×M16—22no—
203C2×M16—21no—
204C2×M16—21no—
205C22×C8—22no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C2×C4×C3112yes—
210C4⋊Q8D4×C3111yescharacteristic
211#127D4×C3111yescharacteristic
212#124C2×C4×C3112yes—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C42C23×C3111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C3111yescharacteristic
225C4⋊C8D4×C3111yescharacteristic
226C4⋊C8D4×C3111yescharacteristic
227C4⋊C8D4×C3111yescharacteristic
228#103—24no—
229#102—24no—
230C22⋊C8—22no—
231C22⋊C8—22no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234#97C2×C4×C3112yes—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8—21no—
238C31#943311yescharacteristic, direct product factor, Sylow
239#41—42no—
240#41—42no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—81no—
245C2×Q8C22⋊C4×C3112yes—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊C4×C3112yes—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4C2×D4×C3111yescharacteristic
253C22×C4#41×C3111yescharacteristic
254C22×C4#41×C3111yescharacteristic
255M16—41no—
256M16—41no—
257M16—82no—
258M16—81no—
259M16—81no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—82no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C42C22×C4×C3111yescharacteristic
277C42C2×D4×C3111yescharacteristic
278C42C2×D4×C3111yescharacteristic
279C42C2×D4×C3111yescharacteristic
280C23—22no—
281C23C31×#12311yescharacteristic
282Q8—42no—
283Q8—82no—
284Q8—81no—
285Q8—81no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—82no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C3111yescharacteristic
304C2×C4C4×D4×C3111yescharacteristic
305C2×C4C4×D4×C3111yescharacteristic
306C2×C4C31×#12011yescharacteristic
307C2×C4C31×#12111yescharacteristic
308C2×C4C31×#12111yescharacteristic
309C8—42no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—41no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22C31×#38611yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4C31×#45511yescharacteristic
329C4C31×#45511yescharacteristic
330C4C31×#47111yescharacteristic
331C4C31×#47111yescharacteristic
332C4C31×#47211yescharacteristic
333C4C31×#47311yescharacteristic
334C2—41no—
335C2—82no—
336C2C31×#188511yescharacteristic
337C2C31×#190711yescharacteristic
338C2C31×#190811yescharacteristic
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
4. C31×#1548C2semidirect
5. C31×#1546C2semidirect
6. C31×#1299C2semidirect
7. C31×#1299C2semidirect
110. #9433C31direct (N × H)
150. #1548C2×C31semidirect
151. #1546C2×C31semidirect
152. #1299C2×C31semidirect
153. #1299C2×C31semidirect
238. C31#9433direct (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×#29792
C31×#15602
C31×#15482
C31×#15462
C31×#12992
#943331