Finite Group Databasebeta

← C31×#10283 #21467042

Subgroups — C31×#10283 #21467042

Order 7936.

626 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3227C211yesmaximal, characteristic
2C31×#3206C211yesmaximal, characteristic
3C31×#2868C211yesmaximal, characteristic, complemented
4C31×#1962C211yesmaximal, characteristic
5C31×#1549C211yesmaximal, characteristic, complemented
6C31×#1548C211yesmaximal, characteristic, complemented
7C31×#1276C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×C4⋊Q8—22no—
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C31×C4⋊Q8C2211yescharacteristic
12C31×#498—21no—
13C31×#492—21no—
14C31×#487—21no—
15C31×#486—21no—
16C31×#481—22no—
17C31×#476—22no—
18C31×#461—22no—
19C31×#448—22no—
20C31×#431C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#423C2211yescharacteristic
23C2×C31×#104—22no—
24C31×#384—22no—
25C31×#384—22no—
26C43×C31C2211yescharacteristic
27C31×#333—22no—
28C31×#332—22no—
29C2×#41×C31—21no—
30C22×Q8×C31—21no—
31C22×Q8×C31D412yes—
32C2×SD16×C31—24no—
33C2×M16×C31—21no—
34C31×C4⋊Q8—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—48no—
43C31×C4⋊Q8D411yescharacteristic
44C31×#127D411yescharacteristic
45C31×#124—21no—
46C31×#121—21no—
47C31×#121—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C2×C4⋊C4×C31—28no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31D412yes—
55C2×C42×C31—21no—
56C2×C42×C31—21no—
57C2×C42×C31D412yes—
58C2×C42×C31C2311yescharacteristic
59C31×#106—24no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8D412yes—
63C31×C4⋊C8D412yes—
64C31×#104—44no—
65C31×#103—24no—
66C31×#102—24no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71#41×C31—42no—
72#41×C31—42no—
73C2×Q8×C31—22no—
74C2×Q8×C31—21no—
75C2×Q8×C31—22no—
76C2×Q8×C31—44no—
77C2×Q8×C31—44no—
78C2×Q8×C31—41no—
79C2×Q8×C31—41no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—41no—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—41no—
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D411yescharacteristic
91SD16×C31—84no—
92M16×C31—42no—
93C2×C8×C31—22no—
94C2×C8×C31—22no—
95C2×C8×C31—41no—
96C4⋊C4×C31—22no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—416no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—41no—
109C42×C31—24no—
110C42×C31—24no—
111C42×C31—22no—
112C42×C31SD1614yescomplemented
113C42×C31C2×D411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31C2×D411yescharacteristic
116C42×C31#4111yescharacteristic
117#10283C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—41no—
119C23×C31#12011yescharacteristic
120Q8×C31—44no—
121Q8×C31—42no—
122Q8×C31—82no—
123Q8×C31—82no—
124Q8×C31—82no—
125D4×C31—42no—
126D4×C31—42no—
127D4×C31—42no—
128D4×C31—82no—
129C2×C4×C31—24no—
130C2×C4×C31—24no—
131C2×C4×C31—24no—
132C2×C4×C31—22no—
133C2×C4×C31—22no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—41no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31#12011yescharacteristic
142C2×C4×C31#12011yescharacteristic
143C2×C4×C31#12111yescharacteristic
144C2×C4×C31#12111yescharacteristic
145C2×C4×C31#12111yescharacteristic
146C2×C4×C31#12711yescharacteristic
147C2×C4×C31C2×SD1612yes—
148C2×C4×C31#13712yes—
149C8×C31—42no—
150C8×C31—42no—
151C8×C31—81no—
152#3227C2×C3111yescharacteristic
153#3206C2×C3111yescharacteristic
154#2868C2×C3111yescharacteristic, complemented
155#1962C2×C3111yescharacteristic
156#1549C2×C3111yescharacteristic, complemented
157#1548C2×C3111yescharacteristic, complemented
158#1276C2×C3111yescharacteristic, complemented
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—81no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31#39211yescharacteristic
165C22×C31#44812yes—
166C4×C31—28no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—82no—
170C4×C31—82no—
171C4×C31—81no—
172C4×C31#45312yes—
173C4×C31#45612yes—
174C4×C31#46112yes—
175C4×C31#49211yescharacteristic
176C4×C31#49711yescharacteristic
177#532C22×C3111yescharacteristic
178C2×C4⋊Q8—22no—
179C2×C4⋊Q8C22×C3111yescharacteristic
180C2×C4⋊Q8C22×C3111yescharacteristic
181#498—21no—
182#492—21no—
183#487—21no—
184#486—21no—
185#481—22no—
186#476—22no—
187#461—22no—
188#448—22no—
189#431C22×C3111yescharacteristic
190#431C22×C3111yescharacteristic
191#423C22×C3111yescharacteristic
192C2×#104—22no—
193#384—22no—
194#384—22no—
195C43C22×C3111yescharacteristic
196#333—22no—
197#332—22no—
198C2×C31—22no—
199C2×C31—161no—
200C2×C31#200211yescharacteristic
201C2×C31#200511yescharacteristic
202C2×C31#201311yescharacteristic
203C2×#41—21no—
204C22×Q8—21no—
205C22×Q8D4×C3112yes—
206C2×SD16—24no—
207C2×M16—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—48no—
217C4⋊Q8D4×C3111yescharacteristic
218#127D4×C3111yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C3112yes—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C3112yes—
232C2×C42C23×C3111yescharacteristic
233#106—24no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8D4×C3112yes—
237C4⋊C8D4×C3112yes—
238#104—44no—
239#103—24no—
240#102—24no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C4×C8—21no—
244C4×C8—21no—
245C31#1028311yescharacteristic, direct product factor, Sylow
246#41—42no—
247#41—42no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4C2×D4×C3111yescharacteristic
264C22×C4C2×D4×C3111yescharacteristic
265C22×C4C2×D4×C3111yescharacteristic
266SD16—84no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—416no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—24no—
285C42—24no—
286C42—22no—
287C42SD16×C3114yescomplemented
288C42C2×D4×C3111yescharacteristic
289C42C2×D4×C3111yescharacteristic
290C42C2×D4×C3111yescharacteristic
291C42#41×C3111yescharacteristic
292C23—41no—
293C23C31×#12011yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—82no—
297Q8—82no—
298Q8—82no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C31×#12011yescharacteristic
316C2×C4C31×#12011yescharacteristic
317C2×C4C31×#12111yescharacteristic
318C2×C4C31×#12111yescharacteristic
319C2×C4C31×#12111yescharacteristic
320C2×C4C31×#12711yescharacteristic
321C2×C4C2×SD16×C3112yes—
322C2×C4C31×#13712yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C31×#39211yescharacteristic
332C22C31×#44812yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—81no—
339C4C31×#45312yes—
340C4C31×#45612yes—
341C4C31×#46112yes—
342C4C31×#49211yescharacteristic
343C4C31×#49711yescharacteristic
344C2—22no—
345C2—161no—
346C2C31×#200211yescharacteristic
347C2C31×#200511yescharacteristic
348C2C31×#201311yescharacteristic
subgroupG/H
center, socleC22×C31#392
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
3. C31×#2868C2semidirect
5. C31×#1549C2semidirect
6. C31×#1548C2semidirect
7. C31×#1276C2semidirect
112. C42×C31SD16semidirect
117. #10283C31direct (N × H)
154. #2868C2×C31semidirect
156. #1549C2×C31semidirect
157. #1548C2×C31semidirect
158. #1276C2×C31semidirect
245. C31#10283direct (N × H)
287. C42SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32272
C31×#32062
C31×#28682
C31×#19622
C31×#15492
C31×#15482
C31×#12762
#1028331