Finite Group Databasebeta

← C31×#9291 #21466050

Subgroups — C31×#9291 #21466050

Order 7936.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3226C211yesmaximal, characteristic
2C31×#2932C211yesmaximal, characteristic
3C31×#1960C211yesmaximal, characteristic, complemented
4C31×#1546C211yesmaximal, characteristic, complemented
5C31×#1517C211yesmaximal, characteristic
6C31×#1286C211yesmaximal, characteristic, complemented
7C31×#1275C211yesmaximal, characteristic, complemented
8C2×C31×#131—21no—
9C31×#532C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C31×#500C412yescomplemented
12C31×#486C412yescomplemented
13C31×#480—22no—
14C31×#474—22no—
15C31×#435—22no—
16C31×#435—22no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C2×C31×#103—21no—
21C2×C31×#103—21no—
22C31×#408—21no—
23C2×C31×#97C2211yescharacteristic
24C31×#382C2211yescharacteristic
25C31×#332—22no—
26C31×#327—22no—
27C2×#41×C31—21no—
28C22×Q8×C31—21no—
29C31×#131—42no—
30C31×#131—42no—
31C2×M16×C31—22no—
32C2×M16×C31—21no—
33C22×C8×C31—22no—
34C22×C8×C31D411yescharacteristic
35C22×C8×C31D411yescharacteristic
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8C2×C412yes—
40C31×C4⋊Q8C2×C411yescharacteristic
41C31×#127C2×C411yescharacteristic
42C31×#124—21no—
43C31×#121—21no—
44C31×#121D412yes—
45C4×D4×C31—21no—
46C4×D4×C31D412yes—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×#107—24no—
52C31×C4⋊C8—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8D412yes—
56C31×#103—42no—
57C31×#103—42no—
58C31×#102—24no—
59C31×C22⋊C8—24no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×#97—21no—
63C31×#97—21no—
64C4×C8×C31—21no—
65C4×C8×C31C2×C412yes—
66C31×#95—21no—
67C31×#95—21no—
68#41×C31—41no—
69#41×C31—41no—
70#41×C31—41no—
71#41×C31—41no—
72C2×Q8×C31—21no—
73C2×Q8×C31—22no—
74C2×Q8×C31—41no—
75C2×Q8×C31—41no—
76C2×Q8×C31—41no—
77C2×Q8×C31—41no—
78C2×Q8×C31—41no—
79C2×D4×C31—22no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31C22⋊C412yes—
83C22×C4×C31—22no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4111yescharacteristic
89M16×C31—44no—
90M16×C31—41no—
91M16×C31—41no—
92C2×C8×C31—21no—
93C2×C8×C31—21no—
94C2×C8×C31—22no—
95C2×C8×C31—21no—
96C2×C8×C31—22no—
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—44no—
100C2×C8×C31—41no—
101C2×C8×C31D812yes—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31C22⋊C412yes—
110C22⋊C4×C31—22no—
111C22⋊C4×C31—22no—
112C42×C31C22×C411yescharacteristic
113C42×C31C2×D411yescharacteristic
114C42×C31C2×D411yescharacteristic
115C42×C31#4111yescharacteristic
116#9291C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—22no—
118C23×C31#12111yescharacteristic
119Q8×C31—41no—
120Q8×C31—41no—
121Q8×C31—42no—
122Q8×C31—42no—
123Q8×C31—81no—
124Q8×C31—81no—
125D4×C31—42no—
126D4×C31—42no—
127D4×C31—42no—
128D4×C31—41no—
129D4×C31—41no—
130D4×C31—81no—
131C2×C4×C31—22no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31—81no—
141C2×C4×C31—81no—
142C2×C4×C31C2×C22⋊C411yescharacteristic
143C2×C4×C31C4×D411yescharacteristic
144C2×C4×C31C4×D411yescharacteristic
145C2×C4×C31#12011yescharacteristic
146C2×C4×C31#12111yescharacteristic
147C2×C4×C31#12311yescharacteristic
148C2×C4×C31C2×D811yescharacteristic
149C2×C4×C31#13511yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
152C8×C31—22no—
153C8×C31—42no—
154C8×C31—42no—
155C8×C31—41no—
156C8×C31—81no—
157#3226C2×C3111yescharacteristic
158#2932C2×C3111yescharacteristic
159#1960C2×C3111yescharacteristic, complemented
160#1546C2×C3111yescharacteristic, complemented
161#1517C2×C3111yescharacteristic
162#1286C2×C3111yescharacteristic, complemented
163#1275C2×C3111yescharacteristic, complemented
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—42no—
167C22×C31—42no—
168C22×C31—42no—
169C22×C31#38611yescharacteristic
170C22×C31#45911yescharacteristic
171C22×C31#46311yescharacteristic
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—42no—
177C4×C31—82no—
178C4×C31—161no—
179C4×C31C4×D811yescharacteristic
180C4×C31#44211yescharacteristic
181C4×C31#44711yescharacteristic
182C4×C31#44911yescharacteristic
183C2×#131—21no—
184#532C22×C3111yescharacteristic
185C2×C4⋊Q8C22×C3111yescharacteristic
186#500C4×C3112yescomplemented
187#486C4×C3112yescomplemented
188#480—22no—
189#474—22no—
190#435—22no—
191#435—22no—
192#431C22×C3111yescharacteristic
193#431C22×C3111yescharacteristic
194#423C22×C3111yescharacteristic
195C2×#103—21no—
196C2×#103—21no—
197#408—21no—
198C2×#97C22×C3111yescharacteristic
199#382C22×C3111yescharacteristic
200#332—22no—
201#327—22no—
202C2×C31—21no—
203C2×C31—21no—
204C2×C31—82no—
205C2×C31#187911yescharacteristic
206C2×C31#190211yescharacteristic
207C2×C31#190911yescharacteristic
208C2×#41—21no—
209C22×Q8—21no—
210#131—42no—
211#131—42no—
212C2×M16—22no—
213C2×M16—21no—
214C22×C8—22no—
215C22×C8D4×C3111yescharacteristic
216C22×C8D4×C3111yescharacteristic
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8C2×C4×C3112yes—
221C4⋊Q8C2×C4×C3111yescharacteristic
222#127C2×C4×C3111yescharacteristic
223#124—21no—
224#121—21no—
225#121D4×C3112yes—
226C4×D4—21no—
227C4×D4D4×C3112yes—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42C23×C3111yescharacteristic
232#107—24no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8D4×C3112yes—
237#103—42no—
238#103—42no—
239#102—24no—
240C22⋊C8—24no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—21no—
244#97—21no—
245C4×C8—21no—
246C4×C8C2×C4×C3112yes—
247#95—21no—
248#95—21no—
249C31#929111yescharacteristic, direct product factor, Sylow
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊C4×C3112yes—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4C2×D4×C3111yescharacteristic
270C22×C4#41×C3111yescharacteristic
271M16—44no—
272M16—41no—
273M16—41no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—22no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8D8×C3112yes—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C3112yes—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C42C22×C4×C3111yescharacteristic
295C42C2×D4×C3111yescharacteristic
296C42C2×D4×C3111yescharacteristic
297C42#41×C3111yescharacteristic
298C23—22no—
299C23C31×#12111yescharacteristic
300Q8—41no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—42no—
307D4—42no—
308D4—42no—
309D4—41no—
310D4—41no—
311D4—81no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C3111yescharacteristic
324C2×C4C4×D4×C3111yescharacteristic
325C2×C4C4×D4×C3111yescharacteristic
326C2×C4C31×#12011yescharacteristic
327C2×C4C31×#12111yescharacteristic
328C2×C4C31×#12311yescharacteristic
329C2×C4C2×D8×C3111yescharacteristic
330C2×C4C31×#13511yescharacteristic
331C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
333C8—22no—
334C8—42no—
335C8—42no—
336C8—41no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22C31×#38611yescharacteristic
344C22C31×#45911yescharacteristic
345C22C31×#46311yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—82no—
352C4—161no—
353C4C4×D8×C3111yescharacteristic
354C4C31×#44211yescharacteristic
355C4C31×#44711yescharacteristic
356C4C31×#44911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C31×#187911yescharacteristic
361C2C31×#190211yescharacteristic
362C2C31×#190911yescharacteristic
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
3. C31×#1960C2semidirect
4. C31×#1546C2semidirect
6. C31×#1286C2semidirect
7. C31×#1275C2semidirect
11. C31×#500C4semidirect
12. C31×#486C4semidirect
116. #9291C31direct (N × H)
159. #1960C2×C31semidirect
160. #1546C2×C31semidirect
162. #1286C2×C31semidirect
163. #1275C2×C31semidirect
186. #500C4×C31semidirect
187. #486C4×C31semidirect
249. C31#9291direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32262
C31×#29322
C31×#19602
C31×#15462
C31×#15172
C31×#12862
C31×#12752
#929131