Finite Group Databasebeta

← C31×#13387 #21470146

Subgroups — C31×#13387 #21470146

Order 7936.

428 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3058C211yesmaximal, characteristic
2C31×#2159C211yesmaximal, characteristic, complemented
3C2×C31×#361C211yesmaximal, characteristic, complemented
4C2×C31×#357C211yesmaximal, characteristic, complemented
5C2×C31×#350C211yesmaximal, characteristic, complemented
6C31×#1816C211yesmaximal, characteristic, complemented
7C31×#1382C211yesmaximal, characteristic, complemented
8C22×D8×C31C2211yescharacteristic
9C2×C31×#131C2211yescharacteristic
10C31×#535—21no—
11C2×C31×M32C2211yescharacteristic
12C22×C16×C31C2211yescharacteristic
13C31×#469—22no—
14C31×#466—21no—
15C31×#466—21no—
16C2×C31×#108C2211yescharacteristic
17C31×#427C2211yescharacteristic
18C2×C31×#107C2211yescharacteristic
19C31×#418—21no—
20C31×#417—21no—
21C31×#367—21no—
22C31×#366—21no—
23C31×#361—22no—
24C31×#357—22no—
25C31×#350—22no—
26C31×#343—21no—
27C2×#41×C31D411yescharacteristic
28C22×D4×C31—21no—
29C2×D8×C31—21no—
30C2×D8×C31—21no—
31C2×D8×C31—21no—
32C2×D8×C31—21no—
33C2×D8×C31—21no—
34C2×D8×C31D412yes—
35C31×#131—21no—
36C31×#131—21no—
37C31×#131—21no—
38C31×#131—21no—
39C2×M16×C31—21no—
40C2×M16×C31—21no—
41C2×M16×C31D411yescharacteristic
42C22×C8×C31—21no—
43C22×C8×C31C2311yescharacteristic
44C31×#127—41no—
45C31×#124—41no—
46C31×#121—22no—
47C31×#121—22no—
48C31×#120—42no—
49C31×#117—21no—
50C2×C4⋊C4×C31—21no—
51C31×M32—21no—
52C31×M32D412yescomplemented
53C2×C16×C31—21no—
54C2×C16×C31—21no—
55C2×C16×C31—21no—
56C2×C16×C31—21no—
57C31×#108—21no—
58C31×#108—21no—
59C31×#107—21no—
60C31×#107—21no—
61C31×#107D411yescharacteristic
62C31×#107D411yescharacteristic
63C31×#106—21no—
64C31×#103—41no—
65C31×#102—22no—
66C31×#102—22no—
67C31×#102—41no—
68C24×C31—41no—
69#41×C31—21no—
70#41×C31—21no—
71#41×C31—21no—
72#41×C31—21no—
73C2×Q8×C31D811yescharacteristic
74C2×D4×C31—21no—
75C2×D4×C31—22no—
76C2×D4×C31—42no—
77C2×D4×C31—42no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—41no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31D811yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—41no—
86C22×C4×C31C2×D411yescharacteristic
87D8×C31—22no—
88D8×C31—22no—
89D8×C31—41no—
90D8×C31—41no—
91M16×C31—21no—
92M16×C31—21no—
93M16×C31—41no—
94M16×C31—41no—
95M16×C31—41no—
96M16×C31—41no—
97C2×C8×C31—21no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31C2×D411yescharacteristic
102C2×C8×C31C2×D411yescharacteristic
103C2×C8×C31C2×D411yescharacteristic
104C2×C8×C31#4111yescharacteristic
105C2×C8×C31#4111yescharacteristic
106C2×C8×C31#4111yescharacteristic
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—41no—
114C42×C31—41no—
115C16×C31—22no—
116C16×C31—41no—
117#13387C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—21no—
119C23×C31—42no—
120C23×C31—81no—
121C23×C31—81no—
122C23×C31—161no—
123C23×C31—161no—
124C23×C31AGL(1,ℤ/8)11yescharacteristic
125Q8×C31—21no—
126Q8×C31—21no—
127D4×C31—21no—
128D4×C31—21no—
129D4×C31—41no—
130D4×C31—41no—
131D4×C31—42no—
132D4×C31—42no—
133D4×C31—81no—
134D4×C31—81no—
135D4×C31—162no—
136D4×C31—162no—
137C2×C4×C31—21no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—81no—
143C2×C4×C31—161no—
144C2×C4×C31#12011yescharacteristic
145C2×C4×C31#12111yescharacteristic
146C2×C4×C31#12311yescharacteristic
147C2×C4×C31C2×D811yescharacteristic
148C2×C4×C31#13511yescharacteristic
149C2×C4×C31#13711yescharacteristic
150C8×C31—41no—
151C8×C31—81no—
152C8×C31#12111yescharacteristic
153C8×C31#12111yescharacteristic
154C8×C31#12311yescharacteristic
155C8×C31#12411yescharacteristic
156#3058C2×C3111yescharacteristic
157#2159C2×C3111yescharacteristic, complemented
158C2×#361C2×C3111yescharacteristic, complemented
159C2×#357C2×C3111yescharacteristic, complemented
160C2×#350C2×C3111yescharacteristic, complemented
161#1816C2×C3111yescharacteristic, complemented
162#1382C2×C3111yescharacteristic, complemented
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—82no—
169C22×C31—82no—
170C22×C31—82no—
171C22×C31—162no—
172C22×C31—162no—
173C22×C31#44711yescharacteristic
174C22×C31#46811yescharacteristic
175C22×C31#48211yescharacteristic
176C4×C31—41no—
177C4×C31—81no—
178C4×C31—81no—
179C4×C31—161no—
180C4×C31#39411yescharacteristic
181C4×C31#45211yescharacteristic
182C4×C31#46611yescharacteristic
183C4×C31#48011yescharacteristic
184C22×D8C22×C3111yescharacteristic
185C2×#131C22×C3111yescharacteristic
186#535—21no—
187C2×M32C22×C3111yescharacteristic
188C22×C16C22×C3111yescharacteristic
189#469—22no—
190#466—21no—
191#466—21no—
192C2×#108C22×C3111yescharacteristic
193#427C22×C3111yescharacteristic
194C2×#107C22×C3111yescharacteristic
195#418—21no—
196#417—21no—
197#367—21no—
198#366—21no—
199#361—22no—
200#357—22no—
201#350—22no—
202#343—21no—
203C2×C31—21no—
204C2×C31—21no—
205C2×C31—81no—
206C2×C31—162no—
207C2×C31#203311yescharacteristic
208C2×C31#219211yescharacteristic
209C2×C31#219411yescharacteristic
210C2×#41D4×C3111yescharacteristic
211C22×D4—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8D4×C3112yes—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16D4×C3111yescharacteristic
225C22×C8—21no—
226C22×C8C23×C3111yescharacteristic
227#127—41no—
228#124—41no—
229#121—22no—
230#121—22no—
231#120—42no—
232#117—21no—
233C2×C4⋊C4—21no—
234M32—21no—
235M32D4×C3112yescomplemented
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240#108—21no—
241#108—21no—
242#107—21no—
243#107—21no—
244#107D4×C3111yescharacteristic
245#107D4×C3111yescharacteristic
246#106—21no—
247#103—41no—
248#102—22no—
249#102—22no—
250#102—41no—
251C31#1338711yescharacteristic, direct product factor, Sylow
252C24—41no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257C2×Q8D8×C3111yescharacteristic
258C2×D4—21no—
259C2×D4—22no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4D8×C3111yescharacteristic
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C2×D4×C3111yescharacteristic
271D8—22no—
272D8—22no—
273D8—41no—
274D8—41no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8C2×D4×C3111yescharacteristic
286C2×C8C2×D4×C3111yescharacteristic
287C2×C8C2×D4×C3111yescharacteristic
288C2×C8#41×C3111yescharacteristic
289C2×C8#41×C3111yescharacteristic
290C2×C8#41×C3111yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C42—41no—
299C16—22no—
300C16—41no—
301C23—21no—
302C23—42no—
303C23—81no—
304C23—81no—
305C23—161no—
306C23—161no—
307C23C31×AGL(1,ℤ/8)11yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318D4—162no—
319D4—162no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—161no—
327C2×C4C31×#12011yescharacteristic
328C2×C4C31×#12111yescharacteristic
329C2×C4C31×#12311yescharacteristic
330C2×C4C2×D8×C3111yescharacteristic
331C2×C4C31×#13511yescharacteristic
332C2×C4C31×#13711yescharacteristic
333C8—41no—
334C8—81no—
335C8C31×#12111yescharacteristic
336C8C31×#12111yescharacteristic
337C8C31×#12311yescharacteristic
338C8C31×#12411yescharacteristic
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—82no—
345C22—82no—
346C22—82no—
347C22—162no—
348C22—162no—
349C22C31×#44711yescharacteristic
350C22C31×#46811yescharacteristic
351C22C31×#48211yescharacteristic
352C4—41no—
353C4—81no—
354C4—81no—
355C4—161no—
356C4C31×#39411yescharacteristic
357C4C31×#45211yescharacteristic
358C4C31×#46611yescharacteristic
359C4C31×#48011yescharacteristic
360C2—21no—
361C2—21no—
362C2—81no—
363C2—162no—
364C2C31×#203311yescharacteristic
365C2C31×#219211yescharacteristic
366C2C31×#219411yescharacteristic
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC31×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#2159C2semidirect
3. C2×C31×#361C2semidirect
4. C2×C31×#357C2semidirect
5. C2×C31×#350C2semidirect
6. C31×#1816C2semidirect
7. C31×#1382C2semidirect
52. C31×M32D4semidirect
117. #13387C31direct (N × H)
157. #2159C2×C31semidirect
158. C2×#361C2×C31semidirect
159. C2×#357C2×C31semidirect
160. C2×#350C2×C31semidirect
161. #1816C2×C31semidirect
162. #1382C2×C31semidirect
235. M32D4×C31semidirect
251. C31#13387direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30582
C31×#21592
C2×C31×#3612
C2×C31×#3572
C2×C31×#3502
C31×#18162
C31×#13822
#1338731