Finite Group Databasebeta

← C31×#14322 #21471081

Subgroups — C31×#14322 #21471081

Order 7936.

1590 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
1C2×C31×#399C211yesmaximal, characteristic
2C2×C31×#389C213yesmaximal, complemented
3C2×C31×#388C213yesmaximal
4C31×#1445C213yesmaximal, complemented
5C31×#1444C211yesmaximal, characteristic, complemented
6C31×#1439C213yesmaximal
7C4×C31×#95C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C31C2213yes—
9C22×C4⋊C4×C31C2213yes—
10C22×C4⋊C4×C31C2213yes—
11C22×C22⋊C4×C31C2211yescharacteristic
12C22×C22⋊C4×C31C2213yes—
13C22×C22⋊C4×C31C2213yes—
14C22×C42×C31C2213yes—
15C31×#399C418yescomplemented
16C31×#389—212no—
17C31×#388—212no—
18C2×C31×#95C2213yes—
19C2×C31×#95C2216yes—
20C2×C31×#95C2213yes—
21C2×C31×#95C2213yes—
22C2×C31×#95C2211yescharacteristic
23C25×C31C2311yescharacteristic
24C23×C4×C31C2313yes—
25C23×C4×C31C2311yescharacteristic
26C23×C4×C31C2313yes—
27C23×C4×C31C2313yes—
28C23×C4×C31C2313yes—
29C23×C4×C31C2311yescharacteristic
30C2×C4⋊C4×C31—26no—
31C2×C4⋊C4×C31—26no—
32C2×C4⋊C4×C31—26no—
33C2×C4⋊C4×C31—26no—
34C2×C4⋊C4×C31—212no—
35C2×C4⋊C4×C31—46no—
36C2×C4⋊C4×C31C2×C4112yes—
37C2×C22⋊C4×C31—26no—
38C2×C22⋊C4×C31—26no—
39C2×C22⋊C4×C31—26no—
40C2×C22⋊C4×C31—26no—
41C2×C22⋊C4×C31—46no—
42C2×C22⋊C4×C31C2×C4112yes—
43C2×C42×C31—46no—
44C2×C42×C31D4112yes—
45C31×#95—26no—
46C31×#95—26no—
47C31×#95—212no—
48C31×#95—26no—
49C31×#95C2×C414yes—
50C24×C31—23no—
51C24×C31—23no—
52C24×C31—23no—
53C24×C31—21no—
54C24×C31—21no—
55C24×C31—23no—
56C24×C31C22×C412yes—
57C24×C31C2411yescharacteristic
58C22×C4×C31—23no—
59C22×C4×C31—26no—
60C22×C4×C31—26no—
61C22×C4×C31—21no—
62C22×C4×C31—23no—
63C22×C4×C31—26no—
64C22×C4×C31—26no—
65C22×C4×C31—23no—
66C22×C4×C31—26no—
67C22×C4×C31—26no—
68C22×C4×C31—23no—
69C22×C4×C31—23no—
70C22×C4×C31—23no—
71C22×C4×C31—23no—
72C22×C4×C31—26no—
73C22×C4×C31—26no—
74C22×C4×C31—23no—
75C22×C4×C31—21no—
76C22×C4×C31—23no—
77C22×C4×C31—23no—
78C22×C4×C31C22×C416yes—
79C22×C4×C31C22×C416yes—
80C22×C4×C31C2×D416yes—
81C22×C4×C31C2×D416yes—
82C22×C4×C31C2×D416yes—
83C22×C4×C31#4116yes—
84C4⋊C4×C31—224no—
85C4⋊C4×C31—412no—
86C4⋊C4×C31—412no—
87C22⋊C4×C31—224no—
88C22⋊C4×C31—412no—
89C22⋊C4×C31—44no—
90C42×C31—412no—
91#14322C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—26no—
93C23×C31—22no—
94C23×C31—26no—
95C23×C31—41no—
96C23×C31—43no—
97C23×C31—43no—
98C23×C31—43no—
99C23×C31—43no—
100C23×C31—43no—
101C23×C31—46no—
102C23×C31—43no—
103C23×C31—43no—
104C23×C31C23×C411yescharacteristic
105C23×C31C22×D413yes—
106C23×C31C2×#4113yes—
107C23×C31H(5,𝔽2)13yes—
108C23×C312−1+411yescharacteristic
109C23×C312−1+411yescharacteristic
110C23×C312−1+413yes—
111C2×C4×C31—212no—
112C2×C4×C31—26no—
113C2×C4×C31—26no—
114C2×C4×C31—26no—
115C2×C4×C31—26no—
116C2×C4×C31—212no—
117C2×C4×C31—26no—
118C2×C4×C31—212no—
119C2×C4×C31—26no—
120C2×C4×C31—26no—
121C2×C4×C31—26no—
122C2×C4×C31—43no—
123C2×C4×C31—43no—
124C2×C4×C31—46no—
125C2×C4×C31—46no—
126C2×C4×C31—46no—
127C2×C4×C31—41no—
128C2×C4×C31—43no—
129C2×C4×C31—43no—
130C2×C4×C31—46no—
131C2×C4×C31—43no—
132C2×C4×C31—43no—
133C2×C4×C31—43no—
134C2×C4×C31—46no—
135C2×C4×C31C4×D4112yes—
136C2×C4×C31#12714yes—
137C2×#399C2×C3111yescharacteristic
138C2×#389C2×C3113yescomplemented
139C2×#388C2×C3113yes—
140#1445C2×C3113yescomplemented
141#1444C2×C3111yescharacteristic, complemented
142#1439C2×C3113yes—
143C4×#95C2×C3111yescharacteristic, complemented
144C22×C31—42no—
145C22×C31—46no—
146C22×C31—46no—
147C22×C31—81no—
148C22×C31—81no—
149C22×C31—83no—
150C22×C31—83no—
151C22×C31C2×C4×D413yes—
152C22×C31#51911yescharacteristic
153C22×C31#52013yes—
154C22×C31C2×#12711yescharacteristic
155C22×C31#53213yes—
156C22×C31#53413yes—
157C22×C31#53613yes—
158C22×C31#53613yes—
159C22×C31#53713yes—
160C22×C31#53916yes—
161C22×C31#54113yes—
162C22×C31#54213yes—
163C4×C31—212no—
164C4×C31—24no—
165C4×C31—46no—
166C4×C31—46no—
167C4×C31—83no—
168C4×C31—81no—
169C22×C4⋊C4C22×C3113yes—
170C22×C4⋊C4C22×C3113yes—
171C22×C4⋊C4C22×C3113yes—
172C22×C22⋊C4C22×C3111yescharacteristic
173C22×C22⋊C4C22×C3113yes—
174C22×C22⋊C4C22×C3113yes—
175C22×C42C22×C3113yes—
176#399C4×C3118yescomplemented
177#389—212no—
178#388—212no—
179C2×#95C22×C3113yes—
180C2×#95C22×C3116yes—
181C2×#95C22×C3113yes—
182C2×#95C22×C3113yes—
183C2×#95C22×C3111yescharacteristic
184C2×C31—82no—
185C2×C31C4×#12711yescharacteristic
186C2×C31#232213yes—
187C2×C31#232313yes—
188C2×C31#265611yescharacteristic
189C2×C31#265811yescharacteristic
190C2×C31#266313yes—
191C2×C31#266413yes—
192C25C23×C3111yescharacteristic
193C23×C4C23×C3113yes—
194C23×C4C23×C3111yescharacteristic
195C23×C4C23×C3113yes—
196C23×C4C23×C3113yes—
197C23×C4C23×C3113yes—
198C23×C4C23×C3111yescharacteristic
199C2×C4⋊C4—26no—
200C2×C4⋊C4—26no—
201C2×C4⋊C4—26no—
202C2×C4⋊C4—26no—
203C2×C4⋊C4—212no—
204C2×C4⋊C4—46no—
205C2×C4⋊C4C2×C4×C31112yes—
206C2×C22⋊C4—26no—
207C2×C22⋊C4—26no—
208C2×C22⋊C4—26no—
209C2×C22⋊C4—26no—
210C2×C22⋊C4—46no—
211C2×C22⋊C4C2×C4×C31112yes—
212C2×C42—46no—
213C2×C42D4×C31112yes—
214#95—26no—
215#95—26no—
216#95—212no—
217#95—26no—
218#95C2×C4×C3114yes—
219C31#1432211yescharacteristic, direct product factor, Sylow
220C24—23no—
221C24—23no—
222C24—23no—
223C24—21no—
224C24—21no—
225C24—23no—
226C24C22×C4×C3112yes—
227C24C24×C3111yescharacteristic
228C22×C4—23no—
229C22×C4—26no—
230C22×C4—26no—
231C22×C4—21no—
232C22×C4—23no—
233C22×C4—26no—
234C22×C4—26no—
235C22×C4—23no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—23no—
242C22×C4—26no—
243C22×C4—26no—
244C22×C4—23no—
245C22×C4—21no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4C22×C4×C3116yes—
249C22×C4C22×C4×C3116yes—
250C22×C4C2×D4×C3116yes—
251C22×C4C2×D4×C3116yes—
252C22×C4C2×D4×C3116yes—
253C22×C4#41×C3116yes—
254C4⋊C4—224no—
255C4⋊C4—412no—
256C4⋊C4—412no—
257C22⋊C4—224no—
258C22⋊C4—412no—
259C22⋊C4—44no—
260C42—412no—
261C23—26no—
262C23—22no—
263C23—26no—
264C23—41no—
265C23—43no—
266C23—43no—
267C23—43no—
268C23—43no—
269C23—43no—
270C23—46no—
271C23—43no—
272C23—43no—
273C23C23×C4×C3111yescharacteristic
274C23C22×D4×C3113yes—
275C23C2×#41×C3113yes—
276C23C31×H(5,𝔽2)13yes—
277C23C31×2−1+411yescharacteristic
278C23C31×2−1+411yescharacteristic
279C23C31×2−1+413yes—
280C2×C4—212no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—26no—
285C2×C4—212no—
286C2×C4—26no—
287C2×C4—212no—
288C2×C4—26no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—43no—
292C2×C4—43no—
293C2×C4—46no—
294C2×C4—46no—
295C2×C4—46no—
296C2×C4—41no—
297C2×C4—43no—
298C2×C4—43no—
299C2×C4—46no—
300C2×C4—43no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—46no—
304C2×C4C4×D4×C31112yes—
305C2×C4C31×#12714yes—
306C22—46no—
307C22—46no—
308C22—42no—
309C22—81no—
310C22—81no—
311C22—83no—
312C22—83no—
313C22C2×C4×D4×C3113yes—
314C22C31×#51911yescharacteristic
315C22C31×#52013yes—
316C22C2×C31×#12711yescharacteristic
317C22C31×#53213yes—
318C22C31×#53413yes—
319C22C31×#53613yes—
320C22C31×#53613yes—
321C22C31×#53713yes—
322C22C31×#53916yes—
323C22C31×#54113yes—
324C22C31×#54213yes—
325C4—212no—
326C4—24no—
327C4—46no—
328C4—46no—
329C4—83no—
330C4—81no—
331C2—82no—
332C2C4×C31×#12711yescharacteristic
333C2C31×#232213yes—
334C2C31×#232313yes—
335C2C31×#265611yescharacteristic
336C2C31×#265811yescharacteristic
337C2C31×#266313yes—
338C2C31×#266413yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
4. C31×#1445C2semidirect
5. C31×#1444C2semidirect
7. C4×C31×#95C2semidirect
15. C31×#399C4semidirect
91. #14322C31direct (N × H)
138. C2×#389C2×C31semidirect
140. #1445C2×C31semidirect
141. #1444C2×C31semidirect
143. C4×#95C2×C31semidirect
176. #399C4×C31semidirect
219. C31#14322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3992
C2×C31×#3892
C2×C31×#3882
C31×#14452
C31×#14442
C31×#14392
C4×C31×#952
#1432231