Finite Group Databasebeta

← C31×#15171 #21471930

Subgroups — C31×#15171 #21471930

Order 7936.

1302 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#401C211yesmaximal, characteristic, complemented
2C2×C31×#396C211yesmaximal, characteristic
3C31×#1442C213yesmaximal, complemented
4C31×#1440C213yesmaximal
5C31×#1437C213yesmaximal
6C31×#1436C213yesmaximal, complemented
7C4×C31×#95C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C31C2213yes—
9C22×C22⋊C4×C31C2211yescharacteristic
10C22×C22⋊C4×C31C2213yes—
11C22×C22⋊C4×C31C2213yes—
12C22×C42×C31C2213yes—
13C31×#401—24no—
14C31×#396—24no—
15C2×C31×#95C2213yes—
16C2×C31×#95C2213yes—
17C2×C31×#95C2213yes—
18C2×C31×#95C2213yes—
19C2×C31×#95C2213yes—
20C2×C31×#95C2213yes—
21C2×C31×#95C2213yes—
22C2×C31×#95C2211yescharacteristic
23C25×C31C2311yescharacteristic
24C23×C4×C31C2311yescharacteristic
25C23×C4×C31C2313yes—
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—43no—
33C2×C22⋊C4×C31—26no—
34C2×C22⋊C4×C31—26no—
35C2×C22⋊C4×C31—26no—
36C2×C22⋊C4×C31—26no—
37C2×C22⋊C4×C31—26no—
38C2×C22⋊C4×C31—43no—
39C2×C22⋊C4×C31—43no—
40C2×C42×C31—26no—
41C2×C42×C31—43no—
42C2×C42×C31—43no—
43C31×#95—26no—
44C31×#95—26no—
45C31×#95—26no—
46C31×#95—26no—
47C31×#95—26no—
48C31×#95—26no—
49C31×#95—43no—
50C31×#95D414yes—
51C24×C31—21no—
52C24×C31—23no—
53C24×C31—23no—
54C24×C31—23no—
55C24×C31—23no—
56C24×C31—21no—
57C24×C31#4112yes—
58C24×C31C2411yescharacteristic
59C22×C4×C31—23no—
60C22×C4×C31—21no—
61C22×C4×C31—23no—
62C22×C4×C31—23no—
63C22×C4×C31—23no—
64C22×C4×C31—23no—
65C22×C4×C31—23no—
66C22×C4×C31—23no—
67C22×C4×C31—23no—
68C22×C4×C31—23no—
69C22×C4×C31—23no—
70C22×C4×C31—23no—
71C22×C4×C31—23no—
72C22×C4×C31—23no—
73C22×C4×C31—23no—
74C22×C4×C31—23no—
75C22×C4×C31—23no—
76C22×C4×C31—23no—
77C22×C4×C31—23no—
78C22×C4×C31—23no—
79C22×C4×C31—21no—
80C22×C4×C31—23no—
81C22×C4×C31—23no—
82C22×C4×C31—23no—
83C22×C4×C31—23no—
84C22×C4×C31—23no—
85C22×C4×C31—23no—
86C22×C4×C31—23no—
87C22×C4×C31—23no—
88C22×C4×C31—23no—
89C22×C4×C31C2×D416yes—
90C22×C4×C31#4116yes—
91C22×C4×C31#4116yes—
92C22×C4×C31#4116yes—
93C4⋊C4×C31—412no—
94C22⋊C4×C31—412no—
95C22⋊C4×C31—412no—
96C22⋊C4×C31—44no—
97C42×C31—412no—
98#15171C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31—26no—
100C23×C31—22no—
101C23×C31—26no—
102C23×C31—41no—
103C23×C31—43no—
104C23×C31—43no—
105C23×C31—43no—
106C23×C31—43no—
107C23×C31—43no—
108C23×C31—43no—
109C23×C31—43no—
110C23×C31—43no—
111C23×C31—43no—
112C23×C31C22×D411yescharacteristic
113C23×C31C2×#4113yes—
114C23×C31C2×#4113yes—
115C23×C31C2×#4111yescharacteristic
116C23×C31C2×#4113yes—
117C23×C31H(5,𝔽2)13yes—
118C23×C312−1+411yescharacteristic
119C2×C4×C31—26no—
120C2×C4×C31—26no—
121C2×C4×C31—26no—
122C2×C4×C31—26no—
123C2×C4×C31—26no—
124C2×C4×C31—26no—
125C2×C4×C31—26no—
126C2×C4×C31—26no—
127C2×C4×C31—26no—
128C2×C4×C31—26no—
129C2×C4×C31—26no—
130C2×C4×C31—43no—
131C2×C4×C31—43no—
132C2×C4×C31—43no—
133C2×C4×C31—43no—
134C2×C4×C31—43no—
135C2×C4×C31—43no—
136C2×C4×C31—43no—
137C2×C4×C31—43no—
138C2×C4×C31—43no—
139C2×C4×C31—43no—
140C2×C4×C31—43no—
141C2×C4×C31—43no—
142C2×C4×C31—41no—
143C2×C4×C31—43no—
144C2×C4×C31—43no—
145C2×C4×C31—43no—
146C2×C4×C31—43no—
147C2×C4×C31—43no—
148C2×C4×C31—43no—
149C2×C4×C31—43no—
150C2×C4×C31—43no—
151C2×C4×C31—43no—
152C2×C4×C31#12614yes—
153C2×#401C2×C3111yescharacteristic, complemented
154C2×#396C2×C3111yescharacteristic
155#1442C2×C3113yescomplemented
156#1440C2×C3113yes—
157#1437C2×C3113yes—
158#1436C2×C3113yescomplemented
159C4×#95C2×C3111yescharacteristic, complemented
160C22×C31—46no—
161C22×C31—46no—
162C22×C31—42no—
163C22×C31—83no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—83no—
167C22×C31C2×#12611yescharacteristic
168C22×C31#52913yes—
169C22×C31#52913yes—
170C22×C31#52913yes—
171C22×C31#53213yes—
172C22×C31#53813yes—
173C22×C31#53913yes—
174C22×C31#54613yes—
175C22×C31#54811yescharacteristic
176C22×C31#55113yes—
177C22×C31#55313yes—
178C22×C31#55313yes—
179C22×C31#55613yes—
180C4×C31—24no—
181C4×C31—46no—
182C4×C31—46no—
183C4×C31—46no—
184C4×C31—83no—
185C4×C31—81no—
186C22×C4⋊C4C22×C3113yes—
187C22×C22⋊C4C22×C3111yescharacteristic
188C22×C22⋊C4C22×C3113yes—
189C22×C22⋊C4C22×C3113yes—
190C22×C42C22×C3113yes—
191#401—24no—
192#396—24no—
193C2×#95C22×C3113yes—
194C2×#95C22×C3113yes—
195C2×#95C22×C3113yes—
196C2×#95C22×C3113yes—
197C2×#95C22×C3113yes—
198C2×#95C22×C3113yes—
199C2×#95C22×C3113yes—
200C2×#95C22×C3111yescharacteristic
201C2×C31—82no—
202C2×C31#240111yescharacteristic
203C2×C31#255913yes—
204C2×C31#256013yes—
205C2×C31#257613yes—
206C2×C31#259413yes—
207C2×C31#264311yescharacteristic
208C2×C31#286011yescharacteristic
209C25C23×C3111yescharacteristic
210C23×C4C23×C3111yescharacteristic
211C23×C4C23×C3113yes—
212C23×C4C23×C3113yes—
213C23×C4C23×C3113yes—
214C23×C4C23×C3113yes—
215C23×C4C23×C3111yescharacteristic
216C2×C4⋊C4—26no—
217C2×C4⋊C4—26no—
218C2×C4⋊C4—43no—
219C2×C22⋊C4—26no—
220C2×C22⋊C4—26no—
221C2×C22⋊C4—26no—
222C2×C22⋊C4—26no—
223C2×C22⋊C4—26no—
224C2×C22⋊C4—43no—
225C2×C22⋊C4—43no—
226C2×C42—26no—
227C2×C42—43no—
228C2×C42—43no—
229#95—26no—
230#95—26no—
231#95—26no—
232#95—26no—
233#95—26no—
234#95—26no—
235#95—43no—
236#95D4×C3114yes—
237C31#1517111yescharacteristic, direct product factor, Sylow
238C24—21no—
239C24—23no—
240C24—23no—
241C24—23no—
242C24—23no—
243C24—21no—
244C24#41×C3112yes—
245C24C24×C3111yescharacteristic
246C22×C4—23no—
247C22×C4—21no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—21no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4C2×D4×C3116yes—
277C22×C4#41×C3116yes—
278C22×C4#41×C3116yes—
279C22×C4#41×C3116yes—
280C4⋊C4—412no—
281C22⋊C4—412no—
282C22⋊C4—412no—
283C22⋊C4—44no—
284C42—412no—
285C23—26no—
286C23—22no—
287C23—26no—
288C23—41no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23—43no—
297C23—43no—
298C23C22×D4×C3111yescharacteristic
299C23C2×#41×C3113yes—
300C23C2×#41×C3113yes—
301C23C2×#41×C3111yescharacteristic
302C23C2×#41×C3113yes—
303C23C31×H(5,𝔽2)13yes—
304C23C31×2−1+411yescharacteristic
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—41no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4C31×#12614yes—
339C22—46no—
340C22—42no—
341C22—46no—
342C22—83no—
343C22—81no—
344C22—81no—
345C22—83no—
346C22C2×C31×#12611yescharacteristic
347C22C31×#52913yes—
348C22C31×#52913yes—
349C22C31×#52913yes—
350C22C31×#53213yes—
351C22C31×#53813yes—
352C22C31×#53913yes—
353C22C31×#54613yes—
354C22C31×#54811yescharacteristic
355C22C31×#55113yes—
356C22C31×#55313yes—
357C22C31×#55313yes—
358C22C31×#55613yes—
359C4—24no—
360C4—46no—
361C4—46no—
362C4—46no—
363C4—81no—
364C4—83no—
365C2—82no—
366C2C31×#240111yescharacteristic
367C2C31×#255913yes—
368C2C31×#256013yes—
369C2C31×#257613yes—
370C2C31×#259413yes—
371C2C31×#264311yescharacteristic
372C2C31×#286011yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#401C2semidirect
3. C31×#1442C2semidirect
6. C31×#1436C2semidirect
7. C4×C31×#95C2semidirect
98. #15171C31direct (N × H)
153. C2×#401C2×C31semidirect
155. #1442C2×C31semidirect
158. #1436C2×C31semidirect
159. C4×#95C2×C31semidirect
237. C31#15171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4012
C2×C31×#3962
C31×#14422
C31×#14402
C31×#14372
C31×#14362
C4×C31×#952
#1517131