Finite Group Databasebeta

← C31×#7606 #21464365

Subgroups — C31×#7606 #21464365

Order 7936.

892 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic, complemented
3C31×#1728C211yesmaximal, characteristic, complemented
4C31×#1270C214yesmaximal, complemented
5C23×D4×C31C411yescharacteristic
6C22×M16×C31—21no—
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C22⋊C4×C31—21no—
9C22×C22⋊C4×C31—21no—
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8—21no—
12C31×#390—21no—
13C31×#390—21no—
14C31×#390C412yes—
15C31×#390C2212yes—
16C31×#336—21no—
17C31×#336—21no—
18C31×#336C2212yescomplemented
19C31×#336C2212yescomplemented
20C25×C31—21no—
21C22×D4×C31—24no—
22C22×D4×C31—21no—
23C22×D4×C31—42no—
24C22×D4×C31—42no—
25C22×D4×C31C2×C412yes—
26C23×C4×C31—21no—
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C2×M16×C31—24no—
31C2×M16×C31—42no—
32C2×M16×C31—42no—
33C22×C8×C31—22no—
34C22×C8×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—42no—
37C2×C4⋊C4×C31C2×C412yes—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—44no—
43C2×C22⋊C4×C31—42no—
44C2×C22⋊C4×C31—42no—
45C2×C42×C31—42no—
46C2×C42×C31C2×C411yescharacteristic
47C2×C42×C31D411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31C2311yescharacteristic
50C31×C22⋊C8—42no—
51C24×C31—24no—
52C24×C31—22no—
53C24×C31—42no—
54C24×C31—42no—
55C24×C31—42no—
56C24×C31—42no—
57C24×C31—42no—
58C24×C31—42no—
59C24×C31C22⋊C411yescharacteristic
60C2×D4×C31—24no—
61C2×D4×C31—22no—
62C2×D4×C31—416no—
63C2×D4×C31—42no—
64C2×D4×C31—42no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31M1614yescomplemented
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—41no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31D812yes—
84C22×C4×C31SD1612yes—
85C22×C4×C31C22×C411yescharacteristic
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88M16×C31—48no—
89C2×C8×C31—24no—
90C2×C8×C31—42no—
91C2×C8×C31—42no—
92C2×C8×C31—42no—
93C2×C8×C31—42no—
94C2×C8×C31—42no—
95C4⋊C4×C31—42no—
96C4⋊C4×C31—42no—
97C22⋊C4×C31—44no—
98C22⋊C4×C31—44no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—44no—
102C42×C31—41no—
103C42×C31—41no—
104C42×C31—41no—
105C42×C31—41no—
106#7606C3111yesmaximal, characteristic, direct product factor, Sylow
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—24no—
112C23×C31—48no—
113C23×C31—48no—
114C23×C31—48no—
115C23×C31—42no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—84no—
122C23×C31—84no—
123C23×C31—84no—
124C23×C31—84no—
125C23×C31#9912yes—
126C23×C31#10212yes—
127C23×C31#10412yes—
128C23×C31C2×C22⋊C411yescharacteristic
129D4×C31—44no—
130D4×C31—48no—
131D4×C31—44no—
132C2×C4×C31—28no—
133C2×C4×C31—24no—
134C2×C4×C31—24no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—44no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—84no—
153C2×C4×C31#10012yes—
154C2×C4×C31#10212yes—
155C2×C4×C31C2×M1612yes—
156C2×C4×C31C2×D811yescharacteristic
157C2×C4×C31C2×SD1611yescharacteristic
158C2×C4×C31AGL(1,ℤ/8)12yes—
159C8×C31—44no—
160C8×C31—82no—
161C2×#390C2×C3111yescharacteristic
162#1817C2×C3111yescharacteristic, complemented
163#1728C2×C3111yescharacteristic, complemented
164#1270C2×C3114yescomplemented
165C22×C31—22no—
166C22×C31—22no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—44no—
172C22×C31—44no—
173C22×C31—44no—
174C22×C31—816no—
175C22×C31—82no—
176C22×C31—82no—
177C22×C31—82no—
178C22×C31—82no—
179C22×C31#32714yes—
180C22×C31#40711yescharacteristic
181C22×C31C2×#9911yescharacteristic
182C22×C31C2×#10011yescharacteristic
183C22×C31C2×#10211yescharacteristic
184C22×C31#41811yescharacteristic
185C22×C31C2×#10411yescharacteristic
186C22×C31#42111yescharacteristic
187C4×C31—22no—
188C4×C31—22no—
189C4×C31—21no—
190C4×C31—22no—
191C4×C31—21no—
192C4×C31—22no—
193C4×C31—41no—
194C4×C31—82no—
195C23×D4C4×C3111yescharacteristic
196C22×M16—21no—
197C22×C4⋊C4C4×C3111yescharacteristic
198C22×C22⋊C4—21no—
199C22×C22⋊C4—21no—
200C22×C42C22×C3111yescharacteristic
201C2×C22⋊C8—21no—
202#390—21no—
203#390—21no—
204#390C4×C3112yes—
205#390C22×C3112yes—
206#336—21no—
207#336—21no—
208#336C22×C3112yescomplemented
209#336C22×C3112yescomplemented
210C2×C31—24no—
211C2×C31—84no—
212C2×C31#146211yescharacteristic
213C2×C31#148611yescharacteristic
214C2×C31#149011yescharacteristic
215C2×C31C2×#32711yescharacteristic
216C2×C31#151011yescharacteristic
217C2×C31#152711yescharacteristic
218C2×C31#154511yescharacteristic
219C25—21no—
220C22×D4—24no—
221C22×D4—21no—
222C22×D4—42no—
223C22×D4—42no—
224C22×D4C2×C4×C3112yes—
225C23×C4—21no—
226C23×C4C2×C4×C3111yescharacteristic
227C23×C4D4×C3111yescharacteristic
228C23×C4D4×C3111yescharacteristic
229C2×M16—24no—
230C2×M16—42no—
231C2×M16—42no—
232C22×C8—22no—
233C22×C8—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4C2×C4×C3112yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4—42no—
244C2×C42—42no—
245C2×C42C2×C4×C3111yescharacteristic
246C2×C42D4×C3111yescharacteristic
247C2×C42D4×C3111yescharacteristic
248C2×C42C23×C3111yescharacteristic
249C22⋊C8—42no—
250C31#760611yescharacteristic, direct product factor, Sylow
251C24—24no—
252C24—22no—
253C24—42no—
254C24—42no—
255C24—42no—
256C24—42no—
257C24—42no—
258C24—42no—
259C24C22⋊C4×C3111yescharacteristic
260C2×D4—24no—
261C2×D4—22no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—416no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4M16×C3114yescomplemented
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4C22⋊C4×C3111yescharacteristic
281C22×C4C22⋊C4×C3111yescharacteristic
282C22×C4C22⋊C4×C3111yescharacteristic
283C22×C4D8×C3112yes—
284C22×C4SD16×C3112yes—
285C22×C4C22×C4×C3111yescharacteristic
286C22×C4C2×D4×C3111yescharacteristic
287C22×C4C2×D4×C3111yescharacteristic
288M16—48no—
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—44no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—24no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—84no—
321C23—84no—
322C23—84no—
323C23—84no—
324C23C31×#9912yes—
325C23C31×#10212yes—
326C23C31×#10412yes—
327C23C2×C22⋊C4×C3111yescharacteristic
328D4—44no—
329D4—48no—
330D4—44no—
331C2×C4—28no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—84no—
352C2×C4C31×#10012yes—
353C2×C4C31×#10212yes—
354C2×C4C2×M16×C3112yes—
355C2×C4C2×D8×C3111yescharacteristic
356C2×C4C2×SD16×C3111yescharacteristic
357C2×C4C31×AGL(1,ℤ/8)12yes—
358C8—44no—
359C8—82no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—44no—
367C22—44no—
368C22—44no—
369C22—816no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22C31×#32714yes—
375C22C31×#40711yescharacteristic
376C22C2×C31×#9911yescharacteristic
377C22C2×C31×#10011yescharacteristic
378C22C2×C31×#10211yescharacteristic
379C22C31×#41811yescharacteristic
380C22C2×C31×#10411yescharacteristic
381C22C31×#42111yescharacteristic
382C4—22no—
383C4—22no—
384C4—21no—
385C4—22no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—82no—
390C2—24no—
391C2—84no—
392C2C31×#146211yescharacteristic
393C2C31×#148611yescharacteristic
394C2C31×#149011yescharacteristic
395C2C2×C31×#32711yescharacteristic
396C2C31×#151011yescharacteristic
397C2C31×#152711yescharacteristic
398C2C31×#154511yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×D4×C31C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1817C2semidirect
3. C31×#1728C2semidirect
4. C31×#1270C2semidirect
18. C31×#336C22semidirect
19. C31×#336C22semidirect
67. C2×D4×C31M16semidirect
106. #7606C31direct (N × H)
162. #1817C2×C31semidirect
163. #1728C2×C31semidirect
164. #1270C2×C31semidirect
208. #336C22×C31semidirect
209. #336C22×C31semidirect
250. C31#7606direct (N × H)
267. C2×D4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C31×#18172
C31×#17282
C31×#12702
#760631