Finite Group Databasebeta

← C31×#9025 #21465784

Subgroups — C31×#9025 #21465784

Order 7936.

768 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic
3C31×#1823C212yesmaximal, complemented
4C2×C31×#323C211yesmaximal, characteristic
5C31×#1294C212yesmaximal, complemented
6C22×C4⋊C4×C31C2211yescharacteristic
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31—21no—
9C22×C22⋊C4×C31C2211yescharacteristic
10C2×C31×C22⋊C8C2212yes—
11C31×#397—22no—
12C31×#397C414yescomplemented
13C31×#385—24no—
14C31×#380—21no—
15C31×#380C2212yes—
16C2×C31×#95—21no—
17C2×C31×#95C2211yescharacteristic
18C31×#340—24no—
19C31×#323—22no—
20C25×C31D411yescharacteristic
21C23×C4×C31—21no—
22C23×C4×C31—21no—
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31C2×C412yescomplemented
32C2×C4⋊C4×C31D414yes—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—24no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—42no—
39C2×C22⋊C4×C31—42no—
40C2×C22⋊C4×C31—42no—
41C2×C22⋊C4×C31—42no—
42C2×C22⋊C4×C31C2×C412yes—
43C2×C22⋊C4×C31D412yes—
44C31×C22⋊C8—22no—
45C31×C22⋊C8—22no—
46C31×#95—22no—
47C31×#95—24no—
48C31×#95—21no—
49C31×#95—22no—
50C31×#95C2×C412yescomplemented
51C24×C31—21no—
52C24×C31—21no—
53C24×C31—21no—
54C24×C31—21no—
55C24×C31—42no—
56C24×C31—42no—
57C24×C31C22⋊C412yes—
58C24×C31D812yes—
59C24×C31SD1612yes—
60C24×C31C2×D411yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—24no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—44no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—82no—
80C22×C4×C31—82no—
81C22×C4×C31C22⋊C412yes—
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D412yes—
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31#4112yes—
86C2×C8×C31—44no—
87C2×C8×C31—42no—
88C4⋊C4×C31—24no—
89C4⋊C4×C31—44no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—82no—
92C22⋊C4×C31—24no—
93C22⋊C4×C31—24no—
94C22⋊C4×C31—44no—
95C22⋊C4×C31—48no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98#9025C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31—22no—
100C23×C31—22no—
101C23×C31—22no—
102C23×C31—22no—
103C23×C31—22no—
104C23×C31—22no—
105C23×C31—22no—
106C23×C31—22no—
107C23×C31—42no—
108C23×C31—42no—
109C23×C31—44no—
110C23×C31—44no—
111C23×C31—42no—
112C23×C31—42no—
113C23×C31—82no—
114C23×C31—82no—
115C23×C31—81no—
116C23×C31—81no—
117C23×C31#10214yes—
118C23×C31C2×C22⋊C411yescharacteristic
119C23×C31#12011yescharacteristic
120C23×C31#12311yescharacteristic
121C23×C31C2×D811yescharacteristic
122C23×C31C2×SD1611yescharacteristic
123C23×C31AGL(1,ℤ/8)11yescharacteristic
124C23×C31#13711yescharacteristic
125C2×C4×C31—24no—
126C2×C4×C31—22no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—44no—
139C2×C4×C31—44no—
140C2×C4×C31—44no—
141C2×C4×C31—81no—
142C2×C4×C31—82no—
143C2×C4×C31—82no—
144C2×C4×C31—88no—
145C2×C4×C31—81no—
146C2×C4×C31—81no—
147C2×C4×C31—81no—
148C2×C4×C31—81no—
149C2×C4×C31C4×D412yes—
150C2×C4×C31#12112yes—
151C8×C31—82no—
152C2×#397C2×C3111yescharacteristic
153#2315C2×C3111yescharacteristic
154#1823C2×C3112yescomplemented
155C2×#323C2×C3111yescharacteristic
156#1294C2×C3112yescomplemented
157C22×C31—22no—
158C22×C31—22no—
159C22×C31—22no—
160C22×C31—22no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—24no—
166C22×C31—44no—
167C22×C31—44no—
168C22×C31—44no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—82no—
172C22×C31—82no—
173C22×C31—82no—
174C22×C31#38611yescharacteristic
175C22×C31C2×#10211yescharacteristic
176C22×C31#41711yescharacteristic
177C22×C31#44711yescharacteristic
178C22×C31#44811yescharacteristic
179C22×C31#45512yes—
180C22×C31#45812yes—
181C22×C31#48011yescharacteristic
182C22×C31#48111yescharacteristic
183C4×C31—22no—
184C4×C31—22no—
185C4×C31—42no—
186C4×C31—82no—
187C4×C31—84no—
188C4×C31—82no—
189C22×C4⋊C4C22×C3111yescharacteristic
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C22⋊C4C22×C3111yescharacteristic
193C2×C22⋊C8C22×C3112yes—
194#397—22no—
195#397C4×C3114yescomplemented
196#385—24no—
197#380—21no—
198#380C22×C3112yes—
199C2×#95—21no—
200C2×#95C22×C3111yescharacteristic
201#340—24no—
202#323—22no—
203C2×C31—21no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—21no—
207C2×C31—44no—
208C2×C31#160712yes—
209C2×C31#160812yes—
210C2×C31#187411yescharacteristic
211C2×C31#188511yescharacteristic
212C2×C31#189011yescharacteristic
213C25D4×C3111yescharacteristic
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4D4×C3111yescharacteristic
218C23×C4C23×C3111yescharacteristic
219C22×C8—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C2×C4×C3112yescomplemented
225C2×C4⋊C4D4×C3114yes—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—42no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4—42no—
234C2×C22⋊C4—42no—
235C2×C22⋊C4C2×C4×C3112yes—
236C2×C22⋊C4D4×C3112yes—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#95—22no—
240#95—24no—
241#95—21no—
242#95—22no—
243#95C2×C4×C3112yescomplemented
244C31#902511yescharacteristic, direct product factor, Sylow
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—42no—
250C24—42no—
251C24C22⋊C4×C3112yes—
252C24D8×C3112yes—
253C24SD16×C3112yes—
254C24C2×D4×C3111yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—82no—
274C22×C4—82no—
275C22×C4C22⋊C4×C3112yes—
276C22×C4C22×C4×C3111yescharacteristic
277C22×C4C2×D4×C3112yes—
278C22×C4C2×D4×C3111yescharacteristic
279C22×C4#41×C3112yes—
280C2×C8—44no—
281C2×C8—42no—
282C4⋊C4—24no—
283C4⋊C4—44no—
284C4⋊C4—42no—
285C4⋊C4—82no—
286C22⋊C4—24no—
287C22⋊C4—24no—
288C22⋊C4—44no—
289C22⋊C4—48no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—42no—
301C23—42no—
302C23—44no—
303C23—44no—
304C23—42no—
305C23—42no—
306C23—82no—
307C23—82no—
308C23—81no—
309C23—81no—
310C23C31×#10214yes—
311C23C2×C22⋊C4×C3111yescharacteristic
312C23C31×#12011yescharacteristic
313C23C31×#12311yescharacteristic
314C23C2×D8×C3111yescharacteristic
315C23C2×SD16×C3111yescharacteristic
316C23C31×AGL(1,ℤ/8)11yescharacteristic
317C23C31×#13711yescharacteristic
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—88no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C4×D4×C3112yes—
343C2×C4C31×#12112yes—
344C8—82no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—24no—
354C22—44no—
355C22—44no—
356C22—44no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—82no—
362C22C31×#38611yescharacteristic
363C22C2×C31×#10211yescharacteristic
364C22C31×#41711yescharacteristic
365C22C31×#44711yescharacteristic
366C22C31×#44811yescharacteristic
367C22C31×#45512yes—
368C22C31×#45812yes—
369C22C31×#48011yescharacteristic
370C22C31×#48111yescharacteristic
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—84no—
376C4—82no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2C31×#160712yes—
383C2C31×#160812yes—
384C2C31×#187411yescharacteristic
385C2C31×#188511yescharacteristic
386C2C31×#189011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1823C2semidirect
5. C31×#1294C2semidirect
12. C31×#397C4semidirect
31. C2×C4⋊C4×C31C2×C4semidirect
50. C31×#95C2×C4semidirect
98. #9025C31direct (N × H)
154. #1823C2×C31semidirect
156. #1294C2×C31semidirect
195. #397C4×C31semidirect
224. C2×C4⋊C4C2×C4×C31semidirect
243. #95C2×C4×C31semidirect
244. C31#9025direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C31×#23152
C31×#18232
C2×C31×#3232
C31×#12942
#902531