Finite Group Databasebeta

← C31×#9021 #21465780

Subgroups — C31×#9021 #21465780

Order 7936.

812 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#399C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic
3C31×#1824C212yesmaximal, complemented
4C2×C31×#323C211yesmaximal, characteristic
5C31×#1294C212yesmaximal, complemented
6C22×C4⋊C4×C31—21no—
7C22×C4⋊C4×C31C2211yescharacteristic
8C22×C22⋊C4×C31—21no—
9C22×C22⋊C4×C31—21no—
10C22×C22⋊C4×C31C2211yescharacteristic
11C2×C31×C22⋊C8C2212yes—
12C31×#399—22no—
13C31×#399C414yescomplemented
14C31×#385—24no—
15C31×#380—21no—
16C31×#380C2212yes—
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—24no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—44no—
33C2×C4⋊C4×C31C2×C412yescomplemented
34C2×C4⋊C4×C31D414yes—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—24no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—44no—
41C2×C22⋊C4×C31—42no—
42C2×C22⋊C4×C31—42no—
43C2×C22⋊C4×C31C2×C412yes—
44C2×C22⋊C4×C31D412yes—
45C31×C22⋊C8—22no—
46C31×C22⋊C8—22no—
47C31×#95—22no—
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×C31SD1612yes—
59C24×C31Q1612yes—
60C24×C31C2×D411yescharacteristic
61C22×C4×C31—24no—
62C22×C4×C31—22no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—22no—
66C22×C4×C31—24no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31—44no—
74C22×C4×C31—42no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—82no—
78C22×C4×C31—82no—
79C22×C4×C31C22⋊C412yes—
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D412yes—
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31#4112yes—
84C2×C8×C31—44no—
85C2×C8×C31—42no—
86C4⋊C4×C31—24no—
87C4⋊C4×C31—48no—
88C4⋊C4×C31—44no—
89C4⋊C4×C31—42no—
90C4⋊C4×C31—82no—
91C22⋊C4×C31—24no—
92C22⋊C4×C31—24no—
93C22⋊C4×C31—48no—
94C22⋊C4×C31—44no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—42no—
97#9021C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—22no—
99C23×C31—22no—
100C23×C31—22no—
101C23×C31—22no—
102C23×C31—22no—
103C23×C31—22no—
104C23×C31—22no—
105C23×C31—22no—
106C23×C31—42no—
107C23×C31—42no—
108C23×C31—44no—
109C23×C31—44no—
110C23×C31—42no—
111C23×C31—42no—
112C23×C31—82no—
113C23×C31—82no—
114C23×C31—81no—
115C23×C31—81no—
116C23×C31#10314yes—
117C23×C31C2×C22⋊C411yescharacteristic
118C23×C31#12011yescharacteristic
119C23×C31#12311yescharacteristic
120C23×C31C2×SD1611yescharacteristic
121C23×C31C2×Q1611yescharacteristic
122C23×C31AGL(1,ℤ/8)11yescharacteristic
123C23×C31#13711yescharacteristic
124C2×C4×C31—24no—
125C2×C4×C31—24no—
126C2×C4×C31—22no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—42no—
130C2×C4×C31—44no—
131C2×C4×C31—44no—
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—42no—
139C2×C4×C31—44no—
140C2×C4×C31—44no—
141C2×C4×C31—44no—
142C2×C4×C31—81no—
143C2×C4×C31—82no—
144C2×C4×C31—88no—
145C2×C4×C31—82no—
146C2×C4×C31C4×D412yes—
147C2×C4×C31#12112yes—
148C8×C31—82no—
149C2×#399C2×C3111yescharacteristic
150#2315C2×C3111yescharacteristic
151#1824C2×C3112yescomplemented
152C2×#323C2×C3111yescharacteristic
153#1294C2×C3112yescomplemented
154C22×C31—22no—
155C22×C31—22no—
156C22×C31—22no—
157C22×C31—22no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—24no—
163C22×C31—44no—
164C22×C31—44no—
165C22×C31—44no—
166C22×C31—42no—
167C22×C31—42no—
168C22×C31—82no—
169C22×C31—82no—
170C22×C31—82no—
171C22×C31#38611yescharacteristic
172C22×C31C2×#10311yescharacteristic
173C22×C31#41711yescharacteristic
174C22×C31#45011yescharacteristic
175C22×C31#45111yescharacteristic
176C22×C31#45312yes—
177C22×C31#45812yes—
178C22×C31#48311yescharacteristic
179C22×C31#48411yescharacteristic
180C4×C31—22no—
181C4×C31—22no—
182C4×C31—44no—
183C4×C31—42no—
184C4×C31—84no—
185C4×C31—82no—
186C22×C4⋊C4—21no—
187C22×C4⋊C4C22×C3111yescharacteristic
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4C22×C3111yescharacteristic
191C2×C22⋊C8C22×C3112yes—
192#399—22no—
193#399C4×C3114yescomplemented
194#385—24no—
195#380—21no—
196#380C22×C3112yes—
197C2×#95C22×C3111yescharacteristic
198#340—24no—
199#323—22no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—21no—
203C2×C31—21no—
204C2×C31—44no—
205C2×C31#161312yes—
206C2×C31#161412yes—
207C2×C31#187211yescharacteristic
208C2×C31#188711yescharacteristic
209C2×C31#189011yescharacteristic
210C25D4×C3111yescharacteristic
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4D4×C3111yescharacteristic
215C23×C4C23×C3111yescharacteristic
216C22×C8—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—44no—
223C2×C4⋊C4C2×C4×C3112yescomplemented
224C2×C4⋊C4D4×C3114yes—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—44no—
231C2×C22⋊C4—42no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4C2×C4×C3112yes—
234C2×C22⋊C4D4×C3112yes—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#95—22no—
238#95—21no—
239#95—22no—
240#95C2×C4×C3112yescomplemented
241C31#902111yescharacteristic, direct product factor, Sylow
242C24—21no—
243C24—21no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—42no—
248C24C22⋊C4×C3112yes—
249C24SD16×C3112yes—
250C24Q16×C3112yes—
251C24C2×D4×C3111yescharacteristic
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—82no—
269C22×C4—82no—
270C22×C4C22⋊C4×C3112yes—
271C22×C4C22×C4×C3111yescharacteristic
272C22×C4C2×D4×C3112yes—
273C22×C4C2×D4×C3111yescharacteristic
274C22×C4#41×C3112yes—
275C2×C8—44no—
276C2×C8—42no—
277C4⋊C4—24no—
278C4⋊C4—44no—
279C4⋊C4—48no—
280C4⋊C4—42no—
281C4⋊C4—82no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—48no—
285C22⋊C4—44no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23—44no—
299C23—44no—
300C23—42no—
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23C31×#10314yes—
307C23C2×C22⋊C4×C3111yescharacteristic
308C23C31×#12011yescharacteristic
309C23C31×#12311yescharacteristic
310C23C2×SD16×C3111yescharacteristic
311C23C2×Q16×C3111yescharacteristic
312C23C31×AGL(1,ℤ/8)11yescharacteristic
313C23C31×#13711yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—82no—
334C2×C4—88no—
335C2×C4—82no—
336C2×C4C4×D4×C3112yes—
337C2×C4C31×#12112yes—
338C8—82no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22C31×#38611yescharacteristic
357C22C2×C31×#10311yescharacteristic
358C22C31×#41711yescharacteristic
359C22C31×#45011yescharacteristic
360C22C31×#45111yescharacteristic
361C22C31×#45312yes—
362C22C31×#45812yes—
363C22C31×#48311yescharacteristic
364C22C31×#48411yescharacteristic
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—84no—
370C4—82no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2C31×#161312yes—
377C2C31×#161412yes—
378C2C31×#187211yescharacteristic
379C2C31×#188711yescharacteristic
380C2C31×#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×#1824C2semidirect
5. C31×#1294C2semidirect
13. C31×#399C4semidirect
33. C2×C4⋊C4×C31C2×C4semidirect
50. C31×#95C2×C4semidirect
97. #9021C31direct (N × H)
151. #1824C2×C31semidirect
153. #1294C2×C31semidirect
193. #399C4×C31semidirect
223. C2×C4⋊C4C2×C4×C31semidirect
240. #95C2×C4×C31semidirect
241. C31#9021direct (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
C31×#23152
C31×#18242
C2×C31×#3232
C31×#12942
#902131