Finite Group Databasebeta

← C31×#9050 #21465809

Subgroups — C31×#9050 #21465809

Order 7936.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3101C211yesmaximal, characteristic
2C31×#2961C211yesmaximal, characteristic, complemented
3C31×#1955C211yesmaximal, characteristic
4C31×#1542C211yesmaximal, characteristic, complemented
5C31×#1486C211yesmaximal, characteristic
6C31×#1301C211yesmaximal, characteristic, complemented
7C31×#1281C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C4×D4×C31C2211yescharacteristic
10C31×#483C412yes—
11C31×#476—21no—
12C31×#461—21no—
13C31×#450C412yes—
14C31×#446—22no—
15C31×#446—22no—
16C4×SD16×C31—22no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#424—21no—
20C31×#423C2211yescharacteristic
21C2×C31×C4⋊C8C2211yescharacteristic
22C2×C31×C22⋊C8—21no—
23C2×C31×C22⋊C8—21no—
24C31×#405—21no—
25C2×C31×#97C2211yescharacteristic
26C31×#333—21no—
27C31×#332—21no—
28C31×D4⋊C8—22no—
29C22×D4×C31C2×C411yescharacteristic
30C23×C4×C31—21no—
31C2×SD16×C31—22no—
32C2×M16×C31—21no—
33C22×C8×C31—21no—
34C22×C8×C31D411yescharacteristic
35C22×C8×C31D411yescharacteristic
36C31×C4⋊Q8D411yescharacteristic
37C31×C4⋊Q8D411yescharacteristic
38C31×#125—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8C2×C412yes—
41C4×Q8×C31—21no—
42C4×Q8×C31D412yes—
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C4×D4×C31—21no—
47C31×#117—21no—
48C2×C4⋊C4×C31C2×C411yescharacteristic
49C2×C22⋊C4×C31—21no—
50C2×C42×C31C2311yescharacteristic
51C31×#106—22no—
52C31×C4⋊C8—24no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8D412yes—
59C31×#103—22no—
60C31×#102—22no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8—42no—
63C31×C22⋊C8—42no—
64C31×C22⋊C8C2×C412yes—
65C31×#97—22no—
66C31×#97—21no—
67C31×#97—21no—
68C4×C8×C31—22no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71C24×C31—21no—
72C2×Q8×C31—21no—
73C2×Q8×C31C22⋊C412yes—
74C2×D4×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—42no—
77C22×C4×C31—21no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31C22×C411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31#4111yescharacteristic
87SD16×C31—44no—
88M16×C31—41no—
89M16×C31—41no—
90C2×C8×C31—21no—
91C2×C8×C31—21no—
92C2×C8×C31—22no—
93C2×C8×C31—22no—
94C2×C8×C31—21no—
95C2×C8×C31—21no—
96C2×C8×C31—21no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31SD1612yescomplemented
102C4⋊C4×C31—22no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31C22⋊C412yes—
110C22⋊C4×C31—22no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C42×C31—22no—
114C42×C31C2×D411yescharacteristic
115C42×C31C2×D411yescharacteristic
116C42×C31C2×D411yescharacteristic
117C42×C31#4111yescharacteristic
118#9050C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—22no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31C4×D411yescharacteristic
127Q8×C31—42no—
128Q8×C31—81no—
129D4×C31—22no—
130D4×C31—22no—
131D4×C31—41no—
132D4×C31—41no—
133C2×C4×C31—22no—
134C2×C4×C31—22no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—81no—
141C2×C4×C31—81no—
142C2×C4×C31—81no—
143C2×C4×C31—81no—
144C2×C4×C31C2×C22⋊C411yescharacteristic
145C2×C4×C31C4×D411yescharacteristic
146C2×C4×C31#12011yescharacteristic
147C2×C4×C31#12111yescharacteristic
148C2×C4×C31#12111yescharacteristic
149C2×C4×C31#12311yescharacteristic
150C2×C4×C31C2×SD1611yescharacteristic
151C2×C4×C31#13511yescharacteristic
152C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C31#13711yescharacteristic
154C8×C31—22no—
155C8×C31—42no—
156C8×C31—41no—
157C8×C31—42no—
158C8×C31—81no—
159C8×C31—81no—
160#3101C2×C3111yescharacteristic
161#2961C2×C3111yescharacteristic, complemented
162#1955C2×C3111yescharacteristic
163#1542C2×C3111yescharacteristic, complemented
164#1486C2×C3111yescharacteristic
165#1301C2×C3111yescharacteristic, complemented
166#1281C2×C3111yescharacteristic, complemented
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31#38611yescharacteristic
177C22×C31C4×SD1611yescharacteristic
178C22×C31#44011yescharacteristic
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—42no—
184C4×C31—42no—
185C4×C31—81no—
186C4×C31#44811yescharacteristic
187C4×C31#44911yescharacteristic
188C4×C31#46011yescharacteristic
189C4×C31#46411yescharacteristic
190#533C22×C3111yescharacteristic
191C2×C4×D4C22×C3111yescharacteristic
192#483C4×C3112yes—
193#476—21no—
194#461—21no—
195#450C4×C3112yes—
196#446—22no—
197#446—22no—
198C4×SD16—22no—
199#431C22×C3111yescharacteristic
200#431C22×C3111yescharacteristic
201#424—21no—
202#423C22×C3111yescharacteristic
203C2×C4⋊C8C22×C3111yescharacteristic
204C2×C22⋊C8—21no—
205C2×C22⋊C8—21no—
206#405—21no—
207C2×#97C22×C3111yescharacteristic
208#333—21no—
209#332—21no—
210D4⋊C8—22no—
211C2×C31—21no—
212C2×C31—21no—
213C2×C31—82no—
214C2×C31#188011yescharacteristic
215C2×C31#188111yescharacteristic
216C2×C31#189111yescharacteristic
217C22×D4C2×C4×C3111yescharacteristic
218C23×C4—21no—
219C2×SD16—22no—
220C2×M16—21no—
221C22×C8—21no—
222C22×C8D4×C3111yescharacteristic
223C22×C8D4×C3111yescharacteristic
224C4⋊Q8D4×C3111yescharacteristic
225C4⋊Q8D4×C3111yescharacteristic
226#125—21no—
227C22⋊Q8—21no—
228C22⋊Q8C2×C4×C3112yes—
229C4×Q8—21no—
230C4×Q8D4×C3112yes—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235#117—21no—
236C2×C4⋊C4C2×C4×C3111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C42C23×C3111yescharacteristic
239#106—22no—
240C4⋊C8—24no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C3112yes—
247#103—22no—
248#102—22no—
249C22⋊C8—21no—
250C22⋊C8—42no—
251C22⋊C8—42no—
252C22⋊C8C2×C4×C3112yes—
253#97—22no—
254#97—21no—
255#97—21no—
256C4×C8—22no—
257C4×C8—21no—
258C4×C8—21no—
259C31#905011yescharacteristic, direct product factor, Sylow
260C24—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C3112yes—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—42no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22×C4×C3111yescharacteristic
274C22×C4C2×D4×C3111yescharacteristic
275C22×C4#41×C3111yescharacteristic
276SD16—44no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8SD16×C3112yescomplemented
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4C22⋊C4×C3112yes—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—22no—
303C42C2×D4×C3111yescharacteristic
304C42C2×D4×C3111yescharacteristic
305C42C2×D4×C3111yescharacteristic
306C42#41×C3111yescharacteristic
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C4×D4×C3111yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C2×C22⋊C4×C3111yescharacteristic
333C2×C4C4×D4×C3111yescharacteristic
334C2×C4C31×#12011yescharacteristic
335C2×C4C31×#12111yescharacteristic
336C2×C4C31×#12111yescharacteristic
337C2×C4C31×#12311yescharacteristic
338C2×C4C2×SD16×C3111yescharacteristic
339C2×C4C31×#13511yescharacteristic
340C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
341C2×C4C31×#13711yescharacteristic
342C8—22no—
343C8—42no—
344C8—41no—
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C31×#38611yescharacteristic
358C22C4×SD16×C3111yescharacteristic
359C22C31×#44011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—81no—
367C4C31×#44811yescharacteristic
368C4C31×#44911yescharacteristic
369C4C31×#46011yescharacteristic
370C4C31×#46411yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2C31×#188011yescharacteristic
375C2C31×#188111yescharacteristic
376C2C31×#189111yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2961C2semidirect
4. C31×#1542C2semidirect
6. C31×#1301C2semidirect
7. C31×#1281C2semidirect
101. C2×C8×C31SD16semidirect
118. #9050C31direct (N × H)
161. #2961C2×C31semidirect
163. #1542C2×C31semidirect
165. #1301C2×C31semidirect
166. #1281C2×C31semidirect
259. C31#9050direct (N × H)
290. C2×C8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#31012
C31×#29612
C31×#19552
C31×#15422
C31×#14862
C31×#13012
C31×#12812
#905031