Finite Group Databasebeta

← C31×#9158 #21465917

Subgroups — C31×#9158 #21465917

Order 7936.

980 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2847C211yesmaximal, characteristic
2C2×C31×#381C211yesmaximal, characteristic, complemented
3C31×#1779C211yesmaximal, characteristic, complemented
4C2×C31×#327C212yesmaximal, complemented
5C31×#1294C212yesmaximal, complemented
6C24×C4×C31C2211yescharacteristic
7C2×C31×#121C412yescomplemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#120—21no—
10C22×C22⋊C4×C31—21no—
11C2×C31×C22⋊C8—22no—
12C2×C31×C22⋊C8C2212yes—
13C31×#386—21no—
14C31×#386—22no—
15C31×#381—24no—
16C31×#380C412yescomplemented
17C31×#380C2211yescharacteristic
18C2×C31×#95—21no—
19C2×C31×#95C2212yes—
20C31×#327—24no—
21C25×C31D411yescharacteristic
22C22×D4×C31—22no—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—22no—
26C23×C4×C31—22no—
27C23×C4×C31—22no—
28C23×C4×C31—44no—
29C23×C4×C31C2×C412yes—
30C23×C4×C31D412yes—
31C23×C4×C31D411yescharacteristic
32C23×C4×C31C2311yescharacteristic
33C22×C8×C31—22no—
34C31×#121—22no—
35C31×#121—22no—
36C31×#121—44no—
37C31×#120—44no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C412yes—
40C2×C22⋊C4×C31—24no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—44no—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—44no—
49C31×#95—24no—
50C31×#95—22no—
51C31×#95—22no—
52C31×#95—21no—
53C31×#95D414yescomplemented
54C24×C31—24no—
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—22no—
58C24×C31—22no—
59C24×C31—21no—
60C24×C31—42no—
61C24×C31C22⋊C412yes—
62C24×C31C2×D411yescharacteristic
63C2×D4×C31—22no—
64C2×D4×C31—42no—
65C2×D4×C31—44no—
66C2×D4×C31—44no—
67C2×D4×C31—44no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—42no—
71C2×D4×C31—42no—
72C22×C4×C31—24no—
73C22×C4×C31—24no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—24no—
77C22×C4×C31—24no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—24no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—48no—
86C22×C4×C31—48no—
87C22×C4×C31—44no—
88C22×C4×C31—44no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31C22⋊C412yes—
92C22×C4×C31C22×C411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D412yes—
95C22×C4×C31#4112yes—
96C2×C8×C31—44no—
97C2×C8×C31—42no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—42no—
100C22⋊C4×C31—44no—
101C22⋊C4×C31—48no—
102C22⋊C4×C31—44no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—42no—
105#9158C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—22no—
107C23×C31—22no—
108C23×C31—24no—
109C23×C31—24no—
110C23×C31—22no—
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—22no—
115C23×C31—22no—
116C23×C31—48no—
117C23×C31—48no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—42no—
122C23×C31—41no—
123C23×C31—42no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—42no—
127C23×C31#9914yes—
128C23×C31C2×C22⋊C411yescharacteristic
129C23×C31#12011yescharacteristic
130C23×C31#12311yescharacteristic
131C23×C31#13512yes—
132C23×C31AGL(1,ℤ/8)12yes—
133D4×C31—82no—
134D4×C31—88no—
135D4×C31—82no—
136D4×C31—82no—
137C2×C4×C31—22no—
138C2×C4×C31—22no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—48no—
145C2×C4×C31—48no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—44no—
149C2×C4×C31—44no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—44no—
157C2×C4×C31—84no—
158C2×C4×C31—84no—
159C2×C4×C31C4×D412yes—
160C2×C4×C31#12112yes—
161C8×C31—82no—
162#2847C2×C3111yescharacteristic
163C2×#381C2×C3111yescharacteristic, complemented
164#1779C2×C3111yescharacteristic, complemented
165C2×#327C2×C3112yescomplemented
166#1294C2×C3112yescomplemented
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—24no—
172C22×C31—24no—
173C22×C31—24no—
174C22×C31—24no—
175C22×C31—24no—
176C22×C31—48no—
177C22×C31—48no—
178C22×C31—42no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—82no—
186C22×C31—82no—
187C22×C31#38611yescharacteristic
188C22×C31C2×#9912yes—
189C22×C31#41611yescharacteristic
190C22×C31#41811yescharacteristic
191C22×C31#42112yes—
192C22×C31#44912yes—
193C22×C31#48212yes—
194C4×C31—22no—
195C4×C31—22no—
196C4×C31—42no—
197C4×C31—84no—
198C4×C31—81no—
199C4×C31—82no—
200C24×C4C22×C3111yescharacteristic
201C2×#121C4×C3112yescomplemented
202C2×#121C22×C3111yescharacteristic
203C2×#120—21no—
204C22×C22⋊C4—21no—
205C2×C22⋊C8—22no—
206C2×C22⋊C8C22×C3112yes—
207#386—21no—
208#386—22no—
209#381—24no—
210#380C4×C3112yescomplemented
211#380C22×C3111yescharacteristic
212C2×#95—21no—
213C2×#95C22×C3112yes—
214#327—24no—
215C2×C31—22no—
216C2×C31—22no—
217C2×C31—44no—
218C2×C31—161no—
219C2×C31#151012yes—
220C2×C31#151612yes—
221C2×C31#187511yescharacteristic
222C2×C31#189711yescharacteristic
223C2×C31#189811yescharacteristic
224C25D4×C3111yescharacteristic
225C22×D4—22no—
226C22×D4—21no—
227C22×D4C2×C4×C3111yescharacteristic
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—44no—
232C23×C4C2×C4×C3112yes—
233C23×C4D4×C3112yes—
234C23×C4D4×C3111yescharacteristic
235C23×C4C23×C3111yescharacteristic
236C22×C8—22no—
237#121—22no—
238#121—22no—
239#121—44no—
240#120—44no—
241C2×C4⋊C4C2×C4×C3111yescharacteristic
242C2×C4⋊C4C2×C4×C3112yes—
243C2×C22⋊C4—24no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—44no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—44no—
252#95—24no—
253#95—22no—
254#95—22no—
255#95—21no—
256#95D4×C3114yescomplemented
257C31#915811yescharacteristic, direct product factor, Sylow
258C24—24no—
259C24—21no—
260C24—21no—
261C24—22no—
262C24—22no—
263C24—21no—
264C24—42no—
265C24C22⋊C4×C3112yes—
266C24C2×D4×C3111yescharacteristic
267C2×D4—22no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—48no—
290C22×C4—48no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C22⋊C4×C3112yes—
296C22×C4C22×C4×C3111yescharacteristic
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4C2×D4×C3112yes—
299C22×C4#41×C3112yes—
300C2×C8—44no—
301C2×C8—42no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—48no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—24no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—48no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23—42no—
329C23—41no—
330C23C31×#9914yes—
331C23C2×C22⋊C4×C3111yescharacteristic
332C23C31×#12011yescharacteristic
333C23C31×#12311yescharacteristic
334C23C31×#13512yes—
335C23C31×AGL(1,ℤ/8)12yes—
336D4—82no—
337D4—88no—
338D4—82no—
339D4—82no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—41no—
360C2×C4—84no—
361C2×C4—84no—
362C2×C4C4×D4×C3112yes—
363C2×C4C31×#12112yes—
364C8—82no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—24no—
370C22—24no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—82no—
384C22—82no—
385C22C31×#38611yescharacteristic
386C22C2×C31×#9912yes—
387C22C31×#41611yescharacteristic
388C22C31×#41811yescharacteristic
389C22C31×#42112yes—
390C22C31×#44912yes—
391C22C31×#48212yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—84no—
396C4—81no—
397C4—82no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—161no—
402C2C31×#151012yes—
403C2C31×#151612yes—
404C2C31×#187511yescharacteristic
405C2C31×#189711yescharacteristic
406C2C31×#189811yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#381C2semidirect
3. C31×#1779C2semidirect
4. C2×C31×#327C2semidirect
5. C31×#1294C2semidirect
7. C2×C31×#121C4semidirect
16. C31×#380C4semidirect
53. C31×#95D4semidirect
105. #9158C31direct (N × H)
163. C2×#381C2×C31semidirect
164. #1779C2×C31semidirect
165. C2×#327C2×C31semidirect
166. #1294C2×C31semidirect
201. C2×#121C4×C31semidirect
210. #380C4×C31semidirect
256. #95D4×C31semidirect
257. C31#9158direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28472
C2×C31×#3812
C31×#17792
C2×C31×#3272
C31×#12942
#915831