Finite Group Databasebeta

← C31×#9472 #21466231

Subgroups — C31×#9472 #21466231

Order 7936.

912 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2973C211yesmaximal, characteristic, complemented
2C31×#2408C211yesmaximal, characteristic
3C31×#1799C211yesmaximal, characteristic, complemented
4C31×#1786C212yesmaximal, complemented
5C31×#1289C212yesmaximal, complemented
6C23×D4×C31C2211yescharacteristic
7C2×C31×#121—21no—
8C2×C31×#120—21no—
9C2×C4×D4×C31C2211yescharacteristic
10C31×#435—24no—
11C31×#432—21no—
12C2×C31×#102—24no—
13C2×C31×#99—21no—
14C31×#407—21no—
15C2×C31×C22⋊C8C2212yes—
16C31×#394C412yescomplemented
17C31×#392C412yescomplemented
18C31×#390—21no—
19C31×#380C2212yes—
20C31×#380C2211yescharacteristic
21C31×#379—21no—
22C31×#342—21no—
23C25×C31—21no—
24C22×D4×C31—22no—
25C22×D4×C31—22no—
26C22×D4×C31—21no—
27C22×D4×C31—22no—
28C22×D4×C31—44no—
29C22×D4×C31C2×C412yes—
30C22×D4×C31D411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C23×C4×C31C2311yescharacteristic
33C2×M16×C31—22no—
34C22×C8×C31D414yescomplemented
35C31×#121—44no—
36C31×#120—44no—
37C4×D4×C31—22no—
38C4×D4×C31—22no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—22no—
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31C2×C411yescharacteristic
48C2×C22⋊C4×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C31×C4⋊C8—22no—
51C31×#102—48no—
52C31×#99—42no—
53C31×C22⋊C8—22no—
54C31×C22⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×#97—22no—
57C31×#95—22no—
58C31×#95C2×C412yes—
59C24×C31—22no—
60C24×C31—44no—
61C24×C31—42no—
62C24×C31—42no—
63C24×C31—41no—
64C24×C31—41no—
65C24×C31—82no—
66C24×C31C22⋊C411yescharacteristic
67C24×C31C2×D411yescharacteristic
68C2×D4×C31—28no—
69C2×D4×C31—24no—
70C2×D4×C31—22no—
71C2×D4×C31—21no—
72C2×D4×C31—22no—
73C2×D4×C31—21no—
74C2×D4×C31—24no—
75C2×D4×C31—44no—
76C2×D4×C31—42no—
77C2×D4×C31—44no—
78C2×D4×C31—48no—
79C2×D4×C31—44no—
80C2×D4×C31—44no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—82no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C22×C411yescharacteristic
94C22×C4×C31C2×D412yes—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31#4112yes—
97M16×C31—82no—
98C2×C8×C31—24no—
99C2×C8×C31—44no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—44no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—22no—
105C22⋊C4×C31—44no—
106C22⋊C4×C31—44no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—42no—
110C22⋊C4×C31—82no—
111C42×C31—21no—
112C42×C31—21no—
113#9472C3111yesmaximal, characteristic, direct product factor, Sylow
114C23×C31—24no—
115C23×C31—21no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—42no—
123C23×C31—48no—
124C23×C31—42no—
125C23×C31—42no—
126C23×C31—42no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—84no—
130C23×C31—88no—
131C23×C31—84no—
132C23×C31—84no—
133C23×C31—82no—
134C23×C31—82no—
135C23×C31C2×C22⋊C411yescharacteristic
136C23×C31#12112yes—
137C23×C31AGL(1,ℤ/8)11yescharacteristic
138C23×C31AGL(1,ℤ/8)12yes—
139C23×C31#13711yescharacteristic
140D4×C31—28no—
141D4×C31—44no—
142D4×C31—44no—
143D4×C31—42no—
144D4×C31—42no—
145D4×C31—44no—
146D4×C31—88no—
147C2×C4×C31—24no—
148C2×C4×C31—22no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—81no—
163C2×C4×C31—82no—
164C2×C4×C31—82no—
165C2×C4×C31—82no—
166C2×C4×C31C4×D412yes—
167C2×C4×C31#12011yescharacteristic
168C2×C4×C31#12311yescharacteristic
169C8×C31—44no—
170#2973C2×C3111yescharacteristic, complemented
171#2408C2×C3111yescharacteristic
172#1799C2×C3111yescharacteristic, complemented
173#1786C2×C3112yescomplemented
174#1289C2×C3112yescomplemented
175C22×C31—21no—
176C22×C31—22no—
177C22×C31—21no—
178C22×C31—22no—
179C22×C31—42no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31—42no—
183C22×C31—44no—
184C22×C31—44no—
185C22×C31—41no—
186C22×C31—44no—
187C22×C31—41no—
188C22×C31—41no—
189C22×C31—81no—
190C22×C31—82no—
191C22×C31—82no—
192C22×C31—88no—
193C22×C31—88no—
194C22×C31—82no—
195C22×C31—82no—
196C22×C31#38611yescharacteristic
197C22×C31#41711yescharacteristic
198C22×C31#41811yescharacteristic
199C22×C31#46812yes—
200C22×C31#46912yes—
201C4×C31—21no—
202C4×C31—22no—
203C4×C31—41no—
204C4×C31—41no—
205C4×C31—41no—
206C4×C31—82no—
207C4×C31—162no—
208C4×C31B(4,𝔽2)12yes—
209C23×D4C22×C3111yescharacteristic
210C2×#121—21no—
211C2×#120—21no—
212C2×C4×D4C22×C3111yescharacteristic
213#435—24no—
214#432—21no—
215C2×#102—24no—
216C2×#99—21no—
217#407—21no—
218C2×C22⋊C8C22×C3112yes—
219#394C4×C3112yescomplemented
220#392C4×C3112yescomplemented
221#390—21no—
222#380C22×C3112yes—
223#380C22×C3111yescharacteristic
224#379—21no—
225#342—21no—
226C2×C31—21no—
227C2×C31—22no—
228C2×C31—21no—
229C2×C31—22no—
230C2×C31—81no—
231C2×C31—84no—
232C2×C31#188911yescharacteristic
233C2×C31#189511yescharacteristic
234C2×C31#191011yescharacteristic
235C25—21no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—21no—
239C22×D4—22no—
240C22×D4—44no—
241C22×D4C2×C4×C3112yes—
242C22×D4D4×C3111yescharacteristic
243C23×C4D4×C3111yescharacteristic
244C23×C4C23×C3111yescharacteristic
245C2×M16—22no—
246C22×C8D4×C3114yescomplemented
247#121—44no—
248#120—44no—
249C4×D4—22no—
250C4×D4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4C2×C4×C3111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4C2×C4×C3111yescharacteristic
260C2×C22⋊C4D4×C3111yescharacteristic
261C2×C42D4×C3111yescharacteristic
262C4⋊C8—22no—
263#102—48no—
264#99—42no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268#97—22no—
269#95—22no—
270#95C2×C4×C3112yes—
271C31#947211yescharacteristic, direct product factor, Sylow
272C24—22no—
273C24—44no—
274C24—42no—
275C24—42no—
276C24—41no—
277C24—41no—
278C24—82no—
279C24C22⋊C4×C3111yescharacteristic
280C24C2×D4×C3111yescharacteristic
281C2×D4—28no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—24no—
288C2×D4—44no—
289C2×D4—42no—
290C2×D4—44no—
291C2×D4—48no—
292C2×D4—44no—
293C2×D4—44no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—82no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4C22⋊C4×C3111yescharacteristic
304C22×C4C22⋊C4×C3111yescharacteristic
305C22×C4C22⋊C4×C3111yescharacteristic
306C22×C4C22×C4×C3111yescharacteristic
307C22×C4C2×D4×C3112yes—
308C22×C4C2×D4×C3111yescharacteristic
309C22×C4#41×C3112yes—
310M16—82no—
311C2×C8—24no—
312C2×C8—44no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—44no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—44no—
319C22⋊C4—44no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—82no—
324C42—21no—
325C42—21no—
326C23—24no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—48no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—84no—
342C23—88no—
343C23—84no—
344C23—84no—
345C23—82no—
346C23—82no—
347C23C2×C22⋊C4×C3111yescharacteristic
348C23C31×#12112yes—
349C23C31×AGL(1,ℤ/8)11yescharacteristic
350C23C31×AGL(1,ℤ/8)12yes—
351C23C31×#13711yescharacteristic
352D4—28no—
353D4—44no—
354D4—44no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—88no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4C4×D4×C3112yes—
379C2×C4C31×#12011yescharacteristic
380C2×C4C31×#12311yescharacteristic
381C8—44no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—44no—
391C22—44no—
392C22—41no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—88no—
400C22—88no—
401C22—82no—
402C22—82no—
403C22C31×#38611yescharacteristic
404C22C31×#41711yescharacteristic
405C22C31×#41811yescharacteristic
406C22C31×#46812yes—
407C22C31×#46912yes—
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4—162no—
415C4C31×B(4,𝔽2)12yes—
416C2—21no—
417C2—22no—
418C2—21no—
419C2—22no—
420C2—81no—
421C2—84no—
422C2C31×#188911yescharacteristic
423C2C31×#189511yescharacteristic
424C2C31×#191011yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2408C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2973C2semidirect
3. C31×#1799C2semidirect
4. C31×#1786C2semidirect
5. C31×#1289C2semidirect
16. C31×#394C4semidirect
17. C31×#392C4semidirect
34. C22×C8×C31D4semidirect
113. #9472C31direct (N × H)
170. #2973C2×C31semidirect
172. #1799C2×C31semidirect
173. #1786C2×C31semidirect
174. #1289C2×C31semidirect
219. #394C4×C31semidirect
220. #392C4×C31semidirect
246. C22×C8D4×C31semidirect
271. C31#9472direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29732
C31×#24082
C31×#17992
C31×#17862
C31×#12892
#947231