Finite Group Databasebeta

← C31×#18319 #21475078

Subgroups — C31×#18319 #21475078

Order 7936.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#543C211yesmaximal, characteristic
2C31×#3195C212yesmaximal, complemented
3C31×#2561C211yesmaximal, characteristic
4C31×#1608C214yesmaximal, complemented
5C31×#1602C214yesmaximal, complemented
6C31×#1508C212yesmaximal, complemented
7C31×#1462C211yesmaximal, characteristic
8C31×#543—24no—
9C31×#543—22no—
10C31×#543C2214yes—
11C2×C31×C22⋊Q8—22no—
12C2×C31×C22⋊Q8—21no—
13C2×C31×C22⋊Q8—22no—
14C2×C31×C22⋊Q8C2212yes—
15C2×C31×C22⋊Q8C2211yescharacteristic
16C22×C22⋊C4×C31—21no—
17C22×C22⋊C4×C31C2211yescharacteristic
18C31×#483—22no—
19C31×#483C2214yescomplemented
20C31×#470—24no—
21C31×#451—22no—
22C31×#451C2214yescomplemented
23C31×#407C2212yes—
24C31×#397C2212yes—
25C31×#393C2212yes—
26C31×#388—22no—
27C31×#381—21no—
28C31×#379—21no—
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#328C2218yescomplemented
31C31×#323C2214yes—
32C25×C31D411yescharacteristic
33C22×Q8×C31—21no—
34C22×Q8×C31D412yes—
35C22×Q8×C31C2311yescharacteristic
36C23×C4×C31—21no—
37C23×C4×C31—21no—
38C23×C4×C31D411yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C2×Q16×C31—24no—
41C2×M16×C31—22no—
42C31×C22⋊Q8—28no—
43C31×C22⋊Q8—28no—
44C31×C22⋊Q8—24no—
45C31×C22⋊Q8—28no—
46C31×C22⋊Q8—24no—
47C31×C22⋊Q8—22no—
48C31×C22⋊Q8—22no—
49C31×C22⋊Q8—28no—
50C31×C22⋊Q8—22no—
51C31×C22⋊Q8—22no—
52C31×C22⋊Q8D414yes—
53C31×C22⋊Q8C2314yes—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31D412yes—
59C2×C4⋊C4×C31C2311yescharacteristic
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—21no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31D412yes—
71C2×C22⋊C4×C31C2312yes—
72C2×C42×C31—21no—
73C31×#106—24no—
74C31×#103—24no—
75C31×#103—24no—
76C31×C22⋊C8—22no—
77C31×C22⋊C8C2314yes—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95C2312yes—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—24no—
84C24×C31—42no—
85C24×C31—81no—
86C24×C31C2×D411yescharacteristic
87C24×C31C2×D412yes—
88C2×Q8×C31—24no—
89C2×Q8×C31—22no—
90C2×Q8×C31—22no—
91C2×Q8×C31—81no—
92C2×Q8×C31—82no—
93C2×Q8×C31—82no—
94C2×Q8×C31C2×D414yes—
95C22×C4×C31—22no—
96C22×C4×C31—21no—
97C22×C4×C31—22no—
98C22×C4×C31—24no—
99C22×C4×C31—24no—
100C22×C4×C31—21no—
101C22×C4×C31—22no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—42no—
105C22×C4×C31—81no—
106C22×C4×C31—82no—
107C22×C4×C31—82no—
108C22×C4×C31C2×D412yes—
109C22×C4×C31C2×D411yescharacteristic
110C22×C4×C31C2×D412yes—
111C22×C4×C31C2×D412yes—
112C22×C4×C31C2411yescharacteristic
113Q16×C31—84no—
114M16×C31—82no—
115C2×C8×C31—24no—
116C4⋊C4×C31—24no—
117C4⋊C4×C31—28no—
118C4⋊C4×C31—24no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—24no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—42no—
123C4⋊C4×C31C2×D414yes—
124C22⋊C4×C31—28no—
125C22⋊C4×C31—24no—
126C22⋊C4×C31—24no—
127C22⋊C4×C31—24no—
128C22⋊C4×C31—24no—
129C22⋊C4×C31—42no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—44no—
133C22⋊C4×C31—82no—
134C42×C31—81no—
135#18319C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—24no—
137C23×C31—24no—
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—22no—
141C23×C31—22no—
142C23×C31—41no—
143C23×C31—42no—
144C23×C31—42no—
145C23×C31—42no—
146C23×C31—42no—
147C23×C31—81no—
148C23×C31—81no—
149C23×C31—88no—
150C23×C31#12011yescharacteristic
151C23×C31#12011yescharacteristic
152C23×C31#13714yes—
153C23×C31C22×D411yescharacteristic
154Q8×C31—44no—
155Q8×C31—44no—
156Q8×C31—82no—
157Q8×C31—84no—
158C2×C4×C31—24no—
159C2×C4×C31—22no—
160C2×C4×C31—24no—
161C2×C4×C31—41no—
162C2×C4×C31—42no—
163C2×C4×C31—42no—
164C2×C4×C31—41no—
165C2×C4×C31—44no—
166C2×C4×C31—42no—
167C2×C4×C31—44no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—81no—
177C2×C4×C31—84no—
178C2×C4×C31—84no—
179C2×C4×C31#12012yes—
180C2×C4×C31C22×D412yes—
181C8×C31—44no—
182C2×#543C2×C3111yescharacteristic
183#3195C2×C3112yescomplemented
184#2561C2×C3111yescharacteristic
185#1608C2×C3114yescomplemented
186#1602C2×C3114yescomplemented
187#1508C2×C3112yescomplemented
188#1462C2×C3111yescharacteristic
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—24no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—44no—
198C22×C31—44no—
199C22×C31—48no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—82no—
203C22×C31—84no—
204C22×C31#45512yes—
205C22×C31C2×#12011yescharacteristic
206C22×C31C2×#13712yes—
207C4×C31—22no—
208C4×C31—22no—
209C4×C31—42no—
210C4×C31—44no—
211C4×C31—44no—
212C4×C31—82no—
213C4×C31—81no—
214C4×C31—81no—
215#543—24no—
216#543—22no—
217#543C22×C3114yes—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8C22×C3112yes—
222C2×C22⋊Q8C22×C3111yescharacteristic
223C22×C22⋊C4—21no—
224C22×C22⋊C4C22×C3111yescharacteristic
225#483—22no—
226#483C22×C3114yescomplemented
227#470—24no—
228#451—22no—
229#451C22×C3114yescomplemented
230#407C22×C3112yes—
231#397C22×C3112yes—
232#393C22×C3112yes—
233#388—22no—
234#381—21no—
235#379—21no—
236C4×C22⋊C4C22×C3111yescharacteristic
237#328C22×C3118yescomplemented
238#323C22×C3114yes—
239C2×C31—22no—
240C2×C31—22no—
241C2×C31—41no—
242C2×C31—44no—
243C2×C31#300411yescharacteristic
244C2×C31C2×#45511yescharacteristic
245C2×C31#302611yescharacteristic
246C25D4×C3111yescharacteristic
247C22×Q8—21no—
248C22×Q8D4×C3112yes—
249C22×Q8C23×C3111yescharacteristic
250C23×C4—21no—
251C23×C4—21no—
252C23×C4D4×C3111yescharacteristic
253C23×C4C23×C3111yescharacteristic
254C2×Q16—24no—
255C2×M16—22no—
256C22⋊Q8—28no—
257C22⋊Q8—28no—
258C22⋊Q8—24no—
259C22⋊Q8—28no—
260C22⋊Q8—24no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—28no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8D4×C3114yes—
267C22⋊Q8C23×C3114yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C3112yes—
273C2×C4⋊C4C23×C3111yescharacteristic
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4D4×C3112yes—
285C2×C22⋊C4C23×C3112yes—
286C2×C42—21no—
287#106—24no—
288#103—24no—
289#103—24no—
290C22⋊C8—22no—
291C22⋊C8C23×C3114yes—
292#95—22no—
293#95—22no—
294#95C23×C3112yes—
295C31#1831911yescharacteristic, direct product factor, Sylow
296C24—21no—
297C24—21no—
298C24—24no—
299C24—42no—
300C24—81no—
301C24C2×D4×C3111yescharacteristic
302C24C2×D4×C3112yes—
303C2×Q8—24no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—81no—
307C2×Q8—82no—
308C2×Q8—82no—
309C2×Q8C2×D4×C3114yes—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—81no—
321C22×C4—82no—
322C22×C4—82no—
323C22×C4C2×D4×C3112yes—
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3112yes—
326C22×C4C2×D4×C3112yes—
327C22×C4C24×C3111yescharacteristic
328Q16—84no—
329M16—82no—
330C2×C8—24no—
331C4⋊C4—24no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—42no—
338C4⋊C4C2×D4×C3114yes—
339C22⋊C4—28no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—42no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—44no—
348C22⋊C4—82no—
349C42—81no—
350C23—24no—
351C23—24no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23—88no—
364C23C31×#12011yescharacteristic
365C23C31×#12011yescharacteristic
366C23C31×#13714yes—
367C23C22×D4×C3111yescharacteristic
368Q8—44no—
369Q8—44no—
370Q8—82no—
371Q8—84no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—84no—
392C2×C4—84no—
393C2×C4C31×#12012yes—
394C2×C4C22×D4×C3112yes—
395C8—44no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—42no—
408C22—42no—
409C22—82no—
410C22—84no—
411C22C31×#45512yes—
412C22C2×C31×#12011yescharacteristic
413C22C2×C31×#13712yes—
414C4—22no—
415C4—22no—
416C4—42no—
417C4—44no—
418C4—44no—
419C4—82no—
420C4—81no—
421C4—81no—
422C2—22no—
423C2—22no—
424C2—41no—
425C2—44no—
426C2C31×#300411yescharacteristic
427C2C2×C31×#45511yescharacteristic
428C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC25×C31D4
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
2. C31×#3195C2semidirect
4. C31×#1608C2semidirect
5. C31×#1602C2semidirect
6. C31×#1508C2semidirect
19. C31×#483C22semidirect
22. C31×#451C22semidirect
30. C31×#328C22semidirect
135. #18319C31direct (N × H)
183. #3195C2×C31semidirect
185. #1608C2×C31semidirect
186. #1602C2×C31semidirect
187. #1508C2×C31semidirect
226. #483C22×C31semidirect
229. #451C22×C31semidirect
237. #328C22×C31semidirect
295. C31#18319direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C31×#31952
C31×#25612
C31×#16082
C31×#16022
C31×#15082
C31×#14622
#1831931