Finite Group Databasebeta

← C31×#8360 #21465119

Subgroups — C31×#8360 #21465119

Order 7936.

846 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#555C211yesmaximal, characteristic
2C31×#1826C212yesmaximal, complemented
3C4×C31×#99C211yesmaximal, characteristic, complemented
4C31×#1507C212yesmaximal, complemented
5C31×#1465C211yesmaximal, characteristic, complemented
6C31×#555—24no—
7C31×#555—24no—
8C2×C31×C4⋊Q8C411yescharacteristic, complemented
9C2×C31×#124—21no—
10C2×C31×#124—21no—
11C2×C31×#121—21no—
12C2×C31×#121C411yescharacteristic, complemented
13C2×C31×#121C2211yescharacteristic
14C2×C4×D4×C31C411yescharacteristic, complemented
15C2×C4×D4×C31C2211yescharacteristic
16C2×C31×#117—21no—
17C2×C31×#117C411yescharacteristic, complemented
18C2×C31×#117C2211yescharacteristic
19C2×C31×#99—21no—
20C31×#407C2212yes—
21C4×C22⋊C4×C31C2212yes—
22C31×#342—21no—
23C31×#339—24no—
24C31×#327—24no—
25C31×#324—21no—
26C31×#323—21no—
27C22×Q8×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31C2×C411yescharacteristic
31C22×D4×C31D411yescharacteristic
32C23×C4×C31—21no—
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C2×M16×C31—22no—
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8—22no—
38C31×#124—28no—
39C31×#124—28no—
40C31×#121—28no—
41C31×#121—22no—
42C31×#121—22no—
43C31×#121—22no—
44C31×#121D414yes—
45C4×D4×C31—22no—
46C4×D4×C31—22no—
47C4×D4×C31—22no—
48C4×D4×C31—22no—
49C31×#117—28no—
50C31×#117—22no—
51C31×#117—22no—
52C31×#117—22no—
53C31×#117D414yes—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31C2×C411yescharacteristic
56C2×C4⋊C4×C31C2×C411yescharacteristic
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31D411yescharacteristic
66C2×C22⋊C4×C31D411yescharacteristic
67C2×C42×C31—21no—
68C2×C42×C31—21no—
69C2×C42×C31—22no—
70C2×C42×C31C2×C411yescharacteristic
71C31×#99—24no—
72C31×C22⋊C8—22no—
73C31×C22⋊C8—22no—
74C31×#95—22no—
75C24×C31—21no—
76C24×C31C22⋊C411yescharacteristic
77C24×C31C2×D411yescharacteristic
78C2×Q8×C31—24no—
79C2×Q8×C31—82no—
80C2×D4×C31—22no—
81C2×D4×C31—24no—
82C2×D4×C31—24no—
83C2×D4×C31—22no—
84C2×D4×C31—21no—
85C2×D4×C31—41no—
86C2×D4×C31—42no—
87C2×D4×C31—82no—
88C2×D4×C31—82no—
89C2×D4×C31C22⋊C412yes—
90C22×C4×C31—24no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31C22⋊C411yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22×C411yescharacteristic
105C22×C4×C31C2×D412yes—
106C22×C4×C31C2×D412yes—
107C22×C4×C31C2×D411yescharacteristic
108M16×C31—44no—
109C2×C8×C31—42no—
110C4⋊C4×C31—24no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—22no—
115C4⋊C4×C31C22⋊C412yes—
116C4⋊C4×C31C22⋊C412yes—
117C4⋊C4×C31C22⋊C412yes—
118C22⋊C4×C31—24no—
119C22⋊C4×C31—24no—
120C22⋊C4×C31—24no—
121C22⋊C4×C31—24no—
122C22⋊C4×C31—22no—
123C22⋊C4×C31—24no—
124C22⋊C4×C31—22no—
125C22⋊C4×C31—24no—
126C22⋊C4×C31—42no—
127C42×C31—24no—
128C42×C31—21no—
129C42×C31—21no—
130C42×C31—24no—
131C42×C31—44no—
132#8360C3111yesmaximal, characteristic, direct product factor, Sylow
133C23×C31—21no—
134C23×C31—21no—
135C23×C31—21no—
136C23×C31—22no—
137C23×C31—21no—
138C23×C31—21no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31—42no—
142C23×C31—42no—
143C23×C31—41no—
144C23×C31—41no—
145C23×C31—41no—
146C23×C31—41no—
147C23×C31C2×C22⋊C411yescharacteristic
148C23×C31#12012yes—
149Q8×C31—84no—
150D4×C31—44no—
151D4×C31—42no—
152D4×C31—42no—
153D4×C31—84no—
154D4×C31—84no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—24no—
158C2×C4×C31—22no—
159C2×C4×C31—21no—
160C2×C4×C31—22no—
161C2×C4×C31—21no—
162C2×C4×C31—22no—
163C2×C4×C31—22no—
164C2×C4×C31—41no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—48no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—42no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—44no—
176C2×C4×C31—82no—
177C2×C4×C31—82no—
178C2×C4×C31#10412yes—
179C2×C4×C31C2×C22⋊C411yescharacteristic
180C2×C4×C31C2×C22⋊C411yescharacteristic
181C2×C4×C31#12012yes—
182C8×C31—82no—
183C2×#555C2×C3111yescharacteristic
184#1826C2×C3112yescomplemented
185C4×#99C2×C3111yescharacteristic, complemented
186#1507C2×C3112yescomplemented
187#1465C2×C3111yescharacteristic, complemented
188C22×C31—21no—
189C22×C31—21no—
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—22no—
193C22×C31—41no—
194C22×C31—42no—
195C22×C31—41no—
196C22×C31—42no—
197C22×C31—42no—
198C22×C31—41no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—82no—
204C22×C31—82no—
205C22×C31#37911yescharacteristic
206C22×C31C2×#10411yescharacteristic
207C22×C31#42111yescharacteristic
208C4×C31—22no—
209C4×C31—21no—
210C4×C31—22no—
211C4×C31—42no—
212C4×C31—42no—
213C4×C31—41no—
214C4×C31—41no—
215C4×C31—42no—
216C4×C31—84no—
217C4×C31#41012yes—
218#555—24no—
219#555—24no—
220C2×C4⋊Q8C4×C3111yescharacteristic, complemented
221C2×#124—21no—
222C2×#124—21no—
223C2×#121—21no—
224C2×#121C4×C3111yescharacteristic, complemented
225C2×#121C22×C3111yescharacteristic
226C2×C4×D4C4×C3111yescharacteristic, complemented
227C2×C4×D4C22×C3111yescharacteristic
228C2×#117—21no—
229C2×#117C4×C3111yescharacteristic, complemented
230C2×#117C22×C3111yescharacteristic
231C2×#99—21no—
232#407C22×C3112yes—
233C4×C22⋊C4C22×C3112yes—
234#342—21no—
235#339—24no—
236#327—24no—
237#324—21no—
238#323—21no—
239C2×C31—21no—
240C2×C31—21no—
241C2×C31—42no—
242C2×C31—81no—
243C2×C31—82no—
244C2×C31#178211yescharacteristic
245C2×C31#178911yescharacteristic
246C2×C31#179511yescharacteristic
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C2×C4×C3111yescharacteristic
251C22×D4D4×C3111yescharacteristic
252C23×C4—21no—
253C23×C4C2×C4×C3111yescharacteristic
254C23×C4C23×C3111yescharacteristic
255C2×M16—22no—
256C4⋊Q8—22no—
257C4⋊Q8—22no—
258#124—28no—
259#124—28no—
260#121—28no—
261#121—22no—
262#121—22no—
263#121—22no—
264#121D4×C3114yes—
265C4×D4—22no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—22no—
269#117—28no—
270#117—22no—
271#117—22no—
272#117—22no—
273#117D4×C3114yes—
274C2×C4⋊C4—21no—
275C2×C4⋊C4C2×C4×C3111yescharacteristic
276C2×C4⋊C4C2×C4×C3111yescharacteristic
277C2×C4⋊C4C2×C4×C3111yescharacteristic
278C2×C4⋊C4D4×C3111yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4D4×C3111yescharacteristic
286C2×C22⋊C4D4×C3111yescharacteristic
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42C2×C4×C3111yescharacteristic
291#99—24no—
292C22⋊C8—22no—
293C22⋊C8—22no—
294#95—22no—
295C31#836011yescharacteristic, direct product factor, Sylow
296C24—21no—
297C24C22⋊C4×C3111yescharacteristic
298C24C2×D4×C3111yescharacteristic
299C2×Q8—24no—
300C2×Q8—82no—
301C2×D4—22no—
302C2×D4—24no—
303C2×D4—24no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—42no—
308C2×D4—82no—
309C2×D4—82no—
310C2×D4C22⋊C4×C3112yes—
311C22×C4—24no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C22⋊C4×C3111yescharacteristic
323C22×C4C22⋊C4×C3111yescharacteristic
324C22×C4C22⋊C4×C3111yescharacteristic
325C22×C4C22×C4×C3111yescharacteristic
326C22×C4C2×D4×C3112yes—
327C22×C4C2×D4×C3112yes—
328C22×C4C2×D4×C3111yescharacteristic
329M16—44no—
330C2×C8—42no—
331C4⋊C4—24no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4C22⋊C4×C3112yes—
337C4⋊C4C22⋊C4×C3112yes—
338C4⋊C4C22⋊C4×C3112yes—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C22⋊C4—24no—
347C22⋊C4—42no—
348C42—24no—
349C42—21no—
350C42—21no—
351C42—24no—
352C42—44no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C2×C22⋊C4×C3111yescharacteristic
368C23C31×#12012yes—
369Q8—84no—
370D4—44no—
371D4—42no—
372D4—42no—
373D4—84no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—48no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4C31×#10412yes—
399C2×C4C2×C22⋊C4×C3111yescharacteristic
400C2×C4C2×C22⋊C4×C3111yescharacteristic
401C2×C4C31×#12012yes—
402C8—82no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22C31×#37911yescharacteristic
421C22C2×C31×#10411yescharacteristic
422C22C31×#42111yescharacteristic
423C4—22no—
424C4—21no—
425C4—22no—
426C4—42no—
427C4—42no—
428C4—41no—
429C4—41no—
430C4—42no—
431C4—84no—
432C4C31×#41012yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—82no—
437C2—81no—
438C2C31×#178211yescharacteristic
439C2C31×#178911yescharacteristic
440C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#555C2
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×#1826C2semidirect
3. C4×C31×#99C2semidirect
4. C31×#1507C2semidirect
5. C31×#1465C2semidirect
8. C2×C31×C4⋊Q8C4semidirect
12. C2×C31×#121C4semidirect
14. C2×C4×D4×C31C4semidirect
17. C2×C31×#117C4semidirect
132. #8360C31direct (N × H)
184. #1826C2×C31semidirect
185. C4×#99C2×C31semidirect
186. #1507C2×C31semidirect
187. #1465C2×C31semidirect
220. C2×C4⋊Q8C4×C31semidirect
224. C2×#121C4×C31semidirect
226. C2×C4×D4C4×C31semidirect
229. C2×#117C4×C31semidirect
295. C31#8360direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5552
C31×#18262
C4×C31×#992
C31×#15072
C31×#14652
#836031