Finite Group Databasebeta

← C31×#35119 #21491878

Subgroups — C31×#35119 #21491878

Order 7936.

2262 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C212yesmaximal, complemented
2C31×#2854C214yesmaximal, complemented
3C31×#2659C211yesmaximal, characteristic, complemented
4C31×#2656C211yesmaximal, characteristic
5C31×#2639C212yesmaximal, complemented
6C31×#2611C214yesmaximal, complemented
7C31×#2610C214yesmaximal, complemented
8C31×#2604C214yesmaximal, complemented
9C31×#2603C214yesmaximal, complemented
10C31×#2325C214yesmaximal, complemented
11C2×C31×#376C211yesmaximal, characteristic, complemented
12C31×#529—216no—
13C2×C31×#126C2214yes—
14C2×C31×#125C2212yes—
15C2×C31×#124C2212yes—
16C2×C31×#123C2214yes—
17C2×C31×C22⋊Q8C2212yes—
18C2×C31×#121C2214yes—
19C2×C31×#121C2212yes—
20C2×C4×Q8×C31C2212yes—
21C2×C4×D4×C31C2214yes—
22C2×C4×D4×C31C2212yes—
23C2×C31×#117C2214yes—
24C22×C42×C31C2212yes—
25C22×C42×C31C2211yescharacteristic
26C31×#400C2214yes—
27C31×#399C2214yes—
28C31×#398C2214yes—
29C31×#397C2214yes—
30C31×#395C2214yes—
31C31×#394C2214yes—
32C31×#393C2214yes—
33C31×#392C2214yes—
34C31×#390C2214yes—
35C31×#390C2214yes—
36C31×#389C2214yes—
37C31×#389C2214yes—
38C31×#388C2218yes—
39C31×#388C2218yes—
40C31×#388C2218yes—
41C31×#387C2218yes—
42C31×#386C2218yes—
43C31×#386C2218yes—
44C31×#385C2218yes—
45C31×#380C2214yes—
46C31×#376C2214yes—
47C31×#376C2214yes—
48C2×C31×#95C2212yes—
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C22×Q8×C31C2312yes—
52C22×D4×C31C2314yes—
53C22×D4×C31C2312yes—
54C22×D4×C31C2314yes—
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2312yes—
57C23×C4×C31C2314yes—
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C31×#126—216no—
62C31×#125—28no—
63C31×#124—28no—
64C31×#123—216no—
65C31×C22⋊Q8—28no—
66C31×#121—28no—
67C31×#121—216no—
68C4×Q8×C31—28no—
69C4×D4×C31—216no—
70C4×D4×C31—28no—
71C31×#117—216no—
72C2×C4⋊C4×C31C2314yes—
73C2×C4⋊C4×C31C2312yes—
74C2×C4⋊C4×C31C2312yes—
75C2×C4⋊C4×C31C2314yes—
76C2×C4⋊C4×C31C2314yes—
77C2×C4⋊C4×C31C2314yes—
78C2×C4⋊C4×C31C2314yes—
79C2×C4⋊C4×C31C2314yes—
80C2×C4⋊C4×C31C2314yes—
81C2×C22⋊C4×C31C2314yes—
82C2×C22⋊C4×C31C2318yes—
83C2×C22⋊C4×C31C2314yes—
84C2×C22⋊C4×C31C2314yes—
85C2×C22⋊C4×C31C2314yes—
86C2×C22⋊C4×C31C2314yes—
87C2×C22⋊C4×C31C2318yes—
88C2×C22⋊C4×C31C2318yes—
89C2×C42×C31—28no—
90C2×C42×C31D418yescomplemented
91C2×C42×C31C2314yes—
92C2×C42×C31C2314yes—
93C2×C42×C31C2314yes—
94C2×C42×C31C2312yes—
95C2×C42×C31C2312yes—
96C31×#95C2314yes—
97C31×#95C2318yes—
98C31×#95C2314yes—
99C31×#95C2318yes—
100C31×#95C2318yes—
101C31×#95C2318yes—
102C24×C31C2414yes—
103C24×C31C2411yescharacteristic
104C2×Q8×C31—24no—
105C2×Q8×C31—44no—
106C2×D4×C31—28no—
107C2×D4×C31—216no—
108C2×D4×C31—24no—
109C2×D4×C31—28no—
110C2×D4×C31—44no—
111C2×D4×C31—44no—
112C2×D4×C31—44no—
113C22×C4×C31—24no—
114C22×C4×C31—24no—
115C22×C4×C31—28no—
116C22×C4×C31—42no—
117C22×C4×C31—42no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—44no—
121C22×C4×C31—44no—
122C22×C4×C31—42no—
123C22×C4×C31—42no—
124C22×C4×C31—42no—
125C22×C4×C31C2×D414yes—
126C22×C4×C31C2×D414yes—
127C22×C4×C31C2×D414yes—
128C22×C4×C31#4118yes—
129C22×C4×C31C2414yes—
130C22×C4×C31C2414yes—
131C22×C4×C31C2414yes—
132C22×C4×C31C2414yes—
133C22×C4×C31C2412yes—
134C22×C4×C31C2412yes—
135C22×C4×C31C2411yescharacteristic
136C22×C4×C31C2411yescharacteristic
137C22×C4×C31C2414yes—
138C4⋊C4×C31—28no—
139C4⋊C4×C31—28no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—28no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—28no—
144C4⋊C4×C31—28no—
145C4⋊C4×C31—44no—
146C4⋊C4×C31—44no—
147C22⋊C4×C31—28no—
148C22⋊C4×C31—28no—
149C22⋊C4×C31—28no—
150C22⋊C4×C31—28no—
151C22⋊C4×C31—28no—
152C22⋊C4×C31—216no—
153C22⋊C4×C31—48no—
154C22⋊C4×C31—48no—
155C42×C31—28no—
156C42×C31—28no—
157C42×C31—28no—
158C42×C31C2×D418yes—
159C42×C31C2×D418yes—
160#35119C3111yesmaximal, characteristic, direct product factor, Sylow
161C23×C31—21no—
162C23×C31—22no—
163C23×C31—21no—
164C23×C31—24no—
165C23×C31—28no—
166C23×C31—24no—
167C23×C31—28no—
168C23×C31—24no—
169C23×C31C22×D412yes—
170C23×C31C2×#4114yes—
171C23×C31C2511yescharacteristic
172Q8×C31—48no—
173D4×C31—48no—
174D4×C31—416no—
175D4×C31—88no—
176C2×C4×C31—28no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—28no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—28no—
193C2×C4×C31—24no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31—48no—
197C2×C4×C31—416no—
198C2×C4×C31—48no—
199C2×C4×C31C22×D414yes—
200C2×C4×C31C22×D412yes—
201C2×C4×C31C22×D412yes—
202C2×C4×C31C22×D414yes—
203C2×C4×C31C2×#4118yes—
204C2×#529C2×C3112yescomplemented
205#2854C2×C3114yescomplemented
206#2659C2×C3111yescharacteristic, complemented
207#2656C2×C3111yescharacteristic
208#2639C2×C3112yescomplemented
209#2611C2×C3114yescomplemented
210#2610C2×C3114yescomplemented
211#2604C2×C3114yescomplemented
212#2603C2×C3114yescomplemented
213#2325C2×C3114yescomplemented
214C2×#376C2×C3111yescharacteristic, complemented
215C22×C31—22no—
216C22×C31—22no—
217C22×C31—24no—
218C22×C31—24no—
219C22×C31—44no—
220C22×C31—44no—
221C22×C31—44no—
222C22×C31—48no—
223C22×C31—48no—
224C22×C31#53214yes—
225C22×C31C23×D411yescharacteristic
226C22×C31C22×#4112yes—
227C22×C31#58511yescharacteristic
228C22×C31#58512yes—
229C22×C31#58511yescharacteristic
230C4×C31—22no—
231C4×C31—22no—
232C4×C31—24no—
233C4×C31—24no—
234C4×C31—28no—
235C4×C31—44no—
236C4×C31—44no—
237C4×C31—44no—
238C4×C31—44no—
239#529—216no—
240C2×#126C22×C3114yes—
241C2×#125C22×C3112yes—
242C2×#124C22×C3112yes—
243C2×#123C22×C3114yes—
244C2×C22⋊Q8C22×C3112yes—
245C2×#121C22×C3114yes—
246C2×#121C22×C3112yes—
247C2×C4×Q8C22×C3112yes—
248C2×C4×D4C22×C3114yes—
249C2×C4×D4C22×C3112yes—
250C2×#117C22×C3114yes—
251C22×C42C22×C3112yes—
252C22×C42C22×C3111yescharacteristic
253#400C22×C3114yes—
254#399C22×C3114yes—
255#398C22×C3114yes—
256#397C22×C3114yes—
257#395C22×C3114yes—
258#394C22×C3114yes—
259#393C22×C3114yes—
260#392C22×C3114yes—
261#390C22×C3114yes—
262#390C22×C3114yes—
263#389C22×C3114yes—
264#389C22×C3114yes—
265#388C22×C3118yes—
266#388C22×C3118yes—
267#388C22×C3118yes—
268#387C22×C3118yes—
269#386C22×C3118yes—
270#386C22×C3118yes—
271#385C22×C3118yes—
272#380C22×C3114yes—
273#376C22×C3114yes—
274#376C22×C3114yes—
275C2×#95C22×C3112yes—
276C2×#95C22×C3111yescharacteristic
277C2×#95C22×C3111yescharacteristic
278C2×C31—24no—
279C2×C31—84no—
280C2×C31C2×#53211yescharacteristic
281C2×C31#344911yescharacteristic
282C2×C31#344911yescharacteristic
283C2×C31#349112yes—
284C2×C31#349312yes—
285C22×Q8C23×C3112yes—
286C22×D4C23×C3114yes—
287C22×D4C23×C3112yes—
288C22×D4C23×C3114yes—
289C23×C4C23×C3111yescharacteristic
290C23×C4C23×C3114yes—
291C23×C4C23×C3112yes—
292C23×C4C23×C3111yescharacteristic
293C23×C4C23×C3111yescharacteristic
294C23×C4C23×C3112yes—
295#126—216no—
296#125—28no—
297#124—28no—
298#123—216no—
299C22⋊Q8—28no—
300#121—28no—
301#121—216no—
302C4×Q8—28no—
303C4×D4—216no—
304C4×D4—28no—
305#117—216no—
306C2×C4⋊C4C23×C3114yes—
307C2×C4⋊C4C23×C3114yes—
308C2×C4⋊C4C23×C3112yes—
309C2×C4⋊C4C23×C3114yes—
310C2×C4⋊C4C23×C3112yes—
311C2×C4⋊C4C23×C3114yes—
312C2×C4⋊C4C23×C3114yes—
313C2×C4⋊C4C23×C3114yes—
314C2×C4⋊C4C23×C3114yes—
315C2×C22⋊C4C23×C3114yes—
316C2×C22⋊C4C23×C3114yes—
317C2×C22⋊C4C23×C3114yes—
318C2×C22⋊C4C23×C3114yes—
319C2×C22⋊C4C23×C3114yes—
320C2×C22⋊C4C23×C3118yes—
321C2×C22⋊C4C23×C3118yes—
322C2×C22⋊C4C23×C3118yes—
323C2×C42—28no—
324C2×C42D4×C3118yescomplemented
325C2×C42C23×C3114yes—
326C2×C42C23×C3114yes—
327C2×C42C23×C3114yes—
328C2×C42C23×C3112yes—
329C2×C42C23×C3112yes—
330#95C23×C3118yes—
331#95C23×C3114yes—
332#95C23×C3114yes—
333#95C23×C3118yes—
334#95C23×C3118yes—
335#95C23×C3118yes—
336C31#3511911yescharacteristic, direct product factor, Sylow
337C24C24×C3114yes—
338C24C24×C3111yescharacteristic
339C2×Q8—24no—
340C2×Q8—44no—
341C2×D4—28no—
342C2×D4—216no—
343C2×D4—24no—
344C2×D4—28no—
345C2×D4—44no—
346C2×D4—44no—
347C2×D4—44no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—28no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4C2×D4×C3114yes—
361C22×C4C2×D4×C3114yes—
362C22×C4C2×D4×C3114yes—
363C22×C4#41×C3118yes—
364C22×C4C24×C3114yes—
365C22×C4C24×C3114yes—
366C22×C4C24×C3114yes—
367C22×C4C24×C3114yes—
368C22×C4C24×C3112yes—
369C22×C4C24×C3112yes—
370C22×C4C24×C3111yescharacteristic
371C22×C4C24×C3111yescharacteristic
372C22×C4C24×C3114yes—
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—24no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—28no—
386C22⋊C4—28no—
387C22⋊C4—216no—
388C22⋊C4—48no—
389C22⋊C4—48no—
390C42—28no—
391C42—28no—
392C42—28no—
393C42C2×D4×C3118yes—
394C42C2×D4×C3118yes—
395C23—21no—
396C23—22no—
397C23—21no—
398C23—24no—
399C23—28no—
400C23—24no—
401C23—28no—
402C23—24no—
403C23C22×D4×C3112yes—
404C23C2×#41×C3114yes—
405C23C25×C3111yescharacteristic
406Q8—48no—
407D4—48no—
408D4—416no—
409D4—88no—
410C2×C4—28no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—28no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—416no—
432C2×C4—48no—
433C2×C4C22×D4×C3114yes—
434C2×C4C22×D4×C3112yes—
435C2×C4C22×D4×C3112yes—
436C2×C4C22×D4×C3114yes—
437C2×C4C2×#41×C3118yes—
438C22—22no—
439C22—22no—
440C22—24no—
441C22—24no—
442C22—44no—
443C22—44no—
444C22—44no—
445C22—48no—
446C22—48no—
447C22C31×#53214yes—
448C22C23×D4×C3111yescharacteristic
449C22C22×#41×C3112yes—
450C22C31×#58511yescharacteristic
451C22C31×#58512yes—
452C22C31×#58511yescharacteristic
453C4—22no—
454C4—22no—
455C4—24no—
456C4—24no—
457C4—28no—
458C4—44no—
459C4—44no—
460C4—44no—
461C4—44no—
462C2—24no—
463C2—84no—
464C2C2×C31×#53211yescharacteristic
465C2C31×#344911yescharacteristic
466C2C31×#344911yescharacteristic
467C2C31×#349112yes—
468C2C31×#349312yes—
subgroupG/H
center, socleC23×C31C25
commutator, Frattini, cosocleC23C25×C31
prime radicalC31×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#529C2semidirect
2. C31×#2854C2semidirect
3. C31×#2659C2semidirect
5. C31×#2639C2semidirect
6. C31×#2611C2semidirect
7. C31×#2610C2semidirect
8. C31×#2604C2semidirect
9. C31×#2603C2semidirect
10. C31×#2325C2semidirect
11. C2×C31×#376C2semidirect
90. C2×C42×C31D4semidirect
160. #35119C31direct (N × H)
204. C2×#529C2×C31semidirect
205. #2854C2×C31semidirect
206. #2659C2×C31semidirect
208. #2639C2×C31semidirect
209. #2611C2×C31semidirect
210. #2610C2×C31semidirect
211. #2604C2×C31semidirect
212. #2603C2×C31semidirect
213. #2325C2×C31semidirect
214. C2×#376C2×C31semidirect
324. C2×C42D4×C31semidirect
336. C31#35119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C31×#28542
C31×#26592
C31×#26562
C31×#26392
C31×#26112
C31×#26102
C31×#26042
C31×#26032
C31×#23252
C2×C31×#3762
#3511931