Finite Group Databasebeta

← C31×#34594 #21491353

Subgroups — C31×#34594 #21491353

Order 7936.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C212yesmaximal, complemented
2C31×#2664C214yesmaximal, complemented
3C31×#2662C214yesmaximal, complemented
4C31×#2659C211yesmaximal, characteristic, complemented
5C31×#2656C211yesmaximal, characteristic
6C31×#2639C212yesmaximal, complemented
7C31×#2618C214yesmaximal, complemented
8C31×#2396C214yesmaximal, complemented
9C31×#2392C214yesmaximal, complemented
10C4×C31×#121C214yesmaximal, complemented
11C2×C4×C4⋊C4×C31C211yesmaximal, 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×C31C2212yes—
22C2×C4×D4×C31C2214yes—
23C2×C4×D4×C31C2214yes—
24C2×C31×#117C2214yes—
25C22×C4⋊C4×C31C2212yes—
26C22×C42×C31C2212yes—
27C22×C42×C31C2211yescharacteristic
28C31×#400C2214yes—
29C31×#399C2214yes—
30C31×#398C2218yes—
31C31×#398C2214yes—
32C31×#397C2214yes—
33C31×#396C2218yes—
34C31×#396C2218yes—
35C31×#395C2214yes—
36C31×#394C2218yes—
37C31×#394C2214yes—
38C31×#393C2214yes—
39C31×#392C2214yes—
40C31×#390C2214yes—
41C31×#389C2214yes—
42C31×#388C2218yes—
43C31×#386C2218yes—
44C31×#380C2214yes—
45C4×C4⋊C4×C31C2214yes—
46C4×C4⋊C4×C31C2214yes—
47C4×C4⋊C4×C31C2214yes—
48C4×C22⋊C4×C31C2218yes—
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C22×Q8×C31C2312yes—
52C22×D4×C31C2314yes—
53C22×D4×C31C2312yes—
54C22×D4×C31C2314yes—
55C23×C4×C31C2314yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2312yes—
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—
71C4×D4×C31—48no—
72C31×#117—216no—
73C2×C4⋊C4×C31—28no—
74C2×C4⋊C4×C31C2314yes—
75C2×C4⋊C4×C31C2314yes—
76C2×C4⋊C4×C31C2314yes—
77C2×C4⋊C4×C31C2318yes—
78C2×C4⋊C4×C31C2312yes—
79C2×C4⋊C4×C31C2314yes—
80C2×C4⋊C4×C31C2312yes—
81C2×C4⋊C4×C31C2314yes—
82C2×C4⋊C4×C31C2314yes—
83C2×C4⋊C4×C31C2314yes—
84C2×C22⋊C4×C31C2318yes—
85C2×C22⋊C4×C31C2314yes—
86C2×C22⋊C4×C31C2314yes—
87C2×C22⋊C4×C31C2314yes—
88C2×C22⋊C4×C31C2314yes—
89C2×C22⋊C4×C31C2314yes—
90C2×C22⋊C4×C31C2318yes—
91C2×C22⋊C4×C31C2318yes—
92C2×C42×C31—44no—
93C2×C42×C31D418yescomplemented
94C2×C42×C31C2314yes—
95C2×C42×C31C2314yes—
96C2×C42×C31C2314yes—
97C2×C42×C31C2312yes—
98C2×C42×C31C2312yes—
99C31×#95C2318yes—
100C31×#95C2314yes—
101C31×#95C2318yes—
102C31×#95C2318yes—
103C31×#95C2314yes—
104C24×C31C2414yes—
105C24×C31C2411yescharacteristic
106C2×Q8×C31—24no—
107C2×Q8×C31—44no—
108C2×D4×C31—28no—
109C2×D4×C31—216no—
110C2×D4×C31—24no—
111C2×D4×C31—28no—
112C2×D4×C31—44no—
113C2×D4×C31—44no—
114C2×D4×C31—44no—
115C22×C4×C31—24no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—24no—
119C22×C4×C31—28no—
120C22×C4×C31—28no—
121C22×C4×C31—28no—
122C22×C4×C31—42no—
123C22×C4×C31—42no—
124C22×C4×C31—42no—
125C22×C4×C31—42no—
126C22×C4×C31—42no—
127C22×C4×C31C2×D414yes—
128C22×C4×C31C2×D414yes—
129C22×C4×C31C2×D414yes—
130C22×C4×C31#4118yes—
131C22×C4×C31C2414yes—
132C22×C4×C31C2414yes—
133C22×C4×C31C2414yes—
134C22×C4×C31C2414yes—
135C22×C4×C31C2412yes—
136C22×C4×C31C2411yescharacteristic
137C22×C4×C31C2412yes—
138C22×C4×C31C2414yes—
139C22×C4×C31C2411yescharacteristic
140C4⋊C4×C31—28no—
141C4⋊C4×C31—28no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—28no—
144C4⋊C4×C31—24no—
145C4⋊C4×C31—28no—
146C4⋊C4×C31—216no—
147C4⋊C4×C31—28no—
148C4⋊C4×C31—44no—
149C4⋊C4×C31—44no—
150C22⋊C4×C31—28no—
151C22⋊C4×C31—28no—
152C22⋊C4×C31—28no—
153C22⋊C4×C31—28no—
154C22⋊C4×C31—28no—
155C22⋊C4×C31—216no—
156C22⋊C4×C31—48no—
157C22⋊C4×C31—48no—
158C42×C31—28no—
159C42×C31—28no—
160C42×C31—44no—
161C42×C31C2×D418yes—
162C42×C31C2×D418yes—
163#34594C3111yesmaximal, characteristic, direct product factor, Sylow
164C23×C31—21no—
165C23×C31—21no—
166C23×C31—22no—
167C23×C31—24no—
168C23×C31—28no—
169C23×C31—24no—
170C23×C31—24no—
171C23×C31—28no—
172C23×C31C22×D412yes—
173C23×C31C2×#4114yes—
174C23×C31C2511yescharacteristic
175Q8×C31—48no—
176D4×C31—48no—
177D4×C31—416no—
178D4×C31—416no—
179C2×C4×C31—28no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—21no—
183C2×C4×C31—21no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—28no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—28no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—28no—
197C2×C4×C31—44no—
198C2×C4×C31—48no—
199C2×C4×C31—48no—
200C2×C4×C31—416no—
201C2×C4×C31C22×D414yes—
202C2×C4×C31C22×D412yes—
203C2×C4×C31C22×D414yes—
204C2×C4×C31C22×D412yes—
205C2×C4×C31C2×#4118yes—
206C2×C4×C31H(5,𝔽2)12yes—
207C2×C4×C312−1+412yes—
208C2×#529C2×C3112yescomplemented
209#2664C2×C3114yescomplemented
210#2662C2×C3114yescomplemented
211#2659C2×C3111yescharacteristic, complemented
212#2656C2×C3111yescharacteristic
213#2639C2×C3112yescomplemented
214#2618C2×C3114yescomplemented
215#2396C2×C3114yescomplemented
216#2392C2×C3114yescomplemented
217C4×#121C2×C3114yescomplemented
218C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
219C22×C31—22no—
220C22×C31—22no—
221C22×C31—24no—
222C22×C31—24no—
223C22×C31—44no—
224C22×C31—44no—
225C22×C31—44no—
226C22×C31—48no—
227C22×C31—48no—
228C22×C31#53214yes—
229C22×C31C23×D411yescharacteristic
230C22×C31C22×#4112yes—
231C22×C31C2×H(5,𝔽2)11yescharacteristic
232C22×C31C2×2−1+411yescharacteristic
233C22×C31#58512yes—
234C4×C31—24no—
235C4×C31—22no—
236C4×C31—24no—
237C4×C31—28no—
238C4×C31—44no—
239C4×C31—44no—
240C4×C31—44no—
241C4×C31—44no—
242C4×C31#53714yes—
243#529—216no—
244C2×#126C22×C3114yes—
245C2×#125C22×C3112yes—
246C2×#124C22×C3112yes—
247C2×#123C22×C3114yes—
248C2×C22⋊Q8C22×C3112yes—
249C2×#121C22×C3114yes—
250C2×#121C22×C3112yes—
251C2×C4×Q8C22×C3112yes—
252C2×C4×D4C22×C3112yes—
253C2×C4×D4C22×C3114yes—
254C2×C4×D4C22×C3114yes—
255C2×#117C22×C3114yes—
256C22×C4⋊C4C22×C3112yes—
257C22×C42C22×C3112yes—
258C22×C42C22×C3111yescharacteristic
259#400C22×C3114yes—
260#399C22×C3114yes—
261#398C22×C3118yes—
262#398C22×C3114yes—
263#397C22×C3114yes—
264#396C22×C3118yes—
265#396C22×C3118yes—
266#395C22×C3114yes—
267#394C22×C3118yes—
268#394C22×C3114yes—
269#393C22×C3114yes—
270#392C22×C3114yes—
271#390C22×C3114yes—
272#389C22×C3114yes—
273#388C22×C3118yes—
274#386C22×C3118yes—
275#380C22×C3114yes—
276C4×C4⋊C4C22×C3114yes—
277C4×C4⋊C4C22×C3114yes—
278C4×C4⋊C4C22×C3114yes—
279C4×C22⋊C4C22×C3118yes—
280C2×#95C22×C3111yescharacteristic
281C2×#95C22×C3111yescharacteristic
282C2×C31—24no—
283C2×C31—84no—
284C2×C31C2×#53211yescharacteristic
285C2×C31C2×#53711yescharacteristic
286C2×C31#344911yescharacteristic
287C2×C31#345912yes—
288C2×C31#346112yes—
289C22×Q8C23×C3112yes—
290C22×D4C23×C3114yes—
291C22×D4C23×C3112yes—
292C22×D4C23×C3114yes—
293C23×C4C23×C3114yes—
294C23×C4C23×C3111yescharacteristic
295C23×C4C23×C3111yescharacteristic
296C23×C4C23×C3112yes—
297C23×C4C23×C3111yescharacteristic
298C23×C4C23×C3112yes—
299#126—216no—
300#125—28no—
301#124—28no—
302#123—216no—
303C22⋊Q8—28no—
304#121—28no—
305#121—216no—
306C4×Q8—28no—
307C4×D4—216no—
308C4×D4—28no—
309C4×D4—48no—
310#117—216no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4C23×C3118yes—
313C2×C4⋊C4C23×C3114yes—
314C2×C4⋊C4C23×C3114yes—
315C2×C4⋊C4C23×C3112yes—
316C2×C4⋊C4C23×C3114yes—
317C2×C4⋊C4C23×C3112yes—
318C2×C4⋊C4C23×C3114yes—
319C2×C4⋊C4C23×C3114yes—
320C2×C4⋊C4C23×C3114yes—
321C2×C4⋊C4C23×C3114yes—
322C2×C22⋊C4C23×C3114yes—
323C2×C22⋊C4C23×C3114yes—
324C2×C22⋊C4C23×C3114yes—
325C2×C22⋊C4C23×C3114yes—
326C2×C22⋊C4C23×C3114yes—
327C2×C22⋊C4C23×C3118yes—
328C2×C22⋊C4C23×C3118yes—
329C2×C22⋊C4C23×C3118yes—
330C2×C42—44no—
331C2×C42D4×C3118yescomplemented
332C2×C42C23×C3114yes—
333C2×C42C23×C3114yes—
334C2×C42C23×C3114yes—
335C2×C42C23×C3112yes—
336C2×C42C23×C3112yes—
337#95C23×C3114yes—
338#95C23×C3114yes—
339#95C23×C3118yes—
340#95C23×C3118yes—
341#95C23×C3118yes—
342C31#3459411yescharacteristic, direct product factor, Sylow
343C24C24×C3114yes—
344C24C24×C3111yescharacteristic
345C2×Q8—24no—
346C2×Q8—44no—
347C2×D4—28no—
348C2×D4—216no—
349C2×D4—24no—
350C2×D4—28no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C2×D4×C3114yes—
367C22×C4C2×D4×C3114yes—
368C22×C4C2×D4×C3114yes—
369C22×C4#41×C3118yes—
370C22×C4C24×C3114yes—
371C22×C4C24×C3114yes—
372C22×C4C24×C3114yes—
373C22×C4C24×C3114yes—
374C22×C4C24×C3112yes—
375C22×C4C24×C3111yescharacteristic
376C22×C4C24×C3112yes—
377C22×C4C24×C3114yes—
378C22×C4C24×C3111yescharacteristic
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—24no—
384C4⋊C4—28no—
385C4⋊C4—216no—
386C4⋊C4—28no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C22⋊C4—216no—
395C22⋊C4—48no—
396C22⋊C4—48no—
397C42—28no—
398C42—28no—
399C42—44no—
400C42C2×D4×C3118yes—
401C42C2×D4×C3118yes—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C3112yes—
411C23C2×#41×C3114yes—
412C23C25×C3111yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C3114yes—
440C2×C4C22×D4×C3112yes—
441C2×C4C22×D4×C3114yes—
442C2×C4C22×D4×C3112yes—
443C2×C4C2×#41×C3118yes—
444C2×C4C31×H(5,𝔽2)12yes—
445C2×C4C31×2−1+412yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22C31×#53214yes—
456C22C23×D4×C3111yescharacteristic
457C22C22×#41×C3112yes—
458C22C2×C31×H(5,𝔽2)11yescharacteristic
459C22C2×C31×2−1+411yescharacteristic
460C22C31×#58512yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4C31×#53714yes—
470C2—24no—
471C2—84no—
472C2C2×C31×#53211yescharacteristic
473C2C2×C31×#53711yescharacteristic
474C2C31×#344911yescharacteristic
475C2C31×#345912yes—
476C2C31×#346112yes—
subgroupG/H
centerC22×C4×C31C24
commutator, Frattini, cosocleC23C25×C31
socleC23×C31C25
prime radicalC31×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#529C2semidirect
2. C31×#2664C2semidirect
3. C31×#2662C2semidirect
4. C31×#2659C2semidirect
6. C31×#2639C2semidirect
7. C31×#2618C2semidirect
8. C31×#2396C2semidirect
9. C31×#2392C2semidirect
10. C4×C31×#121C2semidirect
11. C2×C4×C4⋊C4×C31C2semidirect
93. C2×C42×C31D4semidirect
163. #34594C31direct (N × H)
208. C2×#529C2×C31semidirect
209. #2664C2×C31semidirect
210. #2662C2×C31semidirect
211. #2659C2×C31semidirect
213. #2639C2×C31semidirect
214. #2618C2×C31semidirect
215. #2396C2×C31semidirect
216. #2392C2×C31semidirect
217. C4×#121C2×C31semidirect
218. C2×C4×C4⋊C4C2×C31semidirect
331. C2×C42D4×C31semidirect
342. C31#34594direct (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×#26642
C31×#26622
C31×#26592
C31×#26562
C31×#26392
C31×#26182
C31×#23962
C31×#23922
C4×C31×#1212
C2×C4×C4⋊C4×C312
#3459431