Finite Group Databasebeta

← C31×#61935 #21518694

Subgroups — C31×#61935 #21518694

Order 7936.

1746 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3548C211yesmaximal, characteristic, complemented
2C31×#3509C211yesmaximal, characteristic, complemented
3C31×#3397C214yesmaximal, complemented
4C31×#3392C214yesmaximal, complemented
5C31×#3372C214yesmaximal, complemented
6C31×#3360C214yesmaximal, complemented
7C31×#3221C214yesmaximal, complemented
8C31×#3206C212yesmaximal, complemented
9C31×#3126C214yesmaximal, complemented
10C31×#3106C212yesmaximal, complemented
11C31×#2986C211yesmaximal, characteristic, complemented
12C31×#562—22no—
13C31×#557C2214yes—
14C31×#556C2214yes—
15C31×#554C2214yes—
16C31×#552—24no—
17C31×#550C2214yes—
18C31×#547—22no—
19C31×#541—22no—
20C31×#540C2214yes—
21C31×#537—24no—
22C31×#536C2212yes—
23C31×#533—22no—
24C31×#533C2211yescharacteristic
25C31×#532C2212yes—
26C2×C31×C4⋊Q8C2211yescharacteristic
27C31×#519C2212yes—
28C4×#41×C31C2211yescharacteristic
29C31×#496C2214yes—
30C31×#492C2214yes—
31C31×#492C2214yes—
32C31×#491C2214yes—
33C31×#488C2214yes—
34C31×#487C2214yes—
35C31×#482C2214yes—
36C31×#479C2218yes—
37C31×#477C2212yes—
38C31×#476C2212yes—
39C31×#463C2218yes—
40C31×#461C2214yes—
41C31×#461C2218yes—
42C31×#461C2214yes—
43C31×#460C2212yes—
44C31×#460C2218yes—
45C31×#459C2212yes—
46C31×#449C2214yes—
47C31×#448C2218yes—
48C31×#446C2214yes—
49C8×Q8×C31C2214yes—
50C31×#440C2218yes—
51C4×SD16×C31C2218yes—
52C4×SD16×C31C2214yes—
53C4×D8×C31C2214yes—
54C31×#433C2214yes—
55C31×#431C2212yes—
56C2×#41×C31—24no—
57C2×#41×C31—22no—
58C2×#41×C31C2311yescharacteristic
59C22×Q8×C31C2312yes—
60C2×SD16×C31C2318yes—
61C2×SD16×C31C2314yes—
62C2×SD16×C31C2318yes—
63C2×D8×C31C2314yes—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8D412yes—
67C31×C4⋊Q8C2314yes—
68C31×C4⋊Q8C2314yes—
69C31×C4⋊Q8C2312yes—
70C31×#127C2312yes—
71C31×#127C2314yes—
72C31×#126—28no—
73C31×#125—24no—
74C31×#125—28no—
75C31×#125D412yes—
76C31×#125C2314yes—
77C31×#124—22no—
78C31×#124C2314yes—
79C31×#123—28no—
80C31×#123—24no—
81C31×C22⋊Q8—24no—
82C31×C22⋊Q8—24no—
83C31×C22⋊Q8—24no—
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8D414yes—
86C31×#121—22no—
87C31×#121—24no—
88C31×#121—28no—
89C31×#121—28no—
90C31×#121C2314yes—
91C4×Q8×C31—24no—
92C4×Q8×C31—24no—
93C4×Q8×C31C2312yes—
94C4×Q8×C31C2318yes—
95C4×Q8×C31C2314yes—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31C2312yes—
99C4×D4×C31C2314yes—
100C4×D4×C31C2318yes—
101C31×#117—24no—
102C31×#117—24no—
103C31×#117—21no—
104C31×#117C2311yescharacteristic
105C31×#117C2312yes—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—24no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C31×#107C2314yes—
111C31×#106C2314yes—
112C31×C4⋊C8C2312yes—
113C31×C4⋊C8C2312yes—
114C31×C4⋊C8C2318yes—
115C31×#103C2318yes—
116C31×#103C2314yes—
117C31×#103C2318yes—
118C31×#102C2314yes—
119C31×#102C2314yes—
120C31×#102C2314yes—
121C31×C22⋊C8C2314yes—
122C31×#97C2314yes—
123C4×C8×C31C2314yes—
124C4×C8×C31C2314yes—
125#41×C31—42no—
126#41×C31—84no—
127#41×C31—88no—
128C2×Q8×C31—22no—
129C2×Q8×C31—22no—
130C2×Q8×C31—44no—
131C2×Q8×C31C2×D414yes—
132C2×Q8×C31C2414yes—
133C2×Q8×C31C2411yescharacteristic
134C2×D4×C31—21no—
135C2×D4×C31—24no—
136C2×D4×C31—22no—
137C2×D4×C31—28no—
138C2×D4×C31—22no—
139C2×D4×C31C2411yescharacteristic
140C2×D4×C31C2414yes—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—24no—
145C22×C4×C31—28no—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2411yescharacteristic
148SD16×C31—48no—
149SD16×C31—48no—
150SD16×C31—44no—
151D8×C31—44no—
152C2×C8×C31C2414yes—
153C2×C8×C31C2414yes—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—24no—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—28no—
160C4⋊C4×C31—28no—
161C4⋊C4×C31C2×D414yes—
162C4⋊C4×C31C2×D414yes—
163C4⋊C4×C31C2×D418yes—
164C4⋊C4×C31C2412yes—
165C4⋊C4×C31C2414yes—
166C22⋊C4×C31—21no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—28no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31C2×D414yes—
173C42×C31—21no—
174C42×C31—22no—
175C42×C31—28no—
176C42×C31C2×D411yescharacteristic
177C42×C31C2×D411yescharacteristic
178C42×C31C2412yes—
179C42×C31C2414yes—
180#61935C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—21no—
182C23×C31—24no—
183C23×C31C22×D411yescharacteristic
184Q8×C31—28no—
185Q8×C31—28no—
186Q8×C31—22no—
187Q8×C31—44no—
188Q8×C31—82no—
189D4×C31—22no—
190D4×C31—24no—
191D4×C31—24no—
192D4×C31—42no—
193D4×C31—44no—
194D4×C31—82no—
195D4×C31—88no—
196D4×C31—84no—
197C2×C4×C31—24no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—24no—
201C2×C4×C31—21no—
202C2×C4×C31—24no—
203C2×C4×C31—42no—
204C2×C4×C31—44no—
205C2×C4×C31—44no—
206C2×C4×C31—48no—
207C2×C4×C31—88no—
208C2×C4×C31C22×D411yescharacteristic
209C2×C4×C31C22×D418yes—
210C2×C4×C31C22×D412yes—
211C2×C4×C31C22×D412yes—
212C2×C4×C31C2511yescharacteristic
213C8×C31—24no—
214C8×C31—24no—
215#3548C2×C3111yescharacteristic, complemented
216#3509C2×C3111yescharacteristic, complemented
217#3397C2×C3114yescomplemented
218#3392C2×C3114yescomplemented
219#3372C2×C3114yescomplemented
220#3360C2×C3114yescomplemented
221#3221C2×C3114yescomplemented
222#3206C2×C3112yescomplemented
223#3126C2×C3114yescomplemented
224#3106C2×C3112yescomplemented
225#2986C2×C3111yescharacteristic, complemented
226C22×C31—21no—
227C22×C31—22no—
228C22×C31—41no—
229C22×C31—44no—
230C22×C31—44no—
231C22×C31—42no—
232C22×C31—44no—
233C22×C31C23×D411yescharacteristic
234C4×C31—21no—
235C4×C31—22no—
236C4×C31—28no—
237C4×C31—41no—
238C4×C31—44no—
239C4×C31—42no—
240C4×C31—44no—
241C4×C31#57714yes—
242C4×C31#58512yes—
243#562—22no—
244#557C22×C3114yes—
245#556C22×C3114yes—
246#554C22×C3114yes—
247#552—24no—
248#550C22×C3114yes—
249#547—22no—
250#541—22no—
251#540C22×C3114yes—
252#537—24no—
253#536C22×C3112yes—
254#533—22no—
255#533C22×C3111yescharacteristic
256#532C22×C3112yes—
257C2×C4⋊Q8C22×C3111yescharacteristic
258#519C22×C3112yes—
259C4×#41C22×C3111yescharacteristic
260#496C22×C3114yes—
261#492C22×C3114yes—
262#492C22×C3114yes—
263#491C22×C3114yes—
264#488C22×C3114yes—
265#487C22×C3114yes—
266#482C22×C3114yes—
267#479C22×C3118yes—
268#477C22×C3112yes—
269#476C22×C3112yes—
270#463C22×C3118yes—
271#461C22×C3114yes—
272#461C22×C3118yes—
273#461C22×C3114yes—
274#460C22×C3112yes—
275#460C22×C3118yes—
276#459C22×C3112yes—
277#449C22×C3114yes—
278#448C22×C3118yes—
279#446C22×C3114yes—
280C8×Q8C22×C3114yes—
281#440C22×C3118yes—
282C4×SD16C22×C3118yes—
283C4×SD16C22×C3114yes—
284C4×D8C22×C3114yes—
285#433C22×C3114yes—
286#431C22×C3112yes—
287C2×C31—41no—
288C2×C31—81no—
289C2×C31—84no—
290C2×C31#348711yescharacteristic
291C2×C31C2×#57712yes—
292C2×#41—24no—
293C2×#41—22no—
294C2×#41C23×C3111yescharacteristic
295C22×Q8C23×C3112yes—
296C2×SD16C23×C3118yes—
297C2×SD16C23×C3114yes—
298C2×SD16C23×C3118yes—
299C2×D8C23×C3114yes—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8D4×C3112yes—
303C4⋊Q8C23×C3114yes—
304C4⋊Q8C23×C3114yes—
305C4⋊Q8C23×C3112yes—
306#127C23×C3112yes—
307#127C23×C3114yes—
308#126—28no—
309#125—24no—
310#125—28no—
311#125D4×C3112yes—
312#125C23×C3114yes—
313#124—22no—
314#124C23×C3114yes—
315#123—28no—
316#123—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—28no—
321C22⋊Q8D4×C3114yes—
322#121—22no—
323#121—24no—
324#121—28no—
325#121—28no—
326#121C23×C3114yes—
327C4×Q8—24no—
328C4×Q8—24no—
329C4×Q8C23×C3112yes—
330C4×Q8C23×C3118yes—
331C4×Q8C23×C3114yes—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4C23×C3112yes—
335C4×D4C23×C3114yes—
336C4×D4C23×C3118yes—
337#117—24no—
338#117—24no—
339#117—21no—
340#117C23×C3111yescharacteristic
341#117C23×C3112yes—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C42—21no—
345C2×C42C23×C3111yescharacteristic
346#107C23×C3114yes—
347#106C23×C3114yes—
348C4⋊C8C23×C3112yes—
349C4⋊C8C23×C3112yes—
350C4⋊C8C23×C3118yes—
351#103C23×C3118yes—
352#103C23×C3114yes—
353#103C23×C3118yes—
354#102C23×C3114yes—
355#102C23×C3114yes—
356#102C23×C3114yes—
357C22⋊C8C23×C3114yes—
358#97C23×C3114yes—
359C4×C8C23×C3114yes—
360C4×C8C23×C3114yes—
361C31#6193511yescharacteristic, direct product factor, Sylow
362#41—42no—
363#41—84no—
364#41—88no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—44no—
368C2×Q8C2×D4×C3114yes—
369C2×Q8C24×C3114yes—
370C2×Q8C24×C3111yescharacteristic
371C2×D4—21no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—28no—
375C2×D4—22no—
376C2×D4C24×C3111yescharacteristic
377C2×D4C24×C3114yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—24no—
382C22×C4—28no—
383C22×C4C2×D4×C3112yes—
384C22×C4C24×C3111yescharacteristic
385SD16—48no—
386SD16—48no—
387SD16—44no—
388D8—44no—
389C2×C8C24×C3114yes—
390C2×C8C24×C3114yes—
391C4⋊C4—22no—
392C4⋊C4—24no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4C2×D4×C3114yes—
399C4⋊C4C2×D4×C3114yes—
400C4⋊C4C2×D4×C3118yes—
401C4⋊C4C24×C3112yes—
402C4⋊C4C24×C3114yes—
403C22⋊C4—21no—
404C22⋊C4—22no—
405C22⋊C4—28no—
406C22⋊C4—24no—
407C22⋊C4—28no—
408C22⋊C4—24no—
409C22⋊C4C2×D4×C3114yes—
410C42—21no—
411C42—22no—
412C42—28no—
413C42C2×D4×C3111yescharacteristic
414C42C2×D4×C3111yescharacteristic
415C42C24×C3112yes—
416C42C24×C3114yes—
417C23—21no—
418C23—24no—
419C23C22×D4×C3111yescharacteristic
420Q8—28no—
421Q8—28no—
422Q8—22no—
423Q8—44no—
424Q8—82no—
425D4—22no—
426D4—24no—
427D4—24no—
428D4—42no—
429D4—44no—
430D4—82no—
431D4—88no—
432D4—84no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—48no—
443C2×C4—88no—
444C2×C4C22×D4×C3111yescharacteristic
445C2×C4C22×D4×C3118yes—
446C2×C4C22×D4×C3112yes—
447C2×C4C22×D4×C3112yes—
448C2×C4C25×C3111yescharacteristic
449C8—24no—
450C8—24no—
451C22—21no—
452C22—22no—
453C22—41no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—44no—
458C22C23×D4×C3111yescharacteristic
459C4—21no—
460C4—22no—
461C4—28no—
462C4—41no—
463C4—44no—
464C4—44no—
465C4—42no—
466C4C31×#57714yes—
467C4C31×#58512yes—
468C2—41no—
469C2—81no—
470C2—84no—
471C2C31×#348711yescharacteristic
472C2C2×C31×#57712yes—
subgroupG/H
center, socleC22×C31C23×D4
commutator, Frattini, cosocleC2×C4C25×C31
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C31×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3548C2semidirect
2. C31×#3509C2semidirect
3. C31×#3397C2semidirect
4. C31×#3392C2semidirect
5. C31×#3372C2semidirect
6. C31×#3360C2semidirect
7. C31×#3221C2semidirect
8. C31×#3206C2semidirect
9. C31×#3126C2semidirect
10. C31×#3106C2semidirect
11. C31×#2986C2semidirect
180. #61935C31direct (N × H)
215. #3548C2×C31semidirect
216. #3509C2×C31semidirect
217. #3397C2×C31semidirect
218. #3392C2×C31semidirect
219. #3372C2×C31semidirect
220. #3360C2×C31semidirect
221. #3221C2×C31semidirect
222. #3206C2×C31semidirect
223. #3126C2×C31semidirect
224. #3106C2×C31semidirect
225. #2986C2×C31semidirect
361. C31#61935direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35482
C31×#35092
C31×#33972
C31×#33922
C31×#33722
C31×#33602
C31×#32212
C31×#32062
C31×#31262
C31×#31062
C31×#29862
#6193531