Finite Group Databasebeta

← C31×#22478 #21479237

Subgroups — C31×#22478 #21479237

Order 7936.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#552C211yesmaximal, characteristic
2C31×#2344C212yesmaximal, complemented
3C31×#1996C212yesmaximal, complemented
4C31×#1899C214yesmaximal
5C31×#1820C212yesmaximal, complemented
6C31×#1799C211yesmaximal, characteristic
7C4×C31×#99C211yesmaximal, characteristic
8C31×#1740C212yesmaximal, complemented
9C31×#552—22no—
10C31×#552—24no—
11C31×#552—22no—
12C2×C31×#126C412yescomplemented
13C2×C31×#125C412yescomplemented
14C2×C31×#125C411yescharacteristic, complemented
15C2×C31×#123C2212yes—
16C2×C31×C22⋊Q8C411yescharacteristic, complemented
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C31C411yescharacteristic, complemented
19C2×C4×D4×C31C2211yescharacteristic
20C2×C31×#117C411yescharacteristic, complemented
21C2×C31×#117C2214yes—
22C2×C31×#117C2212yes—
23C22×C4⋊C4×C31C2211yescharacteristic
24C2×C31×#99C2212yes—
25C2×C31×#99C2212yes—
26C31×#389—22no—
27C31×#387—24no—
28C31×#381C2214yes—
29C31×#380C2212yes—
30C4×C4⋊C4×C31—22no—
31C4×C22⋊C4×C31C2212yes—
32C31×#342C2212yes—
33C31×#342C2211yescharacteristic
34C31×#342C2214yes—
35C31×#342C2214yes—
36C31×#342C2211yescharacteristic
37C22×Q8×C31C2×C411yescharacteristic
38C22×D4×C31C2311yescharacteristic
39C23×C4×C31C2×C411yescharacteristic
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C31×#126—24no—
43C31×#126—24no—
44C31×#125—24no—
45C31×#125—24no—
46C31×#125—22no—
47C31×#125—22no—
48C31×#123—24no—
49C31×#123—24no—
50C31×C22⋊Q8—22no—
51C31×C22⋊Q8—22no—
52C31×C22⋊Q8—22no—
53C31×C22⋊Q8—22no—
54C4×Q8×C31—22no—
55C4×Q8×C31—21no—
56C4×Q8×C31—21no—
57C4×D4×C31—22no—
58C4×D4×C31—22no—
59C31×#117—24no—
60C31×#117—24no—
61C31×#117—22no—
62C31×#117—21no—
63C31×#117—21no—
64C31×#117—28no—
65C31×#117—44no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31C2×C411yescharacteristic
69C2×C4⋊C4×C31C2×C412yes—
70C2×C4⋊C4×C31C2×C412yes—
71C2×C4⋊C4×C31C2×C411yescharacteristic
72C2×C4⋊C4×C31C2×C412yes—
73C2×C4⋊C4×C31C2×C412yes—
74C2×C4⋊C4×C31C2×C412yes—
75C2×C4⋊C4×C31C2×C411yescharacteristic
76C2×C4⋊C4×C31C2×C411yescharacteristic
77C2×C4⋊C4×C31C2×C412yes—
78C2×C4⋊C4×C31D412yes—
79C2×C4⋊C4×C31D414yes—
80C2×C4⋊C4×C31D412yes—
81C2×C22⋊C4×C31C2×C412yes—
82C2×C22⋊C4×C31C2×C411yescharacteristic
83C2×C22⋊C4×C31C2×C412yes—
84C2×C22⋊C4×C31C2314yes—
85C2×C22⋊C4×C31C2312yes—
86C2×C22⋊C4×C31C2311yescharacteristic
87C2×C22⋊C4×C31C2312yes—
88C2×C22⋊C4×C31C2312yes—
89C2×C42×C31—24no—
90C2×C42×C31—22no—
91C2×C42×C31C2×C412yes—
92C2×C42×C31C2×C412yes—
93C2×C42×C31C2×C411yescharacteristic
94C31×#99—24no—
95C31×#99—42no—
96C31×#95—22no—
97C31×#95—24no—
98C31×#95—22no—
99C31×#95—24no—
100C24×C31C22×C411yescharacteristic
101C24×C31C2411yescharacteristic
102C2×Q8×C31—21no—
103C2×Q8×C31—21no—
104C2×Q8×C31—42no—
105C2×D4×C31—22no—
106C2×D4×C31—22no—
107C2×D4×C31—21no—
108C2×D4×C31—21no—
109C22×C4×C31—24no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—24no—
117C22×C4×C31—42no—
118C22×C4×C31—42no—
119C22×C4×C31C22×C411yescharacteristic
120C22×C4×C31C22×C412yes—
121C22×C4×C31C22×C411yescharacteristic
122C22×C4×C31C22×C412yes—
123C22×C4×C31C22×C411yescharacteristic
124C22×C4×C31C22×C411yescharacteristic
125C22×C4×C31C22×C412yes—
126C22×C4×C31C22×C412yes—
127C22×C4×C31C22×C411yescharacteristic
128C22×C4×C31C2×D414yes—
129C22×C4×C31C2×D414yes—
130C22×C4×C31C2×D412yes—
131C22×C4×C31C2×D412yes—
132C4⋊C4×C31—24no—
133C4⋊C4×C31—21no—
134C4⋊C4×C31—21no—
135C4⋊C4×C31—24no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—24no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—48no—
142C4⋊C4×C31—44no—
143C4⋊C4×C31C22⋊C412yes—
144C4⋊C4×C31C22⋊C411yescharacteristic
145C4⋊C4×C31C22⋊C411yescharacteristic
146C4⋊C4×C31C22⋊C412yes—
147C4⋊C4×C31C22⋊C412yes—
148C4⋊C4×C31C22⋊C414yes—
149C4⋊C4×C31C22⋊C414yes—
150C22⋊C4×C31—22no—
151C22⋊C4×C31—24no—
152C22⋊C4×C31—22no—
153C22⋊C4×C31—22no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—22no—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—22no—
158C22⋊C4×C31—24no—
159C22⋊C4×C31—24no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31#4114yes—
162C42×C31—22no—
163C42×C31—22no—
164C42×C31—22no—
165C42×C31—22no—
166C42×C31—21no—
167C42×C31—21no—
168C42×C31—48no—
169C42×C31—44no—
170#22478C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—21no—
172C23×C31—21no—
173C23×C31—21no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31C23×C411yescharacteristic
179C23×C31C22×D412yes—
180C23×C31C2×#4112yes—
181C23×C31H(5,𝔽2)11yescharacteristic
182C23×C312−1+411yescharacteristic
183Q8×C31—42no—
184Q8×C31—42no—
185D4×C31—42no—
186D4×C31—42no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—22no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—22no—
197C2×C4×C31—21no—
198C2×C4×C31—21no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—24no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—44no—
217C2×C4×C31—42no—
218C2×C4×C31—44no—
219C2×C4×C31—44no—
220C2×C4×C31—42no—
221C2×C4×C31C2×C22⋊C412yes—
222C2×C4×C31C2×C22⋊C412yes—
223C2×C4×C31C2×C22⋊C411yescharacteristic
224C2×C4×C31C2×C22⋊C414yes—
225C2×C4×C31C2×C22⋊C412yes—
226C2×C4×C31C2×C22⋊C411yescharacteristic
227C2×#552C2×C3111yescharacteristic
228#2344C2×C3112yescomplemented
229#1996C2×C3112yescomplemented
230#1899C2×C3114yes—
231#1820C2×C3112yescomplemented
232#1799C2×C3111yescharacteristic
233C4×#99C2×C3111yescharacteristic
234#1740C2×C3112yescomplemented
235C22×C31—22no—
236C22×C31—21no—
237C22×C31—22no—
238C22×C31—21no—
239C22×C31—42no—
240C22×C31—41no—
241C22×C31—41no—
242C22×C31—41no—
243C22×C31—41no—
244C22×C31—41no—
245C22×C31—81no—
246C22×C31—81no—
247C22×C31C22×C22⋊C411yescharacteristic
248C22×C31C4×#4111yescharacteristic
249C22×C31#52011yescharacteristic
250C22×C31#54612yes—
251C22×C31#54712yes—
252C4×C31—22no—
253C4×C31—24no—
254C4×C31—22no—
255C4×C31—21no—
256C4×C31—22no—
257C4×C31—44no—
258C4×C31—41no—
259C4×C31—41no—
260C4×C31—42no—
261C4×C31—41no—
262C4×C31—42no—
263C4×C31—84no—
264C4×C31—82no—
265C4×C31#41012yes—
266#552—22no—
267#552—24no—
268#552—22no—
269C2×#126C4×C3112yescomplemented
270C2×#125C4×C3112yescomplemented
271C2×#125C4×C3111yescharacteristic, complemented
272C2×#123C22×C3112yes—
273C2×C22⋊Q8C4×C3111yescharacteristic, complemented
274C2×C22⋊Q8C22×C3111yescharacteristic
275C2×C4×Q8C4×C3111yescharacteristic, complemented
276C2×C4×D4C22×C3111yescharacteristic
277C2×#117C4×C3111yescharacteristic, complemented
278C2×#117C22×C3114yes—
279C2×#117C22×C3112yes—
280C22×C4⋊C4C22×C3111yescharacteristic
281C2×#99C22×C3112yes—
282C2×#99C22×C3112yes—
283#389—22no—
284#387—24no—
285#381C22×C3114yes—
286#380C22×C3112yes—
287C4×C4⋊C4—22no—
288C4×C22⋊C4C22×C3112yes—
289#342C22×C3112yes—
290#342C22×C3111yescharacteristic
291#342C22×C3114yes—
292#342C22×C3114yes—
293#342C22×C3111yescharacteristic
294C2×C31—22no—
295C2×C31—22no—
296C2×C31—21no—
297C2×C31—21no—
298C2×C31—81no—
299C2×C31#233911yescharacteristic
300C2×C31C2×#41011yescharacteristic
301C2×C31#288411yescharacteristic
302C22×Q8C2×C4×C3111yescharacteristic
303C22×D4C23×C3111yescharacteristic
304C23×C4C2×C4×C3111yescharacteristic
305C23×C4C23×C3112yes—
306C23×C4C23×C3111yescharacteristic
307#126—24no—
308#126—24no—
309#125—24no—
310#125—24no—
311#125—22no—
312#125—22no—
313#123—24no—
314#123—24no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C4×Q8—22no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×D4—22no—
323C4×D4—22no—
324#117—24no—
325#117—24no—
326#117—22no—
327#117—21no—
328#117—21no—
329#117—28no—
330#117—44no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4C2×C4×C3111yescharacteristic
334C2×C4⋊C4C2×C4×C3112yes—
335C2×C4⋊C4C2×C4×C3112yes—
336C2×C4⋊C4C2×C4×C3111yescharacteristic
337C2×C4⋊C4C2×C4×C3112yes—
338C2×C4⋊C4C2×C4×C3112yes—
339C2×C4⋊C4C2×C4×C3112yes—
340C2×C4⋊C4C2×C4×C3111yescharacteristic
341C2×C4⋊C4C2×C4×C3111yescharacteristic
342C2×C4⋊C4C2×C4×C3112yes—
343C2×C4⋊C4D4×C3112yes—
344C2×C4⋊C4D4×C3114yes—
345C2×C4⋊C4D4×C3112yes—
346C2×C22⋊C4C2×C4×C3112yes—
347C2×C22⋊C4C2×C4×C3111yescharacteristic
348C2×C22⋊C4C2×C4×C3112yes—
349C2×C22⋊C4C23×C3114yes—
350C2×C22⋊C4C23×C3112yes—
351C2×C22⋊C4C23×C3111yescharacteristic
352C2×C22⋊C4C23×C3112yes—
353C2×C22⋊C4C23×C3112yes—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42C2×C4×C3112yes—
357C2×C42C2×C4×C3112yes—
358C2×C42C2×C4×C3111yescharacteristic
359#99—24no—
360#99—42no—
361#95—22no—
362#95—24no—
363#95—22no—
364#95—24no—
365C31#2247811yescharacteristic, direct product factor, Sylow
366C24C22×C4×C3111yescharacteristic
367C24C24×C3111yescharacteristic
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4C22×C4×C3111yescharacteristic
386C22×C4C22×C4×C3112yes—
387C22×C4C22×C4×C3111yescharacteristic
388C22×C4C22×C4×C3112yes—
389C22×C4C22×C4×C3111yescharacteristic
390C22×C4C22×C4×C3111yescharacteristic
391C22×C4C22×C4×C3112yes—
392C22×C4C22×C4×C3112yes—
393C22×C4C22×C4×C3111yescharacteristic
394C22×C4C2×D4×C3114yes—
395C22×C4C2×D4×C3114yes—
396C22×C4C2×D4×C3112yes—
397C22×C4C2×D4×C3112yes—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—48no—
408C4⋊C4—44no—
409C4⋊C4C22⋊C4×C3112yes—
410C4⋊C4C22⋊C4×C3111yescharacteristic
411C4⋊C4C22⋊C4×C3111yescharacteristic
412C4⋊C4C22⋊C4×C3112yes—
413C4⋊C4C22⋊C4×C3112yes—
414C4⋊C4C22⋊C4×C3114yes—
415C4⋊C4C22⋊C4×C3114yes—
416C22⋊C4—22no—
417C22⋊C4—24no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4#41×C3114yes—
428C42—22no—
429C42—22no—
430C42—22no—
431C42—22no—
432C42—21no—
433C42—21no—
434C42—48no—
435C42—44no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C23×C4×C3111yescharacteristic
444C23C22×D4×C3112yes—
445C23C2×#41×C3112yes—
446C23C31×H(5,𝔽2)11yescharacteristic
447C23C31×2−1+411yescharacteristic
448Q8—42no—
449Q8—42no—
450D4—42no—
451D4—42no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4C2×C22⋊C4×C3112yes—
487C2×C4C2×C22⋊C4×C3112yes—
488C2×C4C2×C22⋊C4×C3111yescharacteristic
489C2×C4C2×C22⋊C4×C3114yes—
490C2×C4C2×C22⋊C4×C3112yes—
491C2×C4C2×C22⋊C4×C3111yescharacteristic
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C22×C22⋊C4×C3111yescharacteristic
505C22C4×#41×C3111yescharacteristic
506C22C31×#52011yescharacteristic
507C22C31×#54612yes—
508C22C31×#54712yes—
509C4—22no—
510C4—24no—
511C4—22no—
512C4—21no—
513C4—22no—
514C4—44no—
515C4—41no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—84no—
521C4—82no—
522C4C31×#41012yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2C31×#233911yescharacteristic
529C2C2×C31×#41011yescharacteristic
530C2C31×#288411yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2344C2semidirect
3. C31×#1996C2semidirect
5. C31×#1820C2semidirect
8. C31×#1740C2semidirect
12. C2×C31×#126C4semidirect
13. C2×C31×#125C4semidirect
14. C2×C31×#125C4semidirect
16. C2×C31×C22⋊Q8C4semidirect
18. C2×C4×Q8×C31C4semidirect
20. C2×C31×#117C4semidirect
170. #22478C31direct (N × H)
228. #2344C2×C31semidirect
229. #1996C2×C31semidirect
231. #1820C2×C31semidirect
234. #1740C2×C31semidirect
269. C2×#126C4×C31semidirect
270. C2×#125C4×C31semidirect
271. C2×#125C4×C31semidirect
273. C2×C22⋊Q8C4×C31semidirect
275. C2×C4×Q8C4×C31semidirect
277. C2×#117C4×C31semidirect
365. C31#22478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5522
C31×#23442
C31×#19962
C31×#18992
C31×#18202
C31×#17992
C4×C31×#992
C31×#17402
#2247831