Finite Group Databasebeta

← C31×#14446 #21471205

Subgroups — C31×#14446 #21471205

Order 7936.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C2×C31×#387C212yesmaximal
3C31×#1445C212yesmaximal
4C31×#1442C212yesmaximal
5C31×#1441C212yesmaximal
6C31×#1436C212yesmaximal
7C31×#1436C212yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic
9C31×C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4×C31C2212yes—
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2212yes—
18C22×C42×C31C2211yescharacteristic
19C31×#389C418yescomplemented
20C31×#387—28no—
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C23×C4×C31C2312yes—
34C23×C4×C31C2312yes—
35C23×C4×C31C2312yes—
36C23×C4×C31C2312yes—
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C2×C4⋊C4×C31—24no—
43C2×C4⋊C4×C31—22no—
44C2×C4⋊C4×C31—22no—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—41no—
49C2×C4⋊C4×C31—41no—
50C2×C4⋊C4×C31—41no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31—41no—
53C2×C4⋊C4×C31—41no—
54C2×C4⋊C4×C31—41no—
55C2×C4⋊C4×C31—41no—
56C2×C4⋊C4×C31—41no—
57C2×C4⋊C4×C31—41no—
58C2×C4⋊C4×C31C2×C414yes—
59C2×C4⋊C4×C31C2×C418yes—
60C2×C4⋊C4×C31C2×C414yes—
61C2×C4⋊C4×C31D414yes—
62C2×C4⋊C4×C31Q814yes—
63C2×C42×C31—24no—
64C2×C42×C31—41no—
65C2×C42×C31—41no—
66C2×C42×C31—42no—
67C2×C42×C31—42no—
68C2×C42×C31C2×C414yes—
69C31×#95—24no—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—42no—
77C31×#95—42no—
78C31×#95—42no—
79C31×#95—42no—
80C31×#95C2×C418yes—
81C24×C31C2411yescharacteristic
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31C22×C414yes—
133C22×C4×C31C22×C414yes—
134C22×C4×C31C22×C412yes—
135C22×C4×C31C22×C412yes—
136C22×C4×C31C22×C412yes—
137C22×C4×C31C2×D414yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×Q814yes—
140C22×C4×C31C2×Q812yes—
141C22×C4×C31#4112yes—
142C22×C4×C31#4112yes—
143C22×C4×C31#4112yes—
144C22×C4×C31#4112yes—
145C4⋊C4×C31—28no—
146C4⋊C4×C31—216no—
147C4⋊C4×C31—44no—
148C4⋊C4×C31—44no—
149C4⋊C4×C31—44no—
150C4⋊C4×C31—44no—
151C4⋊C4×C31—44no—
152C42×C31—44no—
153C42×C31—48no—
154#14446C3111yesmaximal, characteristic, direct product factor, Sylow
155C23×C31C23×C411yescharacteristic
156C23×C31C22×D411yescharacteristic
157C23×C31C22×Q811yescharacteristic
158C23×C31C2×#4111yescharacteristic
159C23×C31C2×#4111yescharacteristic
160C23×C31C2×#4111yescharacteristic
161C23×C31C2×#4111yescharacteristic
162C23×C31H(5,𝔽2)11yescharacteristic
163C23×C31H(5,𝔽2)11yescharacteristic
164C23×C31H(5,𝔽2)11yescharacteristic
165C23×C31H(5,𝔽2)11yescharacteristic
166C23×C312−1+411yescharacteristic
167C23×C312−1+411yescharacteristic
168C23×C312−1+411yescharacteristic
169C23×C312−1+411yescharacteristic
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—24no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31#11714yes—
231C2×C4×C31C4×D414yes—
232C2×C4×C31C4×Q814yes—
233C2×#389C2×C3111yescharacteristic
234C2×#387C2×C3112yes—
235#1445C2×C3112yes—
236#1442C2×C3112yes—
237#1441C2×C3112yes—
238#1436C2×C3112yes—
239#1436C2×C3112yes—
240C4⋊#95C2×C3111yescharacteristic
241C4⋊#95C2×C3111yescharacteristic
242C22×C31C2×#11711yescharacteristic
243C22×C31C2×C4×D411yescharacteristic
244C22×C31C2×C4×Q811yescharacteristic
245C22×C31#51811yescharacteristic
246C22×C31#51911yescharacteristic
247C22×C31#52011yescharacteristic
248C22×C31#52011yescharacteristic
249C22×C31#53411yescharacteristic
250C22×C31#53711yescharacteristic
251C22×C31#53811yescharacteristic
252C22×C31#53811yescharacteristic
253C22×C31#53911yescharacteristic
254C22×C31#53911yescharacteristic
255C22×C31#53911yescharacteristic
256C22×C31#53911yescharacteristic
257C22×C31#53911yescharacteristic
258C22×C31#53911yescharacteristic
259C22×C31#54311yescharacteristic
260C22×C31#54411yescharacteristic
261C22×C31#54711yescharacteristic
262C22×C31#54711yescharacteristic
263C22×C31D4×Q811yescharacteristic
264C22×C31#55011yescharacteristic
265C22×C31#55411yescharacteristic
266C22×C31#55511yescharacteristic
267C22×C31#55611yescharacteristic
268C22×C31#55611yescharacteristic
269C22×C31#55611yescharacteristic
270C22×C31#55711yescharacteristic
271C22×C31#55711yescharacteristic
272C22×C31#55911yescharacteristic
273C22×C31#56211yescharacteristic
274C22×C31#56311yescharacteristic
275C22×C31#56311yescharacteristic
276C22×C31#56411yescharacteristic
277C4×C31—24no—
278C4×C31—24no—
279C4×C31—24no—
280C4×C31—44no—
281C4×C31—44no—
282C4×C31—44no—
283C4×C31—44no—
284C4×C31—82no—
285C4×C31—82no—
286C22×C4⋊C4C22×C3112yes—
287C22×C4⋊C4C22×C3111yescharacteristic
288C22×C4⋊C4C22×C3111yescharacteristic
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C4⋊C4C22×C3111yescharacteristic
293C22×C42C22×C3112yes—
294C22×C42C22×C3111yescharacteristic
295#389C4×C3118yescomplemented
296#387—28no—
297C2×#95C22×C3112yes—
298C2×#95C22×C3112yes—
299C2×#95C22×C3112yes—
300C2×#95C22×C3112yes—
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×#95C22×C3112yes—
305C2×#95C22×C3112yes—
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×C31#231311yescharacteristic
310C2×C31#232511yescharacteristic
311C2×C31#232911yescharacteristic
312C2×C31#235411yescharacteristic
313C2×C31#235511yescharacteristic
314C2×C31#236511yescharacteristic
315C2×C31#238211yescharacteristic
316C2×C31#272411yescharacteristic
317C2×C31#272611yescharacteristic
318C2×C31#272711yescharacteristic
319C2×C31#273211yescharacteristic
320C2×C31#280511yescharacteristic
321C2×C31#280811yescharacteristic
322C2×C31#280911yescharacteristic
323C2×C31#281011yescharacteristic
324C23×C4C23×C3112yes—
325C23×C4C23×C3112yes—
326C23×C4C23×C3112yes—
327C23×C4C23×C3112yes—
328C23×C4C23×C3112yes—
329C23×C4C23×C3112yes—
330C23×C4C23×C3111yescharacteristic
331C23×C4C23×C3111yescharacteristic
332C23×C4C23×C3111yescharacteristic
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4C2×C4×C3114yes—
350C2×C4⋊C4C2×C4×C3118yes—
351C2×C4⋊C4C2×C4×C3114yes—
352C2×C4⋊C4D4×C3114yes—
353C2×C4⋊C4Q8×C3114yes—
354C2×C42—24no—
355C2×C42—41no—
356C2×C42—41no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42C2×C4×C3114yes—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95C2×C4×C3118yes—
372C31#1444611yescharacteristic, direct product factor, Sylow
373C24C24×C3111yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4C22×C4×C3114yes—
425C22×C4C22×C4×C3114yes—
426C22×C4C22×C4×C3112yes—
427C22×C4C22×C4×C3112yes—
428C22×C4C22×C4×C3112yes—
429C22×C4C2×D4×C3114yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×Q8×C3114yes—
432C22×C4C2×Q8×C3112yes—
433C22×C4#41×C3112yes—
434C22×C4#41×C3112yes—
435C22×C4#41×C3112yes—
436C22×C4#41×C3112yes—
437C4⋊C4—28no—
438C4⋊C4—216no—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—44no—
442C4⋊C4—44no—
443C4⋊C4—44no—
444C42—44no—
445C42—48no—
446C23C23×C4×C3111yescharacteristic
447C23C22×D4×C3111yescharacteristic
448C23C22×Q8×C3111yescharacteristic
449C23C2×#41×C3111yescharacteristic
450C23C2×#41×C3111yescharacteristic
451C23C2×#41×C3111yescharacteristic
452C23C2×#41×C3111yescharacteristic
453C23C31×H(5,𝔽2)11yescharacteristic
454C23C31×H(5,𝔽2)11yescharacteristic
455C23C31×H(5,𝔽2)11yescharacteristic
456C23C31×H(5,𝔽2)11yescharacteristic
457C23C31×2−1+411yescharacteristic
458C23C31×2−1+411yescharacteristic
459C23C31×2−1+411yescharacteristic
460C23C31×2−1+411yescharacteristic
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C31×#11714yes—
522C2×C4C4×D4×C3114yes—
523C2×C4C4×Q8×C3114yes—
524C22C2×C31×#11711yescharacteristic
525C22C2×C4×D4×C3111yescharacteristic
526C22C2×C4×Q8×C3111yescharacteristic
527C22C31×#51811yescharacteristic
528C22C31×#51911yescharacteristic
529C22C31×#52011yescharacteristic
530C22C31×#52011yescharacteristic
531C22C31×#53411yescharacteristic
532C22C31×#53711yescharacteristic
533C22C31×#53811yescharacteristic
534C22C31×#53811yescharacteristic
535C22C31×#53911yescharacteristic
536C22C31×#53911yescharacteristic
537C22C31×#53911yescharacteristic
538C22C31×#53911yescharacteristic
539C22C31×#53911yescharacteristic
540C22C31×#53911yescharacteristic
541C22C31×#54311yescharacteristic
542C22C31×#54411yescharacteristic
543C22C31×#54711yescharacteristic
544C22C31×#54711yescharacteristic
545C22D4×Q8×C3111yescharacteristic
546C22C31×#55011yescharacteristic
547C22C31×#55411yescharacteristic
548C22C31×#55511yescharacteristic
549C22C31×#55611yescharacteristic
550C22C31×#55611yescharacteristic
551C22C31×#55611yescharacteristic
552C22C31×#55711yescharacteristic
553C22C31×#55711yescharacteristic
554C22C31×#55911yescharacteristic
555C22C31×#56211yescharacteristic
556C22C31×#56311yescharacteristic
557C22C31×#56311yescharacteristic
558C22C31×#56411yescharacteristic
559C4—24no—
560C4—24no—
561C4—24no—
562C4—44no—
563C4—44no—
564C4—44no—
565C4—44no—
566C4—82no—
567C4—82no—
568C2C31×#231311yescharacteristic
569C2C31×#232511yescharacteristic
570C2C31×#232911yescharacteristic
571C2C31×#235411yescharacteristic
572C2C31×#235511yescharacteristic
573C2C31×#236511yescharacteristic
574C2C31×#238211yescharacteristic
575C2C31×#272411yescharacteristic
576C2C31×#272611yescharacteristic
577C2C31×#272711yescharacteristic
578C2C31×#273211yescharacteristic
579C2C31×#280511yescharacteristic
580C2C31×#280811yescharacteristic
581C2C31×#280911yescharacteristic
582C2C31×#281011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
19. C31×#389C4semidirect
154. #14446C31direct (N × H)
295. #389C4×C31semidirect
372. C31#14446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3872
C31×#14452
C31×#14422
C31×#14412
C31×#14362
C31×C4⋊#952
#1444631