Finite Group Databasebeta

← C31×#13949 #21470708

Subgroups — C31×#13949 #21470708

Order 7936.

1326 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#387C212yesmaximal
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
3C31×#1442C212yesmaximal
4C31×#1441C212yesmaximal
5C31×#1436C212yesmaximal
6C31×C4⋊#95C211yesmaximal, characteristic
7C31×C4⋊#95C211yesmaximal, characteristic
8C31×#1434C211yesmaximal, characteristic
9C31×#1434C211yesmaximal, characteristic
10C31×#1434C211yesmaximal, characteristic
11C4×C31×#95C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C42×C31C2212yes—
17C22×C42×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C31×#387—28no—
21C4×C4⋊C4×C31C418yescomplemented
22C2×C31×#95C2211yescharacteristic
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2212yes—
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2312yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31C2×C414yes—
57C2×C4⋊C4×C31C2×C414yes—
58C2×C4⋊C4×C31D414yes—
59C2×C4⋊C4×C31Q814yes—
60C2×C42×C31—22no—
61C2×C42×C31—22no—
62C2×C42×C31—24no—
63C2×C42×C31—24no—
64C2×C42×C31—42no—
65C2×C42×C31—42no—
66C2×C42×C31—42no—
67C2×C42×C31C2×C414yes—
68C2×C42×C31C2×C414yes—
69C2×C42×C31C2×C414yes—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—22no—
76C31×#95—22no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—22no—
81C31×#95—22no—
82C31×#95—42no—
83C31×#95C2×C414yes—
84C31×#95C2×C414yes—
85C24×C31C2411yescharacteristic
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
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—21no—
108C22×C4×C31—21no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
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×C412yes—
133C22×C4×C31C22×C412yes—
134C22×C4×C31C22×C412yes—
135C22×C4×C31C22×C412yes—
136C22×C4×C31C22×C412yes—
137C22×C4×C31C22×C412yes—
138C22×C4×C31C22×C412yes—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×Q812yes—
143C22×C4×C31C2×Q812yes—
144C22×C4×C31C2×Q812yes—
145C22×C4×C31#4114yes—
146C22×C4×C31#4114yes—
147C22×C4×C31#4112yes—
148C22×C4×C31#4112yes—
149C22×C4×C31#4112yes—
150C22×C4×C31#4112yes—
151C4⋊C4×C31—28no—
152C4⋊C4×C31—48no—
153C4⋊C4×C31—48no—
154C4⋊C4×C31C4⋊C4116yescomplemented
155C42×C31—28no—
156C42×C31—44no—
157C42×C31—44no—
158C42×C31—48no—
159#13949C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31C23×C411yescharacteristic
161C23×C31C22×D411yescharacteristic
162C23×C31C22×Q811yescharacteristic
163C23×C31C2×#4111yescharacteristic
164C23×C31C2×#4111yescharacteristic
165C23×C31C2×#4111yescharacteristic
166C23×C31C2×#4111yescharacteristic
167C23×C31C2×#4112yes—
168C23×C31C2×#4112yes—
169C23×C31H(5,𝔽2)12yes—
170C23×C312−1+412yes—
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—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—24no—
200C2×C4×C31—24no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—24no—
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—42no—
231C2×C4×C31C2×C4⋊C414yes—
232C2×C4×C31C2×C4⋊C414yes—
233C2×C4×C31C2×C4⋊C414yes—
234C2×C4×C31#11714yes—
235C2×C4×C31#11714yes—
236C2×#387C2×C3112yes—
237C2×C4×C4⋊C4C2×C3111yescharacteristic
238#1442C2×C3112yes—
239#1441C2×C3112yes—
240#1436C2×C3112yes—
241C4⋊#95C2×C3111yescharacteristic
242C4⋊#95C2×C3111yescharacteristic
243#1434C2×C3111yescharacteristic
244#1434C2×C3111yescharacteristic
245#1434C2×C3111yescharacteristic
246C4×#95C2×C3111yescharacteristic
247C22×C31C22×C4⋊C411yescharacteristic
248C22×C31C2×#11711yescharacteristic
249C22×C31C2×#11711yescharacteristic
250C22×C31C4×#4111yescharacteristic
251C22×C31C4×#4111yescharacteristic
252C22×C31#51811yescharacteristic
253C22×C31#51911yescharacteristic
254C22×C31#52912yes—
255C22×C31#52912yes—
256C22×C31#53211yescharacteristic
257C22×C31#53211yescharacteristic
258C22×C31#53311yescharacteristic
259C22×C31#53311yescharacteristic
260C22×C31#53912yes—
261C22×C31#53912yes—
262C22×C31#54612yes—
263C22×C31#54812yes—
264C22×C31#55112yes—
265C22×C31#55212yes—
266C22×C31#55312yes—
267C22×C31#55412yes—
268C22×C31#55612yes—
269C22×C31#55712yes—
270C4×C31—24no—
271C4×C31—24no—
272C4×C31—24no—
273C4×C31—24no—
274C4×C31—24no—
275C4×C31—44no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—44no—
279C4×C31—82no—
280C4×C31—82no—
281C22×C4⋊C4C22×C3112yes—
282C22×C4⋊C4C22×C3112yes—
283C22×C4⋊C4C22×C3111yescharacteristic
284C22×C4⋊C4C22×C3111yescharacteristic
285C22×C42C22×C3112yes—
286C22×C42C22×C3111yescharacteristic
287C22×C42C22×C3111yescharacteristic
288C22×C42C22×C3111yescharacteristic
289#387—28no—
290C4×C4⋊C4C4×C3118yescomplemented
291C2×#95C22×C3111yescharacteristic
292C2×#95C22×C3111yescharacteristic
293C2×#95C22×C3112yes—
294C2×#95C22×C3111yescharacteristic
295C2×#95C22×C3111yescharacteristic
296C2×#95C22×C3112yes—
297C2×#95C22×C3112yes—
298C2×#95C22×C3112yes—
299C2×#95C22×C3112yes—
300C2×#95C22×C3112yes—
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×#95C22×C3111yescharacteristic
305C2×#95C22×C3111yescharacteristic
306C2×C31#228511yescharacteristic
307C2×C31#229811yescharacteristic
308C2×C31#231311yescharacteristic
309C2×C31#234911yescharacteristic
310C2×C31#235111yescharacteristic
311C2×C31#235311yescharacteristic
312C2×C31#235611yescharacteristic
313C2×C31#255812yes—
314C2×C31#256012yes—
315C2×C31#258812yes—
316C2×C31#259012yes—
317C23×C4C23×C3112yes—
318C23×C4C23×C3112yes—
319C23×C4C23×C3111yescharacteristic
320C23×C4C23×C3111yescharacteristic
321C23×C4C23×C3112yes—
322C23×C4C23×C3112yes—
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3111yescharacteristic
325C23×C4C23×C3111yescharacteristic
326C23×C4C23×C3111yescharacteristic
327C23×C4C23×C3111yescharacteristic
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C2×C4×C3114yes—
337C2×C4⋊C4C2×C4×C3114yes—
338C2×C4⋊C4D4×C3114yes—
339C2×C4⋊C4Q8×C3114yes—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C2×C4×C3114yes—
348C2×C42C2×C4×C3114yes—
349C2×C42C2×C4×C3114yes—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—22no—
356#95—22no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—22no—
361#95—22no—
362#95—42no—
363#95C2×C4×C3114yes—
364#95C2×C4×C3114yes—
365C31#1394911yescharacteristic, direct product factor, Sylow
366C24C24×C3111yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
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×C4C22×C4×C3112yes—
414C22×C4C22×C4×C3112yes—
415C22×C4C22×C4×C3112yes—
416C22×C4C22×C4×C3112yes—
417C22×C4C22×C4×C3112yes—
418C22×C4C22×C4×C3112yes—
419C22×C4C22×C4×C3112yes—
420C22×C4C2×D4×C3112yes—
421C22×C4C2×D4×C3112yes—
422C22×C4C2×D4×C3112yes—
423C22×C4C2×Q8×C3112yes—
424C22×C4C2×Q8×C3112yes—
425C22×C4C2×Q8×C3112yes—
426C22×C4#41×C3114yes—
427C22×C4#41×C3114yes—
428C22×C4#41×C3112yes—
429C22×C4#41×C3112yes—
430C22×C4#41×C3112yes—
431C22×C4#41×C3112yes—
432C4⋊C4—28no—
433C4⋊C4—48no—
434C4⋊C4—48no—
435C4⋊C4C4⋊C4×C31116yescomplemented
436C42—28no—
437C42—44no—
438C42—44no—
439C42—48no—
440C23C23×C4×C3111yescharacteristic
441C23C22×D4×C3111yescharacteristic
442C23C22×Q8×C3111yescharacteristic
443C23C2×#41×C3111yescharacteristic
444C23C2×#41×C3111yescharacteristic
445C23C2×#41×C3111yescharacteristic
446C23C2×#41×C3111yescharacteristic
447C23C2×#41×C3112yes—
448C23C2×#41×C3112yes—
449C23C31×H(5,𝔽2)12yes—
450C23C31×2−1+412yes—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
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—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
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×C4C2×C4⋊C4×C3114yes—
512C2×C4C2×C4⋊C4×C3114yes—
513C2×C4C2×C4⋊C4×C3114yes—
514C2×C4C31×#11714yes—
515C2×C4C31×#11714yes—
516C22C22×C4⋊C4×C3111yescharacteristic
517C22C2×C31×#11711yescharacteristic
518C22C2×C31×#11711yescharacteristic
519C22C4×#41×C3111yescharacteristic
520C22C4×#41×C3111yescharacteristic
521C22C31×#51811yescharacteristic
522C22C31×#51911yescharacteristic
523C22C31×#52912yes—
524C22C31×#52912yes—
525C22C31×#53211yescharacteristic
526C22C31×#53211yescharacteristic
527C22C31×#53311yescharacteristic
528C22C31×#53311yescharacteristic
529C22C31×#53912yes—
530C22C31×#53912yes—
531C22C31×#54612yes—
532C22C31×#54812yes—
533C22C31×#55112yes—
534C22C31×#55212yes—
535C22C31×#55312yes—
536C22C31×#55412yes—
537C22C31×#55612yes—
538C22C31×#55712yes—
539C4—24no—
540C4—24no—
541C4—24no—
542C4—24no—
543C4—24no—
544C4—42no—
545C4—42no—
546C4—44no—
547C4—44no—
548C4—82no—
549C4—82no—
550C2C31×#228511yescharacteristic
551C2C31×#229811yescharacteristic
552C2C31×#231311yescharacteristic
553C2C31×#234911yescharacteristic
554C2C31×#235111yescharacteristic
555C2C31×#235311yescharacteristic
556C2C31×#235611yescharacteristic
557C2C31×#255812yes—
558C2C31×#256012yes—
559C2C31×#258812yes—
560C2C31×#259012yes—
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
21. C4×C4⋊C4×C31C4semidirect
154. C4⋊C4×C31C4⋊C4semidirect
159. #13949C31direct (N × H)
290. C4×C4⋊C4C4×C31semidirect
365. C31#13949direct (N × H)
435. C4⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C4×C4⋊C4×C312
C31×#14422
C31×#14412
C31×#14362
C31×C4⋊#952
C31×#14342
C4×C31×#952
#1394931