Finite Group Databasebeta

← C31×#14024 #21470783

Subgroups — C31×#14024 #21470783

Order 7936.

2054 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C4⋊Q8C211yesmaximal, characteristic
2C22×C4×Q8×C31C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C31×#391C211yesmaximal, characteristic
5C2×C31×#391C211yesmaximal, characteristic
6C31×#1441C214yesmaximal
7C31×#1436C214yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic
9C4×C31×#95C211yesmaximal, characteristic
10C23×Q8×C31C2211yescharacteristic
11C23×Q8×C31C2211yescharacteristic
12C2×C31×C4⋊Q8—24no—
13C2×C31×C4⋊Q8—24no—
14C2×C31×C4⋊Q8C418yescomplemented
15C2×C4×Q8×C31—24no—
16C2×C4×Q8×C31—24no—
17C2×C4×Q8×C31—24no—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2214yes—
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C42×C31C2212yes—
23C22×C42×C31C2211yescharacteristic
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C31×#391—24no—
27C31×#391—24no—
28C31×#391—24no—
29C2×C31×#95C2212yes—
30C2×C31×#95C2214yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2214yes—
33C2×C31×#95C2214yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C22×Q8×C31—22no—
37C22×Q8×C31—22no—
38C22×Q8×C31—22no—
39C22×Q8×C31—22no—
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31C2×C414yes—
47C22×Q8×C31C2×C414yes—
48C22×Q8×C31D414yes—
49C22×Q8×C31D414yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C31×C4⋊Q8—232no—
60C4×Q8×C31—232no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—28no—
67C2×C4⋊C4×C31—28no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31C2×C4116yes—
72C2×C4⋊C4×C31D414yes—
73C2×C42×C31—24no—
74C2×C42×C31—24no—
75C2×C42×C31—24no—
76C2×C42×C31—22no—
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—22no—
81C2×C42×C31—22no—
82C2×C42×C31—22no—
83C2×C42×C31C2×C414yes—
84C2×C42×C31D414yes—
85C31×#95—28no—
86C31×#95—28no—
87C31×#95—24no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—28no—
91C31×#95Q818yescomplemented
92C24×C31C2411yescharacteristic
93C2×Q8×C31—28no—
94C2×Q8×C31—28no—
95C2×Q8×C31—28no—
96C2×Q8×C31—28no—
97C2×Q8×C31—28no—
98C2×Q8×C31—28no—
99C2×Q8×C31—28no—
100C2×Q8×C31—28no—
101C2×Q8×C31—28no—
102C2×Q8×C31—44no—
103C2×Q8×C31—44no—
104C2×Q8×C31—44no—
105C2×Q8×C31—44no—
106C2×Q8×C31C22⋊C4116yes—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
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—21no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—24no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—24no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—24no—
141C22×C4×C31—22no—
142C22×C4×C31—24no—
143C22×C4×C31C22×C414yes—
144C22×C4×C31C22×C414yes—
145C22×C4×C31C22×C414yes—
146C22×C4×C31C22×C412yes—
147C22×C4×C31C2×D414yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D414yes—
150C22×C4×C31C2×D414yes—
151C22×C4×C31C2×D412yes—
152C22×C4×C31C2×D412yes—
153C22×C4×C31C2×D412yes—
154C22×C4×C31C2×D412yes—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×Q814yes—
157C22×C4×C31C2×Q814yes—
158C22×C4×C31C2×Q814yes—
159C22×C4×C31#4114yes—
160C22×C4×C31#4112yes—
161C22×C4×C31#4112yes—
162C4⋊C4×C31—216no—
163C4⋊C4×C31—232no—
164C4⋊C4×C31—28no—
165C4⋊C4×C31—44no—
166C42×C31—216no—
167C42×C31—28no—
168C42×C31—28no—
169C42×C31—44no—
170#14024C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31C23×C411yescharacteristic
172C23×C31C22×D411yescharacteristic
173C23×C31C22×D411yescharacteristic
174C23×C31C22×D411yescharacteristic
175C23×C31C22×D411yescharacteristic
176C23×C31C22×Q812yes—
177C23×C31C2×#4111yescharacteristic
178C23×C31C2×#4111yescharacteristic
179C23×C31C2×#4112yes—
180C23×C312−1+412yes—
181C23×C312−1+412yes—
182Q8×C31—232no—
183Q8×C31—416no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—22no—
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—24no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—24no—
207C2×C4×C31—22no—
208C2×C4×C31—28no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
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—44no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—44no—
228C2×C4×C31—44no—
229C2×C4×C31C2×C22⋊C418yes—
230C2×C4×C31C2×C22⋊C414yes—
231C2×C4×C31C4×D414yes—
232C2×C4×C31C4×D414yes—
233C2×C4×C31C4×Q818yescomplemented
234C2×C4×C31#12014yes—
235C2×C4×C31#12114yes—
236C2×C4×C31#12114yes—
237C2×C4×C31#12314yes—
238C2×C4×C31C4⋊Q814yescomplemented
239C22×C4⋊Q8C2×C3111yescharacteristic
240C22×C4×Q8C2×C3111yescharacteristic
241C2×#391C2×C3111yescharacteristic
242C2×#391C2×C3111yescharacteristic
243C2×#391C2×C3111yescharacteristic
244#1441C2×C3114yes—
245#1436C2×C3114yes—
246C4⋊#95C2×C3111yescharacteristic
247C4×#95C2×C3111yescharacteristic
248C22×C31C22×C22⋊C411yescharacteristic
249C22×C31C2×C4×D411yescharacteristic
250C22×C31C2×C4×D411yescharacteristic
251C22×C31C2×C4×Q812yes—
252C22×C31#51912yes—
253C22×C31C2×#12011yescharacteristic
254C22×C31C2×#12111yescharacteristic
255C22×C31C2×#12111yescharacteristic
256C22×C31C2×#12311yescharacteristic
257C22×C31C2×C4⋊Q811yescharacteristic
258C22×C31#53211yescharacteristic
259C22×C31#53312yes—
260C22×C31#53611yescharacteristic
261C22×C31#53611yescharacteristic
262C22×C31#54112yes—
263C22×C31#54712yes—
264C22×C31#54812yes—
265C22×C31#54812yes—
266C22×C31D4×Q812yes—
267C22×C31D4×Q812yes—
268C22×C31D4×Q812yes—
269C22×C31#55612yes—
270C22×C31#55712yes—
271C4×C31—28no—
272C4×C31—24no—
273C4×C31—28no—
274C4×C31—44no—
275C4×C31—42no—
276C4×C31—44no—
277C4×C31—44no—
278C4×C31—82no—
279C4×C31#38618yes—
280C23×Q8C22×C3111yescharacteristic
281C23×Q8C22×C3111yescharacteristic
282C2×C4⋊Q8—24no—
283C2×C4⋊Q8—24no—
284C2×C4⋊Q8C4×C3118yescomplemented
285C2×C4×Q8—24no—
286C2×C4×Q8—24no—
287C2×C4×Q8—24no—
288C22×C4⋊C4C22×C3112yes—
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3114yes—
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C42C22×C3112yes—
293C22×C42C22×C3111yescharacteristic
294C22×C42C22×C3111yescharacteristic
295C22×C42C22×C3111yescharacteristic
296#391—24no—
297#391—24no—
298#391—24no—
299C2×#95C22×C3112yes—
300C2×#95C22×C3114yes—
301C2×#95C22×C3112yes—
302C2×#95C22×C3114yes—
303C2×#95C22×C3114yes—
304C2×#95C22×C3112yes—
305C2×#95C22×C3112yes—
306C2×C31C2×#38611yescharacteristic
307C2×C31C4×C4⋊Q811yescharacteristic
308C2×C31#232711yescharacteristic
309C2×C31Q8×C22⋊C412yes—
310C2×C31#236512yes—
311C2×C31#242912yes—
312C2×C31#243211yescharacteristic
313C2×C31#243411yescharacteristic
314C2×C31#244612yes—
315C2×C31#254511yescharacteristic
316C2×C31#254611yescharacteristic
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8C2×C4×C3114yes—
328C22×Q8C2×C4×C3114yes—
329C22×Q8D4×C3114yes—
330C22×Q8D4×C3114yes—
331C23×C4C23×C3112yes—
332C23×C4C23×C3112yes—
333C23×C4C23×C3112yes—
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3112yes—
336C23×C4C23×C3112yes—
337C23×C4C23×C3112yes—
338C23×C4C23×C3111yescharacteristic
339C23×C4C23×C3111yescharacteristic
340C4⋊Q8—232no—
341C4×Q8—232no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4C2×C4×C31116yes—
353C2×C4⋊C4D4×C3114yes—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42C2×C4×C3114yes—
365C2×C42D4×C3114yes—
366#95—28no—
367#95—28no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95Q8×C3118yescomplemented
373C31#1402411yescharacteristic, direct product factor, Sylow
374C24C24×C3111yescharacteristic
375C2×Q8—28no—
376C2×Q8—28no—
377C2×Q8—28no—
378C2×Q8—28no—
379C2×Q8—28no—
380C2×Q8—28no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—28no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8C22⋊C4×C31116yes—
389C22×C4—21no—
390C22×C4—21no—
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—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
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×C4C22×C4×C3114yes—
426C22×C4C22×C4×C3114yes—
427C22×C4C22×C4×C3114yes—
428C22×C4C22×C4×C3112yes—
429C22×C4C2×D4×C3114yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3114yes—
432C22×C4C2×D4×C3114yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×D4×C3112yes—
435C22×C4C2×D4×C3112yes—
436C22×C4C2×D4×C3112yes—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×Q8×C3114yes—
439C22×C4C2×Q8×C3114yes—
440C22×C4C2×Q8×C3114yes—
441C22×C4#41×C3114yes—
442C22×C4#41×C3112yes—
443C22×C4#41×C3112yes—
444C4⋊C4—216no—
445C4⋊C4—232no—
446C4⋊C4—28no—
447C4⋊C4—44no—
448C42—216no—
449C42—28no—
450C42—28no—
451C42—44no—
452C23C23×C4×C3111yescharacteristic
453C23C22×D4×C3111yescharacteristic
454C23C22×D4×C3111yescharacteristic
455C23C22×D4×C3111yescharacteristic
456C23C22×D4×C3111yescharacteristic
457C23C22×Q8×C3112yes—
458C23C2×#41×C3111yescharacteristic
459C23C2×#41×C3111yescharacteristic
460C23C2×#41×C3112yes—
461C23C31×2−1+412yes—
462C23C31×2−1+412yes—
463Q8—232no—
464Q8—416no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—24no—
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—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4C2×C22⋊C4×C3118yes—
511C2×C4C2×C22⋊C4×C3114yes—
512C2×C4C4×D4×C3114yes—
513C2×C4C4×D4×C3114yes—
514C2×C4C4×Q8×C3118yescomplemented
515C2×C4C31×#12014yes—
516C2×C4C31×#12114yes—
517C2×C4C31×#12114yes—
518C2×C4C31×#12314yes—
519C2×C4C31×C4⋊Q814yescomplemented
520C22C22×C22⋊C4×C3111yescharacteristic
521C22C2×C4×D4×C3111yescharacteristic
522C22C2×C4×D4×C3111yescharacteristic
523C22C2×C4×Q8×C3112yes—
524C22C31×#51912yes—
525C22C2×C31×#12011yescharacteristic
526C22C2×C31×#12111yescharacteristic
527C22C2×C31×#12111yescharacteristic
528C22C2×C31×#12311yescharacteristic
529C22C2×C31×C4⋊Q811yescharacteristic
530C22C31×#53211yescharacteristic
531C22C31×#53312yes—
532C22C31×#53611yescharacteristic
533C22C31×#53611yescharacteristic
534C22C31×#54112yes—
535C22C31×#54712yes—
536C22C31×#54812yes—
537C22C31×#54812yes—
538C22D4×Q8×C3112yes—
539C22D4×Q8×C3112yes—
540C22D4×Q8×C3112yes—
541C22C31×#55612yes—
542C22C31×#55712yes—
543C4—28no—
544C4—24no—
545C4—28no—
546C4—44no—
547C4—42no—
548C4—44no—
549C4—44no—
550C4—82no—
551C4C31×#38618yes—
552C2C2×C31×#38611yescharacteristic
553C2C4×C31×C4⋊Q811yescharacteristic
554C2C31×#232711yescharacteristic
555C2Q8×C22⋊C4×C3112yes—
556C2C31×#236512yes—
557C2C31×#242912yes—
558C2C31×#243211yescharacteristic
559C2C31×#243411yescharacteristic
560C2C31×#244612yes—
561C2C31×#254511yescharacteristic
562C2C31×#254611yescharacteristic
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
14. C2×C31×C4⋊Q8C4semidirect
91. C31×#95Q8semidirect
170. #14024C31direct (N × H)
233. C2×C4×C31C4×Q8semidirect
238. C2×C4×C31C4⋊Q8semidirect
284. C2×C4⋊Q8C4×C31semidirect
372. #95Q8×C31semidirect
373. C31#14024direct (N × H)
514. C2×C4C4×Q8×C31semidirect
519. C2×C4C31×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C4⋊Q82
C22×C4×Q8×C312
C2×C31×#3912
C31×#14412
C31×#14362
C31×C4⋊#952
C4×C31×#952
#1402431