Finite Group Databasebeta

← #28393941

Subgroups — #28393941

Order 14464.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D113C211yesmaximal, characteristic, complemented
2C2×#16813595C211yesmaximal, characteristic, complemented
3C2×#16813593C211yesmaximal, characteristic, complemented
4C2×#16813590C211yesmaximal, characteristic, complemented
5C2×#16813590C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
7#20298514C211yesmaximal, characteristic, complemented
8#20298512C211yesmaximal, characteristic, complemented
9#20298506C211yesmaximal, characteristic, complemented
10#20298476C211yesmaximal, characteristic, complemented
11#20298474C211yesmaximal, characteristic, complemented
12#20298474C211yesmaximal, characteristic, complemented
13#20298472C211yesmaximal, characteristic, complemented
14#20298453C211yesmaximal, characteristic, complemented
15#392×C113C211yesmaximal, characteristic, complemented
16C24×D113C2211yescharacteristic
17C24×D113C2211yescharacteristic
18C22×D452C2211yescharacteristic
19C22×C22⋊D113C2211yescharacteristic
20C22×C22⋊D113C2211yescharacteristic
21C22×C22⋊D113C2211yescharacteristic
22C22×C22⋊D113C2211yescharacteristic, complemented
23C22×C22⋊D113C2211yescharacteristic, complemented
24C2×D4×D113—24no—
25C2×D4×D113—24no—
26C2×D4×D113—24no—
27C22×C4×D113C2211yescharacteristic
28C22×C4×D113C2211yescharacteristic, complemented
29C22×C4×D113C2211yescharacteristic, complemented
30#16813595—24no—
31#16813593—24no—
32#16813590—24no—
33#16813590—24no—
34C2×C4⋊Dic113C2211yescharacteristic, complemented
35C2×#14268626C2211yescharacteristic, complemented
36C2×C22⋊Dic113C2211yescharacteristic, complemented
37C2×C22⋊Dic113C2211yescharacteristic, complemented
38C2×C22⋊Dic113C2211yescharacteristic, complemented
39C2×C22⋊Dic113C2211yescharacteristic, complemented
40C2×C22⋊Dic113C2211yescharacteristic, complemented
41C2×#14268624C2211yescharacteristic
42C2×#14268624C2211yescharacteristic
43C2×#14268624C2211yescharacteristic
44C2×#14268624C2211yescharacteristic, complemented
45C2×#14268624C2211yescharacteristic, complemented
46C2×#14268624C2211yescharacteristic, complemented
47C2×#14268624C2211yescharacteristic, complemented
48C22⋊C4×D113—24no—
49#16813529C2211yescharacteristic, complemented
50#16813529C2211yescharacteristic, complemented
51#16813529C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C22×D4×C113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic, complemented
55C2×C22⋊C4×C113C2211yescharacteristic, complemented
56C2×C22⋊C4×C113C2211yescharacteristic, complemented
57C2×C22⋊C4×C113C2211yescharacteristic, complemented
58#95×C113C2211yescharacteristic, complemented
59C23×D113—22no—
60C23×D113—22no—
61C23×D113—22no—
62C23×D113—22no—
63C23×D113—22no—
64C23×D113—22no—
65C23×D113—22no—
66C23×D113—22no—
67C23×D113—22no—
68C23×D113—41no—
69C23×D113—41no—
70C23×D113—41no—
71C23×D113—41no—
72C23×D113D414yescomplemented
73C23×D113C2311yescharacteristic
74C23×D113C2311yescharacteristic
75C23×D113C2311yescharacteristic
76C2×D452—22no—
77C2×D452—22no—
78C2×D452D414yescomplemented
79C2×C22⋊D113—22no—
80C2×C22⋊D113—22no—
81C2×C22⋊D113—22no—
82C2×C22⋊D113—22no—
83C2×C22⋊D113—22no—
84C2×C22⋊D113—22no—
85C2×C22⋊D113—22no—
86C2×C22⋊D113—22no—
87C2×C22⋊D113—22no—
88C2×C22⋊D113—22no—
89C2×C22⋊D113—22no—
90C2×C22⋊D113—22no—
91C2×C22⋊D113—22no—
92C2×C22⋊D113—41no—
93C2×C22⋊D113D414yescomplemented
94D4×D113—232no—
95C22×Dic113C2311yescharacteristic
96C22×Dic113C2311yescharacteristic
97C22×Dic113C2311yescharacteristic
98C22×Dic113C2311yescharacteristic
99C22×Dic113C2311yescharacteristic
100C2×C4×D113—22no—
101C2×C4×D113—22no—
102C2×C4×D113—22no—
103C2×C4×D113—22no—
104C2×C4×D113—22no—
105C2×C4×D113—22no—
106C2×C4×D113—22no—
107C2×C4×D113—41no—
108C2×C4×D113—41no—
109C4⋊Dic113—22no—
110#14268626—22no—
111C22⋊Dic113—22no—
112C22⋊Dic113—22no—
113C22⋊Dic113—22no—
114C22⋊Dic113—22no—
115C22⋊Dic113—22no—
116#14268624—22no—
117#14268624—22no—
118#14268624—22no—
119#14268624—22no—
120#14268624—22no—
121#14268624—41no—
122#14268624D414yescomplemented
123C24×C113C2311yescharacteristic
124C24×C113C2311yescharacteristic
125C24×C113C2311yescharacteristic
126C2×D4×C113—22no—
127C2×D4×C113—22no—
128C2×D4×C113—22no—
129C2×D4×C113—22no—
130C2×D4×C113—22no—
131C2×D4×C113—22no—
132C2×D4×C113—41no—
133C2×D4×C113—41no—
134C2×D4×C113—41no—
135C22×C4×C113C2311yescharacteristic
136C22×C4×C113C2311yescharacteristic
137C22×C4×C113C2311yescharacteristic
138C22×C4×C113C2311yescharacteristic
139C22⋊C4×C113—22no—
140C22⋊C4×C113—22no—
141C22⋊C4×C113—41no—
142C23×C113—21no—
143C23×C113—21no—
144C23×C113—21no—
145C23×C113—21no—
146C23×C113—21no—
147C23×C113—21no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—21no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—21no—
154C23×C113—21no—
155C23×C113—21no—
156C23×C113—21no—
157C23×C113—21no—
158C23×C113—21no—
159C23×C113—21no—
160C23×C113—21no—
161C23×C113C2×D412yes—
162C23×C113C2×D412yes—
163C23×C113C2411yescharacteristic
164C22×D113—21no—
165C22×D113—21no—
166C22×D113—21no—
167C22×D113—21no—
168C22×D113—21no—
169C22×D113—21no—
170C22×D113—21no—
171C22×D113—21no—
172C22×D113—28no—
173C22×D113—21no—
174C22×D113—21no—
175C22×D113—21no—
176C22×D113—21no—
177C22×D113—21no—
178C22×D113—21no—
179C22×D113—28no—
180C22×D113—28no—
181C22×D113—44no—
182C22×D113—44no—
183C22×D113—44no—
184C22×D113—44no—
185C22×D113—44no—
186C22×D113—44no—
187C22×D113—44no—
188C22×D113—44no—
189C22×D113—44no—
190C22×D113—44no—
191C22×D113—44no—
192C22×D113C2×D412yes—
193C22×D113C2×D412yes—
194C22×D113C2×D412yes—
195C22×D113C2×D412yes—
196C22×D113C2×D412yes—
197C22×D113C2×D412yes—
198C22×D113#4112yes—
199D4×C113—28no—
200D4×C113—44no—
201D4×C113—44no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—21no—
205C2×C4×C113—21no—
206C2×C4×C113—21no—
207C2×C4×C113—21no—
208C2×C4×C113—21no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113C2×D412yes—
213C2×C4×C113C2×D412yescomplemented
214C22⋊D113—28no—
215C22⋊D113—28no—
216C22⋊D113—44no—
217C22⋊D113—44no—
218C22⋊D113—44no—
219C2×Dic113—21no—
220C2×Dic113—21no—
221C2×Dic113—21no—
222C2×Dic113—21no—
223C2×Dic113—21no—
224C2×Dic113—21no—
225C2×Dic113—21no—
226C2×Dic113—21no—
227C2×Dic113—21no—
228C2×Dic113—21no—
229C2×Dic113—21no—
230C2×Dic113—21no—
231C2×Dic113—21no—
232C2×Dic113C2×D412yes—
233C2×Dic113C2×D412yescomplemented
234D452—28no—
235C4×D113—28no—
236C4×D113—44no—
237C4×D113—44no—
238C22×C113—22no—
239C22×C113—22no—
240C22×C113—22no—
241C22×C113—22no—
242C22×C113—22no—
243C22×C113—22no—
244C22×C113—41no—
245C22×C113—41no—
246C22×C113—41no—
247C22×C113—41no—
248C22×C113—41no—
249C22×C113—41no—
250C22×C113—41no—
251C22×C113—41no—
252C22×C113—41no—
253C22×C113—41no—
254C22×C113—41no—
255C22×C113—41no—
256C22×C113—41no—
257C22×C113—41no—
258C22×C113—41no—
259C22×C113C22×D411yescharacteristic
260C22×C113C22×D411yescharacteristic
261C22×C113C22×D411yescharacteristic
262C22×C113C22×D411yescharacteristic
263C22×C113C2×#4111yescharacteristic
264C22×C113H(5,𝔽2)11yescharacteristic
265C22×C113H(5,𝔽2)11yescharacteristic
266C2×D113—22no—
267C2×D113—22no—
268C2×D113—22no—
269C2×D113—22no—
270C2×D113—22no—
271C2×D113—22no—
272C2×D113—22no—
273C2×D113—22no—
274C2×D113—22no—
275C2×D113—22no—
276C2×D113—22no—
277C2×D113—22no—
278C2×D113—22no—
279C2×D113—22no—
280C2×D113—22no—
281C2×D113—416no—
282C2×D113—416no—
283C2×D113—41no—
284C2×D113—41no—
285C2×D113—41no—
286C2×D113—41no—
287C2×D113#12014yescomplemented
288C2×D113#12114yescomplemented
289C4×C113—22no—
290C4×C113—22no—
291C4×C113—41no—
292C4×C113—41no—
293Dic113—22no—
294Dic113—22no—
295Dic113—41no—
296Dic113—41no—
297Dic113—41no—
298C2×C113—42no—
299C2×C113—42no—
300C2×C113—81no—
301C2×C113C2×#12011yescharacteristic
302C2×C113C2×#12111yescharacteristic
303C2×C113#53411yescharacteristic
304C2×C113D4211yescharacteristic
305C2×C113D4211yescharacteristic
306C2×C113#54611yescharacteristic
307C2×C113#54611yescharacteristic
308D113—24no—
309D113—24no—
310D113—42no—
311#2410—1131nomaximal, Sylow
312C113#241011yescharacteristic, complemented, Sylow
313C23×D4—1131no—
314C2×#121—1131no—
315C2×#121—1131no—
316C2×#120—1131no—
317C2×#120—1131no—
318C22×C22⋊C4—1131no—
319#394—1131no—
320#394—1131no—
321#392—1131no—
322#392D11311yescharacteristic, complemented
323#386—1131no—
324#386—1131no—
325#386—1131no—
326#385—1131no—
327#379—1131no—
328C25—1131no—
329C25—1131no—
330C22×D4—1131no—
331C22×D4—1131no—
332C22×D4—1131no—
333C22×D4—1131no—
334C22×D4—1131no—
335C22×D4—1131no—
336C22×D4—2264no—
337C22×D4—2264no—
338C22×D4—2264no—
339C22×D4C2×D11311yescharacteristic
340C22×D4C2×D11311yescharacteristic, complemented
341C22×D4C2×D11311yescharacteristic, complemented
342C23×C4—1131no—
343C23×C4—1131no—
344C23×C4—1131no—
345#121—2264no—
346#121—2264no—
347#120—2264no—
348#120—2264no—
349C2×C4⋊C4—1131no—
350C2×C4⋊C4—1131no—
351C2×C22⋊C4—1131no—
352C2×C22⋊C4—1131no—
353C2×C22⋊C4—1131no—
354C2×C22⋊C4—1131no—
355C2×C22⋊C4—1131no—
356C2×C22⋊C4—1131no—
357C2×C22⋊C4—1131no—
358C2×C22⋊C4—1131no—
359C2×C22⋊C4—1131no—
360C2×C22⋊C4—1131no—
361C2×C22⋊C4—1131no—
362C2×C22⋊C4—1131no—
363C2×C22⋊C4—2264no—
364C2×C22⋊C4C2×D11311yescharacteristic, complemented
365C2×C22⋊C4C2×D11311yescharacteristic, complemented
366C2×C22⋊C4C2×D11311yescharacteristic, complemented
367#95—1131no—
368#95—1131no—
369#95—1131no—
370#95C2×D11311yescharacteristic, complemented
371C24—1131no—
372C24—1131no—
373C24—1134no—
374C24—1131no—
375C24—4521no—
376C24—4521no—
377C24—4521no—
378C24—4521no—
379C24—2262no—
380C24—2262no—
381C24—2262no—
382C24—2262no—
383C24—2262no—
384C24—2262no—
385C24—2262no—
386C24—2262no—
387C24—2262no—
388C24C22×D11311yescharacteristic
389C24C22×D11311yescharacteristic
390C24C22×D11311yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—1134no—
401C2×D4—1134no—
402C2×D4—4521no—
403C2×D4—2262no—
404C2×D4—2262no—
405C2×D4—2262no—
406C2×D4—2262no—
407C2×D4—22632no—
408C2×D4—2262no—
409C2×D4—2262no—
410C2×D4—2262no—
411C2×D4—2262no—
412C2×D4—2262no—
413C2×D4—2262no—
414C2×D4—2262no—
415C2×D4—2262no—
416C2×D4—2262no—
417C2×D4—2262no—
418C2×D4—2262no—
419C22×C4—1131no—
420C22×C4—1131no—
421C22×C4—1131no—
422C22×C4—1131no—
423C22×C4—1131no—
424C22×C4—4521no—
425C22×C4—4521no—
426C22×C4—2262no—
427C22×C4—2262no—
428C22×C4—2262no—
429C22×C4—2262no—
430C22×C4—2262no—
431C22×C4—2262no—
432C22×C4—2262no—
433C22×C4C22×D11311yescharacteristic
434C22×C4C22×D11311yescharacteristic
435C22×C4C22×D11311yescharacteristic
436C22×C4C22×D11311yescharacteristic
437C4⋊C4—2262no—
438C4⋊C4—2262no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—1134no—
443C22⋊C4—4521no—
444C22⋊C4—2262no—
445C22⋊C4—2262no—
446C22⋊C4—2262no—
447C22⋊C4—2262no—
448C22⋊C4—2262no—
449C22⋊C4—2262no—
450C22⋊C4—2262no—
451C22⋊C4—2262no—
452C22⋊C4—2262no—
453C22⋊C4—2262no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—1132no—
474C23—1132no—
475C23—1132no—
476C23—1132no—
477C23—1132no—
478C23—1132no—
479C23—1132no—
480C23—4524no—
481C23—4524no—
482C23—4524no—
483C23—4524no—
484C23—4524no—
485C23—4524no—
486C23—4524no—
487C23—4524no—
488C23—4524no—
489C23—4524no—
490C23—4524no—
491C23—2268no—
492C23—2268no—
493C23—2268no—
494C23—2261no—
495C23—2261no—
496C23—2261no—
497C23—2261no—
498C23—2261no—
499C23—2261no—
500C23—2261no—
501C23—2261no—
502C23—2261no—
503C23—2261no—
504C23—2261no—
505C23—2261no—
506C23—2261no—
507C23—2261no—
508C23D4×D11312yes—
509C23D4×D11312yes—
510C23C23×D11311yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—4524no—
515D4—4524no—
516D4—4524no—
517D4—2268no—
518D4—2268no—
519D4—2268no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—1132no—
531C2×C4—1132no—
532C2×C4—4524no—
533C2×C4—4524no—
534C2×C4—2268no—
535C2×C4—2261no—
536C2×C4—2261no—
537C2×C4—2261no—
538C2×C4—2261no—
539C2×C4—2261no—
540C2×C4—2261no—
541C2×C4—2261no—
542C2×C4—2261no—
543C2×C4—2261no—
544C2×C4—2261no—
545C2×C4—2261no—
546C2×C4—2261no—
547C2×C4—2261no—
548C2×C4D4×D11312yes—
549C2×C4D4×D11312yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—1134no—
572C22—1134no—
573C22—45216no—
574C22—45216no—
575C22—4521no—
576C22—4521no—
577C22—4521no—
578C22—4521no—
579C22—2262no—
580C22—2262no—
581C22—2262no—
582C22—2262no—
583C22—2262no—
584C22—2262no—
585C22—2262no—
586C22—2262no—
587C22—2262no—
588C22—2262no—
589C22—2262no—
590C22—2262no—
591C22—2262no—
592C22—2262no—
593C22—2262no—
594C22C2×D4×D11311yescharacteristic
595C22C2×D4×D11311yescharacteristic
596C22C2×D4×D11311yescharacteristic
597C22C2×D4×D11311yescharacteristic
598C22#41×D11311yescharacteristic
599C22#1681366711yescharacteristic
600C22#1681366711yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—4521no—
606C4—4521no—
607C4—4521no—
608C4—2262no—
609C4—2262no—
610C2—42no—
611C2—42no—
612C2—81no—
613C2—4522no—
614C2—2264no—
615C2—2264no—
616C2#120×D11311yescharacteristic
617C2#121×D11311yescharacteristic
618C2#2029915811yescharacteristic
619C2#2029923011yescharacteristic
620C2#2029923311yescharacteristic
621C2#2029923711yescharacteristic
622C2#2029924511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#392×C113C2
hypercenter#392D113
hypocenterC113#2410
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. C2×#16813595C2semidirect
3. C2×#16813593C2semidirect
4. C2×#16813590C2semidirect
5. C2×#16813590C2semidirect
6. C2×C22⋊C4×D113C2semidirect
7. #20298514C2semidirect
8. #20298512C2semidirect
9. #20298506C2semidirect
10. #20298476C2semidirect
11. #20298474C2semidirect
12. #20298474C2semidirect
13. #20298472C2semidirect
14. #20298453C2semidirect
15. #392×C113C2semidirect
22. C22×C22⋊D113C22semidirect
23. C22×C22⋊D113C22semidirect
28. C22×C4×D113C22semidirect
29. C22×C4×D113C22semidirect
34. C2×C4⋊Dic113C22semidirect
35. C2×#14268626C22semidirect
36. C2×C22⋊Dic113C22semidirect
37. C2×C22⋊Dic113C22semidirect
38. C2×C22⋊Dic113C22semidirect
39. C2×C22⋊Dic113C22semidirect
40. C2×C22⋊Dic113C22semidirect
44. C2×#14268624C22semidirect
45. C2×#14268624C22semidirect
46. C2×#14268624C22semidirect
47. C2×#14268624C22semidirect
49. #16813529C22semidirect
50. #16813529C22semidirect
51. #16813529C22semidirect
53. C22×D4×C113C22semidirect
54. C22×D4×C113C22semidirect
55. C2×C22⋊C4×C113C22semidirect
56. C2×C22⋊C4×C113C22semidirect
57. C2×C22⋊C4×C113C22semidirect
58. #95×C113C22semidirect
72. C23×D113D4semidirect
78. C2×D452D4semidirect
93. C2×C22⋊D113D4semidirect
122. #14268624D4semidirect
213. C2×C4×C113C2×D4semidirect
233. C2×Dic113C2×D4semidirect
287. C2×D113#120semidirect
288. C2×D113#121semidirect
312. C113#2410semidirect
322. #392D113semidirect
340. C22×D4C2×D113semidirect
341. C22×D4C2×D113semidirect
364. C2×C22⋊C4C2×D113semidirect
365. C2×C22⋊C4C2×D113semidirect
366. C2×C22⋊C4C2×D113semidirect
370. #95C2×D113semidirect
549. C2×C4D4×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×#168135952
C2×#168135932
C2×#168135902
C2×C22⋊C4×D1132
#202985142
#202985122
#202985062
#202984762
#202984742
#202984722
#202984532
#392×C1132
#2410113