Finite Group Databasebeta

← #10824799

Subgroups — #10824799

Order 768.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#433C211yesmaximal, characteristic, complemented
2#82236C211yesmaximal, characteristic, complemented
3#82236C211yesmaximal, characteristic, complemented
4C2×#4711C211yesmaximal, characteristic, complemented
5#70484C211yesmaximal, characteristic, complemented
6#70483C211yesmaximal, characteristic, complemented
7#70481C211yesmaximal, characteristic, complemented
8#70464C211yesmaximal, characteristic, complemented
9#69961C211yesmaximal, characteristic
10#69940C211yesmaximal, characteristic, complemented
11#69935C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69814C211yesmaximal, characteristic, complemented
14C4×#821C211yesmaximal, characteristic, complemented
15C4×#821C211yesmaximal, characteristic, complemented
16#23712—31nomaximal, Sylow
17C2×C3×#117C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C22×D24C2211yescharacteristic
21C2×C4×D12C2211yescharacteristic
22C2×C4×D12C2211yescharacteristic
23C3×#433—24no—
24C2×C3×C4⋊C8C2211yescharacteristic
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C2×C3×#97C2211yescharacteristic
29C2×C3×C4×C8C2211yescharacteristic
30#5212C2211yescharacteristic
31#5212C2211yescharacteristic
32C2×#821C2211yescharacteristic
33C2×#821C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#818C2211yescharacteristic
39C2×#817C2211yescharacteristic
40C2×#817C2211yescharacteristic
41#4990—21no—
42#4990—21no—
43#4989—21no—
44#4989—21no—
45#4957—21no—
46#4957—21no—
47#4956—21no—
48#4956—21no—
49#4939C2211yescharacteristic
50#4939C2211yescharacteristic
51C4×C4⋊Dic3C2211yescharacteristic
52C4×C4⋊Dic3C2211yescharacteristic
53#4928C2211yescharacteristic
54#4928C2211yescharacteristic
55#4711—24no—
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62C2×#442—31no—
63C2×#433D311yescharacteristic, complemented
64#2324—31no—
65#2324—31no—
66#2088—31no—
67#2077—31no—
68#2067—31no—
69#2065—31no—
70#2054—31no—
71#2034—31no—
72#2033—31no—
73#1999—31no—
74#1776—31no—
75C4×#102—31no—
76C4×#102—31no—
77C23×C3×C4C2311yescharacteristic
78C22×#67—21no—
79C22×#67—21no—
80C22×D12C2311yescharacteristic
81C22×D12C2311yescharacteristic
82C22×C4×D3—21no—
83C22×C4×D3—21no—
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C3×#117—22no—
89C3×#117—22no—
90C2×C3×C4⋊C4D411yescharacteristic
91C2×C3×C4⋊C4D411yescharacteristic
92C2×C3×C22⋊C4D411yescharacteristic
93C2×C3×C22⋊C4D411yescharacteristic
94C2×C3×C42C2311yescharacteristic
95C2×C3×C42C2311yescharacteristic
96C2×#217—21no—
97C2×#217—21no—
98#930—22no—
99#930—22no—
100#930—22no—
101#930—22no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×C4⋊Dic3C2311yescharacteristic
111C2×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×Dic3⋊C4—21no—
117C2×Dic3⋊C4—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3—21no—
120C2×D24—22no—
121C2×D24—22no—
122C2×D24—22no—
123C4×D12—22no—
124C4×D12—22no—
125C4×D12—22no—
126C4×D12—22no—
127C3×C4⋊C8—22no—
128C3×C4⋊C8—22no—
129C3×C22⋊C8—22no—
130C3×C22⋊C8—22no—
131C3×#97D414yescomplemented
132C3×C4×C8—22no—
133C3⋊#95—21no—
134C3⋊#95—21no—
135C3⋊#95—21no—
136C3⋊#95—21no—
137C3⋊#95—21no—
138C3⋊#95—21no—
139#821—22no—
140#821—22no—
141#821—22no—
142#821—22no—
143#821—22no—
144#821—22no—
145#818—22no—
146#817—22no—
147#817—22no—
148C22×D8—31no—
149C2×#121—31no—
150C2×#121—31no—
151C2×C4×D4—31no—
152C2×C4×D4—31no—
153C2×#117C2×D311yescharacteristic
154#442—64no—
155#433—24no—
156C2×#107—31no—
157C2×#106—31no—
158C2×#106—31no—
159C2×C4⋊C8C2×D311yescharacteristic
160C2×C4⋊C8C2×D311yescharacteristic
161C2×#102—31no—
162C2×#102—31no—
163C2×#102—31no—
164C2×#102—31no—
165C2×#102—31no—
166C2×#102—31no—
167C2×C22⋊C8C2×D311yescharacteristic
168C2×C22⋊C8C2×D311yescharacteristic
169C2×#97C2×D311yescharacteristic
170C2×C4×C8C2×D311yescharacteristic
171#390—31no—
172#390—31no—
173#390—61no—
174#390—61no—
175#389—31no—
176#389—31no—
177#388—61no—
178#388—61no—
179#386—61no—
180#386—61no—
181#385—61no—
182#385—61no—
183#380—31no—
184#380—31no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—31no—
187#340—31no—
188#340—31no—
189#340—31no—
190#340—31no—
191#340—31no—
192#340—31no—
193C24×C3C2×D411yescharacteristic
194C23×D3—21no—
195C23×D3—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2411yescharacteristic
208C2×#67—24no—
209C2×#67—24no—
210C2×#67—81no—
211C2×#67—81no—
212C2×#67—81no—
213C2×#67—81no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12#4112yes—
231C2×D12#4112yes—
232C2×C4×D3—42no—
233C2×C4×D3—42no—
234C2×C4×D3—81no—
235C2×C4×D3—81no—
236C2×C4×D3—81no—
237C2×C4×D3—81no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8C2×D412yes—
249C2×C3×C8C2×D412yes—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—22no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—22no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42C2×D412yes—
257C3×C42#4112yes—
258#217—81no—
259#217—81no—
260(C2×D3)⋊C4—24no—
261(C2×D3)⋊C4—24no—
262(C2×D3)⋊C4—42no—
263(C2×D3)⋊C4—42no—
264(C2×D3)⋊C4—81no—
265(C2×D3)⋊C4—81no—
266(C2×D3)⋊C4—81no—
267(C2×D3)⋊C4—81no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3#4112yes—
279C4⋊Dic3#4112yes—
280Dic3⋊C4—81no—
281Dic3⋊C4—81no—
282C4×Dic3—81no—
283C4×Dic3—81no—
284D24—28no—
285C22×D4—31no—
286C22×D4—31no—
287C22×D4—61no—
288C22×D4—61no—
289C23×C4—61no—
290C23×C4—61no—
291C23×C4C22×D311yescharacteristic
292C2×D8—62no—
293C2×D8—62no—
294C2×D8—62no—
295C22×C8C22×D311yescharacteristic
296C22×C8C22×D311yescharacteristic
297C22×C8C22×D311yescharacteristic
298C22×C8C22×D311yescharacteristic
299#121—62no—
300#121—62no—
301#121—62no—
302#121—62no—
303C4×D4—62no—
304C4×D4—62no—
305C4×D4—62no—
306C4×D4—62no—
307#117—22no—
308#117—22no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—61no—
316C2×C4⋊C4—61no—
317C2×C4⋊C4D1211yescharacteristic
318C2×C4⋊C4D1211yescharacteristic
319C2×C22⋊C4—61no—
320C2×C22⋊C4—61no—
321C2×C22⋊C4—61no—
322C2×C22⋊C4—61no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—61no—
326C2×C22⋊C4—61no—
327C2×C22⋊C4—61no—
328C2×C22⋊C4—61no—
329C2×C22⋊C4D1211yescharacteristic
330C2×C22⋊C4D1211yescharacteristic
331C2×C42—61no—
332C2×C42—61no—
333C2×C42C22×D311yescharacteristic
334C2×C42C22×D311yescharacteristic
335#107—62no—
336#106—62no—
337#106—62no—
338C4⋊C8—22no—
339C4⋊C8—22no—
340#102—62no—
341#102—62no—
342#102—62no—
343#102—62no—
344#102—62no—
345#102—62no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348#97#6714yescomplemented
349C4×C8—22no—
350#95—61no—
351#95—61no—
352#95—61no—
353#95—61no—
354#95—61no—
355#95—61no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3C22×D411yescharacteristic
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4#12112yes—
396C2×C3×C4#12112yes—
397C2×C3×C4C22×D411yescharacteristic
398C2×C3×C4C2×#4111yescharacteristic
399C2×C3×C4C2×#4111yescharacteristic
400C2×C3×C4C2×#4111yescharacteristic
401C2×C3×C4C2×#4111yescharacteristic
402C2×C3×C4C2×#4111yescharacteristic
403#67—84no—
404#67—84no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—41no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423D12—22no—
424D12—22no—
425D12—22no—
426D12—22no—
427D12—41no—
428D12—41no—
429D12—41no—
430D12—41no—
431C4×D3—84no—
432C4×D3—84no—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8—41no—
436C3×C8—41no—
437C24—61no—
438C24—61no—
439C24C2×D1211yescharacteristic
440C2×D4—32no—
441C2×D4—32no—
442C2×D4—64no—
443C2×D4—64no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—241no—
455C2×D4—241no—
456C2×D4—241no—
457C2×D4—241no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—122no—
471C22×C4—122no—
472C22×C4—241no—
473C22×C4—241no—
474C22×C4—241no—
475C22×C4—241no—
476C22×C4C2×D1211yescharacteristic
477C22×C4C2×D1211yescharacteristic
478C22×C4C2×D1211yescharacteristic
479C22×C4C2×D1211yescharacteristic
480C22×C4C2×D1211yescharacteristic
481C22×C4C23×D311yescharacteristic
482D8—68no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8C2×#6712yes—
494C2×C8C2×#6712yes—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—32no—
498C4⋊C4—32no—
499C4⋊C4—61no—
500C4⋊C4—61no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C4⋊C4—61no—
504C4⋊C4—61no—
505C4⋊C4—61no—
506C4⋊C4—61no—
507C4⋊C4—61no—
508C4⋊C4—61no—
509C4⋊C4—241no—
510C4⋊C4—241no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—64no—
514C22⋊C4—64no—
515C22⋊C4—122no—
516C22⋊C4—122no—
517C22⋊C4—241no—
518C22⋊C4—241no—
519C22⋊C4—241no—
520C22⋊C4—241no—
521C22⋊C4—241no—
522C22⋊C4—241no—
523C42—21no—
524C42—21no—
525C42—241no—
526C42—241no—
527C42#23512yes—
528C42C2×#6712yes—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3C2×#12111yescharacteristic
537C22×C3#52511yescharacteristic
538C22×C3#52511yescharacteristic
539C22×C3#57611yescharacteristic
540C22×C3#57611yescharacteristic
541C22×C3#57711yescharacteristic
542C22×C3#57711yescharacteristic
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—42no—
546C2×D3—42no—
547C2×D3—42no—
548C2×D3—42no—
549C2×D3—81no—
550C2×D3—81no—
551C2×D3—81no—
552C2×D3—81no—
553C2×D3—81no—
554C2×D3—81no—
555C2×D3—81no—
556C2×D3—81no—
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4#52511yescharacteristic
563C3×C4#52911yescharacteristic
564C3×C4#52911yescharacteristic
565C3×C4#53211yescharacteristic
566Dic3—42no—
567Dic3—42no—
568Dic3—81no—
569Dic3—81no—
570Dic3—81no—
571Dic3—81no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—62no—
580C23—62no—
581C23—121no—
582C23—121no—
583C23—121no—
584C23—121no—
585C23—121no—
586C23—121no—
587C23—121no—
588C23—121no—
589C23—121no—
590C23—121no—
591C23—121no—
592C23—121no—
593C23C22×D1211yescharacteristic
594D4—62no—
595D4—62no—
596D4—62no—
597D4—62no—
598D4—121no—
599D4—121no—
600D4—121no—
601D4—121no—
602D4—244no—
603D4—244no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—121no—
627C2×C4—121no—
628C2×C4—121no—
629C2×C4—121no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—121no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—121no—
638C2×C4—121no—
639C2×C4—244no—
640C2×C4—244no—
641C2×C4#93012yes—
642C2×C4#93012yes—
643C2×C4C2×#23511yescharacteristic
644C2×C4D3×#4111yescharacteristic
645C2×C4D3×#4111yescharacteristic
646C2×C4D3×#4111yescharacteristic
647C2×C4D3×#4111yescharacteristic
648C2×C4C22×#6711yescharacteristic
649C8—22no—
650C8—22no—
651C8—41no—
652C8—41no—
653C2×C3—81no—
654C2×C3#239211yescharacteristic
655C2×C3#306211yescharacteristic
656C2×C3#306211yescharacteristic
657C2×C3#311811yescharacteristic
658C2×C3#311911yescharacteristic
659C2×C3#312211yescharacteristic
660C2×C3#312511yescharacteristic
661D3—82no—
662D3—82no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—122no—
671C22—122no—
672C22—122no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—241no—
677C22—241no—
678C22—241no—
679C22—241no—
680C22—241no—
681C22—241no—
682C22—241no—
683C22—241no—
684C22#552411yescharacteristic
685C22#552411yescharacteristic
686C22#575111yescharacteristic
687C22#575111yescharacteristic
688C22#575211yescharacteristic
689C22#575211yescharacteristic
690C22C2×#93011yescharacteristic
691C4—22no—
692C4—22no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—122no—
697C4—122no—
698C4—241no—
699C4—241no—
700C4—241no—
701C4—241no—
702C4#552811yescharacteristic
703C4#552811yescharacteristic
704C4#582811yescharacteristic
705C4#583211yescharacteristic
706C3#2371211yescharacteristic, complemented, Sylow
707C2—81no—
708C2—242no—
709C2—242no—
710C2#7938311yescharacteristic
711C2#7938411yescharacteristic
712C2#7938611yescharacteristic
713C2#7938911yescharacteristic
714C2#8227311yescharacteristic
715C2#8380211yescharacteristic
716C2#8380211yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#433C2
socleC23×C3C22×D4
prime radical#69961C2
hypercenterC2×#433D3
hypocenterC3#23712
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×C3×#433C2semidirect
2. #82236C2semidirect
3. #82236C2semidirect
4. C2×#4711C2semidirect
5. #70484C2semidirect
6. #70483C2semidirect
7. #70481C2semidirect
8. #70464C2semidirect
10. #69940C2semidirect
11. #69935C2semidirect
12. #69934C2semidirect
13. #69814C2semidirect
14. C4×#821C2semidirect
15. C4×#821C2semidirect
63. C2×#433D3semidirect
131. C3×#97D4semidirect
348. #97#67semidirect
706. C3#23712semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4332
#822362
C2×#47112
#704842
#704832
#704812
#704642
#699612
#699402
#699352
#699342
#698142
C4×#8212
#237123