Finite Group Databasebeta

← #10845337

Subgroups — #10845337

Order 768.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4891C211yesmaximal, characteristic, complemented
2C2×#67⋊C8C211yesmaximal, characteristic, complemented
3#73941C211yesmaximal, characteristic, complemented
4#73933C211yesmaximal, characteristic
5C3×#2076C211yesmaximal, characteristic, complemented
6#70630C211yesmaximal, characteristic, complemented
7#69934C211yesmaximal, characteristic, complemented
8#69515C211yesmaximal, characteristic, complemented
9#69511C211yesmaximal, characteristic, complemented
10#68883C211yesmaximal, characteristic, complemented
11#68833C211yesmaximal, characteristic, complemented
12#68823C211yesmaximal, characteristic, complemented
13#68804C211yesmaximal, characteristic, complemented
14#68798C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#25342—31nomaximal, Sylow
17C2×#930C2211yescharacteristic
18C2×C4×#67C2211yescharacteristic
19C23×C3⋊C8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#895C2211yescharacteristic
22C2×#893C2211yescharacteristic
23C2×#890C2211yescharacteristic
24C2×C3×#107C2211yescharacteristic
25C2×C3×C22⋊C8C2211yescharacteristic
26C3×#380C2211yescharacteristic
27C3×#380C2211yescharacteristic
28#5212C2211yescharacteristic
29C2×#821C2211yescharacteristic
30C2×#821C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×#818C2211yescharacteristic
33C2×Dic3⋊C8C2211yescharacteristic
34C2×C8×Dic3C2211yescharacteristic
35#4987C2211yescharacteristic
36#4987C2211yescharacteristic
37#4987C2211yescharacteristic
38#4977C2211yescharacteristic
39Dic3×C4⋊C4C2211yescharacteristic
40C2×#809C2211yescharacteristic
41C2×#809C2211yescharacteristic
42C2×#808C2211yescharacteristic
43C2×#808C2211yescharacteristic
44#4961—21no—
45#4960—21no—
46#4956—21no—
47#4944—21no—
48#4891—24no—
49#67⋊C8—24no—
50#4675—21no—
51#4669—21no—
52#4665—21no—
53#4660—21no—
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57#4551C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62C2×#478—31no—
63C2×C8×D4—31no—
64#2562—31no—
65#2535—31no—
66#2077—31no—
67#2076D311yescharacteristic, complemented
68#2034—31no—
69#2033—31no—
70#1991—31no—
71#1949—31no—
72#1893—31no—
73#1893—31no—
74#1808—31no—
75#1807—31no—
76C4×#102—31no—
77C23×C3×C4C2311yescharacteristic
78C22×#67—21no—
79C22×#67D411yescharacteristic
80C22×D12—21no—
81C22×D12C2311yescharacteristic
82C22×C4×D3—21no—
83C22×C4×D3C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C2×C3×C4⋊C4C2311yescharacteristic
87C2×C3×C4⋊C4C2311yescharacteristic
88C2×C3×C4⋊C4C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—21no—
92C2×#217—21no—
93C2×#217D411yescharacteristic
94#930—22no—
95#930—41no—
96C4×#67—22no—
97C4×#67—22no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4D411yescharacteristic
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3C2311yescharacteristic
107C2×C4⋊Dic3C2311yescharacteristic
108C2×C4⋊Dic3C2311yescharacteristic
109C2×Dic3⋊C4—21no—
110C2×Dic3⋊C4D411yescharacteristic
111C2×C4×Dic3—21no—
112C2×C4×Dic3C2311yescharacteristic
113C22×C3⋊C8—22no—
114C22×C3⋊C8—22no—
115C22×C3⋊C8—41no—
116C22×C3⋊C8C2311yescharacteristic
117C22×C3⋊C8C2311yescharacteristic
118C2×D3×C8—22no—
119C2×D3×C8—22no—
120C2×D3×C8—41no—
121#895—22no—
122#895—41no—
123#893—22no—
124#893—22no—
125#890—22no—
126#890—22no—
127C3×#107—22no—
128C3×C22⋊C8—22no—
129C3×#95—21no—
130C3×#95—21no—
131C3⋊#95—21no—
132C3⋊#95—21no—
133C3⋊#95—21no—
134C3⋊#95—21no—
135C3⋊#95—21no—
136C3⋊#95—21no—
137C3⋊#95—21no—
138#821—22no—
139#821—22no—
140(C2×D3)⋊C8—22no—
141#818—41no—
142Dic3⋊C8D414yescomplemented
143C8×Dic3—22no—
144#809—22no—
145#809—22no—
146#808—22no—
147#808—41no—
148C23×C8—31no—
149C23×C8—31no—
150C2×#125—31no—
151C2×#121—31no—
152C2×#121—31no—
153C2×C4×D4—31no—
154C2×C4×D4—31no—
155#478—64no—
156C8×D4—64no—
157C2×#107—31no—
158C2×#107C2×D311yescharacteristic
159C2×#106—31no—
160C2×#106—31no—
161C2×C4⋊C8—31no—
162C2×#102—31no—
163C2×#102—31no—
164C2×#102—31no—
165C2×#102—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8C2×D311yescharacteristic
168C2×C4×C8—31no—
169#400—61no—
170#397—61no—
171#394—61no—
172#392—61no—
173#388—61no—
174#388—61no—
175#386—61no—
176#386—61no—
177#382—31no—
178#380—31no—
179#380—31no—
180#380—31no—
181#380—31no—
182#380C2×D311yescharacteristic
183#380C2×D311yescharacteristic
184C4×C4⋊C4—31no—
185#340—31no—
186#340—31no—
187#340—31no—
188#340—31no—
189#340—31no—
190#340C2×D311yescharacteristic
191#340C2×D311yescharacteristic
192#340C2×D311yescharacteristic
193C24×C3C2×D411yescharacteristic
194C23×D3—21no—
195C23×D3C2×D411yescharacteristic
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×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2411yescharacteristic
208C2×#67—22no—
209C2×#67—22no—
210C2×#67—22no—
211C2×#67—42no—
212C2×#67—42no—
213C2×#67—81no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3C2×D411yescharacteristic
218C22×Dic3C2×D411yescharacteristic
219C22×Dic3C2×D411yescharacteristic
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12—42no—
226C2×D12—42no—
227C2×D12—81no—
228C2×D12#4112yes—
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—42no—
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×C8C2×D412yes—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C22⋊C4—81no—
253C3×C22⋊C4—81no—
254#217—22no—
255#217—42no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—42no—
258(C2×D3)⋊C4—42no—
259(C2×D3)⋊C4—42no—
260(C2×D3)⋊C4—42no—
261(C2×D3)⋊C4—81no—
262(C2×D3)⋊C4—81no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—42no—
270Dic3⋊C4—22no—
271Dic3⋊C4—42no—
272C4×Dic3—81no—
273C4×Dic3C2×D412yes—
274C4×Dic3#4112yes—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—21no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—44no—
280C2×C3⋊C8C2×D412yes—
281C2×C3⋊C8#4112yes—
282D3×C8—44no—
283C22×D4—31no—
284C22×D4—31no—
285C22×D4—61no—
286C22×D4—61no—
287C23×C4—31no—
288C23×C4—61no—
289C23×C4C22×D311yescharacteristic
290C22×C8—31no—
291C22×C8—31no—
292C22×C8—62no—
293C22×C8—62no—
294C22×C8—62no—
295C22×C8—62no—
296C22×C8—121no—
297C22×C8—121no—
298C22×C8C22×D311yescharacteristic
299C22×C8C22×D311yescharacteristic
300#125—62no—
301#125—62no—
302#121—62no—
303#121—62no—
304#121—121no—
305#121—121no—
306C4×D4—62no—
307C4×D4—62no—
308C4×D4—62no—
309C4×D4—62no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—61no—
315C2×C4⋊C4—61no—
316C2×C4⋊C4C22×D311yescharacteristic
317C2×C4⋊C4C22×D311yescharacteristic
318C2×C4⋊C4C22×D311yescharacteristic
319C2×C4⋊C4C22×D311yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—61no—
326C2×C22⋊C4—61no—
327C2×C22⋊C4—61no—
328C2×C22⋊C4—61no—
329C2×C22⋊C4—61no—
330C2×C22⋊C4—61no—
331C2×C42—31no—
332C2×C42—61no—
333#107—22no—
334#107—121no—
335#106—62no—
336#106—121no—
337C4⋊C8—34no—
338#102—62no—
339#102—62no—
340#102—62no—
341#102—62no—
342C22⋊C8—22no—
343C22⋊C8—62no—
344C4×C8—62no—
345#95—21no—
346#95—21no—
347#95—61no—
348#95—61no—
349#95—61no—
350#95—61no—
351#95—61no—
352#95—61no—
353#95—61no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3#13512yes—
361C23×C3C22×D411yescharacteristic
362C22×D3—21no—
363C22×D3—21no—
364C22×D3—21no—
365C22×D3—21no—
366C22×D3—21no—
367C22×D3—21no—
368C22×D3—22no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3#13512yes—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4C22×D411yescharacteristic
396C2×C3×C4C2×#4111yescharacteristic
397C2×C3×C4C2×#4111yescharacteristic
398C2×C3×C4C2×#4111yescharacteristic
399C2×C3×C4H(5,𝔽2)11yescharacteristic
400C2×C3×C42−1+411yescharacteristic
401#67—28no—
402#67—84no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—21no—
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#12112yes—
420C2×Dic3#12112yes—
421D12—22no—
422D12—22no—
423D12—41no—
424D12—41no—
425D12—84no—
426C4×D3—41no—
427C4×D3—41no—
428C4×D3—41no—
429C4×D3—41no—
430C4×D3—84no—
431C3×C8—22no—
432C3×C8—41no—
433C3⋊C8—22no—
434C3⋊C8—22no—
435C24—31no—
436C24—61no—
437C24D3×D411yescharacteristic
438C2×D4—32no—
439C2×D4—62no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—122no—
448C2×D4—122no—
449C2×D4—122no—
450C2×D4—122no—
451C2×D4—241no—
452C2×D4—241no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—122no—
476C22×C4—241no—
477C22×C4—241no—
478C22×C4D3×D411yescharacteristic
479C22×C4C23×D311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—32no—
486C2×C8—32no—
487C2×C8—61no—
488C2×C8—61no—
489C2×C8—61no—
490C2×C8—61no—
491C2×C8—124no—
492C2×C8—124no—
493C2×C8D3×D412yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—62no—
503C4⋊C4—61no—
504C4⋊C4—61no—
505C4⋊C4—61no—
506C4⋊C4—61no—
507C4⋊C4—61no—
508C4⋊C4—61no—
509C4⋊C4—122no—
510C4⋊C4—122no—
511C22⋊C4—62no—
512C22⋊C4—62no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—122no—
516C22⋊C4—122no—
517C22⋊C4—122no—
518C22⋊C4—122no—
519C22⋊C4—122no—
520C22⋊C4—241no—
521C22⋊C4—241no—
522C42—32no—
523C42—32no—
524C42—241no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3C2×#12111yescharacteristic
533C22×C3#54611yescharacteristic
534C22×C3#54711yescharacteristic
535C22×C3C2×#13511yescharacteristic
536C22×C3C2×#13511yescharacteristic
537C22×C3#57611yescharacteristic
538C22×C3#57711yescharacteristic
539C2×D3—22no—
540C2×D3—22no—
541C2×D3—22no—
542C2×D3—41no—
543C2×D3—41no—
544C2×D3—41no—
545C2×D3—41no—
546C2×D3—42no—
547C2×D3—42no—
548C2×D3—42no—
549C2×D3—81no—
550C2×D3—81no—
551C2×D3—81no—
552C2×D3—81no—
553C3×C4—41no—
554C3×C4—81no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4—81no—
558C3×C4#52911yescharacteristic
559C3×C4#54211yescharacteristic
560C3×C4#54611yescharacteristic
561C3×C4#54811yescharacteristic
562Dic3—22no—
563Dic3—22no—
564Dic3—41no—
565Dic3—81no—
566Dic3—81no—
567Dic3—81no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—32no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23—61no—
579C23—61no—
580C23—61no—
581C23—62no—
582C23—121no—
583C23—121no—
584C23—121no—
585C23—121no—
586C23—121no—
587C23—121no—
588C23#91912yes—
589C23C2×D3×D411yescharacteristic
590D4—68no—
591D4—62no—
592D4—62no—
593D4—121no—
594D4—121no—
595D4—244no—
596D4—244no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—32no—
601C2×C4—32no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
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—244no—
639C2×C4C2×D3×D411yescharacteristic
640C2×C4D3×#4111yescharacteristic
641C2×C4D3×#4111yescharacteristic
642C2×C4D3×#4111yescharacteristic
643C2×C4#100911yescharacteristic
644C2×C4#101011yescharacteristic
645C8—22no—
646C8—41no—
647C8—62no—
648C8—62no—
649C2×C3—42no—
650C2×C3#242711yescharacteristic
651C2×C3#305011yescharacteristic
652C2×C3#306211yescharacteristic
653C2×C3#329611yescharacteristic
654C2×C3#329711yescharacteristic
655C2×C3#333711yescharacteristic
656C2×C3#333911yescharacteristic
657D3—42no—
658D3—82no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—62no—
667C22—62no—
668C22—62no—
669C22—121no—
670C22—121no—
671C22—121no—
672C22—121no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—241no—
677C22—241no—
678C22—241no—
679C22—241no—
680C22D3×#12111yescharacteristic
681C22#565411yescharacteristic
682C22#565511yescharacteristic
683C22C2×#91911yescharacteristic
684C22D3×#13511yescharacteristic
685C22#577411yescharacteristic
686C22#577511yescharacteristic
687C4—41no—
688C4—62no—
689C4—62no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—121no—
695C4—241no—
696C4—241no—
697C4—241no—
698C4#565411yescharacteristic
699C4#567711yescharacteristic
700C4#570611yescharacteristic
701C4#571011yescharacteristic
702C3#2534211yescharacteristic, complemented, Sylow
703C2—42no—
704C2—122no—
705C2—242no—
706C2#7746611yescharacteristic
707C2#8075811yescharacteristic
708C2#8086711yescharacteristic
709C2#8138111yescharacteristic
710C2#8138811yescharacteristic
711C2#8146411yescharacteristic
712C2#8148511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2076C2
socleC23×C3C22×D4
prime radical#73933C2
hypercenter#2076D3
hypocenterC3#25342
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

Complements

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

NH ≅ G/Ntype
1. C2×#4891C2semidirect
2. C2×#67⋊C8C2semidirect
3. #73941C2semidirect
5. C3×#2076C2semidirect
6. #70630C2semidirect
7. #69934C2semidirect
8. #69515C2semidirect
9. #69511C2semidirect
10. #68883C2semidirect
11. #68833C2semidirect
12. #68823C2semidirect
13. #68804C2semidirect
14. #68798C2semidirect
15. #68780C2semidirect
67. #2076D3semidirect
142. Dic3⋊C8D4semidirect
702. C3#25342semidirect

Maximal subgroups

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

subgroupindex
C2×#48912
C2×#67⋊C82
#739412
#739332
C3×#20762
#706302
#699342
#695152
#695112
#688832
#688332
#688232
#688042
#687982
#687802
#253423