Finite Group Databasebeta

← #10830625

Subgroups — #10830625

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C2×#5238C211yesmaximal, characteristic, complemented
3C2×#5217C211yesmaximal, characteristic, complemented
4C2×#5057C211yesmaximal, characteristic, complemented
5#82415C211yesmaximal, characteristic, complemented
6C2×C4×#213C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72128C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#71699C211yesmaximal, characteristic, complemented
11#71695C211yesmaximal, characteristic, complemented
12#71684C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14#71614C211yesmaximal, characteristic, complemented
15#71605C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C3×#546—24no—
20C3×#546—24no—
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#120—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C22×C3×C22⋊C4—21no—
30C22×#215C2211yescharacteristic, complemented
31C22×#213C2211yescharacteristic
32C22×#213C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic, complemented
35C2×C4×D12C2211yescharacteristic, complemented
36#5238—24no—
37C2×#835C2211yescharacteristic, complemented
38C2×#835C2211yescharacteristic, complemented
39C2×#835C2211yescharacteristic, complemented
40#5223—21no—
41#5217—24no—
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48#5212C2211yescharacteristic
49#5212C2211yescharacteristic, complemented
50C2×#830C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic, complemented
53C2×#830C2211yescharacteristic, complemented
54#5057—24no—
55C4×#213—24no—
56#4992—21no—
57C2×#809C2211yescharacteristic, complemented
58C2×#807C2211yescharacteristic, complemented
59#4956—21no—
60#4956—21no—
61#4936C2211yescharacteristic, complemented
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546D311yescharacteristic, complemented
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—21no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4D411yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67—21no—
106C22×#67—21no—
107C22×D12C2311yescharacteristic
108C22×C4×D3—21no—
109C3×#124—22no—
110C3×#124D414yescomplemented
111C3×#123—28no—
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8—22no—
114C3×#121—28no—
115C3×#121—22no—
116C3×#121—22no—
117C3×#120—28no—
118C3×C4×D4—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×C4×D4D414yescomplemented
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C22⋊C4—28no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4D411yescharacteristic
132C2×C3×C22⋊C4D411yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×#217—21no—
135C2×#217—21no—
136C2×#215—22no—
137C2×#215—22no—
138C2×#215—41no—
139C2×#213—22no—
140C2×#213—22no—
141C2×#213—22no—
142C2×#213—22no—
143C2×#213—41no—
144C2×#213D414yescomplemented
145#930—22no—
146#930—22no—
147#930—41no—
148#930—41no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C4×D12—22no—
160C4×D12—22no—
161#835—22no—
162#835—22no—
163#835—41no—
164#832—22no—
165#832—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169#832—41no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173C3⋊#95—21no—
174#830—22no—
175#830—22no—
176#830—41no—
177#830—41no—
178#809—22no—
179#807—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41C2×D311yescharacteristic
183C23×D4C2×D311yescharacteristic
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—24no—
188#546—24no—
189C2×#124C2×D311yescharacteristic
190C2×#123—21no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×#121—21no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121C2×D311yescharacteristic
196C2×#120—21no—
197C2×C4×D4—31no—
198C2×C4×D4C2×D311yescharacteristic
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—21no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3—24no—
233C24×C3—21no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3C2×D411yescharacteristic
241C24×C3C2×D411yescharacteristic
242C23×D3—21no—
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—24no—
255C2×C3×D4—22no—
256C2×C3×D4—24no—
257C2×C3×D4—22no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—41no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—44no—
275C2×C3×D4—81no—
276C2×C3×D4—81no—
277C2×C3×D4C2×D412yes—
278C2×C3×D4C2×D412yes—
279C2×C3×D4C2×D412yes—
280C2×C3×D4#4112yes—
281C22×C3×C4—24no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—24no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4—81no—
300C22×C3×C4—81no—
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C2×#67—42no—
310C2×#67—81no—
311C2×#67—81no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12C2×D412yes—
321C2×C4×D3—42no—
322C2×C4×D3—81no—
323C2×C4×D3—81no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4C2×D412yes—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—24no—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—22no—
335C3×C42C2×D412yes—
336C3×C42C2×D412yes—
337#217—81no—
338#217—81no—
339#215—44no—
340#213—28no—
341#213—44no—
342(C2×D3)⋊C4—42no—
343(C2×D3)⋊C4—42no—
344(C2×D3)⋊C4—42no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8C2×D412yes—
363C25—21no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—41no—
369C2×#41—41no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—31no—
379C22×D4—41no—
380C22×D4—41no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4#6711yescharacteristic
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—61no—
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
394C2×D8—34no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8—31no—
403C22×C8—31no—
404#124—22no—
405#124#6714yescomplemented
406#123—28no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—28no—
410#121—22no—
411#121—22no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—28no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4#6714yescomplemented
423C2×C4⋊C4—21no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4#6711yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—28no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4#6711yescharacteristic
441C2×C22⋊C4#6711yescharacteristic
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—62no—
445#103—62no—
446#103—62no—
447#103—121no—
448#102—62no—
449#102—62no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—62no—
456C22⋊C8—62no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C4×C8—62no—
460#95—61no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—22no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—22no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—48no—
482C23×C3—48no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—84no—
494C23×C3—84no—
495C23×C3—84no—
496C23×C3—84no—
497C23×C3—84no—
498C23×C3#13512yes—
499C23×C3C22×D411yescharacteristic
500C22×D3—22no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—44no—
517C3×D4—48no—
518C3×D4—48no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—84no—
522C3×D4#12114yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—48no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—84no—
549C2×C3×C4#12012yes—
550C2×C3×C4#12012yes—
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C2×#4111yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C2×C3×C4H(5,𝔽2)11yescharacteristic
557#67—84no—
558#67—84no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568D12—22no—
569D12—22no—
570D12—41no—
571D12—41no—
572C4×D3—84no—
573C3⋊C8—22no—
574C3⋊C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—21no—
578C24—24no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—61no—
585C24—81no—
586C24—81no—
587C24C2×#6711yescharacteristic
588C24C2×#6711yescharacteristic
589#41—44no—
590#41—44no—
591#41—44no—
592#41—44no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8C2×#6712yes—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—22no—
602C2×D4—24no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—32no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—122no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4D3×D412yes—
636C2×D4#23712yes—
637C2×D4C2×#6712yes—
638C2×D4C2×#6712yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—122no—
663C22×C4—241no—
664C22×C4—241no—
665C22×C4C2×#6711yescharacteristic
666C22×C4C2×#6711yescharacteristic
667C22×C4C2×#6711yescharacteristic
668C22×C4C2×#6711yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—32no—
674C2×C8—61no—
675C2×C8—61no—
676C2×C8—61no—
677C2×C8—61no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—24no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C2×#6712yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—22no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42C2×#6712yes—
708C42C2×#6712yes—
709C22×C3—24no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—41no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—42no—
725C22×C3—41no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—816no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3C2×#12011yescharacteristic
739C22×C3D4211yescharacteristic
740C22×C3#54611yescharacteristic
741C22×C3C2×#13511yescharacteristic
742C22×C3#57511yescharacteristic
743C22×C3#57611yescharacteristic
744C22×C3#57611yescharacteristic
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—42no—
757C3×C4—42no—
758C3×C4C2×#12111yescharacteristic
759C3×C4#53511yescharacteristic
760C3×C4D4211yescharacteristic
761C3×C4#54611yescharacteristic
762Dic3—81no—
763Dic3—81no—
764Dic3—81no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—22no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—48no—
783C23—48no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—62no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—121no—
801C23—121no—
802C23—121no—
803C23—121no—
804C23—121no—
805C23—121no—
806C23#95012yes—
807C23C22×#6711yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—44no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—62no—
823D4—62no—
824D4—84no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4#93814yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—48no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—84no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—244no—
866C2×C4#95312yes—
867C2×C4#95312yes—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×#23711yescharacteristic
870C2×C4#100411yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4C22×#6711yescharacteristic
873C2×C4C22×#6711yescharacteristic
874C8—62no—
875C8—121no—
876C8—121no—
877C8—121no—
878C2×C3—42no—
879C2×C3—44no—
880C2×C3—81no—
881C2×C3—82no—
882C2×C3#240811yescharacteristic
883C2×C3#300211yescharacteristic
884C2×C3#300811yescharacteristic
885C2×C3#327311yescharacteristic
886C2×C3#328011yescharacteristic
887C2×C3#329711yescharacteristic
888C2×C3#332211yescharacteristic
889D3—82no—
890C22—22no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—122no—
920C22—122no—
921C22—122no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22D4×#6711yescharacteristic
927C22#580611yescharacteristic
928C22C2×#95011yescharacteristic
929C22#582211yescharacteristic
930C22#583511yescharacteristic
931C22#583511yescharacteristic
932C22C2×#95311yescharacteristic
933C4—22no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—241no—
940C4—241no—
941C4—241no—
942C4C2×#93811yescharacteristic
943C4D4×#6711yescharacteristic
944C4#580511yescharacteristic
945C4#580611yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—242no—
952C2#8349511yescharacteristic
953C2#8350011yescharacteristic
954C2#8350411yescharacteristic
955C2#8350511yescharacteristic
956C2#8405311yescharacteristic
957C2#8408011yescharacteristic
958C2#8410111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#546C2
socleC23×C3C22×D4
hypercenterC2×#546D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×C3×#546C2semidirect
2. C2×#5238C2semidirect
3. C2×#5217C2semidirect
4. C2×#5057C2semidirect
5. #82415C2semidirect
6. C2×C4×#213C2semidirect
7. #72135C2semidirect
8. #72128C2semidirect
9. #71725C2semidirect
10. #71699C2semidirect
11. #71695C2semidirect
12. #71684C2semidirect
13. #71679C2semidirect
14. #71614C2semidirect
15. #71605C2semidirect
30. C22×#215C22semidirect
34. C2×#930C22semidirect
35. C2×C4×D12C22semidirect
37. C2×#835C22semidirect
38. C2×#835C22semidirect
39. C2×#835C22semidirect
49. #5212C22semidirect
52. C2×#830C22semidirect
53. C2×#830C22semidirect
57. C2×#809C22semidirect
58. C2×#807C22semidirect
61. #4936C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
66. C2×#546D3semidirect
110. C3×#124D4semidirect
121. C3×C4×D4D4semidirect
144. C2×#213D4semidirect
405. #124#67semidirect
422. C4×D4#67semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×#52382
C2×#52172
C2×#50572
#824152
C2×C4×#2132
#721352
#721282
#717252
#716992
#716952
#716842
#716792
#716142
#716052
#242453