Finite Group Databasebeta

← #10830633

Subgroups — #10830633

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×#5554C211yesmaximal, characteristic, complemented
2C2×C4×#213C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4781C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic, complemented
6#74239C211yesmaximal, characteristic, complemented
7C3×#1804C211yesmaximal, characteristic, complemented
8#70470C211yesmaximal, characteristic, complemented
9#70199C211yesmaximal, characteristic, complemented
10#70198C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68825C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C2×#930—21no—
22C22×(C2×D3)⋊C4—21no—
23C22×D24C2211yescharacteristic
24C22×#204C2211yescharacteristic, complemented
25#5554—24no—
26#5554—24no—
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic, complemented
31C2×#886—21no—
32C2×#882—21no—
33C2×#875C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic, complemented
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#382C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46C2×#816C2211yescharacteristic, complemented
47C4×#213—24no—
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic, complemented
50C2×#810C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic, complemented
55C2×#807C2211yescharacteristic, complemented
56C2×C4×C3⋊C8C2211yescharacteristic, complemented
57#4844—24no—
58#4781—24no—
59#4773—24no—
60#4674—21no—
61#4671—21no—
62#4665—21no—
63#4665—21no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#546—31no—
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#1804D311yescharacteristic, complemented
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×#237—22no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—41no—
92C2×#237—41no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—41no—
98C2×D3×D4—41no—
99C22×D12—21no—
100C22×D12—21no—
101C22×D12—21no—
102C22×D12D411yescharacteristic
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3C2311yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C22×Dic6C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×C4×D4—22no—
112C3×C4×D4D414yescomplemented
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#213—22no—
119C2×#213—22no—
120C2×#213D414yescomplemented
121#930—28no—
122C2×(C2×D3)⋊C4—28no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3D411yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×D24—22no—
140C2×D24—22no—
141C2×D24—41no—
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—41no—
145#897—22no—
146#897—22no—
147#895—22no—
148#895—22no—
149#895—22no—
150#895—22no—
151#895—41no—
152#895—41no—
153#886—28no—
154#882—28no—
155#875—22no—
156#875D414yescomplemented
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12—22no—
161C3×C4⋊C8—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#95—21no—
165C3×#95—21no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—41no—
173(C2×D3)⋊C8—41no—
174#816—22no—
175#810—22no—
176#810—41no—
177#809—22no—
178#809—22no—
179#809—41no—
180#807—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
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×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
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#382C2×D311yescharacteristic, complemented
227#380—31no—
228#380—31no—
229#340C2×D311yescharacteristic, complemented
230#340C2×D311yescharacteristic, complemented
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C23×D3C2×D411yescharacteristic
242C23×D3C2×D411yescharacteristic
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C2×D412yes—
247C2×C3×D4C2×D412yes—
248C2×C3×D4#4112yes—
249C22×C3×C4—21no—
250C22×C3×C4—24no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—81no—
254C22×C3×C4—81no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—24no—
259C2×#67—24no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C22×Dic3—24no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—42no—
268C22×Dic3—42no—
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#237—44no—
272#237—44no—
273#237—44no—
274#237—44no—
275D3×D4—44no—
276D3×D4—44no—
277D3×D4—44no—
278D3×D4—44no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—24no—
292C2×D12—41no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—81no—
298C2×D12—81no—
299C2×D12—81no—
300C2×D12—81no—
301C2×D12C2×D412yes—
302C2×D12C2×D412yes—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—42no—
316C2×C4×D3—81no—
317C2×C4×D3—81no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6C2×D412yes—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4C2×D412yes—
336C3×C22⋊C4—24no—
337C3×C42C2×D412yes—
338C3×C42C2×D412yes—
339#213—28no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—42no—
348(C2×D3)⋊C4—42no—
349(C2×D3)⋊C4—81no—
350(C2×D3)⋊C4—81no—
351C4⋊Dic3—24no—
352C4⋊Dic3—22no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8C2×D412yes—
361D24—44no—
362#204—44no—
363C25—61no—
364C2×#41—62no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—121no—
369C2×#41—121no—
370C22×Q8—31no—
371C22×D4—31no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—62no—
381C22×D4—62no—
382C22×D4—62no—
383C22×D4—121no—
384C22×D4—121no—
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—61no—
390C23×C4—61no—
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×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—62no—
410#121—68no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—22no—
418C4×D4—62no—
419C4×D4—62no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4D1214yescomplemented
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—61no—
426C2×C4⋊C4C22×D311yescharacteristic
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—68no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—22no—
445#103—62no—
446#103—62no—
447#103—121no—
448#102—22no—
449#102—22no—
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—21no—
461#95—21no—
462#95—61no—
463#95—61no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3C22×D411yescharacteristic
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—22no—
479C22×D3—21no—
480C22×D3—22no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—48no—
488C22×D3—48no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—84no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3#13512yes—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4#12114yes—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—84no—
525C2×C3×C4#12012yes—
526C2×C3×C4#12012yes—
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C2×#4111yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533#67—48no—
534#67—48no—
535C2×Dic3—21no—
536C2×Dic3—22no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—48no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548D12—22no—
549D12—22no—
550D12—22no—
551D12—22no—
552D12—44no—
553D12—41no—
554D12—41no—
555D12—41no—
556D12—41no—
557D12—84no—
558D12—84no—
559D12—84no—
560C4×D3—41no—
561C4×D3—41no—
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—84no—
569Dic6—22no—
570Dic6—22no—
571Dic6—41no—
572Dic6—41no—
573C3×C8—41no—
574C3×C8—41no—
575C3⋊C8—22no—
576C3⋊C8—41no—
577C24—21no—
578C24—31no—
579C24—31no—
580C24—64no—
581C24—61no—
582C24—61no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—122no—
587C24—241no—
588C24—241no—
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—32no—
594C2×Q8—61no—
595C2×Q8—61no—
596C2×Q8—61no—
597C2×Q8—61no—
598C2×Q8—61no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—32no—
603C2×D4—32no—
604C2×D4—62no—
605C2×D4—64no—
606C2×D4—64no—
607C2×D4—64no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—121no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—124no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—124no—
632C2×D4—241no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4—241no—
636C2×D4C2×D1212yes—
637C2×D4D3×D412yes—
638C2×D4#23912yes—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—64no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—122no—
663C22×C4—122no—
664C22×C4—122no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4D3×D411yescharacteristic
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—32no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—64no—
691C4⋊C4—62no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C2×D1212yes—
695C22⋊C4—24no—
696C22⋊C4—64no—
697C22⋊C4—64no—
698C22⋊C4—62no—
699C22⋊C4—62no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42C2×D1212yes—
708C42D3×D412yes—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3C2×#12011yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3C2×#13511yescharacteristic
720C22×C3#57511yescharacteristic
721C22×C3#57611yescharacteristic
722C22×C3#57611yescharacteristic
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—41no—
734C2×D3—42no—
735C2×D3—41no—
736C2×D3—42no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—816no—
744C2×D3—81no—
745C2×D3—81no—
746C2×D3—81no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4C2×#12111yescharacteristic
758C3×C4#53511yescharacteristic
759C3×C4D4211yescharacteristic
760C3×C4#54611yescharacteristic
761Dic3—42no—
762Dic3—41no—
763Dic3—41no—
764Dic3—81no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—32no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—62no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—62no—
786C23—61no—
787C23—61no—
788C23—128no—
789C23—128no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23—244no—
807C23C2×D3×D411yescharacteristic
808Q8—62no—
809Q8—62no—
810Q8—121no—
811Q8—121no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—62no—
816D4—62no—
817D4—62no—
818D4—62no—
819D4—124no—
820D4—128no—
821D4—128no—
822D4—121no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—244no—
827D4—244no—
828D4—244no—
829D4#89514yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—61no—
844C2×C4—62no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—84no—
851C2×C4—128no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
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#88212yes—
867C2×C4#88212yes—
868C2×C4C22×D1211yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4C2×#23911yescharacteristic
872C2×C4#100911yescharacteristic
873C2×C4#100911yescharacteristic
874C8—41no—
875C8—41no—
876C8—62no—
877C8—121no—
878C2×C3—44no—
879C2×C3#240811yescharacteristic
880C2×C3#300211yescharacteristic
881C2×C3#300811yescharacteristic
882C2×C3#327311yescharacteristic
883C2×C3#328011yescharacteristic
884C2×C3#329711yescharacteristic
885C2×C3#332211yescharacteristic
886D3—42no—
887D3—81no—
888D3—82no—
889D3—82no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—122no—
906C22—122no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—122no—
911C22—121no—
912C22—122no—
913C22—122no—
914C22—121no—
915C22—121no—
916C22—122no—
917C22—2416no—
918C22—241no—
919C22—241no—
920C22—241no—
921C22—241no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22C2×#88211yescharacteristic
927C22#560911yescharacteristic
928C22#563011yescharacteristic
929C22D3×#13511yescharacteristic
930C22#576811yescharacteristic
931C22#577411yescharacteristic
932C22#577411yescharacteristic
933C4—22no—
934C4—22no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—121no—
939C4—121no—
940C4—122no—
941C4—241no—
942C4C2×#89511yescharacteristic
943C4#552511yescharacteristic
944C4#560911yescharacteristic
945C4#563011yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—44no—
948C2—122no—
949C2—241no—
950C2—242no—
951C2—242no—
952C2#7401611yescharacteristic
953C2#7883311yescharacteristic
954C2#7892811yescharacteristic
955C2#8055511yescharacteristic
956C2#8055711yescharacteristic
957C2#8118711yescharacteristic
958C2#8119211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1804C2
socleC23×C3C22×D4
hypercenter#1804D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. C2×#5554C2semidirect
2. C2×C4×#213C2semidirect
3. C2×#4844C2semidirect
4. C2×#4781C2semidirect
5. C2×#4773C2semidirect
6. #74239C2semidirect
7. C3×#1804C2semidirect
8. #70470C2semidirect
9. #70199C2semidirect
10. #70198C2semidirect
11. #69551C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68825C2semidirect
15. #68822C2semidirect
24. C22×#204C22semidirect
30. C2×#895C22semidirect
35. C2×C4×D12C22semidirect
36. C2×C3×C4⋊C8C22semidirect
39. C3×#382C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×#816C22semidirect
49. #4987C22semidirect
50. C2×#810C22semidirect
51. C2×#810C22semidirect
54. C2×#809C22semidirect
55. C2×#807C22semidirect
56. C2×C4×C3⋊C8C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
78. #1804D3semidirect
112. C3×C4×D4D4semidirect
120. C2×#213D4semidirect
156. #875D4semidirect
206. C2×C4⋊C8C2×D3semidirect
226. #382C2×D3semidirect
229. #340C2×D3semidirect
230. #340C2×D3semidirect
422. C4×D4D12semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#55542
C2×C4×#2132
C2×#48442
C2×#47812
C2×#47732
#742392
C3×#18042
#704702
#701992
#701982
#695512
#688872
#688862
#688252
#688222
#242453