Finite Group Databasebeta

← #10830659

Subgroups — #10830659

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5676C211yesmaximal, characteristic
2C2×#5054C211yesmaximal, characteristic, complemented
3C2×#4808C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×C4×#204C211yesmaximal, characteristic, complemented
6#74240C211yesmaximal, characteristic, complemented
7C3×#1958C211yesmaximal, characteristic, complemented
8#70273C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70243C211yesmaximal, characteristic, complemented
11#70205C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#70176C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic, complemented
15#69556C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#216C2211yescharacteristic, complemented
22C2×#938C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#204C2211yescharacteristic
25#5676—24no—
26#5676—24no—
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic, complemented
29C2×#884—21no—
30C2×#883—21no—
31C2×#882—21no—
32C2×D3×C22⋊C4—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic, complemented
41C3×#382C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
49C2×#817C2211yescharacteristic, complemented
50C2×#816C2211yescharacteristic, complemented
51#5054—24no—
52#4987C2211yescharacteristic
53#4987C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57#4808—24no—
58#4776—24no—
59C4×#204—24no—
60#4672—21no—
61#4670—21no—
62#4670—21no—
63#4661—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536—31no—
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958D311yescharacteristic, complemented
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—41no—
97C2×D3×D4—41no—
98C22×D12—21no—
99C22×D12D411yescharacteristic
100C22×D12C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3C2311yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×#124—22no—
109C3×#124D414yes—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116#946—22no—
117#946—22no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—41no—
121#938—22no—
122#938—22no—
123C2×#214—22no—
124C2×#214—22no—
125C2×#214—41no—
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⋊Dic3—21no—
136C2×C4⋊Dic3D411yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C2×#204—22no—
145C2×#204—22no—
146C2×#204D414yescomplemented
147#897—22no—
148#897—22no—
149#897—41no—
150#897—41no—
151#884—28no—
152#883—28no—
153#882—28no—
154D3×C22⋊C4—28no—
155C4×D12—22no—
156C4×D12—22no—
157C4×D12—22no—
158C4×D12D414yes—
159C4×Dic6—22no—
160C4×Dic6—22no—
161C3×#103—22no—
162C3×#103—41no—
163C3×#102—22no—
164C3×#102—41no—
165C3×C4×C8—22no—
166C3×#95—21no—
167C3×#95—21no—
168#835—22no—
169#832—22no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176(C2×D3)⋊C8—41no—
177#817—22no—
178#816—22no—
179#809—22no—
180#809—22no—
181C4⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187#546—64no—
188#546—64no—
189C2×#124C2×D311yescharacteristic
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103C2×D311yescharacteristic, complemented
210C2×#103C2×D311yescharacteristic, complemented
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×C8C2×D311yescharacteristic, complemented
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382C2×D311yescharacteristic, complemented
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—24no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
241C23×D3C2×D411yescharacteristic
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8C2×D412yes—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4C2×D412yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C2×#67—24no—
261C2×#67—24no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—81no—
265C2×#67—81no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#239—44no—
272#239—44no—
273#239—44no—
274#239—44no—
275D3×D4—44no—
276D3×D4—44no—
277D3×D4—44no—
278D3×D4—44no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—24no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—41no—
286C2×D12—42no—
287C2×D12—42no—
288C2×D12C2×D412yes—
289C2×D12C2×D412yes—
290C2×D12#4112yes—
291C2×C4×D3—24no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—24no—
305C2×C4×D3—42no—
306C2×C4×D3—42no—
307C2×C4×D3—81no—
308C2×C4×D3—81no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8C2×D412yes—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C42C2×D412yes—
328C3×C42C2×D412yes—
329#217—24no—
330#216—44no—
331#214—44no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340C4⋊Dic3—22no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—42no—
345C4⋊Dic3—42no—
346C4⋊Dic3C2×D412yes—
347Dic3⋊C4—24no—
348Dic3⋊C4—42no—
349C4×Dic3—42no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356#204—28no—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—61no—
381C23×C4—61no—
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—34no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—121no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—22no—
396#124D1214yes—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—68no—
405#121—62no—
406#121—62no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—68no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—61no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—41no—
441#103—62no—
442#103—62no—
443#102—22no—
444#102—41no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—62no—
449C22⋊C8—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—22no—
454#95—21no—
455#95—21no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—22no—
468C22×D3—21no—
469C22×D3—22no—
470C22×D3—21no—
471C22×D3—22no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—48no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—41no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4#12012yes—
516C2×C3×C4#12012yes—
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C2×#4111yescharacteristic
521C2×C3×C4H(5,𝔽2)11yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523#67—48no—
524#67—84no—
525C2×Dic3—21no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—22no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540D12—22no—
541D12—22no—
542D12—22no—
543D12—44no—
544D12—48no—
545D12#12114yes—
546C4×D3—48no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550C4×D3—41no—
551C4×D3—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—84no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—31no—
567C24—64no—
568C24—61no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—122no—
573C24—241no—
574C24—241no—
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8C2×D1212yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—32no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—62no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—121no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—241no—
617C2×D4—241no—
618C2×D4C2×D1212yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—64no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—64no—
640C22×C4—61no—
641C22×C4—122no—
642C22×C4—122no—
643C22×C4—241no—
644C22×C4—241no—
645C22×C4D3×D411yescharacteristic
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8D3×D412yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—32no—
668C4⋊C4—64no—
669C4⋊C4—62no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—62no—
681C22⋊C4—62no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—122no—
688C42C2×D1212yes—
689C42D3×D412yes—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3C2×#12011yescharacteristic
698C22×C3D4211yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3C2×#13511yescharacteristic
701C22×C3#57511yescharacteristic
702C22×C3#57711yescharacteristic
703C22×C3#57711yescharacteristic
704C2×D3—24no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—41no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—41no—
717C2×D3—42no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—816no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—42no—
736Dic3—41no—
737Dic3—41no—
738Dic3—42no—
739Dic3—81no—
740C23—22no—
741C23—32no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—62no—
750C23—61no—
751C23—62no—
752C23—61no—
753C23—62no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—128no—
765C23—128no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—34no—
787D4—41no—
788D4—41no—
789D4—62no—
790D4—62no—
791D4—62no—
792D4—124no—
793D4—128no—
794D4—128no—
795D4—244no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—62no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—128no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—244no—
834C2×C4#88212yes—
835C2×C4#88212yes—
836C2×C4C22×D1211yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4#100411yescharacteristic
840C2×C4D3×#4111yescharacteristic
841C2×C4#100911yescharacteristic
842C8—22no—
843C8—41no—
844C8—121no—
845C8—121no—
846C2×C3—82no—
847C2×C3#240811yescharacteristic
848C2×C3#300211yescharacteristic
849C2×C3#300911yescharacteristic
850C2×C3#327511yescharacteristic
851C2×C3#328211yescharacteristic
852C2×C3#329611yescharacteristic
853C2×C3#332311yescharacteristic
854D3—42no—
855D3—44no—
856D3—81no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—64no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—121no—
869C22—121no—
870C22—122no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—121no—
875C22—122no—
876C22—121no—
877C22—122no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—2416no—
886C22C2×#88211yescharacteristic
887C22#567611yescharacteristic
888C22#571711yescharacteristic
889C22D3×#13511yescharacteristic
890C22#576811yescharacteristic
891C22#577011yescharacteristic
892C22#577011yescharacteristic
893C4—22no—
894C4—22no—
895C4—42no—
896C4—81no—
897C4—81no—
898C4—121no—
899C4—121no—
900C4—122no—
901C4—122no—
902C4—241no—
903C4D4×D1211yescharacteristic
904C4#555411yescharacteristic
905C4D3×#12111yescharacteristic
906C4#560711yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—82no—
909C2—122no—
910C2—124no—
911C2—241no—
912C2#7643611yescharacteristic
913C2#7883311yescharacteristic
914C2#7883511yescharacteristic
915C2#8165211yescharacteristic
916C2#8165711yescharacteristic
917C2#8183011yescharacteristic
918C2#8183211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1958C2
socleC23×C3C22×D4
prime radicalC2×#5676C2
hypercenter#1958D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#5054C2semidirect
3. C2×#4808C2semidirect
4. C2×#4776C2semidirect
5. C2×C4×#204C2semidirect
6. #74240C2semidirect
7. C3×#1958C2semidirect
8. #70273C2semidirect
9. #70267C2semidirect
10. #70243C2semidirect
11. #70205C2semidirect
12. #70198C2semidirect
13. #70176C2semidirect
14. #69787C2semidirect
15. #69556C2semidirect
21. C22×#216C22semidirect
28. C2×#897C22semidirect
35. C2×C4×Dic6C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
40. C2×C3×C4×C8C22semidirect
41. C3×#382C22semidirect
42. C2×#835C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. C2×(C2×D3)⋊C8C22semidirect
49. C2×#817C22semidirect
50. C2×#816C22semidirect
53. #4987C22semidirect
56. C2×C4⋊(C3⋊C8)C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
76. #1958D3semidirect
146. C2×#204D4semidirect
209. C2×#103C2×D3semidirect
210. C2×#103C2×D3semidirect
221. C2×C4×C8C2×D3semidirect
226. #382C2×D3semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#56762
C2×#50542
C2×#48082
C2×#47762
C2×C4×#2042
#742402
C3×#19582
#702732
#702672
#702432
#702052
#701982
#701762
#697872
#695562
#242473