Finite Group Databasebeta

← #10826973

Subgroups — #10826973

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5627C211yesmaximal, characteristic, complemented
2C2×#5524C211yesmaximal, characteristic, complemented
3C2×#5047C211yesmaximal, characteristic, complemented
4C2×#4808C211yesmaximal, characteristic, complemented
5C2×#4810C211yesmaximal, characteristic, complemented
6C2×#4734C211yesmaximal, characteristic, complemented
7C3×#1873C211yesmaximal, characteristic, complemented
8#71586C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#69955C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68879C211yesmaximal, characteristic, complemented
16#23923—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#216C2211yescharacteristic, complemented
24C22×#215C2211yescharacteristic, complemented
25C2×#930C2211yescharacteristic
26C22×D24C2211yescharacteristic, complemented
27C22×#204C2211yescharacteristic, complemented
28#5627—24no—
29#5627—24no—
30#5524—24no—
31#5524—24no—
32C2×#897C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×#895C2211yescharacteristic
35C2×#895C2211yescharacteristic
36C2×#895C2211yescharacteristic
37C2×#894—21no—
38C2×#893—21no—
39C2×#892C2211yescharacteristic
40C2×#886—21no—
41C2×#882—21no—
42C2×#882—21no—
43C2×#67⋊C4—21no—
44C2×C4×D12—21no—
45C2×C4×D12—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×#830C2211yescharacteristic
50C2×#821C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×#816C2211yescharacteristic, complemented
56#5047—24no—
57C2×#810C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic, complemented
60C2×#809C2211yescharacteristic, complemented
61#4810—24no—
62#4808—24no—
63#4734—24no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C2×#525—31no—
70C2×#452—31no—
71C2×#452—31no—
72C2×#449—31no—
73C2×#449—31no—
74#2001—31no—
75#2000—31no—
76#2000—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1873—31no—
81#1873D311yescharacteristic, complemented
82#1779—31no—
83C24×D3D411yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C23×Dic3D411yescharacteristic
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—22no—
93C2×#239—41no—
94C2×#239—41no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—41no—
100C2×#235—41no—
101C22×D12—21no—
102C22×D12—21no—
103C22×D12—21no—
104C22×D12—21no—
105C22×D12C2311yescharacteristic
106C22×D12C2311yescharacteristic
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—21no—
110C22×C4×D3—21no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3D411yescharacteristic
116C22×C4×D3D411yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×Dic6C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8D414yescomplemented
124C3×#117—22no—
125C3×#117—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C42—21no—
133#946—22no—
134#946—22no—
135C2×#216—22no—
136C2×#216—22no—
137C2×#216—41no—
138C2×#215—22no—
139C2×#215—22no—
140C2×#215—41no—
141#930—22no—
142#930D414yescomplemented
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4—21no—
155C2×C4×Dic3—21no—
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C2×D24—22no—
159C2×D24—22no—
160C2×D24—41no—
161C2×#204—22no—
162C2×#204—22no—
163C2×#204—41no—
164#897—22no—
165#897—22no—
166#897—22no—
167#897D414yescomplemented
168#895—22no—
169#895—22no—
170#895—22no—
171#895—22no—
172#895—22no—
173#895D414yescomplemented
174#894—28no—
175#893—28no—
176#892—22no—
177#892—22no—
178#886—28no—
179#882—28no—
180#882—28no—
181#67⋊C4—28no—
182C4×D12—28no—
183C4×D12—28no—
184C3×#103—22no—
185C3×#103—22no—
186C3×C22⋊C8—22no—
187#830—22no—
188#821—22no—
189(C2×D3)⋊C8—22no—
190(C2×D3)⋊C8—22no—
191(C2×D3)⋊C8—41no—
192(C2×D3)⋊C8—41no—
193#816—22no—
194#810—22no—
195#809—22no—
196#809—22no—
197#809—22no—
198C22×#41—31no—
199C22×#41—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×D8—31no—
205#525—64no—
206#525—64no—
207#525—64no—
208#525—64no—
209C2×#123—61no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121—31no—
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—61no—
222C2×C4×D4—61no—
223C2×C4×D4—61no—
224C2×C4×D4—61no—
225C2×#117—31no—
226C2×#117C2×D311yescharacteristic
227#452—64no—
228#452—64no—
229#449—64no—
230#449—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103C2×D311yescharacteristic, complemented
234C2×#103C2×D311yescharacteristic, complemented
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102—31no—
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245#340—31no—
246#340—31no—
247#340C2×D311yescharacteristic, complemented
248#340C2×D311yescharacteristic, complemented
249C24×C3C2×D411yescharacteristic
250C23×D3—22no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—41no—
256C23×D3—41no—
257C23×D3—41no—
258C23×D3—41no—
259C23×D3C2×D411yescharacteristic
260C23×D3C2×D411yescharacteristic
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8C2×D412yes—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2411yescharacteristic
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—42no—
285C22×Dic3—22no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—22no—
289C22×Dic3—41no—
290C22×Dic3C2×D411yescharacteristic
291C22×Dic3C2×D411yescharacteristic
292#239—44no—
293#239—44no—
294#239—44no—
295#239—44no—
296#235—44no—
297#235—44no—
298#235—44no—
299#235—44no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12—24no—
309C2×D12—24no—
310C2×D12—24no—
311C2×D12—24no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—42no—
315C2×D12—42no—
316C2×D12—42no—
317C2×D12—42no—
318C2×D12—42no—
319C2×D12—42no—
320C2×D12—42no—
321C2×D12—42no—
322C2×D12C2×D412yes—
323C2×D12C2×D412yes—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—24no—
329C2×C4×D3—24no—
330C2×C4×D3—22no—
331C2×C4×D3—22no—
332C2×C4×D3—22no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—22no—
340C2×C4×D3—44no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—41no—
345C2×C4×D3—41no—
346C2×C4×D3—42no—
347C2×C4×D3—42no—
348C2×C4×D3—42no—
349C2×C4×D3—42no—
350C2×C4×D3C2×D412yes—
351C2×C4×D3C2×D412yes—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—21no—
357C2×Dic6C2×D412yes—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C3×C4⋊C4—24no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4C2×D412yes—
369C3×C4⋊C4C2×D412yes—
370C3×C4⋊C4C2×D412yes—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373C3×C42—24no—
374#216—44no—
375#215—44no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384C4⋊Dic3—24no—
385C4⋊Dic3—21no—
386C4⋊Dic3—24no—
387C4⋊Dic3C2×D412yes—
388Dic3⋊C4—24no—
389C4×Dic3—24no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396D24—44no—
397#204—44no—
398C25—31no—
399C2×#41—62no—
400C2×#41—62no—
401C2×#41—62no—
402C2×#41—62no—
403C2×#41—62no—
404C2×#41—62no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—121no—
408C2×#41—121no—
409C2×#41—121no—
410C2×#41—121no—
411C22×Q8—31no—
412C22×Q8C22×D311yescharacteristic
413C22×D4—31no—
414C22×D4—31no—
415C22×D4—61no—
416C22×D4—61no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4—61no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—61no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—61no—
431C23×C4—62no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4C22×D311yescharacteristic
435C2×Q16—62no—
436C2×Q16—62no—
437C2×Q16—121no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—121no—
443C2×SD16—121no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451#123—68no—
452#123—68no—
453C22⋊Q8—22no—
454C22⋊Q8—34no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8D1214yescomplemented
461#121—34no—
462#121—34no—
463#121—62no—
464#121—62no—
465#121—62no—
466#121—62no—
467#121—62no—
468#121—62no—
469#120—68no—
470#120—68no—
471C4×D4—68no—
472C4×D4—68no—
473C4×D4—68no—
474C4×D4—68no—
475#117—22no—
476#117—22no—
477#117—62no—
478#117—62no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—61no—
482C2×C4⋊C4—61no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C42—21no—
498C2×C42—61no—
499#103—22no—
500#103—22no—
501#103—62no—
502#103—62no—
503#102—62no—
504#102—62no—
505#102—62no—
506#102—62no—
507C22⋊C8—22no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—62no—
511C22⋊C8—121no—
512C22⋊C8—121no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3#12012yes—
520C23×C3C22×D411yescharacteristic
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3—44no—
541C22×D3—44no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3#12012yes—
555C22×D3#13512yes—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8—41no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4#12012yes—
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4H(5,𝔽2)11yescharacteristic
584C2×C3×C4H(5,𝔽2)11yescharacteristic
585#67—48no—
586#67—48no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—22no—
590C2×Dic3—21no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—44no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3#12012yes—
600D12—22no—
601D12—22no—
602D12—22no—
603D12—22no—
604D12—48no—
605D12—48no—
606D12—48no—
607D12—48no—
608D12—41no—
609D12—41no—
610D12—41no—
611D12—41no—
612C4×D3—22no—
613C4×D3—22no—
614C4×D3—22no—
615C4×D3—22no—
616C4×D3—44no—
617C4×D3—48no—
618C4×D3—44no—
619C4×D3—48no—
620C4×D3—41no—
621C4×D3—41no—
622C4×D3—41no—
623C4×D3—41no—
624Dic6—22no—
625Dic6—22no—
626Dic6—41no—
627Dic6—41no—
628C3×C8—41no—
629C3×C8—41no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—31no—
633C24—31no—
634C24—62no—
635C24—62no—
636C24—62no—
637C24—61no—
638C24—61no—
639C24—121no—
640C24—121no—
641C24—121no—
642C24—121no—
643C24D3×D411yescharacteristic
644#41—124no—
645#41—124no—
646#41—124no—
647#41—124no—
648#41—124no—
649#41—124no—
650#41—124no—
651#41—124no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—32no—
658C2×Q8—61no—
659C2×Q8—61no—
660C2×Q8—61no—
661C2×Q8—61no—
662C2×Q8—61no—
663C2×Q8C2×D1212yes—
664C2×D4—32no—
665C2×D4—32no—
666C2×D4—64no—
667C2×D4—64no—
668C2×D4—64no—
669C2×D4—64no—
670C2×D4—64no—
671C2×D4—64no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—122no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—122no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—122no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4—122no—
693C2×D4—122no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—31no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—31no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—64no—
709C22×C4—64no—
710C22×C4—62no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—62no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—62no—
719C22×C4—62no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—121no—
727C22×C4—121no—
728C22×C4—124no—
729C22×C4—124no—
730C22×C4—124no—
731C22×C4—124no—
732C22×C4—122no—
733C22×C4—122no—
734C22×C4—122no—
735C22×C4—121no—
736C22×C4—122no—
737C22×C4C2×D1212yes—
738C22×C4D3×D411yescharacteristic
739C22×C4D3×D412yes—
740C22×C4C23×D311yescharacteristic
741Q16—124no—
742SD16—124no—
743SD16—124no—
744D8—124no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—61no—
752C2×C8—61no—
753C2×C8—61no—
754C2×C8—61no—
755C2×C8—61no—
756C2×C8—61no—
757C4⋊C4—24no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—32no—
762C4⋊C4—64no—
763C4⋊C4—64no—
764C4⋊C4—64no—
765C4⋊C4—61no—
766C4⋊C4C2×D1212yes—
767C4⋊C4D3×D412yes—
768C4⋊C4D3×D412yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—64no—
772C22⋊C4—64no—
773C22⋊C4—64no—
774C22⋊C4—64no—
775C22⋊C4—64no—
776C22⋊C4—64no—
777C22⋊C4—64no—
778C22⋊C4—64no—
779C42—24no—
780C42—64no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3C2×#12011yescharacteristic
789C22×C3C2×#12011yescharacteristic
790C22×C3#53411yescharacteristic
791C22×C3C2×#13511yescharacteristic
792C22×C3#57511yescharacteristic
793C22×C3#57511yescharacteristic
794C22×C3#57511yescharacteristic
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—416no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—41no—
806C2×D3—41no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—42no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—81no—
817C2×D3—81no—
818C2×D3—81no—
819C2×D3—81no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C3×C4—22no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4D4211yescharacteristic
830C3×C4D4211yescharacteristic
831C3×C4D4211yescharacteristic
832C3×C4D4211yescharacteristic
833Dic3—22no—
834Dic3—42no—
835Dic3—41no—
836Dic3—42no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—32no—
844C23—32no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—62no—
858C23—62no—
859C23—124no—
860C23—124no—
861C23—124no—
862C23—124no—
863C23—124no—
864C23—124no—
865C23—124no—
866C23—121no—
867C23—121no—
868C23—121no—
869C23—121no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23#88212yes—
879C23C2×D3×D411yescharacteristic
880Q8—22no—
881Q8—22no—
882Q8—41no—
883Q8—41no—
884Q8—62no—
885Q8—62no—
886Q8—121no—
887Q8—121no—
888D4—62no—
889D4—62no—
890D4—62no—
891D4—62no—
892D4—128no—
893D4—128no—
894D4—128no—
895D4—128no—
896D4—128no—
897D4—128no—
898D4—121no—
899D4—121no—
900D4—121no—
901D4—121no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—32no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—61no—
928C2×C4—62no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—62no—
932C2×C4—124no—
933C2×C4—124no—
934C2×C4—128no—
935C2×C4—128no—
936C2×C4—124no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4#88212yes—
946C2×C4C22×D1211yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4C2×D3×D411yescharacteristic
949C2×C4C2×D3×D411yescharacteristic
950C2×C4#100911yescharacteristic
951C2×C4#100911yescharacteristic
952C8—41no—
953C8—41no—
954C8—121no—
955C8—121no—
956C2×C3—42no—
957C2×C3#240311yescharacteristic
958C2×C3#300211yescharacteristic
959C2×C3#300211yescharacteristic
960C2×C3#300511yescharacteristic
961C2×C3#300511yescharacteristic
962C2×C3#319111yescharacteristic
963C2×C3#319711yescharacteristic
964D3—42no—
965D3—42no—
966D3—82no—
967D3—82no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—1216no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—122no—
991C22—122no—
992C22—122no—
993C22—122no—
994C22—122no—
995C22—122no—
996C22—241no—
997C22—241no—
998C22—241no—
999C22—241no—
1000C22—241no—
1001C22—241no—
1002C22—241no—
1003C22—241no—
1004C22C2×#88211yescharacteristic
1005C22D3×#12011yescharacteristic
1006C22#565311yescharacteristic
1007C22D3×#13511yescharacteristic
1008C22#576811yescharacteristic
1009C22#577711yescharacteristic
1010C22#577711yescharacteristic
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—62no—
1017C4—122no—
1018C4—121no—
1019C4—122no—
1020C4D4×D1211yescharacteristic
1021C4D4×D1211yescharacteristic
1022C4#560911yescharacteristic
1023C4#560911yescharacteristic
1024C3#2392311yescharacteristic, complemented, Sylow
1025C2—42no—
1026C2—122no—
1027C2—122no—
1028C2—242no—
1029C2—242no—
1030C2#7488411yescharacteristic
1031C2#7883311yescharacteristic
1032C2#7895911yescharacteristic
1033C2#8022611yescharacteristic
1034C2#8022711yescharacteristic
1035C2#8154011yescharacteristic
1036C2#8154111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
hypercenter#1873D3
hypocenterC3#23923
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
1. C2×#5627C2semidirect
2. C2×#5524C2semidirect
3. C2×#5047C2semidirect
4. C2×#4808C2semidirect
5. C2×#4810C2semidirect
6. C2×#4734C2semidirect
7. C3×#1873C2semidirect
8. #71586C2semidirect
9. #70273C2semidirect
10. #70272C2semidirect
11. #69955C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68881C2semidirect
15. #68879C2semidirect
23. C22×#216C22semidirect
24. C22×#215C22semidirect
26. C22×D24C22semidirect
27. C22×#204C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#103C22semidirect
50. C2×#821C22semidirect
55. C2×#816C22semidirect
57. C2×#810C22semidirect
58. C2×#809C22semidirect
59. C2×#809C22semidirect
60. C2×#809C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
81. #1873D3semidirect
123. C3×C22⋊Q8D4semidirect
142. #930D4semidirect
167. #897D4semidirect
173. #895D4semidirect
233. C2×#103C2×D3semidirect
234. C2×#103C2×D3semidirect
247. #340C2×D3semidirect
248. #340C2×D3semidirect
460. C22⋊Q8D12semidirect
1024. C3#23923semidirect

Maximal subgroups

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

subgroupindex
C2×#56272
C2×#55242
C2×#50472
C2×#48082
C2×#48102
C2×#47342
C3×#18732
#715862
#702732
#702722
#699552
#688872
#688862
#688812
#688792
#239233