Finite Group Databasebeta

← #10830646

Subgroups — #10830646

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5576C211yesmaximal, characteristic
2C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
3C2×#5187C211yesmaximal, characteristic, complemented
4C2×#5186C211yesmaximal, characteristic, complemented
5#82499C211yesmaximal, characteristic, complemented
6C2×#5028C211yesmaximal, characteristic, complemented
7#71627C211yesmaximal, characteristic, complemented
8#70635C211yesmaximal, characteristic, complemented
9#70634C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70272C211yesmaximal, characteristic, complemented
12#70267C211yesmaximal, characteristic, complemented
13#70266C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic, complemented
15#69773C211yesmaximal, characteristic, complemented
16#24246—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×#215C2211yescharacteristic
26#5576—24no—
27#5576—24no—
28C2×#897—21no—
29C2×#897C2211yescharacteristic
30C2×#895—21no—
31C2×#895C2211yescharacteristic
32C2×#875—21no—
33C2×#875C2211yescharacteristic
34C2×C4×D12—21no—
35C2×C4×D12C2211yescharacteristic
36C3×C4×Q16—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43#5187—24no—
44#5186—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×#816C2211yescharacteristic
52C2×#816C2211yescharacteristic
53#5028—24no—
54#4991—21no—
55#4987C2211yescharacteristic
56#4987C2211yescharacteristic
57#4981—21no—
58C2×#810C2211yescharacteristic
59C2×#809C2211yescharacteristic
60#4940—21no—
61#4940—21no—
62#4936C2211yescharacteristic
63C2×C4⋊(C3⋊C8)C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#451—31no—
70C2×C4×Q16D311yescharacteristic, complemented
71#2536—31no—
72#2036—31no—
73#2033—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—41no—
88C2×#239—41no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—22no—
92C2×D3×Q8—22no—
93C2×D3×Q8—41no—
94C2×D3×Q8—41no—
95C22×D12—21no—
96C22×D12—21no—
97C22×D12D411yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16D414yescomplemented
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8D414yes—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C42—21no—
119C2×C3×C42—21no—
120C2×C3×C42C2311yescharacteristic
121#946—22no—
122#946—22no—
123#946—41no—
124#946—41no—
125C2×#216—22no—
126C2×#216—22no—
127C2×#216—41no—
128C2×#215—22no—
129C2×#215—22no—
130C2×#215—41no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4D411yescharacteristic
140C2×(C2×D3)⋊C4D411yescharacteristic
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3D411yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149#897—28no—
150#897—22no—
151#897—22no—
152#895—28no—
153#895—22no—
154#895—22no—
155#875—28no—
156#875—22no—
157#875D414yes—
158C4×D12—28no—
159C4×D12—22no—
160C4×D12—22no—
161C3×#107—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×C4×C8—22no—
165#835—22no—
166#835—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—41no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176(C2×D3)⋊C8—41no—
177#816—22no—
178#816—41no—
179#810—22no—
180#809—22no—
181C4⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C23×Q8—31no—
184C22×Q16—31no—
185C22×Q16C2×D311yescharacteristic
186C22×SD16—31no—
187#548—64no—
188#548—64no—
189C2×#124—31no—
190C2×#124—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×C22⋊Q8—61no—
195C2×#121—31no—
196C2×#121—61no—
197C2×C4×Q8C2×D311yescharacteristic
198C2×C4×Q8C2×D311yescharacteristic
199C2×C4×D4—31no—
200C2×C4×D4—61no—
201#464—64no—
202#452—64no—
203#451—64no—
204C4×Q16—24no—
205C2×#107C2×D311yescharacteristic
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#103—31no—
212C2×#103C2×D311yescharacteristic
213C2×#103C2×D311yescharacteristic
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×C8C2×D311yescharacteristic
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C23×D3—21no—
232C23×D3C2×D411yescharacteristic
233C23×D3C2×D411yescharacteristic
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8C2×D412yes—
243C2×C3×Q8C2×D412yes—
244C2×C3×Q8C2×D412yes—
245C2×C3×Q8#4112yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258#239—44no—
259#239—44no—
260#239—44no—
261#239—44no—
262D3×Q8—44no—
263D3×Q8—44no—
264D3×Q8—44no—
265D3×Q8—44no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—24no—
271C2×D12—24no—
272C2×D12—22no—
273C2×D12—22no—
274C2×D12—21no—
275C2×D12—41no—
276C2×D12—42no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12C2×D412yes—
281C2×C4×D3—24no—
282C2×C4×D3—24no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—24no—
304C2×Dic6—21no—
305C2×Dic6—42no—
306C2×Dic6—42no—
307C2×Dic6C2×D412yes—
308C3×Q16—28no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8C2×D412yes—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—42no—
320C3×C4⋊C4C2×D412yes—
321C3×C42—24no—
322C3×C42—42no—
323C3×C42C2×D412yes—
324C3×C42C2×D412yes—
325#216—44no—
326#215—44no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—22no—
330(C2×D3)⋊C4—22no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—42no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—42no—
337C4⋊Dic3—24no—
338C4⋊Dic3—22no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343Dic3⋊C4—42no—
344Dic3⋊C4—42no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—121no—
356C2×#41—121no—
357C22×Q8—31no—
358C22×Q8—61no—
359C22×Q8—62no—
360C22×Q8—62no—
361C22×Q8—62no—
362C22×Q8—62no—
363C22×Q8—121no—
364C22×Q8—121no—
365C22×Q8C22×D311yescharacteristic
366C22×Q8C22×D311yescharacteristic
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4—61no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—61no—
374C23×C4—61no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—62no—
378C2×Q16—62no—
379C2×Q16—121no—
380C2×Q16D1214yescomplemented
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—121no—
384C22×C8—31no—
385C22×C8—31no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388#124—34no—
389#124—68no—
390#124—62no—
391C22⋊Q8—62no—
392C22⋊Q8—68no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8—121no—
397C22⋊Q8—121no—
398#121—62no—
399#121—68no—
400#121—62no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8#6714yes—
405C4×D4—68no—
406C4×D4—62no—
407C4×D4—62no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—31no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42C22×D311yescharacteristic
431#107—22no—
432C4⋊C8—62no—
433#103—22no—
434#103—22no—
435#103—62no—
436#103—62no—
437#103—62no—
438#103—62no—
439#103—121no—
440#102—62no—
441#102—62no—
442#102—121no—
443C22⋊C8—62no—
444C22⋊C8—62no—
445C22⋊C8—121no—
446C22⋊C8—121no—
447C4×C8—22no—
448#95—61no—
449#95—61no—
450#95—61no—
451#95—61no—
452C23×C3C22×D411yescharacteristic
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—22no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3#13512yes—
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8#12114yes—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4#12012yes—
499C2×C3×C4#12012yes—
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504C2×C3×C4H(5,𝔽2)11yescharacteristic
505C2×C3×C4H(5,𝔽2)11yescharacteristic
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521D12—22no—
522D12—22no—
523D12—44no—
524D12—48no—
525D12—48no—
526D12—41no—
527D12—41no—
528C4×D3—48no—
529C4×D3—48no—
530C4×D3—41no—
531C4×D3—41no—
532C4×D3—41no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538Dic6—22no—
539Dic6—22no—
540Dic6—48no—
541Dic6—41no—
542Dic6—41no—
543C3×C8—22no—
544C3×C8—41no—
545C3⋊C8—41no—
546C3⋊C8—41no—
547C24—31no—
548C24—31no—
549C24—61no—
550#41—124no—
551#41—124no—
552#41—124no—
553#41—124no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—32no—
563C2×Q8—64no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—122no—
570C2×Q8—122no—
571C2×Q8—124no—
572C2×Q8—124no—
573C2×Q8—124no—
574C2×Q8—124no—
575C2×Q8C2×D1212yes—
576C2×Q8C2×D1212yes—
577C2×Q8#23512yes—
578C2×Q8C2×#6712yes—
579C2×D4—32no—
580C2×D4—62no—
581C2×D4—64no—
582C2×D4—64no—
583C2×D4—62no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—121no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—122no—
593C2×D4—122no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624Q16—28no—
625Q16—124no—
626SD16—124no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8C2×D1212yes—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—42no—
644C4⋊C4—64no—
645C4⋊C4—62no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—122no—
651C4⋊C4—122no—
652C4⋊C4C2×#6712yes—
653C22⋊C4—64no—
654C22⋊C4—64no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C42—24no—
664C42—42no—
665C42D3×D412yes—
666C42C2×#6712yes—
667C22×C3C2×#12011yescharacteristic
668C22×C3D4211yescharacteristic
669C22×C3#54611yescharacteristic
670C22×C3C2×#13511yescharacteristic
671C22×C3#57511yescharacteristic
672C22×C3#57811yescharacteristic
673C22×C3#57811yescharacteristic
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—42no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—42no—
685C2×D3—41no—
686C2×D3—42no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—81no—
701C3×C4C2×#12111yescharacteristic
702C3×C4#53511yescharacteristic
703C3×C4D4211yescharacteristic
704C3×C4#54611yescharacteristic
705Dic3—42no—
706Dic3—41no—
707Dic3—41no—
708Dic3—81no—
709Dic3—81no—
710C23—32no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—62no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23C2×D3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—41no—
738Q8—41no—
739Q8—62no—
740Q8—62no—
741Q8—128no—
742Q8—121no—
743Q8—121no—
744Q8#93014yes—
745D4—62no—
746D4—62no—
747D4—124no—
748D4—128no—
749D4—128no—
750D4—121no—
751D4—121no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—128no—
776C2×C4—128no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4#93712yes—
794C2×C4#93712yes—
795C2×C4C22×D1211yescharacteristic
796C2×C4C2×#23511yescharacteristic
797C2×C4C2×D3×D411yescharacteristic
798C2×C4#100911yescharacteristic
799C2×C4#100911yescharacteristic
800C2×C4C22×#6711yescharacteristic
801C8—22no—
802C8—41no—
803C8—121no—
804C8—121no—
805C2×C3#240811yescharacteristic
806C2×C3#300211yescharacteristic
807C2×C3#301111yescharacteristic
808C2×C3#327711yescharacteristic
809C2×C3#328511yescharacteristic
810C2×C3#330011yescharacteristic
811C2×C3#332711yescharacteristic
812D3—42no—
813D3—81no—
814D3—82no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—122no—
828C22—121no—
829C22—122no—
830C22—122no—
831C22—121no—
832C22—241no—
833C22—241no—
834C22—241no—
835C22—241no—
836C22D4×D1211yescharacteristic
837C22#555011yescharacteristic
838C22#576611yescharacteristic
839C22#576611yescharacteristic
840C22D3×#13511yescharacteristic
841C22#576811yescharacteristic
842C22C2×#93711yescharacteristic
843C4—22no—
844C4—22no—
845C4—24no—
846C4—42no—
847C4—42no—
848C4—81no—
849C4—121no—
850C4—121no—
851C4—122no—
852C4—241no—
853C4—241no—
854C4D4×D1211yescharacteristic
855C4#555011yescharacteristic
856C4C2×#93011yescharacteristic
857C4#583011yescharacteristic
858C3#2424611yescharacteristic, complemented, Sylow
859C2—122no—
860C2—241no—
861C2—242no—
862C2#7973011yescharacteristic
863C2#7973211yescharacteristic
864C2#7973611yescharacteristic
865C2#7973811yescharacteristic
866C2#8240311yescharacteristic
867C2#8388411yescharacteristic
868C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×Q16C2
socleC23×C3C22×D4
prime radicalC2×#5576C2
hypercenterC2×C4×Q16D3
hypocenterC3#24246
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Q16C2semidirect
3. C2×#5187C2semidirect
4. C2×#5186C2semidirect
5. #82499C2semidirect
6. C2×#5028C2semidirect
7. #71627C2semidirect
8. #70635C2semidirect
9. #70634C2semidirect
10. #70273C2semidirect
11. #70272C2semidirect
12. #70267C2semidirect
13. #70266C2semidirect
14. #69787C2semidirect
15. #69773C2semidirect
70. C2×C4×Q16D3semidirect
107. C2×C3×Q16D4semidirect
380. C2×Q16D12semidirect
858. C3#24246semidirect

Maximal subgroups

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

subgroupindex
C2×#55762
C2×C3×C4×Q162
C2×#51872
C2×#51862
#824992
C2×#50282
#716272
#706352
#706342
#702732
#702722
#702672
#702662
#697872
#697732
#242463