Finite Group Databasebeta

← C4×#5835 #11659404

Subgroups — C4×#5835 #11659404

Order 768.

2826 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×#5835C211yesmaximal, characteristic
3C4×#1009C211yesmaximal, characteristic, complemented
4#84099C211yesmaximal, characteristic, complemented
5#82564C213yesmaximal, complemented
6#82563C211yesmaximal, characteristic, complemented
7#82562C211yesmaximal, characteristic, complemented
8#82557C213yesmaximal, complemented
9#82538C213yesmaximal, complemented
10#82537C213yesmaximal, complemented
11C4×#949C213yesmaximal, complemented
12C4×#948C211yesmaximal, characteristic, complemented
13C4×#950C213yesmaximal, complemented
14C4×#932C213yesmaximal, complemented
15C2×C4×#213C213yesmaximal, complemented
16C4×#576—31nomaximal, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C3×#520—21no—
20C3×#520C2211yescharacteristic
21C3×#520C2213yescomplemented
22C3×#518—23no—
23C3×#518C2213yescomplemented
24C3×C4×#41—21no—
25C3×C4×#41C2211yescharacteristic
26C3×C4×#41C2213yescomplemented
27C2×C3×C4×D4—23no—
28C2×C3×C4×D4C2213yescomplemented
29#5835C4116yesdirect product factor
30#5827C2211yescharacteristic
31C2×#950C2213yes—
32C2×#949C2213yes—
33C2×#948C2211yescharacteristic
34C2×#948C2211yescharacteristic
35C2×#932C2213yes—
36C22×#213C2213yes—
37#5574—21no—
38C4×#239—21no—
39#5545—23no—
40C4×D3×D4—23no—
41#5523C2213yescomplemented
42#5521C2213yescomplemented
43C4×#235C2213yescomplemented
44C2×C4×D12C2213yescomplemented
45#5233C2213yescomplemented
46#5232C2213yescomplemented
47#5215C2213yescomplemented
48C2×#832C2213yescomplemented
49C4×#216C2211yescharacteristic, complemented
50C4×#216C2213yescomplemented
51#5026C2216yescomplemented
52C4×#215C2213yescomplemented
53C4×#215C2213yescomplemented
54#5018C2216yescomplemented
55C4×#214C2213yescomplemented
56C4×#214C2213yescomplemented
57#5014C2216yescomplemented
58#5014C2216yescomplemented
59C4×#213C2213yescomplemented
60C4×#213C2213yescomplemented
61C4×#213C2216yescomplemented
62C4×#213C2216yescomplemented
63C4×#213C2216yescomplemented
64#5002C2213yescomplemented
65#5001C2213yescomplemented
66#4998C2213yescomplemented
67#4997C2213yescomplemented
68#4997C2213yescomplemented
69#4995C2213yescomplemented
70#4966C2213yescomplemented
71C2×#809C2213yescomplemented
72#4964C2213yescomplemented
73C2×#807C2213yescomplemented
74C4×#208C2213yescomplemented
75C2×C4×C3⋊C8C2213yescomplemented
76C2×#576—31no—
77C4×H(5,𝔽2)—31no—
78C4×H(5,𝔽2)D311yescharacteristic, complemented
79#2951—33no—
80#2948—33no—
81#2946—33no—
82#2946—33no—
83C4×AGL(1,ℤ/8)—33no—
84C4×AGL(1,ℤ/8)—33no—
85C4×#135—33no—
86C2×C4×D8—33no—
87#2913—31no—
88#2897—31no—
89#2897—31no—
90C4×#131—31no—
91C3×H(5,𝔽2)—24no—
92C3×H(5,𝔽2)C2×C418yescomplemented
93C2×C3×#41—21no—
94C2×C3×#41C2313yes—
95C2×C3×#41C2311yescharacteristic
96C22×C3×D4—23no—
97C22×C3×D4C2313yes—
98C23×C3×C4—23no—
99#1009—24no—
100#1009C2×C418yescomplemented
101C2×#239—21no—
102C2×D3×D4—23no—
103C2×#235C2313yes—
104C22×D12C2313yes—
105C22×C4×D3—23no—
106C3×C4×Q8—21no—
107C3×C4×Q8D411yescharacteristic
108C3×C4×Q8D411yescharacteristic
109C3×C4×Q8C2311yescharacteristic
110C3×C4×Q8C2313yes—
111C3×C4×D4—23no—
112C3×C4×D4—23no—
113C3×C4×D4—23no—
114C3×C4×D4—23no—
115C3×C4×D4—23no—
116C3×C4×D4—26no—
117C3×C4×D4—23no—
118C3×C4×D4—23no—
119C3×C4×D4D413yes—
120C3×C4×D4D413yes—
121C3×C4×D4C2313yes—
122C3×C4×D4C2316yes—
123C3×C4×D4C2313yes—
124C3×#117—23no—
125C3×#117—23no—
126C3×#117C2313yes—
127C3×#117C2313yes—
128C2×C3×C4⋊C4—23no—
129C2×C3×C4⋊C4C2313yes—
130C2×C3×C22⋊C4—23no—
131C2×C3×C22⋊C4—26no—
132C2×C3×C42—23no—
133C2×C3×C42C2313yes—
134#950C2×C4124yescomplemented
135#949C2×C4124yescomplemented
136#948—24no—
137#948C2×C418yescomplemented
138Q8×Dic3—21no—
139C2×#216C2311yescharacteristic
140C2×#215C2313yes—
141D4×Dic3—23no—
142C2×#214C2313yes—
143#932C2×C4124yescomplemented
144C2×#213C2×C4124yescomplemented
145C2×#213C2313yes—
146C2×#213C2316yes—
147C4×#67—23no—
148C4×#67—23no—
149C2×(C2×D3)⋊C4—23no—
150#926C2313yes—
151C2×C4⋊Dic3C2313yes—
152C2×#208C2313yes—
153C2×#208C2313yes—
154C22×C3⋊C8C2313yes—
155C22×C3⋊C8C2313yes—
156#893—23no—
157#893—23no—
158#892—23no—
159D3×C4⋊C4—23no—
160#67⋊C4—26no—
161D3×C22⋊C4—26no—
162C4×D12—23no—
163C4×D12—23no—
164C4×D12C2313yes—
165C4×D12C2316yes—
166C4×D12C2313yes—
167#872—23no—
168C42×D3—23no—
169C4×Dic6C2311yescharacteristic
170C4×Dic6C2313yes—
171#835C2313yes—
172#835C2311yescharacteristic
173#832C2313yes—
174#832C2316yes—
175#832C2313yes—
176#810C2313yes—
177#810C2311yescharacteristic
178#809C2313yes—
179#809C2316yes—
180#809C2313yes—
181#808C2313yes—
182#808C2313yes—
183#807C2313yes—
184#807C2316yes—
185#807C2311yescharacteristic
186#803C2316yes—
187C4×C3⋊C8C2311yescharacteristic
188C4×C3⋊C8C2313yes—
189C4×C3⋊C8C2313yes—
190C4×C3⋊C8C2313yes—
191C2×H(5,𝔽2)—31no—
192C2×H(5,𝔽2)C2×D311yescharacteristic
193#576—316no—
194C2×AGL(1,ℤ/8)—33no—
195C2×AGL(1,ℤ/8)—33no—
196C2×#135—33no—
197C22×D8—33no—
198C2×#131—31no—
199C2×#131—31no—
200#520—21no—
201#520—31no—
202#520—33no—
203#520—61no—
204#520C2×D311yescharacteristic
205#520C2×D313yescomplemented
206#518—23no—
207#518—33no—
208#518—63no—
209#518C2×D313yescomplemented
210C4×#41—21no—
211C4×#41—33no—
212C4×#41—61no—
213C4×#41C2×D311yescharacteristic
214C4×#41C2×D313yescomplemented
215C2×C4×D4—23no—
216C2×C4×D4—33no—
217C2×C4×D4—63no—
218C2×C4×D4C2×D313yescomplemented
219#442—36no—
220#442—36no—
221#440—36no—
222#440—36no—
223C4×Q16—31no—
224C4×Q16—33no—
225C4×SD16—33no—
226C4×SD16—33no—
227C4×SD16—33no—
228C4×SD16—33no—
229C4×D8—33no—
230C4×D8—36no—
231C4×D8—36no—
232C4×D8—36no—
233C4×D8—33no—
234#428—33no—
235#428—33no—
236#427—33no—
237C2×#107—33no—
238#418—33no—
239#418—33no—
240#417—33no—
241#417—33no—
242#416—33no—
243#416—33no—
244C2×#102—33no—
245C2×#102—33no—
246#405—33no—
247#405—33no—
248C4×M16—33no—
249C2×C4×C8—33no—
250C24×C3—23no—
251C23×D3—23no—
252C3×#41—28no—
253C3×#41—26no—
254C3×#41C22×C414yes—
255C3×#41C22×C4112yescomplemented
256C3×#41#4114yes—
257C2×C3×Q8C2×D411yescharacteristic
258C2×C3×Q8C2411yescharacteristic
259C2×C3×D4—23no—
260C2×C3×D4—224no—
261C2×C3×D4—23no—
262C2×C3×D4—26no—
263C2×C3×D4C22×C4112yescomplemented
264C2×C3×D4C2×D413yes—
265C2×C3×D4C2413yes—
266C22×C3×C4—23no—
267C22×C3×C4—23no—
268C22×C3×C4—23no—
269C22×C3×C4—23no—
270C22×C3×C4—26no—
271C22×C3×C4—86no—
272C22×C3×C4C2×D413yes—
273C22×C3×C4C2×D413yes—
274C22×C3×C4C2413yes—
275C2×#67—23no—
276C22×Dic3—23no—
277#239—28no—
278D3×D4—224no—
279#235—26no—
280#235C22×C4112yescomplemented
281C2×D12—23no—
282C2×D12—26no—
283C2×D12C22×C4112yescomplemented
284C2×D12C2413yes—
285C2×C4×D3—23no—
286C2×C4×D3—23no—
287C2×C4×D3—23no—
288C2×C4×D3—26no—
289C2×C4×D3—86no—
290C2×Dic6C2411yescharacteristic
291C3×C4⋊C4—23no—
292C3×C4⋊C4—23no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D413yes—
295C3×C4⋊C4C2×D413yes—
296C3×C4⋊C4C2413yes—
297C3×C4⋊C4C2411yescharacteristic
298C3×C22⋊C4—23no—
299C3×C22⋊C4—23no—
300C3×C22⋊C4—26no—
301C3×C22⋊C4—23no—
302C3×C22⋊C4C2×D416yes—
303C3×C42—21no—
304C3×C42—23no—
305C3×C42—23no—
306C3×C42C2×D413yes—
307C3×C42C2×D413yes—
308C3×C42C2411yescharacteristic
309C3×C42C2413yes—
310#217—23no—
311#216C22×C414yescomplemented
312#215C22×C4112yescomplemented
313#214C22×C4112yescomplemented
314#213C22×C4112yescomplemented
315#213C22×C4124yescomplemented
316(C2×D3)⋊C4—23no—
317(C2×D3)⋊C4—23no—
318(C2×D3)⋊C4—26no—
319C4⋊Dic3—23no—
320C4⋊Dic3C2413yes—
321C4⋊Dic3C2411yescharacteristic
322Dic3⋊C4—21no—
323Dic3⋊C4—23no—
324C4×Dic3—21no—
325C4×Dic3—23no—
326C4×Dic3—23no—
327#208—26no—
328#208C22×C4112yescomplemented
329C2×C3⋊C8—26no—
330C2×C3⋊C8C22×C4112yescomplemented
331C2×C3⋊C8C2411yescharacteristic
332C2×C3⋊C8C2413yes—
333C2×C3⋊C8C2411yescharacteristic
334C2×C3⋊C8C2413yes—
335H(5,𝔽2)—24no—
336H(5,𝔽2)—38no—
337H(5,𝔽2)—64no—
338H(5,𝔽2)C4×D318yescomplemented
339C2×#41—21no—
340C2×#41—33no—
341C2×#41—61no—
342C2×#41C22×D313yes—
343C2×#41C22×D311yescharacteristic
344C22×D4—23no—
345C22×D4—33no—
346C22×D4—63no—
347C22×D4C22×D313yes—
348C23×C4—23no—
349C23×C4—63no—
350AGL(1,ℤ/8)—324no—
351AGL(1,ℤ/8)—324no—
352#135—324no—
353C2×Q16—31no—
354C2×SD16—33no—
355C2×SD16—33no—
356C2×D8—324no—
357C2×D8—33no—
358C2×D8—36no—
359#131—38no—
360#131—64no—
361C2×M16—33no—
362C2×M16—33no—
363C22×C8—33no—
364C22×C8—33no—
365C4×Q8—21no—
366C4×Q8—31no—
367C4×Q8—33no—
368C4×Q8—61no—
369C4×Q8#6711yescharacteristic
370C4×Q8#6711yescharacteristic
371C4×Q8C22×D311yescharacteristic
372C4×Q8C22×D313yes—
373C4×D4—23no—
374C4×D4—23no—
375C4×D4—23no—
376C4×D4—23no—
377C4×D4—23no—
378C4×D4—26no—
379C4×D4—23no—
380C4×D4—23no—
381C4×D4—33no—
382C4×D4—36no—
383C4×D4—33no—
384C4×D4—63no—
385C4×D4—63no—
386C4×D4—63no—
387C4×D4—63no—
388C4×D4—63no—
389C4×D4—66no—
390C4×D4—63no—
391C4×D4—63no—
392C4×D4#6713yes—
393C4×D4#6713yes—
394C4×D4C22×D313yes—
395C4×D4C22×D316yes—
396C4×D4C22×D313yes—
397#117—23no—
398#117—23no—
399#117—33no—
400#117—63no—
401#117—63no—
402#117C22×D313yes—
403#117C22×D313yes—
404C2×C4⋊C4—23no—
405C2×C4⋊C4—33no—
406C2×C4⋊C4—63no—
407C2×C4⋊C4C22×D313yes—
408C2×C22⋊C4—23no—
409C2×C22⋊C4—26no—
410C2×C22⋊C4—63no—
411C2×C22⋊C4—66no—
412C2×C42—23no—
413C2×C42—63no—
414C2×C42C22×D313yes—
415#107—33no—
416#107—36no—
417#107—31no—
418#106—33no—
419#106—33no—
420#103—31no—
421#103—33no—
422#103—31no—
423#103—33no—
424#102—33no—
425#102—36no—
426#102—33no—
427#102—33no—
428#102—36no—
429#102—33no—
430#97—36no—
431C4×C8—31no—
432C4×C8—33no—
433C4×C8—33no—
434C4×C8—33no—
435C23×C3—23no—
436C23×C3—212no—
437C23×C3—83no—
438C23×C3—83no—
439C23×C3C22×D413yes—
440C22×D3—23no—
441C22×D3—212no—
442C22×D3—83no—
443C22×D3—83no—
444C3×Q8—21no—
445C3×Q8C4×D414yes—
446C3×Q8C23×C412yes—
447C3×D4—212no—
448C3×D4—212no—
449C3×D4—23no—
450C3×D4C4×D4112yes—
451C3×D4C23×C416yes—
452C2×C3×C4—21no—
453C2×C3×C4—212no—
454C2×C3×C4—26no—
455C2×C3×C4—21no—
456C2×C3×C4—23no—
457C2×C3×C4—43no—
458C2×C3×C4—46no—
459C2×C3×C4—83no—
460C2×C3×C4—86no—
461C2×C3×C4—83no—
462C2×C3×C4C23×C416yes—
463C2×C3×C4C22×D413yes—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D413yes—
466C2×C3×C4C22×D413yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4116yes—
469C2×C3×C4C2511yescharacteristic
470#67—212no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—23no—
474C2×Dic3—83no—
475D12—212no—
476D12—23no—
477D12C23×C416yes—
478C4×D3—212no—
479C4×D3—46no—
480C4×D3—83no—
481C4×D3—86no—
482Dic6—21no—
483Dic6C23×C412yes—
484C3⋊C8—21no—
485C3⋊C8—23no—
486C3⋊C8C23×C412yes—
487C3⋊C8C23×C416yes—
488C24—23no—
489C24—63no—
490#41—28no—
491#41—26no—
492#41—312no—
493#41—68no—
494#41—66no—
495#41C2×C4×D314yes—
496#41C2×C4×D3112yescomplemented
497#41#23514yes—
498C2×Q8—31no—
499C2×Q8C2×#6711yescharacteristic
500C2×Q8C23×D311yescharacteristic
501C2×D4—23no—
502C2×D4—224no—
503C2×D4—26no—
504C2×D4—23no—
505C2×D4—312no—
506C2×D4—33no—
507C2×D4—63no—
508C2×D4—624no—
509C2×D4—66no—
510C2×D4—63no—
511C2×D4C2×C4×D3112yescomplemented
512C2×D4C2×#6713yes—
513C2×D4C23×D313yes—
514C22×C4—23no—
515C22×C4—23no—
516C22×C4—23no—
517C22×C4—23no—
518C22×C4—26no—
519C22×C4—63no—
520C22×C4—63no—
521C22×C4—63no—
522C22×C4—63no—
523C22×C4—66no—
524C22×C4—86no—
525C22×C4—246no—
526C22×C4C2×#6713yes—
527C22×C4C2×#6713yes—
528C22×C4C23×D313yes—
529Q16—34no—
530SD16—312no—
531SD16—312no—
532D8—312no—
533D8—324no—
534M16—312no—
535M16—66no—
536C2×C8—312no—
537C2×C8—31no—
538C2×C8—33no—
539C2×C8—31no—
540C2×C8—33no—
541C2×C8—66no—
542C4⋊C4—23no—
543C4⋊C4—23no—
544C4⋊C4—21no—
545C4⋊C4—31no—
546C4⋊C4—33no—
547C4⋊C4—63no—
548C4⋊C4—63no—
549C4⋊C4—61no—
550C4⋊C4C2×#6713yes—
551C4⋊C4C2×#6713yes—
552C4⋊C4C23×D311yescharacteristic
553C4⋊C4C23×D313yes—
554C22⋊C4—23no—
555C22⋊C4—23no—
556C22⋊C4—26no—
557C22⋊C4—23no—
558C22⋊C4—63no—
559C22⋊C4—63no—
560C22⋊C4—66no—
561C22⋊C4—63no—
562C22⋊C4C2×#6716yes—
563C42—23no—
564C42—23no—
565C42—21no—
566C42—63no—
567C42—63no—
568C42—61no—
569C42C2×#6713yes—
570C42C2×#6713yes—
571C42C23×D313yes—
572C42C23×D311yescharacteristic
573C22×C3—23no—
574C22×C3—23no—
575C22×C3—26no—
576C22×C3—43no—
577C22×C3—43no—
578C22×C3—812no—
579C22×C3C2×C4×D416yes—
580C22×C3C23×D411yescharacteristic
581C2×D3—26no—
582C2×D3—43no—
583C2×D3—43no—
584C2×D3—812no—
585C3×C4—23no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—23no—
589C3×C4—41no—
590C3×C4—43no—
591C3×C4C2×C4×D416yes—
592C3×C4#57612yescomplemented
593C3×C4C24×C411yescharacteristic
594C3×C4C22×#4111yescharacteristic
595Dic3—22no—
596Dic3—41no—
597Dic3—43no—
598C23—23no—
599C23—212no—
600C23—63no—
601C23—612no—
602C23—83no—
603C23—83no—
604C23—243no—
605C23—243no—
606C23C22×#6713yes—
607Q8—21no—
608Q8—32no—
609Q8—61no—
610Q8C4×#6714yes—
611Q8C22×C4×D312yes—
612D4—212no—
613D4—23no—
614D4—212no—
615D4—36no—
616D4—612no—
617D4—63no—
618D4—612no—
619D4C4×#67112yes—
620D4C22×C4×D316yes—
621C2×C4—21no—
622C2×C4—212no—
623C2×C4—26no—
624C2×C4—21no—
625C2×C4—23no—
626C2×C4—43no—
627C2×C4—46no—
628C2×C4—61no—
629C2×C4—612no—
630C2×C4—61no—
631C2×C4—63no—
632C2×C4—86no—
633C2×C4—83no—
634C2×C4—83no—
635C2×C4—126no—
636C2×C4—246no—
637C2×C4—243no—
638C2×C4—243no—
639C2×C4C22×C4×D316yes—
640C2×C4C2×#23516yes—
641C2×C4C22×#6713yes—
642C2×C4C22×#6711yescharacteristic
643C2×C4C22×#6713yes—
644C2×C4C22×#6713yes—
645C2×C4C22×#6711yescharacteristic
646C2×C4C24×D311yescharacteristic
647C8—32no—
648C8—36no—
649C8—61no—
650C8—63no—
651C2×C3—26no—
652C2×C3—46no—
653C2×C3C22×C4×D411yescharacteristic
654C2×C3C2×#57611yescharacteristic
655C2×C3#358411yescharacteristic
656D3—46no—
657C22—23no—
658C22—23no—
659C22—26no—
660C22—43no—
661C22—43no—
662C22—66no—
663C22—812no—
664C22—123no—
665C22—123no—
666C22—2412no—
667C22C2×C4×#6716yes—
668C22C23×#6711yescharacteristic
669C4—21no—
670C4—23no—
671C4—22no—
672C4—23no—
673C4—41no—
674C4—43no—
675C4—62no—
676C4—121no—
677C4—123no—
678C4C2×C4×#6716yes—
679C4#583512yesdirect product factor
680C4C23×C4×D311yescharacteristic
681C4C22×#23511yescharacteristic
682C3C4×#57611yescharacteristic, complemented, Sylow
683C2—26no—
684C2—46no—
685C2—126no—
686C2C22×C4×#6711yescharacteristic
687C2C2×#583511yescharacteristic
688C2#8729711yescharacteristic
subgroupG/H
centerC2×C4C22×#67
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×C4×H(5,𝔽2)C2
socleC22×C3C23×D4
prime radicalC2×#5835C2
cosocleC2×C3×C4C25
hypercenterC4×H(5,𝔽2)D3
hypocenterC3C4×#576
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×C4×H(5,𝔽2)C2semidirect
3. C4×#1009C2semidirect
4. #84099C2semidirect
5. #82564C2semidirect
6. #82563C2semidirect
7. #82562C2semidirect
8. #82557C2semidirect
9. #82538C2semidirect
10. #82537C2semidirect
11. C4×#949C2semidirect
12. C4×#948C2semidirect
13. C4×#950C2semidirect
14. C4×#932C2semidirect
15. C2×C4×#213C2semidirect
21. C3×#520C22semidirect
23. C3×#518C22semidirect
26. C3×C4×#41C22semidirect
28. C2×C3×C4×D4C22semidirect
29. #5835C4direct (N × H)
41. #5523C22semidirect
42. #5521C22semidirect
43. C4×#235C22semidirect
44. C2×C4×D12C22semidirect
45. #5233C22semidirect
46. #5232C22semidirect
47. #5215C22semidirect
48. C2×#832C22semidirect
49. C4×#216C22semidirect
50. C4×#216C22semidirect
51. #5026C22semidirect
52. C4×#215C22semidirect
53. C4×#215C22semidirect
54. #5018C22semidirect
55. C4×#214C22semidirect
56. C4×#214C22semidirect
57. #5014C22semidirect
58. #5014C22semidirect
59. C4×#213C22semidirect
60. C4×#213C22semidirect
61. C4×#213C22semidirect
62. C4×#213C22semidirect
63. C4×#213C22semidirect
64. #5002C22semidirect
65. #5001C22semidirect
66. #4998C22semidirect
67. #4997C22semidirect
68. #4997C22semidirect
69. #4995C22semidirect
70. #4966C22semidirect
71. C2×#809C22semidirect
72. #4964C22semidirect
73. C2×#807C22semidirect
74. C4×#208C22semidirect
75. C2×C4×C3⋊C8C22semidirect
78. C4×H(5,𝔽2)D3semidirect
92. C3×H(5,𝔽2)C2×C4semidirect
100. #1009C2×C4semidirect
134. #950C2×C4semidirect
135. #949C2×C4semidirect
137. #948C2×C4semidirect
143. #932C2×C4semidirect
144. C2×#213C2×C4semidirect
205. #520C2×D3semidirect
209. #518C2×D3semidirect
214. C4×#41C2×D3semidirect
218. C2×C4×D4C2×D3semidirect
255. C3×#41C22×C4semidirect
263. C2×C3×D4C22×C4semidirect
280. #235C22×C4semidirect
283. C2×D12C22×C4semidirect
311. #216C22×C4semidirect
312. #215C22×C4semidirect
313. #214C22×C4semidirect
314. #213C22×C4semidirect
315. #213C22×C4semidirect
328. #208C22×C4semidirect
330. C2×C3⋊C8C22×C4semidirect
338. H(5,𝔽2)C4×D3semidirect
496. #41C2×C4×D3semidirect
511. C2×D4C2×C4×D3semidirect
592. C3×C4#576semidirect
679. C4#5835direct (N × H)
682. C3C4×#576semidirect

Maximal subgroups

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

subgroupindex
C3×C4×H(5,𝔽2)2
C2×#58352
C4×#10092
#840992
#825642
#825632
#825622
#825572
#825382
#825372
C4×#9492
C4×#9482
C4×#9502
C4×#9322
C2×C4×#2132
C4×#5763