Finite Group Databasebeta

← #11867165

Subgroups — #11867165

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3748C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10591180C212yesmaximal, complemented
6#10591179C212yesmaximal, complemented
7#10591167C212yesmaximal, complemented
8#10591166C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591085C211yesmaximal, characteristic, complemented
12#82924—31nomaximal
13#82621—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67—21no—
16C2×C3×#235C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C2×#3748—24no—
19C2×#3748C2211yescharacteristic
20C2×#3748C2211yescharacteristic
21C2×#3748C2212yescomplemented
22C22×C3⋊(C3⋊C8)C2212yescomplemented
23C3×#953—21no—
24C3×#930—21no—
25C3×#930—21no—
26C3×#930C2212yes—
27C3×#930C2212yes—
28C3×#930C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic, complemented
30C3×#929—21no—
31C3×C4×#67—21no—
32C3×C4×#67—21no—
33C2×C3×(C2×D3)⋊C4—21no—
34C3×#926C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C3×#924C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38C2×#3715C2212yescomplemented
39#63823—24no—
40C2×#3713C2212yescomplemented
41#63576C2212yescomplemented
42#63574C2212yescomplemented
43#63565C2212yescomplemented
44#63562C2212yescomplemented
45#63562C2212yescomplemented
46#63562C2212yescomplemented
47C3×#525—31no—
48C2×C3×#121—31no—
49C2×#949—31no—
50C2×#932—31no—
51#5791D311yescharacteristic, complemented
52C2×#930D311yescharacteristic, complemented
53C22×#208—31no—
54C22×#208—31no—
55C22×#208—61no—
56#5232—31no—
57#5215—31no—
58#5049—32no—
59#5048—32no—
60#5042—32no—
61#5041—32no—
62#5039—32no—
63#5039—32no—
64#5038—32no—
65#5038—32no—
66#5001—31no—
67#4995—31no—
68#4966—31no—
69#4964—31no—
70C24×C32D411yescharacteristic
71C23×C3×D3—21no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4D411yescharacteristic
75C22×C32×C4D411yescharacteristic
76C22×C32×C4D411yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C2×C3×#67—21no—
83C2×C3×#67—22no—
84C2×C3×#67—22no—
85C2×C3×#67—44no—
86C22×C3×Dic3—21no—
87C3×#235—22no—
88C3×#235—22no—
89C2×C3×D12—22no—
90C2×C3×D12—22no—
91C2×C3×D12—21no—
92C2×C3×D12C2312yes—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6C2311yescharacteristic
96#3748—22no—
97#3748—24no—
98#3748D414yescomplemented
99C2×C3⋊(C3⋊C8)—24no—
100C2×C3⋊(C3⋊C8)C2312yes—
101C2×C3⋊(C3⋊C8)C2312yes—
102C3×#217—21no—
103C3×#217—21no—
104C3×#217—21no—
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—21no—
108C3×(C2×D3)⋊C4—21no—
109C3×C4⋊Dic3—21no—
110C3×C4⋊Dic3C2311yescharacteristic
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2312yes—
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×C4×Dic3—21no—
116#3715—24no—
117#3713—24no—
118#3055—91noSylow
119C2×C3×#41—31no—
120C22×C3×D4—31no—
121C22×C3×D4—61no—
122C23×C3×C4—21no—
123C23×C3×C4C2×D311yescharacteristic
124C23×C3×C4C2×D311yescharacteristic
125C22×#67—21no—
126C2×#235C2×D311yescharacteristic
127C22×D12C2×D311yescharacteristic
128C3×#123—61no—
129C3×C22⋊Q8—31no—
130C3×C22⋊Q8—31no—
131C3×#121—32no—
132C3×#121—32no—
133C3×#121—31no—
134C3×#121—31no—
135C3×#121—61no—
136C3×#121—61no—
137C3×#120—61no—
138C3×C4×D4—61no—
139C3×C4×D4—61no—
140C3×#117—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—61no—
143#953—21no—
144#949—64no—
145C2×#215—32no—
146C2×#214—32no—
147#932—64no—
148C2×#213—32no—
149C2×#213—32no—
150#930—21no—
151#930—21no—
152#930C2×D312yes—
153#930C2×D312yes—
154#930C2×D311yescharacteristic, complemented
155#930C2×D311yescharacteristic, complemented
156#929—21no—
157C4×#67—21no—
158C4×#67—21no—
159C2×(C2×D3)⋊C4—21no—
160#926C2×D311yescharacteristic
161C2×C4⋊Dic3C2×D311yescharacteristic
162#924C2×D311yescharacteristic, complemented
163#924C2×D311yescharacteristic, complemented
164C2×#208—31no—
165C2×#208—31no—
166C2×#208—31no—
167C2×#208—31no—
168C2×#208—32no—
169C2×#208—32no—
170C2×#208—61no—
171C2×#208—61no—
172C2×#208—62no—
173C2×#208—64no—
174C2×#208—64no—
175C2×#208—68no—
176C22×C3⋊C8—32no—
177C22×C3⋊C8—32no—
178C22×C3⋊C8—62no—
179#835—32no—
180#832—32no—
181#832—32no—
182#832—32no—
183#810—32no—
184#809—32no—
185#809—32no—
186#809—32no—
187#808—32no—
188#808—32no—
189#807—32no—
190#807—32no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—41no—
194C23×C32C2×D411yescharacteristic
195C23×C32C2×D411yescharacteristic
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—22no—
198C22×C3×D3—21no—
199C22×C3×D3—42no—
200C22×C3×D3—42no—
201C22×C3×D3—42no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4C2×D412yes—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4#4112yes—
214C2×C32×C4C2411yescharacteristic
215C3×#67—42no—
216C3×#67—44no—
217C3×#67—42no—
218C3×#67—42no—
219C3×#67—44no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—42no—
225C3×D12—21no—
226C3×D12—22no—
227C3×D12—22no—
228C3×D12—21no—
229C3×D12—42no—
230C3×C4×D3—42no—
231C3×Dic6—21no—
232C3×Dic6—21no—
233C3⋊(C3⋊C8)—22no—
234C3⋊(C3⋊C8)C2×D414yescomplemented
235C2×AGL(1,ℤ/8)—91no—
236C22×M16—91no—
237#525—31no—
238C2×#121—31no—
239#469—92no—
240#468—92no—
241#466—92no—
242#465—92no—
243#428—91no—
244#418—91no—
245#417—91no—
246C24×C3—21no—
247C24×C3—61no—
248C24×C3#6711yescharacteristic
249C24×C3#6711yescharacteristic
250C23×D3—21no—
251C3×#41—62no—
252C3×#41—62no—
253C2×C3×Q8—31no—
254C2×C3×D4—31no—
255C2×C3×D4—32no—
256C2×C3×D4—61no—
257C2×C3×D4—61no—
258C2×C3×D4—61no—
259C2×C3×D4—62no—
260C2×C3×D4—62no—
261C2×C3×D4—62no—
262C2×C3×D4—62no—
263C2×C3×D4—61no—
264C2×C3×D4—124no—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4#6711yescharacteristic
280C22×C3×C4#6711yescharacteristic
281C22×C3×C4#6711yescharacteristic
282C22×C3×C4#6711yescharacteristic
283C22×C3×C4#6711yescharacteristic
284C22×C3×C4#6711yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C2×#67—21no—
292C2×#67—21no—
293C2×#67—21no—
294C2×#67—22no—
295C2×#67—22no—
296C2×#67—44no—
297C22×Dic3—21no—
298#235—22no—
299#235—22no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—21no—
303C2×D12C22×D312yes—
304C2×D12C22×D311yescharacteristic
305C2×C4×D3—21no—
306C2×Dic6C22×D311yescharacteristic
307C3×C4⋊C4—31no—
308C3×C4⋊C4—32no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C22⋊C4—61no—
316C3×C22⋊C4—62no—
317C3×C22⋊C4—62no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—61no—
321#217—21no—
322#217—21no—
323#217—21no—
324#215—64no—
325#214—64no—
326#213—64no—
327#213—64no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—22no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3C22×D311yescharacteristic
334C4⋊Dic3C22×D312yes—
335C4⋊Dic3C22×D311yescharacteristic
336Dic3⋊C4—21no—
337Dic3⋊C4—21no—
338C4×Dic3—21no—
339#208—34no—
340#208—34no—
341#208—64no—
342#208—64no—
343#208—64no—
344#208—68no—
345#208—64no—
346#208—62no—
347#208—62no—
348C2×C3⋊C8—32no—
349C2×C3⋊C8—32no—
350C2×C3⋊C8—32no—
351C2×C3⋊C8—32no—
352C2×C3⋊C8—62no—
353C2×C3⋊C8—62no—
354C2×C3⋊C8—64no—
355C2×C3⋊C8—64no—
356C2×C3⋊C8—68no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—44no—
365C22×C32#12112yes—
366C22×C32AGL(1,ℤ/8)12yescomplemented
367C22×C32C22×D411yescharacteristic
368C2×C3×D3—41no—
369C2×C3×D3—42no—
370C2×C3×D3—42no—
371C2×C3×D3—41no—
372C2×C3×D3—41no—
373C2×C3×D3—42no—
374C2×C3×D3—84no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4#12112yes—
378C32×C4C22×D411yescharacteristic
379C32×C4C2×#4111yescharacteristic
380C3×Dic3—41no—
381C3×Dic3—42no—
382C3×Dic3—41no—
383C3×Dic3—41no—
384C2×#41—31no—
385C22×D4—31no—
386C22×D4—61no—
387C23×C4D3211yescharacteristic
388AGL(1,ℤ/8)—184no—
389C2×SD16—92no—
390C2×D8—92no—
391C2×M16—91no—
392C2×M16—91no—
393C2×M16—92no—
394C2×M16—184no—
395C22×C8—92no—
396#123—61no—
397C22⋊Q8—31no—
398C22⋊Q8—31no—
399#121—32no—
400#121—32no—
401#121—31no—
402#121—31no—
403#121—61no—
404#121—61no—
405#120—61no—
406C4×D4—61no—
407C4×D4—61no—
408#117—31no—
409C2×C4⋊C4—31no—
410C2×C22⋊C4—61no—
411#107—92no—
412#106—92no—
413#103—92no—
414#102—92no—
415#102—92no—
416#102—92no—
417C23×C3—24no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—42no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—42no—
429C23×C3—61no—
430C23×C3—62no—
431C23×C3—122no—
432C23×C3—122no—
433C23×C3—122no—
434C23×C3C2×#6711yescharacteristic
435C23×C3C2×#6711yescharacteristic
436C23×C3C2×#6711yescharacteristic
437C23×C3C2×#6711yescharacteristic
438C23×C3C2×#6711yescharacteristic
439C23×C3C2×#6711yescharacteristic
440C22×D3—21no—
441C22×D3—22no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C3×Q8—61no—
446C3×Q8—61no—
447C3×D4—61no—
448C3×D4—62no—
449C3×D4—62no—
450C3×D4—61no—
451C3×D4—122no—
452C3×D4—124no—
453C3×D4—122no—
454C3×D4—122no—
455C3×D4—124no—
456C3×D4—122no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—62no—
487C2×C3×C4—61no—
488C2×C3×C4—122no—
489C2×C3×C4—122no—
490C2×C3×C4D3×D412yes—
491C2×C3×C4D3×D412yes—
492C2×C3×C4#23712yes—
493C2×C3×C4#23712yes—
494C2×C3×C4C2×#6711yescharacteristic
495C2×C3×C4C2×#6711yescharacteristic
496C2×C3×C4C2×#6711yescharacteristic
497C2×C3×C4C2×#6711yescharacteristic
498C2×C3×C4C2×#6711yescharacteristic
499C2×C3×C4C2×#6711yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502#67—42no—
503#67—44no—
504#67—44no—
505#67—42no—
506#67—42no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—22no—
511C2×Dic3—42no—
512D12—21no—
513D12—22no—
514D12—22no—
515D12—21no—
516D12—42no—
517C4×D3—42no—
518Dic6—21no—
519Dic6—21no—
520C3⋊C8—34no—
521C3⋊C8—34no—
522C3⋊C8—64no—
523C3⋊C8—64no—
524C3⋊C8—62no—
525C3⋊C8—62no—
526C2×C32—22no—
527C2×C32—22no—
528C2×C32—41no—
529C2×C32C2×#12111yescharacteristic
530C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
531C2×C32#57511yescharacteristic
532C3×D3—81no—
533C3×D3—82no—
534C24—61no—
535C24#62511yescharacteristic
536#41—62no—
537#41—62no—
538C2×Q8—31no—
539C2×D4—31no—
540C2×D4—32no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—61no—
548C2×D4—62no—
549C2×D4—124no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4#62511yescharacteristic
555C22×C4#62511yescharacteristic
556C22×C4#62511yescharacteristic
557C22×C4C2×D3211yescharacteristic
558C22×C4C2×D3211yescharacteristic
559C22×C4C2×D3211yescharacteristic
560SD16—184no—
561D8—184no—
562M16—94no—
563M16—184no—
564M16—182no—
565C2×C8—92no—
566C2×C8—92no—
567C2×C8—184no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—32no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C42—61no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—48no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—122no—
612C22×C3—122no—
613C22×C3—121no—
614C22×C3—122no—
615C22×C3—244no—
616C22×C3#93212yescomplemented
617C22×C3#93912yes—
618C22×C3#93912yes—
619C22×C3#94912yescomplemented
620C22×C3C22×#6711yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—42no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—42no—
628C2×D3—84no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—22no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4—122no—
641C3×C4—121no—
642C3×C4#93912yes—
643C3×C4#93912yes—
644C3×C4C2×D3×D411yescharacteristic
645C3×C4C2×D3×D411yescharacteristic
646C3×C4C2×#23711yescharacteristic
647C3×C4C2×#23711yescharacteristic
648Dic3—42no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652C32#305511yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—41no—
656C23—61no—
657C23—62no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23C2×#62511yescharacteristic
662C23C2×#62511yescharacteristic
663C23C2×#62511yescharacteristic
664Q8—61no—
665Q8—61no—
666D4—62no—
667D4—61no—
668D4—61no—
669D4—62no—
670D4—124no—
671D4—122no—
672D4—124no—
673D4—122no—
674D4—122no—
675D4—122no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—122no—
688C2×C4—122no—
689C2×C4#380512yes—
690C2×C4C2×#62511yescharacteristic
691C2×C4C2×#62511yescharacteristic
692C2×C4C2×#62511yescharacteristic
693C2×C4#381112yes—
694C2×C4C22×D3211yescharacteristic
695C8—94no—
696C8—182no—
697C2×C3—24no—
698C2×C3—22no—
699C2×C3—22no—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—42no—
706C2×C3—42no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—241no—
710C2×C3—242no—
711C2×C3C2×#93211yescharacteristic
712C2×C3C2×#93911yescharacteristic
713C2×C3C2×#93911yescharacteristic
714C2×C3C2×#94911yescharacteristic
715C2×C3#582211yescharacteristic
716C2×C3#582211yescharacteristic
717D3—82no—
718D3—81no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—44no—
727C22—121no—
728C22—122no—
729C22—122no—
730C22—121no—
731C22—121no—
732C22—122no—
733C22—244no—
734C22#6382312yescomplemented
735C22#6398012yes—
736C22C22×#62511yescharacteristic
737C4—21no—
738C4—21no—
739C4—121no—
740C4—122no—
741C4—121no—
742C4—121no—
743C4#6398012yes—
744C4C2×#380511yescharacteristic
745C4C2×#381111yescharacteristic
746C3—21no—
747C3#8262111yescharacteristic, complemented
748C3#8292411yescharacteristic, complemented
749C2—22no—
750C2—22no—
751C2—41no—
752C2—242no—
753C2—241no—
754C2C2×#6382311yescharacteristic
755C2#1059478611yescharacteristic
756C2C2×#6398011yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3748C2semidirect
2. C3×#5791C2semidirect
3. C2×C3×#930C2semidirect
4. C2×#63823C2semidirect
5. #10591180C2semidirect
6. #10591179C2semidirect
7. #10591167C2semidirect
8. #10591166C2semidirect
9. #10591139C2semidirect
10. #10591087C2semidirect
11. #10591085C2semidirect
21. C2×#3748C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
28. C3×#930C22semidirect
29. C3×#930C22semidirect
36. C3×#924C22semidirect
37. C3×#924C22semidirect
38. C2×#3715C22semidirect
40. C2×#3713C22semidirect
41. #63576C22semidirect
42. #63574C22semidirect
43. #63565C22semidirect
44. #63562C22semidirect
45. #63562C22semidirect
46. #63562C22semidirect
51. #5791D3semidirect
52. C2×#930D3semidirect
98. #3748D4semidirect
154. #930C2×D3semidirect
155. #930C2×D3semidirect
162. #924C2×D3semidirect
163. #924C2×D3semidirect
234. C3⋊(C3⋊C8)C2×D4semidirect
366. C22×C32AGL(1,ℤ/8)semidirect
616. C22×C3#932semidirect
619. C22×C3#949semidirect
652. C32#3055semidirect
734. C22#63823semidirect
747. C3#82621semidirect
748. C3#82924semidirect

Maximal subgroups

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

subgroupindex
C22×#37482
C3×#57912
C2×C3×#9302
C2×#638232
#105911802
#105911792
#105911672
#105911662
#105911392
#105910872
#105910852
#829243
#826213