Finite Group Databasebeta

← #11866192

Subgroups — #11866192

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63926C211yesmaximal, characteristic, complemented
4#10594010C211yesmaximal, characteristic, complemented
5C3×#5016C211yesmaximal, characteristic, complemented
6C3×#5015C211yesmaximal, characteristic, complemented
7#10591486C211yesmaximal, characteristic, complemented
8#10591476C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590594C211yesmaximal, characteristic, complemented
11#10590551C211yesmaximal, characteristic, complemented
12#10590540C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590355C211yesmaximal, characteristic, complemented
15#10590332C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#80334—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic, complemented
23C4×#638—21no—
24C2×#3752—21no—
25#64102C2211yescharacteristic, complemented
26#64101C2211yescharacteristic
27#64090—21no—
28C22⋊C4×C3⋊D3—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30#64081C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic, complemented
35C3×#875C2211yescharacteristic, complemented
36C3×#874C2211yescharacteristic, complemented
37#63937—24no—
38#63926—24no—
39#63922—21no—
40#63922—21no—
41#63914C2211yescharacteristic, complemented
42#63885—21no—
43#63885—21no—
44#63863C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49C2×#3712C2211yescharacteristic
50C2×#3710C2211yescharacteristic
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67#5715—31no—
68#5674—31no—
69#5545—31no—
70#5545—31no—
71#5545—61no—
72C3×#463—31no—
73C3×#459—31no—
74#5165—31no—
75#5153—31no—
76#5150—31no—
77#5150—31no—
78#5072—31no—
79#5057—31no—
80#5016D311yescharacteristic, complemented
81#5015D311yescharacteristic, complemented
82#4844—31no—
83#4843—31no—
84#4839—31no—
85#4839—31no—
86#4819—31no—
87#4804—31no—
88#4787—31no—
89#4786—31no—
90#4786—31no—
91#4772—31no—
92#4770—31no—
93#4770—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3D414yescomplemented
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—22no—
119#3796—22no—
120#3796—22no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3757—21no—
125#3752—21no—
126#3752—21no—
127#3752—21no—
128#3752D411yescharacteristic
129#3752D411yescharacteristic
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750D411yescharacteristic
132#3750D411yescharacteristic
133C4×C3⋊Dic3—21no—
134C4×C3⋊Dic3C2311yescharacteristic
135C3×#214—22no—
136C3×#213—22no—
137C3×#213—22no—
138C3×#213—22no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147#3717—22no—
148#3714—22no—
149#3714—22no—
150#3714—22no—
151#3712—22no—
152#3710—22no—
153#3041—91noSylow
154C2×#239—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×C3×SD16—31no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C3×#127—31no—
166C3×#124—31no—
167C3×C4×D4—21no—
168C3×C4×D4C2×D311yescharacteristic, complemented
169C3×C4×D4C2×D311yescharacteristic, complemented
170#947—31no—
171C2×#215—31no—
172#940—31no—
173#940—31no—
174#939—61no—
175#939—61no—
176#937—61no—
177#937—61no—
178#936—31no—
179D4×Dic3—31no—
180D4×Dic3—31no—
181D4×Dic3—61no—
182C2×#214C2×D311yescharacteristic, complemented
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213C2×D311yescharacteristic
187C2×#213C2×D311yescharacteristic
188C2×#213C2×D311yescharacteristic, complemented
189C4×#67—61no—
190C4×#67—61no—
191C4×#67—62no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4—62no—
195#914—64no—
196#911—64no—
197D3×D8—64no—
198D3×D8—64no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×#204—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207#893—31no—
208#893—31no—
209#893—61no—
210#892—31no—
211#892—31no—
212#892—61no—
213#884—61no—
214#884—61no—
215#882—61no—
216#882—61no—
217#67⋊C4—61no—
218#67⋊C4—61no—
219#67⋊C4—62no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222D3×C22⋊C4—62no—
223#875C2×D311yescharacteristic, complemented
224#874C2×D311yescharacteristic, complemented
225C4×D12—31no—
226C4×D12—31no—
227C4×D12—61no—
228#872—31no—
229#872—31no—
230#872—61no—
231C3×C4⋊C8—31no—
232C3×C4⋊C8—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102—31no—
237#835—31no—
238#832—31no—
239#832—31no—
240#832—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#816—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249#810C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic, complemented
251#809C2×D311yescharacteristic, complemented
252#809C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
254C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—24no—
258C22×C3⋊D3—81no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—81no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274#638—24no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—81no—
277C2×C3⋊Dic3C2×D411yescharacteristic
278C2×C3⋊Dic3C2×D411yescharacteristic
279C2×C3⋊Dic3C2×D411yescharacteristic
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)C2×D412yes—
282C4×C3⋊D3—81no—
283C4×C3⋊D3—81no—
284C4×C3⋊D3C2×D412yes—
285C4×C3⋊D3#4112yes—
286C2×C3×Dic3—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—81no—
294C3×D12—81no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#625—42no—
299#625—81no—
300#625—81no—
301D3×Dic3—42no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C22×D8—91no—
308#535—91no—
309#518—91no—
310#463—31no—
311#463—91no—
312#463—91no—
313#463—91no—
314#459—31no—
315#459—91no—
316#459—91no—
317#459—91no—
318#424—91no—
319#418—91no—
320#416—91no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—61no—
325C23×D3—62no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—22no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—62no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—62no—
352#239—62no—
353#239—62no—
354#237—62no—
355#237—62no—
356D3×D4—34no—
357D3×D4—34no—
358D3×D4—64no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—64no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×Dic6C22×D311yescharacteristic
386C3×SD16—62no—
387C3×D8—62no—
388C3×D8—62no—
389C3×D8—62no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—22no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—21no—
403C3×C42C22×D311yescharacteristic
404C3×C42C22×D311yescharacteristic
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—62no—
410#215—62no—
411#214—22no—
412#213—22no—
413#213—22no—
414#213—22no—
415#213—62no—
416#213—62no—
417#213—62no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—31no—
443Dic3⋊C4—31no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446C4×Dic3—31no—
447C4×Dic3—31no—
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451C4×Dic3—62no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455C2×C3⋊C8C22×D311yescharacteristic
456D24—62no—
457D24—62no—
458D24—62no—
459#204—62no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—62no—
462D3×C8—62no—
463D3×C8—62no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32C22×D411yescharacteristic
468C2×C3⋊D3—22no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—84no—
474C2×C3⋊D3#12112yes—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484D32—84no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4C2×#4111yescharacteristic
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3⋊Dic3—41no—
493C3⋊Dic3#12112yes—
494C3×Dic3—41no—
495C2×#41—91no—
496C22×D4—91no—
497C22×D4—91no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—31no—
504C2×D8—91no—
505C2×D8—91no—
506C2×D8—91no—
507C2×D8—184no—
508C2×M16—91no—
509C22×C8—91no—
510#127—31no—
511#127—91no—
512#124—31no—
513#124—91no—
514#121—181no—
515#121—181no—
516#120—181no—
517#120—181no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—91no—
521C4×D4—181no—
522C4×D4—181no—
523C4×D4D3211yescharacteristic, complemented
524#117—91no—
525#117—91no—
526C2×C22⋊C4—181no—
527C2×C22⋊C4—181no—
528C4⋊C8—31no—
529C4⋊C8—31no—
530C4⋊C8—91no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—31no—
537#102—91no—
538#102—91no—
539#102—91no—
540C23×C3—22no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—61no—
552C22×D3—64no—
553C22×D3—64no—
554C22×D3—62no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—68no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—242no—
569C22×D3—242no—
570C3×Q8—61no—
571C3×Q8—61no—
572C3×D4—22no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—22no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—241no—
583C3×D4—241no—
584C3×D4D3×D412yes—
585C3×D4D3×D412yes—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—61no—
593C2×C3×C4—81no—
594C2×C3×C4—81no—
595C2×C3×C4—82no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—64no—
603#67—64no—
604#67—68no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—241no—
609#67—241no—
610#67—241no—
611#67—241no—
612C2×Dic3—21no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—62no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—122no—
626C2×Dic3—241no—
627C2×Dic3—241no—
628C2×Dic3—242no—
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—32no—
636D12—32no—
637D12—62no—
638D12—62no—
639D12—61no—
640D12—61no—
641D12—81no—
642D12—81no—
643D12—122no—
644C4×D3—32no—
645C4×D3—32no—
646C4×D3—32no—
647C4×D3—32no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—122no—
651C4×D3—241no—
652C4×D3—241no—
653C4×D3—241no—
654C4×D3—241no—
655C4×D3—242no—
656C4×D3—242no—
657Dic6—21no—
658Dic6—21no—
659C3×C8—61no—
660C3×C8—61no—
661C3×C8—61no—
662C3×C8—61no—
663C3⋊C8—21no—
664C3⋊C8—21no—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C2×C32—42no—
668C2×C32C2×#12111yescharacteristic
669C2×C32#57611yescharacteristic
670C2×C32#57611yescharacteristic
671C3⋊D3—22no—
672C3⋊D3—42no—
673C3×D3—81no—
674C3×D3—81no—
675C3×D3—81no—
676C24—181no—
677C24—181no—
678#41—182no—
679#41—182no—
680C2×Q8—31no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—94no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4C2×D3211yescharacteristic
697C22×C4—21no—
698C22×C4—91no—
699C22×C4—181no—
700C22×C4—181no—
701C22×C4—181no—
702C22×C4—181no—
703SD16—62no—
704SD16—182no—
705D8—62no—
706D8—62no—
707D8—62no—
708D8—182no—
709D8—182no—
710D8—182no—
711M16—182no—
712C2×C8—31no—
713C2×C8—31no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—182no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—91no—
720C4⋊C4C2×D3211yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—91no—
725C22⋊C4—91no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C42—91no—
733C42—181no—
734C42C2×D3211yescharacteristic
735C22×C3—24no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C2×D3—32no—
757C2×D3—32no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—62no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—64no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—244no—
784C2×D3—244no—
785C2×D3—244no—
786C2×D3—244no—
787C2×D3—248no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—42no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—121no—
800C3×C4C2×D3×D411yescharacteristic
801C3×C4C2×D3×D411yescharacteristic
802C3×C4D3×#4111yescharacteristic
803C3×C4D3×#4111yescharacteristic
804Dic3—32no—
805Dic3—32no—
806Dic3—41no—
807Dic3—62no—
808Dic3—61no—
809Dic3—61no—
810Dic3—61no—
811Dic3—61no—
812Dic3—121no—
813Dic3—121no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817C32#304111yescharacteristic, complemented, Sylow
818C23—21no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—91no—
823C23—184no—
824C23—181no—
825C23—362no—
826C23—721no—
827C23—721no—
828C23—721no—
829C23—721no—
830Q8—61no—
831Q8—61no—
832D4—21no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—92no—
840D4—184no—
841D4—181no—
842D4—241no—
843D4—241no—
844D4—362no—
845D4—362no—
846D4—721no—
847D4—721no—
848D4#380212yes—
849C2×C4—21no—
850C2×C4—61no—
851C2×C4—81no—
852C2×C4—91no—
853C2×C4—92no—
854C2×C4—92no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4—721no—
860C2×C4—721no—
861C2×C4—721no—
862C2×C4#381111yescharacteristic
863C2×C4#381111yescharacteristic
864C2×C4C22×D3211yescharacteristic
865C8—61no—
866C8—61no—
867C8—61no—
868C8—61no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—44no—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3—241no—
876C2×C3—241no—
877C2×C3—241no—
878C2×C3D3×#12111yescharacteristic
879C2×C3D3×#12111yescharacteristic
880C2×C3#575711yescharacteristic
881C2×C3#576911yescharacteristic
882C2×C3#577411yescharacteristic
883C2×C3#577411yescharacteristic
884D3—62no—
885D3—62no—
886D3—81no—
887D3—81no—
888D3—81no—
889D3—122no—
890D3—124no—
891D3—122no—
892D3—122no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—92no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—181no—
907C22—181no—
908C22—182no—
909C22—361no—
910C22—361no—
911C22—724no—
912C22—724no—
913C22C2×#381111yescharacteristic
914C4—21no—
915C4—21no—
916C4—41no—
917C4—92no—
918C4—121no—
919C4—181no—
920C4—181no—
921C4—361no—
922C4C2×#380211yescharacteristic
923C4#6430611yescharacteristic
924C3—21no—
925C3#8033411yescharacteristic, complemented
926C3#8053611yescharacteristic, complemented
927C2—42no—
928C2—182no—
929C2—241no—
930C2—241no—
931C2—241no—
932C2—362no—
933C2#1059508111yescharacteristic
934C2#1059510211yescharacteristic
935C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596016C2semidirect
2. C2×#63937C2semidirect
3. C2×#63926C2semidirect
4. #10594010C2semidirect
5. C3×#5016C2semidirect
6. C3×#5015C2semidirect
7. #10591486C2semidirect
8. #10591476C2semidirect
9. #10590611C2semidirect
10. #10590594C2semidirect
11. #10590551C2semidirect
12. #10590540C2semidirect
13. #10590356C2semidirect
14. #10590355C2semidirect
15. #10590332C2semidirect
21. C32×C4×D4C22semidirect
22. D4×C3⋊Dic3C22semidirect
25. #64102C22semidirect
29. C4×C4⋊(C3⋊D3)C22semidirect
31. C2×C3×#214C22semidirect
34. C2×C3×#213C22semidirect
35. C3×#875C22semidirect
36. C3×#874C22semidirect
41. #63914C22semidirect
44. #63863C22semidirect
45. C2×#3717C22semidirect
48. C2×#3714C22semidirect
51. C3×#810C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#809C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. #63572C22semidirect
58. #63572C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
80. #5016D3semidirect
81. #5015D3semidirect
101. D4×C3⋊D3D4semidirect
168. C3×C4×D4C2×D3semidirect
169. C3×C4×D4C2×D3semidirect
182. C2×#214C2×D3semidirect
188. C2×#213C2×D3semidirect
223. #875C2×D3semidirect
224. #874C2×D3semidirect
249. #810C2×D3semidirect
250. #809C2×D3semidirect
251. #809C2×D3semidirect
252. #809C2×D3semidirect
253. C4⋊(C3⋊C8)C2×D3semidirect
254. C4⋊(C3⋊C8)C2×D3semidirect
523. C4×D4D32semidirect
817. C32#3041semidirect
925. C3#80334semidirect
926. C3#80536semidirect

Maximal subgroups

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

subgroupindex
#105960162
C2×#639372
C2×#639262
#105940102
C3×#50162
C3×#50152
#105914862
#105914762
#105906112
#105905942
#105905512
#105905402
#105903562
#105903552
#105903322
#805363
#803343