Finite Group Databasebeta

← #11905972

Subgroups — #11905972

Order 1152.

3945 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C3×#5805C211yesmaximal, characteristic, complemented
4C2×C3×#940C211yesmaximal, characteristic, complemented
5#10595526C218yesmaximal, complemented
6#10595309C212yesmaximal, complemented
7#10595300C212yesmaximal, complemented
8#10595297C214yesmaximal, complemented
9#10595168C212yesmaximal, complemented
10#10595167C212yesmaximal, complemented
11#10595164C214yesmaximal, complemented
12#10595042C211yesmaximal, characteristic, complemented
13#10595029C211yesmaximal, characteristic, complemented
14#10594954C211yesmaximal, characteristic, complemented
15#86316—31nomaximal
16#86195—31nomaximal
17C22×C32×D4C2211yescharacteristic, complemented
18C22×#638C2214yescomplemented
19#64361—28no—
20C2×#3830C2212yescomplemented
21C2×#3830C2212yescomplemented
22C2×D4×C3⋊D3C2212yescomplemented
23C2×D4×C3⋊D3C2212yescomplemented
24C2×#3828C2211yescharacteristic
25C2×#3828C2211yescharacteristic, complemented
26C22×C3×#67C2214yescomplemented
27C2×C3×#235C2211yescharacteristic, complemented
28C22×C3×D12C2211yescharacteristic, complemented
29C2×#3811C2218yescomplemented
30C2×D3×#67C2214yescomplemented
31#64307—28no—
32C2×#3802C2212yescomplemented
33C2×D3×D12C2212yescomplemented
34C2×#3796C2212yescomplemented
35C2×#3795C2212yescomplemented
36C3×#953C2214yescomplemented
37C3×#940C2214yescomplemented
38C3×#940C2212yescomplemented
39C3×#940C2212yescomplemented
40C3×#940C2212yescomplemented
41C3×#938C2214yescomplemented
42C3×#936C2212yescomplemented
43C3×#926C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45#63983C2218yescomplemented
46#63981C2218yescomplemented
47#63980C2218yescomplemented
48#63979C2218yescomplemented
49#63978C2214yescomplemented
50#63977C2214yescomplemented
51#67⋊Dic3C2218yescomplemented
52#63971C2218yescomplemented
53#63958C2218yescomplemented
54#63952C2214yescomplemented
55#63916C2214yescomplemented
56#63911C2212yescomplemented
57#63911C2211yescharacteristic, complemented
58C4×#626C2214yescomplemented
59#63894C2212yescomplemented
60C4×#624C2212yescomplemented
61#63874C2212yescomplemented
62#63866C2211yescharacteristic, complemented
63#63864C2211yescharacteristic, complemented
64#63860C2212yescomplemented
65#63860C2211yescharacteristic, complemented
66#63844C2212yescomplemented
67C2×#1009—31no—
68C2×#1004—31no—
69C2×#1004—31no—
70C2×#1004—31no—
71C2×#1004—61no—
72C3×#535—31no—
73C2×C3×#127—31no—
74#5832—31no—
75#5805—31no—
76#5805D311yescharacteristic, complemented
77C2×#940D311yescharacteristic, complemented
78D4×#67—38no—
79#5718—34no—
80#5717—34no—
81#5716—32no—
82#5715—32no—
83#5715—32no—
84#5715—32no—
85D3×#127—32no—
86D3×#127—32no—
87#5674—32no—
88#5668—32no—
89#5609—34no—
90#5599—34no—
91#5590—38no—
92#5525—31no—
93#5522—31no—
94#5477—31no—
95C4×#235—31no—
96C24×C32C2312yes—
97C23×C3⋊D3C2314yes—
98C23×C3×D3C2312yes—
99C22×D32C2314yes—
100C2×C32×D4—24no—
101C2×C32×D4C2312yes—
102C2×C32×D4C2312yes—
103C22×C32×C4C2311yescharacteristic
104C2×#638—216no—
105C2×#638C2312yes—
106C2×#638C2314yes—
107C2×#638C2314yes—
108C2×#638C2312yes—
109C22×C3⋊Dic3C2314yes—
110#3830—28no—
111#3830—28no—
112D4×C3⋊D3—28no—
113D4×C3⋊D3—28no—
114#3828—24no—
115#3828D418yescomplemented
116C2×C4⋊(C3⋊D3)C2311yescharacteristic
117C2×C4⋊(C3⋊D3)C2311yescharacteristic
118C2×C4×C3⋊D3C2312yes—
119C2×C4×C3⋊D3C2312yes—
120C2×#634C2311yescharacteristic
121C2×#634C2311yescharacteristic
122C2×C3×#67—48no—
123C2×C3×#67C2318yes—
124C2×C3×#67C2312yes—
125C2×C3×#67C2318yes—
126C2×C3×#67C2318yes—
127C22×C3×Dic3C2312yes—
128C3×#235—24no—
129C2×C3×D12—24no—
130C2×C3×D12C2312yes—
131C2×C3×D12C2312yes—
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135#3811—416no—
136D3×#67—216no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2318yes—
140C2×#625C2314yes—
141C2×#624C2314yes—
142C2×D3×Dic3C2314yes—
143#3802—28no—
144D3×D12—28no—
145#3796—28no—
146#3795—28no—
147C3×#217C2312yes—
148C3×#217C2318yes—
149C3×C4⋊Dic3C2312yes—
150C3×C4×Dic3C2312yes—
151C3×C4×Dic3C2311yescharacteristic
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2312yes—
154#3724C2314yes—
155Dic3⋊Dic3C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2318yes—
160Dic32C2314yes—
161#3498—91noSylow
162C2×C3×#41—31no—
163C22×C3×D4—21no—
164C22×C3×D4—34no—
165C22×C3×D4—31no—
166C22×C3×D4C2×D311yescharacteristic, complemented
167C22×C3×D4C2×D311yescharacteristic, complemented
168C22×#67—34no—
169C22×#67—34no—
170C22×#67—34no—
171C22×#67—64no—
172C22×#67C2×D314yescomplemented
173#1009—68no—
174C2×#239—32no—
175#1004—68no—
176#1004—68no—
177#1004—68no—
178#1004—616no—
179C2×#237—32no—
180C2×#237—32no—
181C2×#237—32no—
182C2×#237—32no—
183C2×#237—32no—
184C2×#237—32no—
185C2×#237—62no—
186C2×#237—62no—
187C2×D3×D4—34no—
188C2×D3×D4—32no—
189C2×D3×D4—32no—
190C2×D3×D4—32no—
191C2×D3×D4—32no—
192C2×D3×D4—38no—
193C2×D3×D4—38no—
194C2×D3×D4—32no—
195C2×D3×D4—32no—
196C2×D3×D4—32no—
197C2×D3×D4—62no—
198C2×D3×D4—62no—
199C2×#235—31no—
200C2×#235—31no—
201C2×#235—31no—
202C2×#235—31no—
203C2×#235—32no—
204C2×#235—61no—
205C2×#235—61no—
206C2×#235C2×D311yescharacteristic, complemented
207C22×D12—32no—
208C22×D12C2×D311yescharacteristic, complemented
209C3×#127—32no—
210C3×#127—32no—
211C3×#127—32no—
212C3×#127—34no—
213C3×#124—32no—
214C3×#121—34no—
215C3×#120—34no—
216C3×#117—31no—
217C2×C3×C42—31no—
218#953—34no—
219#953C2×D314yescomplemented
220#947—31no—
221#944—31no—
222#940—38no—
223#940—38no—
224#940—31no—
225#940—32no—
226#940C2×D312yescomplemented
227#940C2×D312yescomplemented
228#940C2×D312yescomplemented
229#940C2×D314yescomplemented
230#939—38no—
231#939—38no—
232#939—34no—
233#939—38no—
234#938—38no—
235#938—34no—
236#938C2×D314yescomplemented
237#937—38no—
238#937—38no—
239#937—38no—
240#936—31no—
241#936—32no—
242#936C2×D312yescomplemented
243D4×Dic3—38no—
244#930—34no—
245C4×#67—34no—
246C4×#67—34no—
247#926C2×D311yescharacteristic, complemented
248C2×C4×Dic3C2×D311yescharacteristic, complemented
249#895—34no—
250#893—32no—
251#887—32no—
252#884—38no—
253#884—38no—
254#882—34no—
255#882—38no—
256#67⋊C4—38no—
257#67⋊C4—34no—
258#875—32no—
259#875—31no—
260#875—31no—
261#874—32no—
262#874—31no—
263C4×D12—34no—
264C4×D12—32no—
265#872—32no—
266#872—32no—
267C42×D3—32no—
268C42×D3—32no—
269#869—31no—
270C4×Dic6—32no—
271C23×C32—24no—
272C23×C32—44no—
273C23×C32C2414yes—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—28no—
276C22×C3⋊D3—48no—
277C22×C3⋊D3C2412yes—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—24no—
280C22×C3×D3—44no—
281C22×C3×D3C2412yes—
282C22×C3×D3C2414yes—
283C2×D32—28no—
284C2×D32—48no—
285C32×D4—24no—
286C32×D4—24no—
287C2×C32×C4C2×D414yescomplemented
288C2×C32×C4C2411yescharacteristic
289C2×C32×C4C2411yescharacteristic
290#638—24no—
291#638—28no—
292#638—28no—
293#638C2×D418yescomplemented
294C2×C3⋊Dic3—28no—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2412yes—
297C4⋊(C3⋊D3)—22no—
298C4⋊(C3⋊D3)C2×D414yescomplemented
299C4×C3⋊D3—24no—
300C4×C3⋊D3C2×D418yescomplemented
301#634—22no—
302#634C2×D414yescomplemented
303C3×#67—24no—
304C3×#67—216no—
305C3×#67—48no—
306C3×#67—48no—
307C2×C3×Dic3—24no—
308C2×C3×Dic3C2414yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×D12—24no—
313C3×D12—24no—
314C3×D12—22no—
315C3×C4×D3—24no—
316C3×Dic6—22no—
317#626—28no—
318#626—28no—
319#626—48no—
320#625—28no—
321#624—28no—
322D3×Dic3—28no—
323C2×H(5,𝔽2)—91no—
324C2×H(5,𝔽2)—91no—
325#550—94no—
326D42—98no—
327D42—94no—
328#535—31no—
329#535—91no—
330#535—92no—
331#535—92no—
332#532—91no—
333#532—92no—
334C2×#127—31no—
335C2×#127—92no—
336C4×#41—91no—
337C24×C3—22no—
338C24×C3—32no—
339C24×C3C22×D312yes—
340C24×C3C22×D312yes—
341C23×D3—34no—
342C23×D3—34no—
343C23×D3—34no—
344C23×D3—34no—
345C23×D3—64no—
346C23×D3C22×D312yes—
347C3×#41—64no—
348C2×C3×Q8—31no—
349C2×C3×D4—28no—
350C2×C3×D4—24no—
351C2×C3×D4—24no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—38no—
355C2×C3×D4—32no—
356C2×C3×D4—38no—
357C2×C3×D4—38no—
358C2×C3×D4—31no—
359C2×C3×D4—32no—
360C2×C3×D4—32no—
361C2×C3×D4—64no—
362C2×C3×D4—128no—
363C2×C3×D4C22×D312yes—
364C2×C3×D4C22×D312yes—
365C2×C3×D4C22×D312yes—
366C2×C3×D4C22×D312yes—
367C22×C3×C4—21no—
368C22×C3×C4—32no—
369C22×C3×C4—32no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—32no—
373C2×#67—32no—
374C2×#67—32no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—32no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—38no—
385C2×#67—48no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—64no—
389C2×#67—64no—
390C2×#67—616no—
391C2×#67—616no—
392C2×#67—616no—
393C2×#67—632no—
394C2×#67C22×D318yes—
395C2×#67C22×D312yes—
396C2×#67C22×D318yes—
397C2×#67C22×D318yes—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—64no—
402C22×Dic3C22×D312yes—
403#239—68no—
404#237—68no—
405#237—68no—
406#237—68no—
407#237—68no—
408#237—68no—
409#237—68no—
410#237—616no—
411#237—616no—
412D3×D4—68no—
413D3×D4—68no—
414D3×D4—68no—
415D3×D4—68no—
416D3×D4—68no—
417D3×D4—68no—
418D3×D4—68no—
419D3×D4—616no—
420D3×D4—616no—
421D3×D4—616no—
422D3×D4—1216no—
423D3×D4—1216no—
424#235—24no—
425#235—38no—
426#235—38no—
427#235—68no—
428#235—68no—
429#235—68no—
430#235—64no—
431#235—64no—
432C2×D12—24no—
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—34no—
436C2×D12—34no—
437C2×D12—31no—
438C2×D12—31no—
439C2×D12—38no—
440C2×D12—61no—
441C2×D12—61no—
442C2×D12—68no—
443C2×D12C22×D312yes—
444C2×D12C22×D311yescharacteristic
445C2×D12C22×D312yes—
446C2×C4×D3—32no—
447C2×C4×D3—32no—
448C2×C4×D3—34no—
449C2×C4×D3—32no—
450C2×C4×D3—32no—
451C2×C4×D3—34no—
452C2×C4×D3—34no—
453C2×C4×D3—62no—
454C2×C4×D3—62no—
455C2×C4×D3C22×D312yes—
456C2×Dic6—31no—
457C2×Dic6—31no—
458C2×Dic6—31no—
459C2×Dic6—31no—
460C2×Dic6—61no—
461C2×Dic6—61no—
462C2×Dic6C22×D311yescharacteristic
463C3×C4⋊C4—32no—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—38no—
466C3×C42—32no—
467C3×C42—31no—
468C3×C42—32no—
469C3×C42—31no—
470#217—34no—
471#217—38no—
472#217C22×D312yes—
473#217C22×D318yes—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—38no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3C22×D312yes—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485C4×Dic3—34no—
486C4×Dic3—34no—
487C4×Dic3C22×D311yescharacteristic
488C4×Dic3C22×D312yes—
489C4×Dic3C22×D311yescharacteristic
490C4×Dic3C22×D312yes—
491C22×C32—24no—
492C22×C32—22no—
493C22×C32—28no—
494C22×C32—84no—
495C22×C32C22×D412yes—
496C22×C32C2511yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—24no—
499C2×C3⋊D3—24no—
500C2×C3⋊D3—88no—
501C2×C3⋊D3C22×D414yes—
502C2×C3×D3—24no—
503C2×C3×D3—22no—
504C2×C3×D3—24no—
505C2×C3×D3—28no—
506C2×C3×D3—84no—
507D32—88no—
508C32×C4C22×D412yes—
509C32×C4C22×D412yes—
510C3⋊Dic3—22no—
511C3⋊Dic3C22×D414yes—
512C3×Dic3—22no—
513C3×Dic3—24no—
514C3×Dic3—22no—
515C3×Dic3H(5,𝔽2)14yescomplemented
516H(5,𝔽2)—188no—
517H(5,𝔽2)—188no—
518C2×#41—31no—
519C2×#41—92no—
520C2×#41—92no—
521C2×#41—92no—
522C2×#41—92no—
523C2×#41—91no—
524C2×#41—91no—
525C22×D4—34no—
526C22×D4—31no—
527C22×D4—92no—
528C22×D4—92no—
529C22×D4—98no—
530C22×D4—94no—
531C22×D4—94no—
532C22×D4—92no—
533C22×D4—92no—
534C22×D4D3211yescharacteristic, complemented
535C4⋊Q8—91no—
536#127—32no—
537#127—32no—
538#127—34no—
539#127—32no—
540#127—91no—
541#127—92no—
542#127—98no—
543#124—32no—
544#124—91no—
545#124—92no—
546#124—91no—
547#121—34no—
548#121—98no—
549#121—98no—
550#121—94no—
551#121—94no—
552#121—98no—
553#120—34no—
554#120—98no—
555#120—94no—
556#120—98no—
557C4×Q8—92no—
558C4×D4—92no—
559C4×D4—94no—
560C4×D4—94no—
561C4×D4—98no—
562#117—31no—
563#117—92no—
564C2×C42—31no—
565C2×C42—92no—
566C23×C3—28no—
567C23×C3—24no—
568C23×C3—24no—
569C23×C3—24no—
570C23×C3—21no—
571C23×C3—34no—
572C23×C3—32no—
573C23×C3—44no—
574C23×C3—44no—
575C23×C3—64no—
576C23×C3—84no—
577C23×C3—124no—
578C23×C3C23×D314yes—
579C23×C3C23×D314yes—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—24no—
583C22×D3—32no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—44no—
588C22×D3—62no—
589C22×D3—62no—
590C22×D3—68no—
591C22×D3—68no—
592C22×D3—68no—
593C22×D3—68no—
594C22×D3—616no—
595C22×D3—128no—
596C22×D3—128no—
597C22×D3—128no—
598C22×D3—128no—
599C22×D3—248no—
600C22×D3C23×D314yes—
601C22×D3C23×D312yes—
602C3×Q8—62no—
603C3×D4—28no—
604C3×D4—28no—
605C3×D4—24no—
606C3×D4—24no—
607C3×D4—24no—
608C3×D4—24no—
609C3×D4—616no—
610C3×D4—64no—
611C3×D4—62no—
612C3×D4—64no—
613C3×D4—64no—
614C3×D4—128no—
615C3×D4—128no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—24no—
619C2×C3×C4—32no—
620C2×C3×C4—34no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—64no—
624C2×C3×C4—64no—
625C2×C3×C4D3×D414yescomplemented
626C2×C3×C4D3×D414yescomplemented
627C2×C3×C4C23×D311yescharacteristic
628C2×C3×C4C23×D311yescharacteristic
629C2×C3×C4C23×D311yescharacteristic
630C2×C3×C4C23×D311yescharacteristic
631#67—24no—
632#67—216no—
633#67—38no—
634#67—38no—
635#67—48no—
636#67—48no—
637#67—68no—
638#67—68no—
639#67—68no—
640#67—68no—
641#67—68no—
642#67—68no—
643#67—68no—
644#67—68no—
645#67—68no—
646#67—616no—
647#67—616no—
648#67—64no—
649#67—64no—
650#67—68no—
651#67—128no—
652C2×Dic3—24no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—68no—
660C2×Dic3—68no—
661C2×Dic3—68no—
662C2×Dic3—616no—
663C2×Dic3C23×D314yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667D12—24no—
668D12—24no—
669D12—22no—
670D12—34no—
671D12—34no—
672D12—64no—
673D12—64no—
674D12—68no—
675D12—68no—
676D12—62no—
677D12—62no—
678D12—128no—
679C4×D3—24no—
680C4×D3—38no—
681C4×D3—38no—
682C4×D3—68no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—68no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—68no—
689Dic6—22no—
690Dic6—34no—
691Dic6—34no—
692Dic6—64no—
693Dic6—64no—
694Dic6—62no—
695Dic6—62no—
696C2×C32—22no—
697C2×C32—44no—
698C2×C32C23×D411yescharacteristic
699C2×C32C2×H(5,𝔽2)12yes—
700C3⋊D3—24no—
701C3⋊D3—42no—
702C3×D3—42no—
703C3×D3—44no—
704C24—32no—
705C24—94no—
706C24—94no—
707C24C2×D3212yes—
708#41—64no—
709#41—98no—
710#41—188no—
711#41—188no—
712#41—188no—
713#41—188no—
714#41—184no—
715C2×Q8—31no—
716C2×Q8—91no—
717C2×Q8—91no—
718C2×D4—24no—
719C2×D4—38no—
720C2×D4—32no—
721C2×D4—38no—
722C2×D4—38no—
723C2×D4—32no—
724C2×D4—32no—
725C2×D4—31no—
726C2×D4—64no—
727C2×D4—94no—
728C2×D4—94no—
729C2×D4—98no—
730C2×D4—92no—
731C2×D4—94no—
732C2×D4—94no—
733C2×D4—92no—
734C2×D4—94no—
735C2×D4—91no—
736C2×D4—91no—
737C2×D4—128no—
738C2×D4—188no—
739C2×D4—188no—
740C2×D4—188no—
741C2×D4—188no—
742C2×D4—1816no—
743C2×D4—1816no—
744C2×D4—3616no—
745C2×D4C2×D3212yes—
746C2×D4C2×D3212yes—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—94no—
750C22×C4—94no—
751C22×C4—92no—
752C22×C4—94no—
753C22×C4—92no—
754C22×C4C2×D3211yescharacteristic
755C4⋊C4—32no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C22⋊C4—32no—
759C22⋊C4—38no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4—98no—
764C42—31no—
765C42—31no—
766C42—32no—
767C42—32no—
768C42—94no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—28no—
772C22×C3—24no—
773C22×C3—24no—
774C22×C3—28no—
775C22×C3—28no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—48no—
779C22×C3—42no—
780C22×C3—64no—
781C22×C3—62no—
782C22×C3—64no—
783C22×C3—68no—
784C22×C3—84no—
785C22×C3—84no—
786C22×C3—88no—
787C22×C3—244no—
788C22×C3C2×D3×D412yes—
789C22×C3C2×D3×D412yes—
790C22×C3C24×D311yescharacteristic
791C22×C3C24×D311yescharacteristic
792C2×D3—22no—
793C2×D3—24no—
794C2×D3—28no—
795C2×D3—24no—
796C2×D3—34no—
797C2×D3—34no—
798C2×D3—64no—
799C2×D3—64no—
800C2×D3—64no—
801C2×D3—64no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—64no—
805C2×D3—64no—
806C2×D3—84no—
807C2×D3—124no—
808C2×D3—124no—
809C2×D3—248no—
810C2×D3—248no—
811C2×D3—248no—
812C2×D3—248no—
813C2×D3—2416no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—34no—
817C3×C4—62no—
818C3×C4—64no—
819C3×C4—62no—
820C3×C4C2×D3×D412yes—
821C3×C4C2×D3×D412yes—
822C3×C4C2×D3×D412yes—
823C3×C4C2×D3×D412yes—
824Dic3—22no—
825Dic3—22no—
826Dic3—24no—
827Dic3—34no—
828Dic3—34no—
829Dic3—64no—
830Dic3—64no—
831Dic3—62no—
832Dic3—62no—
833Dic3#100414yescomplemented
834C32#349811yescharacteristic, complemented, Sylow
835C23—24no—
836C23—32no—
837C23—34no—
838C23—44no—
839C23—64no—
840C23—92no—
841C23—92no—
842C23—124no—
843C23—188no—
844C23—188no—
845C23—368no—
846C23—368no—
847C23C22×D3214yes—
848C23C22×D3211yescharacteristic
849Q8—62no—
850Q8—94no—
851Q8—182no—
852D4—24no—
853D4—24no—
854D4—616no—
855D4—64no—
856D4—64no—
857D4—64no—
858D4—62no—
859D4—98no—
860D4—94no—
861D4—128no—
862D4—128no—
863D4—188no—
864D4—188no—
865D4—188no—
866D4—188no—
867D4—188no—
868D4—184no—
869D4—182no—
870D4—368no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—34no—
874C2×C4—32no—
875C2×C4—64no—
876C2×C4—64no—
877C2×C4—92no—
878C2×C4—98no—
879C2×C4—92no—
880C2×C4—188no—
881C2×C4—188no—
882C2×C4—188no—
883C2×C4—184no—
884C2×C4#381114yescomplemented
885C2×C4C22×D3211yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—21no—
891C2×C3—42no—
892C2×C3—48no—
893C2×C3—44no—
894C2×C3—44no—
895C2×C3—124no—
896C2×C3—122no—
897C2×C3C22×D3×D411yescharacteristic
898C2×C3C22×D3×D411yescharacteristic
899C2×C3C2×#100412yes—
900C2×C3D3×H(5,𝔽2)12yes—
901D3—42no—
902D3—44no—
903D3—64no—
904D3—64no—
905D3—124no—
906D3—124no—
907D3—122no—
908D3—122no—
909C22—22no—
910C22—28no—
911C22—24no—
912C22—68no—
913C22—64no—
914C22—62no—
915C22—64no—
916C22—84no—
917C22—94no—
918C22—184no—
919C22—184no—
920C22—182no—
921C22—244no—
922C22—728no—
923C22—728no—
924C22C2×#381112yes—
925C22C23×D3211yescharacteristic
926C4—34no—
927C4—62no—
928C4—64no—
929C4—62no—
930C4—94no—
931C4—182no—
932C4C2×#381112yes—
933C4C2×#381112yes—
934C3—21no—
935C3#8619511yescharacteristic, complemented
936C3#8631611yescharacteristic, complemented
937C2—22no—
938C2—44no—
939C2—124no—
940C2—122no—
941C2—184no—
942C2—362no—
943C2D3×#100412yes—
944C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64307C2semidirect
3. C3×#5805C2semidirect
4. C2×C3×#940C2semidirect
5. #10595526C2semidirect
6. #10595309C2semidirect
7. #10595300C2semidirect
8. #10595297C2semidirect
9. #10595168C2semidirect
10. #10595167C2semidirect
11. #10595164C2semidirect
12. #10595042C2semidirect
13. #10595029C2semidirect
14. #10594954C2semidirect
17. C22×C32×D4C22semidirect
18. C22×#638C22semidirect
20. C2×#3830C22semidirect
21. C2×#3830C22semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C2×D4×C3⋊D3C22semidirect
25. C2×#3828C22semidirect
26. C22×C3×#67C22semidirect
27. C2×C3×#235C22semidirect
28. C22×C3×D12C22semidirect
29. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
32. C2×#3802C22semidirect
33. C2×D3×D12C22semidirect
34. C2×#3796C22semidirect
35. C2×#3795C22semidirect
36. C3×#953C22semidirect
37. C3×#940C22semidirect
38. C3×#940C22semidirect
39. C3×#940C22semidirect
40. C3×#940C22semidirect
41. C3×#938C22semidirect
42. C3×#936C22semidirect
43. C3×#926C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. #63983C22semidirect
46. #63981C22semidirect
47. #63980C22semidirect
48. #63979C22semidirect
49. #63978C22semidirect
50. #63977C22semidirect
51. #67⋊Dic3C22semidirect
52. #63971C22semidirect
53. #63958C22semidirect
54. #63952C22semidirect
55. #63916C22semidirect
56. #63911C22semidirect
57. #63911C22semidirect
58. C4×#626C22semidirect
59. #63894C22semidirect
60. C4×#624C22semidirect
61. #63874C22semidirect
62. #63866C22semidirect
63. #63864C22semidirect
64. #63860C22semidirect
65. #63860C22semidirect
66. #63844C22semidirect
76. #5805D3semidirect
77. C2×#940D3semidirect
115. #3828D4semidirect
166. C22×C3×D4C2×D3semidirect
167. C22×C3×D4C2×D3semidirect
172. C22×#67C2×D3semidirect
206. C2×#235C2×D3semidirect
208. C22×D12C2×D3semidirect
219. #953C2×D3semidirect
226. #940C2×D3semidirect
227. #940C2×D3semidirect
228. #940C2×D3semidirect
229. #940C2×D3semidirect
236. #938C2×D3semidirect
242. #936C2×D3semidirect
247. #926C2×D3semidirect
248. C2×C4×Dic3C2×D3semidirect
287. C2×C32×C4C2×D4semidirect
293. #638C2×D4semidirect
298. C4⋊(C3⋊D3)C2×D4semidirect
300. C4×C3⋊D3C2×D4semidirect
302. #634C2×D4semidirect
515. C3×Dic3H(5,𝔽2)semidirect
534. C22×D4D32semidirect
625. C2×C3×C4D3×D4semidirect
626. C2×C3×C4D3×D4semidirect
833. Dic3#1004semidirect
834. C32#3498semidirect
884. C2×C4#3811semidirect
935. C3#86195semidirect
936. C3#86316semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#643072
C3×#58052
C2×C3×#9402
#105955262
#105953092
#105953002
#105952972
#105951682
#105951672
#105951642
#105950422
#105950292
#105949542
#863163
#861953