Finite Group Databasebeta

← #11905982

Subgroups — #11905982

Order 1152.

3663 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3#10595996C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5522C211yesmaximal, characteristic, complemented
6#10595029C211yesmaximal, characteristic, complemented
7C2×#63911C211yesmaximal, characteristic, complemented
8#10594621C214yesmaximal, complemented
9#10594524C214yesmaximal, complemented
10#10594277C218yesmaximal, complemented
11#10594001C212yesmaximal, complemented
12#10594000C212yesmaximal, complemented
13D3×#874C212yesmaximal, complemented
14#10593969C212yesmaximal, complemented
15#86316—31nomaximal
16#85846—31nomaximal
17C2×#3828C2211yescharacteristic, complemented
18C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×#3811C2214yescomplemented
23C2×D3×#67C2214yescomplemented
24C22×#626C2214yescomplemented
25#64308—28no—
26#64307—28no—
27C2×#3802C2212yescomplemented
28C2×D3×D12C2212yescomplemented
29C2×D3×D12C2212yescomplemented
30C2×D3×D12C2212yescomplemented
31C2×D3×D12C2218yescomplemented
32C2×#3799C2212yescomplemented
33C2×#3799C2212yescomplemented
34C2×#3796C2212yescomplemented
35C2×#3795C2212yescomplemented
36C32×#117C2211yescharacteristic, complemented
37#64104C2214yescomplemented
38#64091C2214yescomplemented
39#64084C2212yescomplemented
40#64083C2212yescomplemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×#895C2214yescomplemented
43C3×#893C2212yescomplemented
44C3×#887C2212yescomplemented
45C3×#882C2214yescomplemented
46C3×#67⋊C4C2214yescomplemented
47C3×#875C2212yescomplemented
48C3×#874C2212yescomplemented
49C3×#872C2212yescomplemented
50C3×C42×D3C2212yescomplemented
51#63978C2214yescomplemented
52#63923C2218yescomplemented
53#63922C2218yescomplemented
54#63911C2214yescomplemented
55#63911C2212yescomplemented
56#63911C2212yescomplemented
57#63911C2211yescharacteristic, complemented
58#63911C2218yescomplemented
59#63910C2218yescomplemented
60#63906C2218yescomplemented
61C4×#626C2214yescomplemented
62#63886C2218yescomplemented
63#63880C2218yescomplemented
64#63866C2211yescharacteristic, complemented
65#63864C2211yescharacteristic, complemented
66#63860C2211yescharacteristic, complemented
67C2×#1009—31no—
68C2×#1009—31no—
69C2×#1009—31no—
70C2×#1004—31no—
71C3×#535—31no—
72C3×C4×#41—31no—
73#5832—31no—
74C2×#940—31no—
75#5715—32no—
76D3×#127—32no—
77#5674—32no—
78#5668—32no—
79#5609—34no—
80#5599—34no—
81#5590—38no—
82#5577—34no—
83D4×D12—34no—
84D4×D12—38no—
85#5525—31no—
86#5525—31no—
87#5525—32no—
88#5525—32no—
89#5525—61no—
90#5525D311yescharacteristic, complemented
91#5522D311yescharacteristic, complemented
92#5477—31no—
93#5477—32no—
94C2×#874—31no—
95C2×#874—32no—
96C23×C3⋊D3C2312yes—
97C23×C3×D3C2312yes—
98C22×D32C2314yes—
99C22×D32C2314yes—
100C22×C32×C4C2311yescharacteristic
101C2×#638C2312yes—
102#3828—24no—
103C2×C4⋊(C3⋊D3)—24no—
104C2×C4⋊(C3⋊D3)C2312yes—
105C2×C4⋊(C3⋊D3)C2312yes—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2318yes—
108C2×C4×C3⋊D3C2312yes—
109C2×#634C2311yescharacteristic
110C2×C3×#67C2312yes—
111C2×C3×#67C2312yes—
112C22×C3×Dic3C2312yes—
113C3×#235—24no—
114C3×#235D418yescomplemented
115C2×C3×D12—24no—
116C2×C3×D12C2312yes—
117C2×C3×D12C2312yes—
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2318yes—
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6C2311yescharacteristic
125C2×C3×Dic6C2311yescharacteristic
126#3811—216no—
127D3×#67—216no—
128C2×#626—48no—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#626C2318yes—
134C2×#626C2318yes—
135C2×#625C2314yes—
136C2×#624C2314yes—
137C2×D3×Dic3C2314yes—
138#3802—28no—
139D3×D12—28no—
140D3×D12—28no—
141D3×D12—28no—
142D3×D12—416no—
143#3799—28no—
144#3799—28no—
145#3796—28no—
146#3795—28no—
147C32×C4⋊C4C2312yes—
148C32×C22⋊C4C2312yes—
149C32×C42C2312yes—
150#3752C2318yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2318yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2314yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2311yescharacteristic
157C3×C4×Dic3C2311yescharacteristic
158Dic3⋊Dic3C2314yes—
159#3722C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161#3498—91noSylow
162C2×C3×#41—31no—
163C2×C3×#41—31no—
164C22×C3×D4—31no—
165C22×#67—34no—
166C22×#67—34no—
167#1009—68no—
168#1009—68no—
169#1009—68no—
170C2×#239—32no—
171C2×#239—32no—
172C2×#239—32no—
173#1004—68no—
174C2×#237—32no—
175C2×#237—32no—
176C2×D3×D4—34no—
177C2×D3×D4—34no—
178C2×D3×D4—34no—
179C2×D3×D4—32no—
180C2×D3×D4—32no—
181C2×D3×D4—32no—
182C2×D3×D4—32no—
183C2×D3×D4—32no—
184C2×D3×D4—38no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—32no—
188C2×#235—32no—
189C2×#235—32no—
190C2×#235—61no—
191C2×#235C2×D311yescharacteristic
192C2×#235C2×D311yescharacteristic, complemented
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—34no—
196C22×D12—32no—
197C22×D12—32no—
198C22×D12—32no—
199C22×D12—38no—
200C22×D12—61no—
201C22×D12C2×D311yescharacteristic, complemented
202C3×#127—32no—
203C3×#124—32no—
204C3×#121—34no—
205C3×#120—34no—
206C3×C4×Q8—32no—
207C3×C4×D4—32no—
208C3×C4×D4—34no—
209C3×#117—21no—
210C3×#117—32no—
211C3×#117C2×D311yescharacteristic, complemented
212C3×#117C2×D311yescharacteristic, complemented
213C2×C3×C42—31no—
214C2×C3×C42—32no—
215#947—31no—
216#944—31no—
217#940—32no—
218#940—32no—
219#940—31no—
220#940—38no—
221#940—34no—
222#939—34no—
223#939—38no—
224#937—38no—
225#936—31no—
226#930—34no—
227#930—38no—
228C4×#67—34no—
229C2×C4×Dic3C2×D311yescharacteristic, complemented
230#895—38no—
231#895—34no—
232#895—34no—
233#895—38no—
234#895—64no—
235#895C2×D314yescomplemented
236#893C2×D312yescomplemented
237#887C2×D312yescomplemented
238#884—38no—
239#884—38no—
240#882—38no—
241#882—34no—
242#882—34no—
243#882—38no—
244#882—38no—
245#882—64no—
246#882C2×D314yescomplemented
247#67⋊C4—38no—
248#67⋊C4C2×D314yescomplemented
249#875—31no—
250#875—31no—
251#875—32no—
252#875—32no—
253#875—62no—
254#875C2×D312yescomplemented
255#874—32no—
256#874—31no—
257#874—32no—
258#874—38no—
259#874—34no—
260#874—32no—
261#874—32no—
262#874—62no—
263#874C2×D312yescomplemented
264C4×D12—34no—
265C4×D12—38no—
266#872C2×D312yescomplemented
267C42×D3C2×D312yescomplemented
268#869—31no—
269C23×C32C2411yescharacteristic
270C22×C3⋊D3—24no—
271C22×C3⋊D3—44no—
272C22×C3⋊D3C2412yes—
273C22×C3⋊D3C2414yes—
274C22×C3×D3—24no—
275C22×C3×D3—44no—
276C22×C3×D3C2412yes—
277C22×C3×D3C2414yes—
278C22×C3×D3C2412yes—
279C2×D32—28no—
280C2×D32—28no—
281C2×D32—48no—
282C2×D32—48no—
283C2×C32×C4C2×D414yescomplemented
284C2×C32×C4C2414yes—
285C2×C32×C4C2411yescharacteristic
286C2×C32×C4C2411yescharacteristic
287#638—24no—
288C2×C3⋊Dic3C2412yes—
289C4⋊(C3⋊D3)—24no—
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—22no—
292C4⋊(C3⋊D3)—48no—
293C4×C3⋊D3—24no—
294#634—22no—
295C3×#67—24no—
296C3×#67C2×D418yescomplemented
297C2×C3×Dic3—24no—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C3×D12—24no—
303C3×D12—24no—
304C3×D12—22no—
305C3×D12—48no—
306C3×D12C2×D414yescomplemented
307C3×C4×D3—24no—
308C3×C4×D3—28no—
309C3×C4×D3C2×D418yescomplemented
310C3×Dic6—22no—
311C3×Dic6C2×D414yescomplemented
312#626—28no—
313#626—28no—
314#626—28no—
315#626—28no—
316#626—216no—
317#626—48no—
318#625—28no—
319#624—28no—
320D3×Dic3—28no—
321C2×H(5,𝔽2)—91no—
322C2×H(5,𝔽2)—91no—
323#550—94no—
324D42—98no—
325D42—94no—
326#535—31no—
327#535—92no—
328#535—92no—
329#535—91no—
330#532—92no—
331#532—91no—
332C2×#127—92no—
333C2×#127—91no—
334C4×#41—31no—
335C24×C3—32no—
336C23×D3—32no—
337C23×D3—32no—
338C23×D3—34no—
339C23×D3—34no—
340C23×D3—34no—
341C23×D3—34no—
342C23×D3—62no—
343C23×D3C22×D312yes—
344C3×#41—38no—
345C3×#41—64no—
346C2×C3×Q8—31no—
347C2×C3×Q8—31no—
348C2×C3×D4—32no—
349C2×C3×D4—32no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—32no—
353C2×C3×D4—32no—
354C2×C3×D4—38no—
355C2×C3×D4—64no—
356C22×C3×C4—21no—
357C22×C3×C4—32no—
358C22×C3×C4—32no—
359C22×C3×C4—32no—
360C22×C3×C4—34no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—38no—
368C2×#67—34no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—38no—
373C2×#67—62no—
374C2×#67—616no—
375C2×#67—128no—
376C2×#67C22×D312yes—
377C2×#67C22×D312yes—
378C22×Dic3—34no—
379C22×Dic3C22×D312yes—
380#239—68no—
381#239—68no—
382#239—68no—
383#237—68no—
384#237—68no—
385D3×D4—68no—
386D3×D4—68no—
387D3×D4—616no—
388D3×D4—616no—
389D3×D4—616no—
390D3×D4—68no—
391D3×D4—68no—
392D3×D4—68no—
393D3×D4—1216no—
394#235—24no—
395#235—68no—
396#235—68no—
397#235—64no—
398#235—64no—
399#235—68no—
400#235—124no—
401#235D1218yescomplemented
402C2×D12—24no—
403C2×D12—34no—
404C2×D12—38no—
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—34no—
408C2×D12—32no—
409C2×D12—31no—
410C2×D12—32no—
411C2×D12—31no—
412C2×D12—32no—
413C2×D12—32no—
414C2×D12—38no—
415C2×D12—38no—
416C2×D12—38no—
417C2×D12—61no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—68no—
421C2×D12—68no—
422C2×D12—68no—
423C2×D12—64no—
424C2×D12—64no—
425C2×D12—68no—
426C2×D12—124no—
427C2×D12—1216no—
428C2×D12—128no—
429C2×D12C22×D312yes—
430C2×D12C22×D312yes—
431C2×D12C22×D311yescharacteristic
432C2×D12C22×D318yes—
433C2×D12C22×D311yescharacteristic
434C2×C4×D3—34no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—62no—
440C2×C4×D3C22×D314yes—
441C2×C4×D3C22×D312yes—
442C2×C4×D3C22×D312yes—
443C2×Dic6—31no—
444C2×Dic6—31no—
445C2×Dic6—61no—
446C2×Dic6C22×D311yescharacteristic
447C2×Dic6C22×D311yescharacteristic
448C3×C4⋊C4—22no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4C22×D312yes—
451C3×C4⋊C4C22×D312yes—
452C3×C22⋊C4—22no—
453C3×C22⋊C4—38no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4C22×D312yes—
456C3×C22⋊C4C22×D312yes—
457C3×C42—22no—
458C3×C42—31no—
459C3×C42—34no—
460C3×C42—32no—
461C3×C42—31no—
462C3×C42C22×D312yes—
463C3×C42C22×D312yes—
464#217—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—38no—
467(C2×D3)⋊C4—38no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—68no—
471(C2×D3)⋊C4C22×D314yes—
472(C2×D3)⋊C4C22×D318yes—
473C4⋊Dic3—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4C22×D314yes—
476C4×Dic3C22×D311yescharacteristic
477C4×Dic3C22×D314yes—
478C4×Dic3C22×D311yescharacteristic
479C4×Dic3C22×D312yes—
480C22×C32—22no—
481C22×C32C22×D412yes—
482C22×C32C2511yescharacteristic
483C2×C3⋊D3—24no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—28no—
486C2×C3⋊D3—24no—
487C2×C3⋊D3—84no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—22no—
491C2×C3×D3—28no—
492C2×C3×D3—24no—
493C2×C3×D3—84no—
494C2×C3×D3C22×D414yes—
495D32—88no—
496D32—88no—
497C32×C4—24no—
498C32×C4C22×D412yes—
499C32×C4C22×D412yes—
500C3⋊Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—22no—
503C3×Dic3C22×D414yes—
504C3×Dic3H(5,𝔽2)14yescomplemented
505H(5,𝔽2)—188no—
506H(5,𝔽2)—188no—
507C2×#41—31no—
508C2×#41—31no—
509C2×#41—92no—
510C2×#41—92no—
511C2×#41—92no—
512C2×#41—92no—
513C2×#41—91no—
514C22×D4—31no—
515C22×D4—92no—
516C22×D4—92no—
517C22×D4—92no—
518C22×D4—98no—
519C22×D4—94no—
520C22×D4—94no—
521C22×D4—92no—
522C22×D4—94no—
523C22×D4—91no—
524C4⋊Q8—91no—
525#127—32no—
526#127—92no—
527#127—91no—
528#127—92no—
529#127—94no—
530#127—98no—
531#127—92no—
532#124—32no—
533#124—91no—
534#124—91no—
535#124—92no—
536#121—34no—
537#121—98no—
538#121—98no—
539#121—98no—
540#121—94no—
541#121—94no—
542#120—34no—
543#120—98no—
544#120—98no—
545#120—94no—
546C4×Q8—32no—
547C4×D4—32no—
548C4×D4—34no—
549C4×D4—98no—
550C4×D4—94no—
551#117—32no—
552#117D3211yescharacteristic, complemented
553C2×C42—31no—
554C2×C42—32no—
555C23×C3—21no—
556C23×C3—32no—
557C23×C3—32no—
558C23×C3—34no—
559C23×C3—64no—
560C23×C3—124no—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C22×D3—24no—
564C22×D3—32no—
565C22×D3—34no—
566C22×D3—34no—
567C22×D3—32no—
568C22×D3—44no—
569C22×D3—64no—
570C22×D3—62no—
571C22×D3—68no—
572C22×D3—68no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—68no—
576C22×D3—68no—
577C22×D3—124no—
578C22×D3—128no—
579C22×D3—128no—
580C22×D3—128no—
581C22×D3—128no—
582C22×D3—124no—
583C22×D3—124no—
584C22×D3—244no—
585C22×D3C23×D312yes—
586C22×D3C23×D314yes—
587C22×D3C23×D312yes—
588C3×Q8—34no—
589C3×Q8—62no—
590C3×D4—38no—
591C3×D4—34no—
592C3×D4—64no—
593C3×D4—62no—
594C3×D4—64no—
595C3×D4—64no—
596C3×D4—128no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—24no—
600C2×C3×C4—24no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—38no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—68no—
607C2×C3×C4—64no—
608C2×C3×C4—64no—
609C2×C3×C4C2×D1214yescomplemented
610C2×C3×C4D3×D414yescomplemented
611C2×C3×C4C23×D314yes—
612C2×C3×C4C23×D314yes—
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D311yescharacteristic
616C2×C3×C4C23×D311yescharacteristic
617#67—24no—
618#67—68no—
619#67—68no—
620#67—64no—
621#67—64no—
622#67—68no—
623#67—68no—
624#67—68no—
625#67—68no—
626#67—616no—
627#67—124no—
628#67—128no—
629#67C2×D1218yescomplemented
630C2×Dic3—24no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—62no—
634C2×Dic3—68no—
635C2×Dic3C23×D312yes—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639D12—24no—
640D12—24no—
641D12—22no—
642D12—48no—
643D12—68no—
644D12—68no—
645D12—68no—
646D12—616no—
647D12—68no—
648D12—64no—
649D12—64no—
650D12—62no—
651D12—64no—
652D12—62no—
653D12—64no—
654D12—124no—
655D12—124no—
656D12—122no—
657D12—128no—
658D12—128no—
659D12—128no—
660D12—248no—
661D12C2×D1214yescomplemented
662C4×D3—24no—
663C4×D3—28no—
664C4×D3—68no—
665C4×D3—68no—
666C4×D3—64no—
667C4×D3—64no—
668C4×D3—68no—
669C4×D3—124no—
670C4×D3C2×D1218yescomplemented
671Dic6—22no—
672Dic6—62no—
673Dic6—62no—
674Dic6—122no—
675Dic6C2×D1214yescomplemented
676C2×C32—22no—
677C2×C32C23×D411yescharacteristic
678C2×C32C2×H(5,𝔽2)12yes—
679C3⋊D3—42no—
680C3⋊D3—44no—
681C3×D3—24no—
682C3×D3—42no—
683C3×D3—44no—
684C24—32no—
685C24—94no—
686C24—94no—
687C24—92no—
688#41—38no—
689#41—64no—
690#41—188no—
691#41—188no—
692#41—188no—
693#41—188no—
694#41—184no—
695C2×Q8—31no—
696C2×Q8—31no—
697C2×Q8—91no—
698C2×D4—32no—
699C2×D4—32no—
700C2×D4—31no—
701C2×D4—32no—
702C2×D4—32no—
703C2×D4—31no—
704C2×D4—38no—
705C2×D4—64no—
706C2×D4—98no—
707C2×D4—94no—
708C2×D4—94no—
709C2×D4—94no—
710C2×D4—94no—
711C2×D4—98no—
712C2×D4—94no—
713C2×D4—92no—
714C2×D4—92no—
715C2×D4—91no—
716C2×D4—92no—
717C2×D4—98no—
718C2×D4—188no—
719C2×D4—188no—
720C2×D4—188no—
721C2×D4—1816no—
722C2×D4—188no—
723C2×D4—1816no—
724C2×D4—184no—
725C2×D4—3616no—
726C2×D4—368no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—34no—
730C22×C4—32no—
731C22×C4—94no—
732C22×C4—94no—
733C22×C4—92no—
734C22×C4C2×D3211yescharacteristic
735C4⋊C4—34no—
736C4⋊C4—94no—
737C4⋊C4C2×D3212yes—
738C22⋊C4—34no—
739C22⋊C4—38no—
740C22⋊C4—94no—
741C22⋊C4—94no—
742C22⋊C4—98no—
743C22⋊C4C2×D3212yes—
744C42—31no—
745C42—31no—
746C42—34no—
747C42—32no—
748C42C2×D3212yes—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—21no—
753C22×C3—34no—
754C22×C3—42no—
755C22×C3—64no—
756C22×C3—64no—
757C22×C3—62no—
758C22×C3—68no—
759C22×C3—64no—
760C22×C3—244no—
761C22×C3C22×D1212yes—
762C22×C3C2×D3×D412yes—
763C22×C3C24×D311yescharacteristic
764C22×C3C24×D311yescharacteristic
765C2×D3—24no—
766C2×D3—22no—
767C2×D3—24no—
768C2×D3—24no—
769C2×D3—28no—
770C2×D3—64no—
771C2×D3—62no—
772C2×D3—64no—
773C2×D3—62no—
774C2×D3—64no—
775C2×D3—68no—
776C2×D3—64no—
777C2×D3—68no—
778C2×D3—84no—
779C2×D3—122no—
780C2×D3—124no—
781C2×D3—124no—
782C2×D3—128no—
783C2×D3—248no—
784C2×D3—248no—
785C2×D3—248no—
786C2×D3—248no—
787C2×D3—244no—
788C2×D3—244no—
789C2×D3—248no—
790C2×D3C22×D1214yes—
791C3×C4—24no—
792C3×C4—24no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—34no—
796C3×C4—34no—
797C3×C4—44no—
798C3×C4—62no—
799C3×C4—62no—
800C3×C4C22×D1212yes—
801C3×C4C22×D1212yes—
802C3×C4C2×D3×D412yes—
803C3×C4C2×D3×D412yes—
804Dic3—22no—
805Dic3—22no—
806Dic3—62no—
807Dic3—62no—
808Dic3—122no—
809Dic3C22×D1214yes—
810Dic3#100914yescomplemented
811C32#349811yescharacteristic, complemented, Sylow
812C23—32no—
813C23—34no—
814C23—32no—
815C23—64no—
816C23—92no—
817C23—94no—
818C23—124no—
819C23—188no—
820C23—188no—
821C23—184no—
822C23—364no—
823C23—368no—
824C23—368no—
825C23C22×D3211yescharacteristic
826Q8—34no—
827Q8—62no—
828Q8—182no—
829D4—38no—
830D4—34no—
831D4—64no—
832D4—64no—
833D4—64no—
834D4—62no—
835D4—128no—
836D4—188no—
837D4—188no—
838D4—188no—
839D4—1816no—
840D4—188no—
841D4—188no—
842D4—184no—
843D4—182no—
844D4—184no—
845D4—184no—
846D4—368no—
847D4—368no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—38no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—68no—
854C2×C4—64no—
855C2×C4—64no—
856C2×C4—92no—
857C2×C4—188no—
858C2×C4—188no—
859C2×C4—184no—
860C2×C4D3×D1214yescomplemented
861C2×C4C22×D3214yes—
862C2×C4C22×D3211yescharacteristic
863C2×C4C22×D3211yescharacteristic
864C2×C3—22no—
865C2×C3—22no—
866C2×C3—21no—
867C2×C3—22no—
868C2×C3—42no—
869C2×C3—64no—
870C2×C3—122no—
871C2×C3—124no—
872C2×C3C23×D1211yescharacteristic
873C2×C3C22×D3×D411yescharacteristic
874C2×C3C2×#100912yes—
875C2×C3D3×H(5,𝔽2)12yes—
876D3—24no—
877D3—44no—
878D3—42no—
879D3—122no—
880D3—124no—
881D3—124no—
882D3—122no—
883D3—244no—
884D3—242no—
885C22—22no—
886C22—34no—
887C22—64no—
888C22—62no—
889C22—64no—
890C22—64no—
891C22—68no—
892C22—184no—
893C22—182no—
894C22—184no—
895C22—188no—
896C22—244no—
897C22—724no—
898C22—728no—
899C22—728no—
900C22C2×D3×D1212yes—
901C22C23×D3211yescharacteristic
902C4—24no—
903C4—34no—
904C4—34no—
905C4—62no—
906C4—62no—
907C4—182no—
908C4C2×D3×D1212yes—
909C4C2×D3×D1212yes—
910C3—21no—
911C3#8584611yescharacteristic, complemented
912C3#8631611yescharacteristic, complemented
913C2—22no—
914C2—64no—
915C2—124no—
916C2—122no—
917C2—364no—
918C2—362no—
919C2C22×D3×D1211yescharacteristic
920C2D3×#100912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C2×#64307C2semidirect
3. #10595996C2semidirect
4. C3×#5525C2semidirect
5. C3×#5522C2semidirect
6. #10595029C2semidirect
7. C2×#63911C2semidirect
8. #10594621C2semidirect
9. #10594524C2semidirect
10. #10594277C2semidirect
11. #10594001C2semidirect
12. #10594000C2semidirect
13. D3×#874C2semidirect
14. #10593969C2semidirect
17. C2×#3828C22semidirect
18. C22×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×#235C22semidirect
21. C22×C3×D12C22semidirect
22. C2×#3811C22semidirect
23. C2×D3×#67C22semidirect
24. C22×#626C22semidirect
27. C2×#3802C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×D3×D12C22semidirect
31. C2×D3×D12C22semidirect
32. C2×#3799C22semidirect
33. C2×#3799C22semidirect
34. C2×#3796C22semidirect
35. C2×#3795C22semidirect
36. C32×#117C22semidirect
37. #64104C22semidirect
38. #64091C22semidirect
39. #64084C22semidirect
40. #64083C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C3×#895C22semidirect
43. C3×#893C22semidirect
44. C3×#887C22semidirect
45. C3×#882C22semidirect
46. C3×#67⋊C4C22semidirect
47. C3×#875C22semidirect
48. C3×#874C22semidirect
49. C3×#872C22semidirect
50. C3×C42×D3C22semidirect
51. #63978C22semidirect
52. #63923C22semidirect
53. #63922C22semidirect
54. #63911C22semidirect
55. #63911C22semidirect
56. #63911C22semidirect
57. #63911C22semidirect
58. #63911C22semidirect
59. #63910C22semidirect
60. #63906C22semidirect
61. C4×#626C22semidirect
62. #63886C22semidirect
63. #63880C22semidirect
64. #63866C22semidirect
65. #63864C22semidirect
66. #63860C22semidirect
90. #5525D3semidirect
91. #5522D3semidirect
114. C3×#235D4semidirect
192. C2×#235C2×D3semidirect
201. C22×D12C2×D3semidirect
211. C3×#117C2×D3semidirect
212. C3×#117C2×D3semidirect
229. C2×C4×Dic3C2×D3semidirect
235. #895C2×D3semidirect
236. #893C2×D3semidirect
237. #887C2×D3semidirect
246. #882C2×D3semidirect
248. #67⋊C4C2×D3semidirect
254. #875C2×D3semidirect
263. #874C2×D3semidirect
266. #872C2×D3semidirect
267. C42×D3C2×D3semidirect
283. C2×C32×C4C2×D4semidirect
296. C3×#67C2×D4semidirect
306. C3×D12C2×D4semidirect
309. C3×C4×D3C2×D4semidirect
311. C3×Dic6C2×D4semidirect
401. #235D12semidirect
504. C3×Dic3H(5,𝔽2)semidirect
552. #117D32semidirect
609. C2×C3×C4C2×D12semidirect
610. C2×C3×C4D3×D4semidirect
629. #67C2×D12semidirect
661. D12C2×D12semidirect
670. C4×D3C2×D12semidirect
675. Dic6C2×D12semidirect
810. Dic3#1009semidirect
811. C32#3498semidirect
860. C2×C4D3×D12semidirect
911. C3#85846semidirect
912. C3#86316semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C2×#643072
#105959962
C3×#55252
C3×#55222
#105950292
C2×#639112
#105946212
#105945242
#105942772
#105940012
#105940002
D3×#8742
#105939692
#863163
#858463