Finite Group Databasebeta

← #11866344

Subgroups — #11866344

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2#10595347C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10595303C211yesmaximal, characteristic
5#10592862C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10591444C211yesmaximal, characteristic, complemented
10#10591438C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590801C211yesmaximal, characteristic, complemented
14#10590797C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#83969—31nomaximal
17#80385—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64149C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic, complemented
30C3×#915—24no—
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63983—21no—
35#63978—21no—
36#63978—21no—
37D3×#215—24no—
38#63864C2211yescharacteristic
39#63863C2211yescharacteristic
40#63855—21no—
41#63855C2211yescharacteristic
42#63843—21no—
43#63843C2211yescharacteristic, complemented
44Dic3×Dic6—21no—
45Dic3×Dic6C2211yescharacteristic, complemented
46#63841—21no—
47#63841C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63563C2211yescharacteristic
63C2×C3×#137—31no—
64#5830—31no—
65#5812—31no—
66C22×#215—31no—
67C2×#915D311yescharacteristic, complemented
68C2×D3×SD16—31no—
69#5715—31no—
70#5572—31no—
71C3×#460—31no—
72#5233—31no—
73#5185—31no—
74#5185—31no—
75#5185—31no—
76#5185—31no—
77#5166—31no—
78#5163—31no—
79#5163—31no—
80#5163—31no—
81#5163—31no—
82#5163—61no—
83#5163D311yescharacteristic, complemented
84#5131—31no—
85#5119—31no—
86#5075—31no—
87#5028—31no—
88#4845—31no—
89#4839—31no—
90#4772—31no—
91#4770—31no—
92#4767—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×D3×Q8—22no—
105C3×D3×Q8D414yescomplemented
106C3×#237—22no—
107C3×#237—22no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115D3×D12—22no—
116D3×D12—22no—
117C32×SD16—22no—
118C2×C32×C8C2311yescharacteristic
119#3755—22no—
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#216—22no—
126C3×#215—22no—
127C3×#214—22no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×Dic12—22no—
135C3×ΓL(1,𝔽25)—22no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139Dic3⋊Dic3D411yescharacteristic
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3D411yescharacteristic
146(C2×D3)⋊Dic3D411yescharacteristic
147Dic32—21no—
148Dic32—21no—
149Dic32—21no—
150#3717—22no—
151#3715—22no—
152D3×C3⋊C8—22no—
153#3043—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×#237C2×D311yescharacteristic
158C2×D3×D4—31no—
159C22×D12—31no—
160C3×#137—64no—
161C2×C3×Q16—31no—
162C2×C3×Q16—31no—
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16C2×D311yescharacteristic, complemented
167C2×C3×SD16C2×D311yescharacteristic, complemented
168C2×C3×M16—31no—
169C3×#127—31no—
170C3×C4×Q8—31no—
171#947—31no—
172#947—31no—
173Q8×Dic3—31no—
174Q8×Dic3—31no—
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—61no—
178Q8×Dic3—61no—
179Q8×Dic3—61no—
180Q8×Dic3C2×D311yescharacteristic, complemented
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187C2×#215—64no—
188C2×#215C2×D311yescharacteristic
189#940—31no—
190#940—31no—
191#940—61no—
192#940C2×D311yescharacteristic
193#939—61no—
194#939—61no—
195#937—61no—
196#937—61no—
197#937—61no—
198#937—61no—
199#936—31no—
200C2×#214—31no—
201C2×#214C2×D311yescharacteristic, complemented
202#930—61no—
203#930—61no—
204#926—31no—
205#926—31no—
206#926—61no—
207#926—61no—
208C22×C3⋊C8—31no—
209#915—24no—
210D3×SD16—64no—
211C2×Dic12C2×D311yescharacteristic, complemented
212C2×#204—31no—
213C2×ΓL(1,𝔽25)C2×D311yescharacteristic
214C2×D3×C8—31no—
215#892—31no—
216#892—61no—
217#887—31no—
218#887—61no—
219#875—31no—
220#872—31no—
221#872—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—42no—
256C2×D32—81no—
257C2×D32—81no—
258C32×Q8—21no—
259C32×Q8C2×D412yes—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264#638—81no—
265#638—81no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C3×#67—42no—
272C3×#67—81no—
273C3×#67—81no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×C4×D3—24no—
284C3×C4×D3C2×D412yes—
285C3×C4×D3#4112yes—
286C3×Dic6—21no—
287C3×Dic6—24no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6C2×D412yes—
291#626—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—31no—
297C22×SD16—91no—
298#535—91no—
299#519—91no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—31no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—34no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67—121no—
343C22×Dic3—21no—
344D3×Q8—22no—
345D3×Q8#6714yescomplemented
346#237—22no—
347#237—22no—
348D3×D4—62no—
349D3×D4—62no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—21no—
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C3×Q16—62no—
364C3×SD16—22no—
365C3×SD16—22no—
366C3×SD16—42no—
367C3×SD16—62no—
368C3×SD16—62no—
369C3×M16—62no—
370C2×C3×C8—21no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379#217—31no—
380#217—31no—
381#217—61no—
382#217—61no—
383#217—61no—
384#216—22no—
385#215—22no—
386#215—62no—
387#215—62no—
388#215—62no—
389#215—62no—
390#215—122no—
391#214—22no—
392#214—62no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—121no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—121no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438Dic12—22no—
439#204—62no—
440ΓL(1,𝔽25)—22no—
441D3×C8—62no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—22no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—41no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—91no—
471#137—64no—
472C2×Q16—31no—
473C2×Q16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—184no—
480C2×SD16D3211yescharacteristic, complemented
481C2×M16—31no—
482C22×C8—91no—
483#127—31no—
484#127—91no—
485#124—91no—
486#124—91no—
487#121—181no—
488#121—181no—
489#120—181no—
490#120—181no—
491C4×Q8—31no—
492C4×Q8—91no—
493C4×Q8—91no—
494C4×Q8—91no—
495C4×Q8—181no—
496C4×Q8—181no—
497#117—91no—
498#117—91no—
499#117—181no—
500#117—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—91no—
506#103—91no—
507#102—31no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C22×D3—21no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—121no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3D3×D411yescharacteristic
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—22no—
532C3×Q8—32no—
533C3×Q8—41no—
534C3×Q8—64no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8D3×D412yes—
539C3×Q8C2×#6712yes—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—41no—
545C3×D4—41no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—122no—
549C3×D4—241no—
550C3×D4—241no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—31no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—41no—
560C2×C3×C4—64no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—122no—
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—42no—
568#67—81no—
569#67—81no—
570#67—122no—
571#67—241no—
572#67—241no—
573#67—241no—
574#67—241no—
575#67—242no—
576#67—242no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—42no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3D3×D411yescharacteristic
591C2×Dic3D3×D411yescharacteristic
592C2×Dic3D3×D411yescharacteristic
593D12—21no—
594D12—21no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—121no—
600D12—121no—
601D12—122no—
602C4×D3—24no—
603C4×D3#23712yes—
604C4×D3C2×#6712yes—
605Dic6—21no—
606Dic6—24no—
607Dic6—21no—
608Dic6—21no—
609Dic6C2×#6712yes—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—61no—
614C3×C8—61no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—121no—
620C2×C32—81no—
621C2×C32C2×#12111yescharacteristic
622C2×C32#57711yescharacteristic
623C2×C32#57711yescharacteristic
624C3⋊D3—81no—
625C3×D3—22no—
626C3×D3—81no—
627C24—181no—
628#41—62no—
629#41—62no—
630C2×Q8—34no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8—61no—
634C2×Q8—62no—
635C2×Q8C2×D3211yescharacteristic
636C2×D4—31no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—91no—
641C2×D4—182no—
642C2×D4—182no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4C2×D3211yescharacteristic
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—61no—
650Q16—62no—
651Q16—62no—
652SD16—22no—
653SD16—62no—
654SD16—62no—
655SD16—182no—
656SD16—182no—
657SD16—182no—
658M16—62no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—91no—
662C2×C8—182no—
663C2×C8C2×D3211yescharacteristic
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C22⋊C4—91no—
673C22⋊C4—91no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—31no—
680C42—61no—
681C42—91no—
682C42—181no—
683C42—181no—
684C42—181no—
685C42—181no—
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—241no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3—244no—
719C2×D3—244no—
720C2×D3#93912yes—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—32no—
726C3×C4—42no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×#23711yescharacteristic
734C3×C4D3×#4111yescharacteristic
735C3×C4C22×#6711yescharacteristic
736Dic3—21no—
737Dic3—21no—
738Dic3—22no—
739Dic3—41no—
740Dic3—41no—
741Dic3—62no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—241no—
750Dic3#93912yes—
751C32#304311yescharacteristic, complemented, Sylow
752C23—21no—
753C23—31no—
754C23—61no—
755C23—181no—
756C23—362no—
757C23—721no—
758C23—721no—
759Q8—21no—
760Q8—32no—
761Q8—64no—
762Q8—61no—
763Q8—61no—
764Q8—61no—
765Q8D3×#6712yes—
766D4—21no—
767D4—21no—
768D4—61no—
769D4—61no—
770D4—122no—
771D4—181no—
772D4—181no—
773D4—241no—
774D4—241no—
775D4—362no—
776D4—721no—
777D4—721no—
778C2×C4—21no—
779C2×C4—31no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—64no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—122no—
791C2×C4—181no—
792C2×C4C22×D3211yescharacteristic
793C8—21no—
794C8—61no—
795C8—61no—
796C8—181no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—62no—
801C2×C3—81no—
802C2×C3—81no—
803C2×C3—161no—
804C2×C3—241no—
805C2×C3D3×#12111yescharacteristic
806C2×C3#576211yescharacteristic
807C2×C3#577511yescharacteristic
808C2×C3#577811yescharacteristic
809C2×C3#577811yescharacteristic
810C2×C3C2×#93911yescharacteristic
811D3—22no—
812D3—81no—
813D3—241no—
814D3—241no—
815D3—481no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—61no—
821C22—61no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22—724no—
829C22D32×D411yescharacteristic
830C4—22no—
831C4—32no—
832C4—61no—
833C4—61no—
834C4—62no—
835C4—121no—
836C4—121no—
837C4—181no—
838C4—181no—
839C4—361no—
840C4D3×#23711yescharacteristic
841C4C2×D3×#6711yescharacteristic
842C3—21no—
843C3#8038511yescharacteristic, complemented
844C3#8396911yescharacteristic, complemented
845C2—62no—
846C2—81no—
847C2—241no—
848C2—721no—
849C2#1059475111yescharacteristic
850C2#1059475411yescharacteristic
851C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595303C2
hypercenterC2×SD16D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. #10595347C2semidirect
3. C2×D3×#215C2semidirect
5. #10592862C2semidirect
6. C3×#5163C2semidirect
7. #10591612C2semidirect
8. #10591607C2semidirect
9. #10591444C2semidirect
10. #10591438C2semidirect
11. #10591420C2semidirect
12. #10590939C2semidirect
13. #10590801C2semidirect
14. #10590797C2semidirect
15. #10590695C2semidirect
21. C2×C32×SD16C22semidirect
22. Q8×C3⋊Dic3C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
29. C2×C3×#214C22semidirect
31. C2×C3×Dic12C22semidirect
43. #63843C22semidirect
45. Dic3×Dic6C22semidirect
51. #63659C22semidirect
53. #63641C22semidirect
54. C3×#832C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
67. C2×#915D3semidirect
83. #5163D3semidirect
105. C3×D3×Q8D4semidirect
166. C2×C3×SD16C2×D3semidirect
167. C2×C3×SD16C2×D3semidirect
180. Q8×Dic3C2×D3semidirect
181. C2×#216C2×D3semidirect
201. C2×#214C2×D3semidirect
211. C2×Dic12C2×D3semidirect
233. #832C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
345. D3×Q8#67semidirect
480. C2×SD16D32semidirect
751. C32#3043semidirect
843. C3#80385semidirect
844. C3#83969semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
#105953472
C2×D3×#2152
#105953032
#105928622
C3×#51632
#105916122
#105916072
#105914442
#105914382
#105914202
#105909392
#105908012
#105907972
#105906952
#839693
#803853