Finite Group Databasebeta

← #11864633

Subgroups — #11864633

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595398C211yesmaximal, characteristic, complemented
4C2×#63949C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590963C211yesmaximal, characteristic, complemented
13#10590955C211yesmaximal, characteristic, complemented
14#10590944C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83949—31nomaximal
17#80231—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×#3811—21no—
23C2×D3×#67—21no—
24C22×#626—21no—
25C2×#3804—21no—
26#64314—24no—
27#64314—24no—
28C2×D3×D12C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3798C2211yescharacteristic
31C2×#3796C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#914—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63949—24no—
43#63916C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic, complemented
47#63886—21no—
48#63885—21no—
49#63851—21no—
50C2×#3715C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68#5833—31no—
69C2×#950—31no—
70C2×#919—31no—
71C2×#914D311yescharacteristic, complemented
72#5629—31no—
73C3×#452—31no—
74#5238—31no—
75C2×#832—31no—
76#5187—31no—
77#5173—31no—
78#5173D311yescharacteristic, complemented
79#5169—31no—
80#5169—31no—
81#5169—31no—
82#5169—61no—
83#5158—31no—
84#5158—31no—
85#5156—31no—
86#5156—31no—
87#5133—31no—
88#5129—31no—
89#5046—31no—
90#4810—31no—
91#4803—31no—
92#4773—31no—
93D3×#102—31no—
94#4732—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#237—22no—
112C3×#237—22no—
113C3×D3×D4—22no—
114C3×D3×D4D414yescomplemented
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122#3811—28no—
123D3×#67—28no—
124C2×#627D411yescharacteristic
125C2×#626—28no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626D411yescharacteristic
131C2×#626D411yescharacteristic
132C2×#625—21no—
133C2×#625D411yescharacteristic
134C2×#624—21no—
135#3804—28no—
136C2×D3×Dic3—21no—
137C2×D3×Dic3—21no—
138D3×D12—22no—
139D3×D12—22no—
140#3799—22no—
141#3799D414yescomplemented
142#3798—22no—
143#3798—22no—
144#3796—22no—
145#3796—22no—
146C32×SD16—22no—
147C2×C32×C8C2311yescharacteristic
148#3755—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151#3750—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#216—22no—
154C3×#215—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×ΓL(1,𝔽25)—22no—
163Dic3⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3715—22no—
167#3714—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C22×#67—61no—
175#1009—64no—
176#1009—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239C2×D311yescharacteristic, complemented
180#1004—64no—
181#1004—64no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237C2×D311yescharacteristic
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C22×D12—31no—
198C22×D12—61no—
199C3×AGL(1,ℤ/8)—64no—
200C2×C3×Q16—31no—
201C2×C3×SD16—21no—
202C2×C3×SD16—31no—
203C2×C3×SD16C2×D311yescharacteristic, complemented
204C2×C3×SD16C2×D311yescharacteristic, complemented
205C2×C3×D8—31no—
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C3×C22⋊Q8—31no—
209#950—64no—
210#946—31no—
211#946—31no—
212#946—61no—
213#946C2×D311yescharacteristic, complemented
214C2×#216C2×D311yescharacteristic, complemented
215C2×#215—31no—
216C2×#215—31no—
217C2×#215—31no—
218C2×#215—61no—
219C2×#215C2×D311yescharacteristic, complemented
220#939—61no—
221#939—61no—
222#938—31no—
223#938—31no—
224C2×#214—31no—
225C2×#213—31no—
226C2×#213C2×D311yescharacteristic, complemented
227#930—31no—
228#930—61no—
229C2×C4⋊Dic3—31no—
230#924—61no—
231C22×C3⋊C8—31no—
232#919—64no—
233#914—24no—
234C2×D24—31no—
235C2×D24C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
237C2×D3×C8—31no—
238#896—61no—
239#895—31no—
240#895—61no—
241D3×C4⋊C4—31no—
242#884—61no—
243#884—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#832—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—61no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—61no—
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267#816—31no—
268#816C2×D311yescharacteristic, complemented
269#809—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—81no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—21no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3C2×D411yescharacteristic
283C22×C3×D3C2×D411yescharacteristic
284C2×D32—24no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8—21no—
289C32×D4—21no—
290C32×D4C2×D412yes—
291C2×C32×C4—21no—
292C2×C32×C4C2411yescharacteristic
293#638—24no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3C2×D411yescharacteristic
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)C2×D412yes—
298C4×C3⋊D3—21no—
299C4×C3⋊D3—21no—
300C3×#67—24no—
301C3×#67—24no—
302C2×C3×Dic3—24no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—42no—
311C3×D12C2×D412yes—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—42no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
319#627—22no—
320#626—24no—
321#626—24no—
322#626—22no—
323#626—24no—
324#626—22no—
325#626—81no—
326#625—22no—
327#625—81no—
328#624—24no—
329D3×Dic3—24no—
330D3×Dic3—81no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—31no—
337C2×#135—91no—
338#537—91no—
339#452—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—121no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—21no—
362C2×C3×Q8—31no—
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×D4—21no—
366C2×C3×D4—34no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D311yescharacteristic
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—61no—
378C22×C3×C4—61no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—68no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—68no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—121no—
396C22×Dic3—21no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399#239—22no—
400#239—22no—
401#239—34no—
402#239—62no—
403#239—62no—
404#239—62no—
405#237—22no—
406#237—22no—
407#237—62no—
408#237—68no—
409#237—62no—
410D3×D4—22no—
411D3×D4—62no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—68no—
416D3×D4—68no—
417D3×D4—68no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4—122no—
421D3×D4—122no—
422D3×D4#6714yescomplemented
423#235—34no—
424#235—62no—
425#235—62no—
426#235—62no—
427#235—68no—
428#235—62no—
429#235—62no—
430C2×D12—21no—
431C2×D12—31no—
432C2×D12—31no—
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—61no—
436C2×D12—62no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—68no—
440C2×D12—61no—
441C2×D12—62no—
442C2×D12—61no—
443C2×D12C22×D311yescharacteristic
444C2×D12C22×D311yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3C22×D311yescharacteristic
454C2×C4×D3C22×D311yescharacteristic
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6C22×D311yescharacteristic
458C3×Q16—62no—
459C3×SD16—22no—
460C3×SD16—22no—
461C3×SD16—42no—
462C3×SD16—62no—
463C3×D8—62no—
464C3×D8—62no—
465C3×M16—62no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8C22×D311yescharacteristic
470C2×C3×C8C22×D311yescharacteristic
471C3×C4⋊C4—31no—
472C3×C4⋊C4—61no—
473C3×C22⋊C4—61no—
474#217—61no—
475#217—61no—
476#216—22no—
477#215—22no—
478#215—62no—
479#215—62no—
480#215—62no—
481#215—122no—
482#214—62no—
483#213—22no—
484#213—62no—
485(C2×D3)⋊C4—21no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—121no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—61no—
494C4⋊Dic3—61no—
495C4⋊Dic3C22×D311yescharacteristic
496Dic3⋊C4—21no—
497Dic3⋊C4—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—61no—
500Dic3⋊C4—121no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—22no—
508D24—62no—
509ΓL(1,𝔽25)—22no—
510D3×C8—62no—
511C22×C32—22no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—84no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534C2×C3×D3#12012yes—
535D32—84no—
536C32×C4—41no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—21no—
540C3⋊Dic3—41no—
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—64no—
560#135—184no—
561C2×Q16—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16D3211yescharacteristic, complemented
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—91no—
569C2×M16—31no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—31no—
581#103—91no—
582#102—31no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—41no—
597C23×C3—64no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—241no—
601C23×C3—241no—
602C22×D3—21no—
603C22×D3—24no—
604C22×D3—21no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—81no—
615C22×D3—81no—
616C22×D3—121no—
617C22×D3—124no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—242no—
627C22×D3—242no—
628C22×D3D3×D411yescharacteristic
629C22×D3D3×D411yescharacteristic
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—32no—
635C3×Q8—41no—
636C3×Q8—41no—
637C3×Q8—61no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—22no—
641C3×D4—32no—
642C3×D4—41no—
643C3×D4—64no—
644C3×D4—64no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—61no—
648C3×D4—122no—
649C3×D4D3×D412yes—
650C3×D4C2×#6712yes—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—31no—
658C2×C3×C4—41no—
659C2×C3×C4—64no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—122no—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667#67—24no—
668#67—24no—
669#67—64no—
670#67—62no—
671#67—64no—
672#67—64no—
673#67—62no—
674#67—64no—
675#67—64no—
676#67—62no—
677#67—62no—
678#67—124no—
679#67—241no—
680#67—241no—
681#67—241no—
682C2×Dic3—24no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—61no—
688C2×Dic3—64no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—121no—
692C2×Dic3—241no—
693C2×Dic3D3×D411yescharacteristic
694C2×Dic3D3×D411yescharacteristic
695D12—21no—
696D12—21no—
697D12—21no—
698D12—32no—
699D12—32no—
700D12—42no—
701D12—62no—
702D12—62no—
703D12—64no—
704D12—64no—
705D12—62no—
706D12—64no—
707D12—61no—
708D12—61no—
709D12—121no—
710D12—241no—
711D12C2×#6712yes—
712C4×D3—21no—
713C4×D3—21no—
714C4×D3—42no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—64no—
722C4×D3—121no—
723C4×D3—121no—
724C4×D3—241no—
725C4×D3D3×D412yes—
726C4×D3C2×#6712yes—
727Dic6—21no—
728Dic6—62no—
729Dic6—62no—
730Dic6D3×D412yes—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—41no—
734C3×C8—61no—
735C3×C8—61no—
736C3⋊C8—21no—
737C3⋊C8—21no—
738C3⋊C8—61no—
739C3⋊C8—61no—
740C3⋊C8—121no—
741C2×C32—42no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—41no—
746C3⋊D3—42no—
747C3×D3—22no—
748C3×D3—41no—
749C3×D3—42no—
750C3×D3—81no—
751C24—61no—
752C24—181no—
753C24—181no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—94no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—188no—
763#41—182no—
764#41—182no—
765C2×Q8—31no—
766C2×Q8—91no—
767C2×Q8C2×D3211yescharacteristic
768C2×D4—34no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—61no—
772C2×D4—62no—
773C2×D4—61no—
774C2×D4—61no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—91no—
779C2×D4—181no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—181no—
783C2×D4—181no—
784C2×D4—188no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—188no—
789C2×D4—188no—
790C2×D4—182no—
791C2×D4—181no—
792C2×D4C2×D3211yescharacteristic
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—91no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4—181no—
801Q16—62no—
802SD16—22no—
803SD16—62no—
804SD16—182no—
805SD16—182no—
806D8—62no—
807D8—62no—
808D8—182no—
809M16—62no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—91no—
813C2×C8—182no—
814C2×C8C2×D3211yescharacteristic
815C4⋊C4—31no—
816C4⋊C4—61no—
817C4⋊C4—91no—
818C4⋊C4—181no—
819C4⋊C4—181no—
820C22⋊C4—61no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—32no—
828C22×C3—42no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—62no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—244no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—21no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—62no—
866C2×D3—61no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—84no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—122no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—241no—
878C2×D3—241no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—248no—
884C2×D3#93712yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—61no—
891C3×C4—62no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C22×#6711yescharacteristic
898Dic3—22no—
899Dic3—21no—
900Dic3—41no—
901Dic3—61no—
902Dic3—61no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—241no—
907Dic3#93712yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—21no—
910C23—31no—
911C23—31no—
912C23—64no—
913C23—61no—
914C23—61no—
915C23—91no—
916C23—184no—
917C23—184no—
918C23—181no—
919C23—241no—
920C23—241no—
921C23—721no—
922C23—721no—
923C23—721no—
924C23—721no—
925Q8—21no—
926Q8—21no—
927Q8—32no—
928Q8—61no—
929Q8—182no—
930D4—21no—
931D4—32no—
932D4—64no—
933D4—64no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—92no—
938D4—122no—
939D4—182no—
940D4—182no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—182no—
946D4—181no—
947D4—721no—
948D4—721no—
949D4D3×#6712yes—
950C2×C4—21no—
951C2×C4—31no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—31no—
955C2×C4—64no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—91no—
961C2×C4—122no—
962C2×C4—184no—
963C2×C4—184no—
964C2×C4—181no—
965C2×C4—181no—
966C2×C4—181no—
967C2×C4—721no—
968C2×C4C22×D3211yescharacteristic
969C8—21no—
970C8—61no—
971C8—61no—
972C8—181no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—42no—
978C2×C3—62no—
979C2×C3—82no—
980C2×C3—122no—
981C2×C3—121no—
982C2×C3—241no—
983C2×C3D3×#12011yescharacteristic
984C2×C3#576911yescharacteristic
985C2×C3#577411yescharacteristic
986C2×C3#577511yescharacteristic
987C2×C3#577811yescharacteristic
988C2×C3C2×#93711yescharacteristic
989D3—22no—
990D3—41no—
991D3—42no—
992D3—81no—
993D3—122no—
994D3—121no—
995D3—122no—
996D3—121no—
997D3—122no—
998D3—242no—
999C22—22no—
1000C22—32no—
1001C22—41no—
1002C22—41no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—62no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—181no—
1015C22—181no—
1016C22—182no—
1017C22—181no—
1018C22—244no—
1019C22—361no—
1020C22—361no—
1021C22—724no—
1022C22—724no—
1023C22D32×D411yescharacteristic
1024C4—32no—
1025C4—41no—
1026C4—61no—
1027C4—62no—
1028C4—121no—
1029C4—181no—
1030C4—361no—
1031C4D32×D411yescharacteristic
1032C4C2×D3×#6711yescharacteristic
1033C3—21no—
1034C3#8023111yescharacteristic, complemented
1035C3#8394911yescharacteristic, complemented
1036C2—42no—
1037C2—62no—
1038C2—121no—
1039C2—122no—
1040C2—241no—
1041C2—361no—
1042C2—362no—
1043C2#1059475411yescharacteristic
1044C2#1059475511yescharacteristic
1045C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3012
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×#64314C2semidirect
2. C2×C3×#914C2semidirect
3. #10595398C2semidirect
4. C2×#63949C2semidirect
5. #10592868C2semidirect
6. C3×#5173C2semidirect
7. #10591656C2semidirect
8. #10591651C2semidirect
9. #10591456C2semidirect
10. #10591450C2semidirect
11. D3×#832C2semidirect
12. #10590963C2semidirect
13. #10590955C2semidirect
14. #10590944C2semidirect
15. #10590671C2semidirect
19. C2×C3×#239C22semidirect
32. C2×C32×SD16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×D24C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
43. #63916C22semidirect
44. #63908C22semidirect
46. D3×C4⋊Dic3C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#914D3semidirect
78. #5173D3semidirect
114. C3×D3×D4D4semidirect
141. #3799D4semidirect
179. C2×#239C2×D3semidirect
203. C2×C3×SD16C2×D3semidirect
204. C2×C3×SD16C2×D3semidirect
213. #946C2×D3semidirect
214. C2×#216C2×D3semidirect
219. C2×#215C2×D3semidirect
226. C2×#213C2×D3semidirect
235. C2×D24C2×D3semidirect
236. C2×ΓL(1,𝔽25)C2×D3semidirect
253. #832C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
422. D3×D4#67semidirect
565. C2×SD16D32semidirect
908. C32#3012semidirect
1034. C3#80231semidirect
1035. C3#83949semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×C3×#9142
#105953982
C2×#639492
#105928682
C3×#51732
#105916562
#105916512
#105914562
#105914502
D3×#8322
#105909632
#105909552
#105909442
#105906712
#839493
#802313