Finite Group Databasebeta

← #11864155

Subgroups — #11864155

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5170C211yesmaximal, characteristic, complemented
7#10591593C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591520C211yesmaximal, characteristic, complemented
11#10591515C211yesmaximal, characteristic, complemented
12#10590963C211yesmaximal, characteristic, complemented
13#10590944C211yesmaximal, characteristic, complemented
14#10590936C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83946—31nomaximal
17#80040—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23D3×#239—24no—
24D3×#239—24no—
25C2×D3×D12—21no—
26C2×D3×D12C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3799—21no—
30C2×#3799C2211yescharacteristic
31C2×#3796—21no—
32C2×#3796C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34#64147C2211yescharacteristic, complemented
35C2×#3753C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C3×#938C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#914—24no—
41C2×C3×D24C2211yescharacteristic, complemented
42C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43#63970—21no—
44D3×#217—21no—
45#63958—21no—
46#63934—24no—
47#63916C2211yescharacteristic, complemented
48#63908C2211yescharacteristic
49D3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, 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×D3×#41—31no—
66C22×#239—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×#938—31no—
69C2×#932—31no—
70C2×#914—31no—
71C2×#914D311yescharacteristic, complemented
72D3×#121—31no—
73C3×#448—31no—
74#5232—31no—
75#5227—31no—
76#5172—31no—
77#5172—31no—
78#5172—31no—
79#5172—31no—
80#5172—61no—
81#5170—31no—
82#5170D311yescharacteristic, complemented
83#5158—31no—
84#5158—31no—
85#5156—31no—
86#5156—31no—
87#5133—31no—
88#5126—31no—
89#5036—31no—
90#4810—31no—
91#4810—31no—
92#4803—31no—
93#4803—31no—
94#4732—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102#3832—22no—
103#3832—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C3×#239—22no—
111C3×#239D414yescomplemented
112C3×D3×Q8—22no—
113C3×D3×Q8—22no—
114C3×D3×D4—22no—
115C3×D3×D4—22no—
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6—21no—
124C2×C3×Dic6C2311yescharacteristic
125D3×#67—44no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#624—21no—
132C2×#624D411yescharacteristic
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137D3×D12—28no—
138D3×D12—22no—
139D3×D12—22no—
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3799—28no—
144#3799—22no—
145#3799D414yescomplemented
146#3796—28no—
147#3796—22no—
148#3796—22no—
149C32×SD16—22no—
150C2×C32×C8C2311yescharacteristic
151#3757—21no—
152#3753—22no—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#215—22no—
157C3×#214—22no—
158C3×#213—22no—
159C3×C4⋊Dic3C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162C3×D24—22no—
163C3×ΓL(1,𝔽25)—22no—
164Dic3⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166(C2×D3)⋊Dic3—21no—
167#3715—22no—
168#3714—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173C22×C3×D4—31no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—61no—
182C2×#239—61no—
183C2×#239—61no—
184C2×#239—64no—
185C2×#239—64no—
186C2×#239C2×D311yescharacteristic
187C2×D3×Q8C2×D311yescharacteristic, complemented
188C2×#237—31no—
189C2×#237—61no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic, complemented
194C2×#235—31no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3—61no—
202C3×AGL(1,ℤ/8)—64no—
203C2×C3×SD16—21no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×SD16C2×D311yescharacteristic, complemented
208C2×C3×D8—31no—
209C2×C3×D8—31no—
210C2×C3×M16—31no—
211C3×#121—31no—
212C2×#217—61no—
213C2×#215—31no—
214C2×#215C2×D311yescharacteristic, complemented
215#939—61no—
216#938—31no—
217#938—31no—
218#938—31no—
219#938—31no—
220#938—61no—
221#938—61no—
222#938—61no—
223#938C2×D311yescharacteristic
224C2×#214—31no—
225C2×#214C2×D311yescharacteristic, complemented
226#932—64no—
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—31no—
230C2×#213—61no—
231C2×#213C2×D311yescharacteristic, complemented
232#930—31no—
233C2×C4⋊Dic3—31no—
234C2×#208—31no—
235#914—24no—
236#914—64no—
237C2×D24—31no—
238C2×D24C2×D311yescharacteristic, complemented
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#103—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—61no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#832—31no—
255#830—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—61no—
267(C2×D3)⋊C8C2×D311yescharacteristic, complemented
268#816—31no—
269#816C2×D311yescharacteristic, complemented
270#809—31no—
271#809—31no—
272C23×C32—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—42no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—24no—
283C2×D32—22no—
284C2×D32—22no—
285C2×D32—41no—
286C2×D32—42no—
287C2×D32—42no—
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C32×D4—21no—
291C32×D4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2411yescharacteristic
294#638—42no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—24no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301C4×C3⋊D3—21no—
302C4×C3⋊D3—21no—
303C3×#67—42no—
304C3×#67—42no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yescomplemented
314C3×C4×D3—24no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—24no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—24no—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#626—24no—
324#626—24no—
325#626—24no—
326#626—42no—
327#625—42no—
328#624—22no—
329#624—24no—
330D3×Dic3—24no—
331D3×Dic3—22no—
332D3×Dic3—22no—
333D3×Dic3—42no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—31no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—91no—
342#449—91no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—31no—
347#448—91no—
348#447—91no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C3×#41—34no—
360C3×#41—62no—
361C2×C3×Q8—21no—
362C2×C3×Q8—31no—
363C2×C3×Q8—61no—
364C2×C3×Q8—62no—
365C2×C3×Q8—62no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—62no—
373C2×C3×D4—62no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C2×#67—21no—
383C2×#67—21no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—121no—
393C2×#67—124no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398#239—22no—
399#239—34no—
400#239—68no—
401#239—62no—
402#239—68no—
403#239—62no—
404#239—62no—
405#239—62no—
406#239—62no—
407#239—62no—
408#239—62no—
409#239—122no—
410#239—122no—
411#239#6714yescomplemented
412D3×Q8—22no—
413D3×Q8—22no—
414#237—62no—
415#237—68no—
416#237—62no—
417D3×D4—22no—
418D3×D4—22no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—68no—
422D3×D4—124no—
423#235—34no—
424#235—62no—
425#235—68no—
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—68no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—62no—
438C2×D12—61no—
439C2×D12—121no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—21no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—61no—
451C2×C4×D3—62no—
452C2×C4×D3—62no—
453C2×C4×D3—68no—
454C2×C4×D3—68no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3—61no—
463C2×C4×D3—121no—
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—22no—
469C3×SD16—22no—
470C3×SD16—42no—
471C3×SD16—62no—
472C3×SD16—62no—
473C3×D8—62no—
474C3×D8—62no—
475C3×M16—62no—
476C2×C3×C8—21no—
477C2×C3×C8—31no—
478C2×C3×C8—31no—
479C2×C3×C8C22×D311yescharacteristic
480C2×C3×C8C22×D311yescharacteristic
481C3×C4⋊C4—31no—
482C3×C22⋊C4—61no—
483#217—21no—
484#217—61no—
485#217—61no—
486#217—61no—
487#217—61no—
488#217—121no—
489#215—22no—
490#215—62no—
491#214—22no—
492#214—62no—
493#213—22no—
494#213—62no—
495#213—62no—
496#213—62no—
497#213—122no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—61no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—61no—
503C4⋊Dic3—61no—
504C4⋊Dic3C22×D311yescharacteristic
505Dic3⋊C4—61no—
506#208—62no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—31no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—22no—
513D24—62no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—21no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—21no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—84no—
537C2×C3×D3#12012yes—
538C2×C3×D3AGL(1,ℤ/8)12yescomplemented
539D32—44no—
540D32—48no—
541C32×C4—22no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
545C3⋊Dic3—41no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—31no—
559C22×D4—31no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565AGL(1,ℤ/8)—64no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—31no—
569C2×SD16—91no—
570C2×SD16D3211yescharacteristic, complemented
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—31no—
576C2×M16—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—31no—
587#103—91no—
588#103—91no—
589#102—91no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—122no—
605C23×C3—122no—
606C23×C3—122no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—42no—
612C22×D3—42no—
613C22×D3—42no—
614C22×D3—61no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—64no—
618C22×D3—64no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8D3×D412yescomplemented
640C3×Q8C2×#6712yescomplemented
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—32no—
646C3×D4—41no—
647C3×D4—41no—
648C3×D4—64no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—61no—
652C3×D4—122no—
653C3×D4—122no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—31no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—31no—
661C2×C3×C4—41no—
662C2×C3×C4—64no—
663C2×C3×C4—64no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670#67—42no—
671#67—42no—
672#67—64no—
673#67—64no—
674#67—64no—
675#67—122no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—122no—
680#67—242no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—61no—
686C2×Dic3—62no—
687C2×Dic3—64no—
688C2×Dic3—62no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—121no—
692C2×Dic3—122no—
693C2×Dic3D3×D411yescharacteristic
694C2×Dic3D3×D411yescharacteristic
695D12—24no—
696D12—21no—
697D12—21no—
698D12—21no—
699D12—32no—
700D12—32no—
701D12—62no—
702D12—64no—
703D12—64no—
704D12—64no—
705D12—64no—
706D12—64no—
707D12—61no—
708D12—61no—
709D12—121no—
710D12—124no—
711D12—122no—
712D12C2×#6712yescomplemented
713C4×D3—24no—
714C4×D3—21no—
715C4×D3—21no—
716C4×D3—24no—
717C4×D3—62no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—62no—
722C4×D3—64no—
723C4×D3—62no—
724C4×D3—61no—
725C4×D3—61no—
726C4×D3—61no—
727C4×D3—61no—
728C4×D3—62no—
729C4×D3—64no—
730C4×D3—121no—
731C4×D3—121no—
732C4×D3—124no—
733C4×D3—122no—
734C4×D3D3×D412yes—
735C4×D3C2×#6712yes—
736Dic6—24no—
737Dic6—21no—
738Dic6D3×D412yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—41no—
742C3×C8—61no—
743C3×C8—61no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—121no—
749C2×C32—81no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
752C2×C32#57511yescharacteristic
753C3⋊D3—41no—
754C3⋊D3—42no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—61no—
760C24—91no—
761C24—181no—
762#41—34no—
763#41—62no—
764#41—94no—
765#41—182no—
766#41—188no—
767#41—182no—
768#41—182no—
769#41—188no—
770#41—182no—
771#41—182no—
772C2×Q8—31no—
773C2×Q8—61no—
774C2×Q8—62no—
775C2×Q8—62no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—91no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—188no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—181no—
806C22×C4—182no—
807C22×C4—182no—
808C22×C4—181no—
809C22×C4—188no—
810C22×C4—181no—
811C22×C4—181no—
812SD16—22no—
813SD16—62no—
814SD16—62no—
815SD16—182no—
816D8—62no—
817D8—62no—
818D8—182no—
819D8—182no—
820M16—62no—
821M16—182no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8—91no—
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—91no—
828C4⋊C4—181no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—32no—
835C22×C3—32no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—62no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—244no—
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—22no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—62no—
873C2×D3—61no—
874C2×D3—62no—
875C2×D3—61no—
876C2×D3—84no—
877C2×D3—122no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—124no—
882C2×D3—124no—
883C2×D3—128no—
884C2×D3—128no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—241no—
890C2×D3—241no—
891C2×D3#91412yescomplemented
892C2×D3#93712yes—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—42no—
899C3×C4—61no—
900C3×C4—62no—
901C3×C4—121no—
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C22×#6711yescharacteristic
906Dic3—21no—
907Dic3—22no—
908Dic3—41no—
909Dic3—61no—
910Dic3—61no—
911Dic3—121no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#93712yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—61no—
921C23—61no—
922C23—91no—
923C23—122no—
924C23—122no—
925C23—122no—
926C23—182no—
927C23—182no—
928C23—184no—
929C23—181no—
930C23—362no—
931C23—361no—
932C23—362no—
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8D3×#6712yescomplemented
938D4—21no—
939D4—21no—
940D4—32no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—92no—
946D4—122no—
947D4—122no—
948D4—184no—
949D4—184no—
950D4—184no—
951D4—184no—
952D4—181no—
953D4—362no—
954D4—362no—
955D4—362no—
956C2×C4—21no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—31no—
961C2×C4—64no—
962C2×C4—64no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—91no—
968C2×C4—184no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—182no—
972C2×C4—182no—
973C2×C4—184no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—362no—
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—61no—
981C8—61no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—62no—
987C2×C3—62no—
988C2×C3—81no—
989C2×C3—81no—
990C2×C3—122no—
991C2×C3—161no—
992C2×C3—241no—
993C2×C3D3×#12011yescharacteristic
994C2×C3C2×#91411yescharacteristic
995C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
996C2×C3#577311yescharacteristic
997C2×C3#577711yescharacteristic
998C2×C3C2×#93711yescharacteristic
999D3—22no—
1000D3—22no—
1001D3—42no—
1002D3—81no—
1003D3—121no—
1004D3—122no—
1005D3—121no—
1006D3—122no—
1007D3—241no—
1008D3—242no—
1009C22—32no—
1010C22—32no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—62no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—181no—
1025C22—181no—
1026C22—182no—
1027C22—181no—
1028C22—244no—
1029C22—364no—
1030C22—368no—
1031C22—361no—
1032C22—361no—
1033C22D32×D411yescharacteristic
1034C4—22no—
1035C4—32no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—181no—
1040C4—361no—
1041C4D32×D411yescharacteristic
1042C4C2×D3×#6711yescharacteristic
1043C3—21no—
1044C3#8004011yescharacteristic, complemented
1045C3#8394611yescharacteristic, complemented
1046C2—62no—
1047C2—62no—
1048C2—81no—
1049C2—122no—
1050C2—241no—
1051C2—361no—
1052C2—362no—
1053C2D3×#91411yescharacteristic
1054C2#1059474411yescharacteristic
1055C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3006
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×D3×#239C2semidirect
2. C2×C3×#914C2semidirect
3. D3×#938C2semidirect
4. C2×#63934C2semidirect
5. #10592871C2semidirect
6. C3×#5170C2semidirect
7. #10591593C2semidirect
8. #10591583C2semidirect
9. #10591550C2semidirect
10. #10591520C2semidirect
11. #10591515C2semidirect
12. #10590963C2semidirect
13. #10590944C2semidirect
14. #10590936C2semidirect
15. #10590671C2semidirect
18. C2×#3832C22semidirect
20. C2×C3×D3×Q8C22semidirect
21. C2×C3×D3×D4C22semidirect
26. C2×D3×D12C22semidirect
32. C2×#3796C22semidirect
33. C2×C32×SD16C22semidirect
34. #64147C22semidirect
35. C2×#3753C22semidirect
36. C2×C3×#215C22semidirect
38. C2×C3×#214C22semidirect
39. C2×C3×#213C22semidirect
41. C2×C3×D24C22semidirect
42. C2×C3×ΓL(1,𝔽25)C22semidirect
47. #63916C22semidirect
49. D3×C4⋊Dic3C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. C2×#3711C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
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
82. #5170D3semidirect
111. C3×#239D4semidirect
145. #3799D4semidirect
187. C2×D3×Q8C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
207. C2×C3×SD16C2×D3semidirect
214. C2×#215C2×D3semidirect
225. C2×#214C2×D3semidirect
231. C2×#213C2×D3semidirect
238. C2×D24C2×D3semidirect
240. C2×ΓL(1,𝔽25)C2×D3semidirect
252. #835C2×D3semidirect
267. (C2×D3)⋊C8C2×D3semidirect
269. #816C2×D3semidirect
289. C32×Q8C2×D4semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
313. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
411. #239#67semidirect
538. C2×C3×D3AGL(1,ℤ/8)semidirect
570. C2×SD16D32semidirect
639. C3×Q8D3×D4semidirect
640. C3×Q8C2×#67semidirect
712. D12C2×#67semidirect
738. Dic6D3×D4semidirect
891. C2×D3#914semidirect
916. C32#3006semidirect
937. Q8D3×#67semidirect
1044. C3#80040semidirect
1045. C3#83946semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×C3×#9142
D3×#9382
C2×#639342
#105928712
C3×#51702
#105915932
#105915832
#105915502
#105915202
#105915152
#105909632
#105909442
#105909362
#105906712
#839463
#800403