Finite Group Databasebeta

← #11864153

Subgroups — #11864153

Order 1152.

1691 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×#63932C211yesmaximal, characteristic, complemented
5#10592869C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591592C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591519C211yesmaximal, characteristic, complemented
11#10591516C211yesmaximal, characteristic, complemented
12#10590962C211yesmaximal, characteristic, complemented
13#10590945C211yesmaximal, characteristic, complemented
14#10590936C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#83946—31nomaximal
17#80084—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23#64319—24no—
24#64319—24no—
25C2×#3802—21no—
26C2×#3802C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3795—21no—
30C2×#3795—21no—
31C2×#3795C2211yescharacteristic
32C2×#3795C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34#64147C2211yescharacteristic
35C2×#3754C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C3×#938C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, 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#63932—24no—
47#63916C2211yescharacteristic
48#63908C2211yescharacteristic, complemented
49D3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×#938—31no—
69C2×#932—31no—
70C2×#914D311yescharacteristic, complemented
71C2×#911—31no—
72D3×#121—31no—
73C3×#449—31no—
74#5238—31no—
75#5232—31no—
76#5172—31no—
77#5172D311yescharacteristic, complemented
78#5170—31no—
79#5170—31no—
80#5170—31no—
81#5170—61no—
82#5158—31no—
83#5158—31no—
84#5156—31no—
85#5156—31no—
86#5156—31no—
87#5133—31no—
88#5126—31no—
89#5037—31no—
90#4806—31no—
91#4803—31no—
92#4773—31no—
93#4771—31no—
94#4734—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102Q8×C3⋊D3—22no—
103Q8×C3⋊D3—22no—
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C3×#239—22no—
111C3×#239—22no—
112C3×#239—22no—
113C3×#239D414yescomplemented
114C3×D3×D4—22no—
115C3×D3×D4—22no—
116C2×C3×D12—21no—
117C2×C3×D12—21no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125D3×#67—44no—
126C2×#626—21no—
127C2×#625—21no—
128C2×#625—21no—
129C2×#625—21no—
130C2×#625—21no—
131C2×#624D411yescharacteristic
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137#3802—28no—
138#3802—22no—
139#3802—22no—
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3795—28no—
144#3795—28no—
145#3795—22no—
146#3795—22no—
147#3795—22no—
148#3795D414yescomplemented
149C32×SD16—22no—
150C2×C32×C8C2311yescharacteristic
151#3757—21no—
152#3754—22no—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#215—22no—
157C3×#213—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#3716—22no—
168#3713—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173C22×C3×D4—31no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177D3×#41—64no—
178D3×#41—64no—
179C2×#239C2×D311yescharacteristic
180C2×#239C2×D311yescharacteristic, complemented
181C2×D3×Q8—31no—
182C2×D3×Q8—31no—
183C2×D3×Q8—61no—
184C2×#237—31no—
185C2×#237—31no—
186C2×#237—61no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic, complemented
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C2×#235—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×SD16C2×D311yescharacteristic, complemented
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×D8—31no—
208C2×C3×D8—31no—
209C2×C3×D8—31no—
210C2×C3×M16—31no—
211C3×#121—31no—
212C2×#217—61no—
213C2×#215C2×D311yescharacteristic, complemented
214#939—61no—
215#938—31no—
216#938—31no—
217#938—31no—
218#938—31no—
219#938—61no—
220#938—61no—
221#938—61no—
222#938C2×D311yescharacteristic, complemented
223C2×#214—31no—
224C2×#214—31no—
225C2×#214—31no—
226C2×#214—61no—
227#932—64no—
228C2×#213—31no—
229C2×#213—31no—
230C2×#213C2×D311yescharacteristic, complemented
231C2×#213C2×D311yescharacteristic, complemented
232#930—31no—
233C2×C4⋊Dic3—31no—
234C2×#208—31no—
235#914—24no—
236#911—64no—
237C2×D24C2×D311yescharacteristic, complemented
238C2×#204—31no—
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×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#835—61no—
251#835C2×D311yescharacteristic, complemented
252#832—31no—
253#832—31no—
254#832—31no—
255#830—31no—
256#821—31no—
257#821—31no—
258#821C2×D311yescharacteristic, complemented
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#816—31no—
267#816—31no—
268#816—31no—
269#816—61no—
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
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⋊Dic3—21no—
297C2×C3⋊Dic3C2×D411yescharacteristic
298C4×C3⋊D3—24no—
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301#634—24no—
302#634—21no—
303#634C2×D412yescomplemented
304C3×#67—42no—
305C3×#67—42no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—24no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D412yescomplemented
316C3×D12C2×D412yescomplemented
317C3×C4×D3—24no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—24no—
321C3×C4×D3C2×D412yes—
322C3×C4×D3C2×D412yes—
323#626—42no—
324#625—24no—
325#625—24no—
326#625—24no—
327#625—42no—
328#624—22no—
329D3×Dic3—24no—
330D3×Dic3—22no—
331D3×Dic3—22no—
332D3×Dic3—24no—
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—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
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—
361C3×#41—62no—
362C3×#41—62no—
363C2×C3×Q8—21no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
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—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—121no—
396C2×#67—124no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402#239—22no—
403#239—22no—
404#239—22no—
405#239#6714yescomplemented
406D3×Q8—62no—
407D3×Q8—62no—
408D3×Q8—62no—
409D3×Q8—62no—
410D3×Q8—122no—
411D3×Q8—122no—
412#237—34no—
413#237—62no—
414#237—62no—
415#237—68no—
416#237—68no—
417#237—62no—
418D3×D4—22no—
419D3×D4—22no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—68no—
423D3×D4—68no—
424D3×D4—62no—
425D3×D4—62no—
426D3×D4—124no—
427#235—34no—
428#235—62no—
429#235—62no—
430#235—68no—
431#235—68no—
432#235—62no—
433C2×D12—21no—
434C2×D12—21no—
435C2×D12—61no—
436C2×D12C22×D311yescharacteristic
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D311yescharacteristic
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3—31no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—61no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—68no—
451C2×C4×D3—68no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—62no—
457C2×C4×D3—62no—
458C2×C4×D3—61no—
459C2×C4×D3—121no—
460C2×C4×D3C22×D311yescharacteristic
461C2×C4×D3C22×D311yescharacteristic
462C2×Dic6—31no—
463C2×Dic6—31no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6—61no—
467C2×Dic6—121no—
468C3×SD16—22no—
469C3×SD16—22no—
470C3×SD16—42no—
471C3×SD16—62no—
472C3×D8—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#214—62no—
491#214—62no—
492#214—62no—
493#214—122no—
494#213—22no—
495#213—22no—
496#213—62no—
497#213—62no—
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—
513#204—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—21no—
522C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—84no—
538C2×C3×D3#12012yes—
539D32—44no—
540D32—48no—
541C32×C4—22no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
545C3⋊Dic3—22no—
546C3⋊Dic3—41no—
547C3×Dic3—21no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
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—91no—
569C2×SD16—91no—
570C2×SD16D3211yescharacteristic, complemented
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—31no—
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—91no—
587#103—91no—
588#103—91no—
589#102—31no—
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—61no—
605C23×C3—122no—
606C23×C3—122no—
607C23×C3—122no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—31no—
612C22×D3—31no—
613C22×D3—42no—
614C22×D3—42no—
615C22×D3—42no—
616C22×D3—61no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—64no—
621C22×D3—64no—
622C22×D3—62no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3D3×D411yescharacteristic
630C22×D3D3×D411yescharacteristic
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—22no—
634C3×Q8—41no—
635C3×Q8D3×D412yescomplemented
636C3×Q8C2×#6712yescomplemented
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—21no—
641C3×D4—32no—
642C3×D4—32no—
643C3×D4—41no—
644C3×D4—41no—
645C3×D4—64no—
646C3×D4—64no—
647C3×D4—61no—
648C3×D4—61no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—122no—
652C3×D4—122no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—31no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—41no—
661C2×C3×C4—64no—
662C2×C3×C4—64no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—42no—
669#67—42no—
670#67—64no—
671#67—64no—
672#67—64no—
673#67—64no—
674#67—64no—
675#67—64no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—122no—
680#67—122no—
681#67—242no—
682C2×Dic3—21no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—61no—
686C2×Dic3—62no—
687C2×Dic3—64no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—64no—
691C2×Dic3—62no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—122no—
697C2×Dic3D3×D411yescharacteristic
698C2×Dic3D3×D411yescharacteristic
699D12—24no—
700D12—24no—
701D12—21no—
702D12—21no—
703D12—21no—
704D12—21no—
705D12—122no—
706D12D3×D412yescomplemented
707D12C2×#6712yescomplemented
708C4×D3—24no—
709C4×D3—21no—
710C4×D3—21no—
711C4×D3—24no—
712C4×D3—62no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—62no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—62no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—62no—
724C4×D3—121no—
725C4×D3—121no—
726C4×D3—124no—
727C4×D3—122no—
728C4×D3D3×D412yes—
729C4×D3C2×#6712yes—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6—124no—
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—22no—
754C3×D3—22no—
755C3×D3—41no—
756C3×D3—42no—
757C3×D3—42no—
758C3×D3—81no—
759C24—61no—
760C24—91no—
761C24—181no—
762#41—34no—
763#41—62no—
764#41—62no—
765#41—62no—
766#41—94no—
767#41—182no—
768#41—182no—
769#41—182no—
770#41—188no—
771#41—188no—
772C2×Q8—91no—
773C2×Q8—181no—
774C2×Q8—182no—
775C2×Q8—182no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—62no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—181no—
787C2×D4—181no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—188no—
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—181no—
810C22×C4—188no—
811C22×C4—181no—
812SD16—22no—
813SD16—62no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—62no—
818D8—62no—
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—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—62no—
846C22×C3—61no—
847C22×C3—62no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—244no—
859C22×C3C2×D3×D411yescharacteristic
860C22×C3C2×D3×D411yescharacteristic
861C2×D3—21no—
862C2×D3—21no—
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—22no—
866C2×D3—21no—
867C2×D3—22no—
868C2×D3—32no—
869C2×D3—32no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—62no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—84no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—124no—
886C2×D3—124no—
887C2×D3—128no—
888C2×D3—128no—
889C2×D3#93712yes—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—32no—
895C3×C4—42no—
896C3×C4—61no—
897C3×C4—121no—
898C3×C4C2×D3×D411yescharacteristic
899C3×C4C2×D3×D411yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C22×#6711yescharacteristic
902Dic3—21no—
903Dic3—41no—
904Dic3—62no—
905Dic3—61no—
906Dic3—62no—
907Dic3—61no—
908Dic3—122no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—241no—
913Dic3#93712yes—
914C32#300611yescharacteristic, complemented, Sylow
915C23—21no—
916C23—31no—
917C23—31no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—91no—
922C23—122no—
923C23—122no—
924C23—122no—
925C23—182no—
926C23—182no—
927C23—184no—
928C23—361no—
929C23—362no—
930C23—362no—
931Q8—21no—
932Q8—92no—
933Q8—184no—
934Q8—181no—
935Q8D3×#6712yescomplemented
936D4—21no—
937D4—21no—
938D4—32no—
939D4—32no—
940D4—64no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—61no—
946D4—122no—
947D4—122no—
948D4—184no—
949D4—184no—
950D4—184no—
951D4—362no—
952D4—362no—
953D4—362no—
954C2×C4—21no—
955C2×C4—31no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—31no—
959C2×C4—64no—
960C2×C4—64no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—91no—
965C2×C4—184no—
966C2×C4—182no—
967C2×C4—182no—
968C2×C4—184no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—181no—
972C2×C4—181no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—362no—
976C2×C4C22×D3211yescharacteristic
977C8—21no—
978C8—61no—
979C8—61no—
980C8—181no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—62no—
985C2×C3—81no—
986C2×C3—81no—
987C2×C3—122no—
988C2×C3—121no—
989C2×C3—122no—
990C2×C3—161no—
991C2×C3—241no—
992C2×C3D3×#12011yescharacteristic
993C2×C3#576811yescharacteristic
994C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
995C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
996C2×C3#577311yescharacteristic
997C2×C3C2×#93711yescharacteristic
998D3—22no—
999D3—41no—
1000D3—42no—
1001D3—42no—
1002D3—62no—
1003D3—62no—
1004D3—81no—
1005D3—122no—
1006C22—32no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22—61no—
1014C22—62no—
1015C22—62no—
1016C22—61no—
1017C22—92no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—181no—
1026C22—181no—
1027C22—244no—
1028C22—364no—
1029C22—368no—
1030C22D32×D411yescharacteristic
1031C4—22no—
1032C4—32no—
1033C4—61no—
1034C4—121no—
1035C4—181no—
1036C4—182no—
1037C4—361no—
1038C4D32×D411yescharacteristic
1039C4C2×D3×#6711yescharacteristic
1040C3—21no—
1041C3#8008411yescharacteristic, complemented
1042C3#8394611yescharacteristic, complemented
1043C2—62no—
1044C2—81no—
1045C2—121no—
1046C2—122no—
1047C2—122no—
1048C2—182no—
1049C2—241no—
1050C2#1059474011yescharacteristic
1051C2#1059474511yescharacteristic
1052C2D3×#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×#64319C2semidirect
2. C2×C3×#914C2semidirect
3. D3×#938C2semidirect
4. C2×#63932C2semidirect
5. #10592869C2semidirect
6. C3×#5172C2semidirect
7. #10591592C2semidirect
8. #10591586C2semidirect
9. #10591550C2semidirect
10. #10591519C2semidirect
11. #10591516C2semidirect
12. #10590962C2semidirect
13. #10590945C2semidirect
14. #10590936C2semidirect
15. #10590670C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×C3×#239C22semidirect
21. C2×C3×D3×D4C22semidirect
26. C2×#3802C22semidirect
32. C2×#3795C22semidirect
33. C2×C32×SD16C22semidirect
35. C2×#3754C22semidirect
36. C2×C3×#215C22semidirect
37. C3×#938C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
41. C2×C3×D24C22semidirect
42. C2×C3×ΓL(1,𝔽25)C22semidirect
48. #63908C22semidirect
49. D3×C4⋊Dic3C22semidirect
50. C2×#3716C22semidirect
51. C2×#3713C22semidirect
52. C2×#3711C22semidirect
53. #63662C22semidirect
54. #63647C22semidirect
55. #63643C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#914D3semidirect
77. #5172D3semidirect
113. C3×#239D4semidirect
148. #3795D4semidirect
180. C2×#239C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
205. C2×C3×SD16C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
213. C2×#215C2×D3semidirect
222. #938C2×D3semidirect
230. C2×#213C2×D3semidirect
231. C2×#213C2×D3semidirect
237. C2×D24C2×D3semidirect
240. C2×ΓL(1,𝔽25)C2×D3semidirect
251. #835C2×D3semidirect
258. #821C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
289. C32×Q8C2×D4semidirect
303. #634C2×D4semidirect
315. C3×D12C2×D4semidirect
316. C3×D12C2×D4semidirect
405. #239#67semidirect
522. C2×C3⋊D3AGL(1,ℤ/8)semidirect
570. C2×SD16D32semidirect
635. C3×Q8D3×D4semidirect
636. C3×Q8C2×#67semidirect
706. D12D3×D4semidirect
707. D12C2×#67semidirect
914. C32#3006semidirect
935. Q8D3×#67semidirect
1041. C3#80084semidirect
1042. C3#83946semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×C3×#9142
D3×#9382
C2×#639322
#105928692
C3×#51722
#105915922
#105915862
#105915502
#105915192
#105915162
#105909622
#105909452
#105909362
#105906702
#839463
#800843