Finite Group Databasebeta

← #11864126

Subgroups — #11864126

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×#237C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×#63932C211yesmaximal, characteristic, complemented
5#10592857C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic, complemented
7#10591520C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591457C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590964C211yesmaximal, characteristic, complemented
13#10590936C211yesmaximal, characteristic, complemented
14#10590822C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#83946—31nomaximal
17#80003—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23C2×D3×#67—21no—
24C2×#3805—21no—
25C2×#3804—21no—
26C22×D3×Dic3—21no—
27D3×#237—24no—
28D3×#237—24no—
29C2×C4×D32C2211yescharacteristic
30C2×#3796C2211yescharacteristic, complemented
31C2×#3795C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic, complemented
33C2×C32×D8C2211yescharacteristic, complemented
34#64147C2211yescharacteristic, complemented
35C2×#3754C2211yescharacteristic, complemented
36C3×#938C2211yescharacteristic
37C2×C3×#214C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#911—24no—
41C2×C3×#204C2211yescharacteristic, complemented
42C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43#63970—21no—
44D3×#217—21no—
45#63958—21no—
46#63932—24no—
47#63916C2211yescharacteristic, complemented
48#63908C2211yescharacteristic
49D3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×#938—31no—
69C2×#932—31no—
70C2×#911—31no—
71C2×#911D311yescharacteristic, complemented
72D3×#121—31no—
73C3×#447—31no—
74#5232—31no—
75#5217—31no—
76#5172—31no—
77#5172—31no—
78#5170—31no—
79#5170—31no—
80#5158—31no—
81#5158—31no—
82#5158—31no—
83#5158—31no—
84#5158—61no—
85#5156—31no—
86#5156D311yescharacteristic, complemented
87#5133—31no—
88#5126—31no—
89#5040—31no—
90#4781—31no—
91#4781—31no—
92#4771—31no—
93#4771—31no—
94#4738—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C22×D32D411yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102C2×#638—21no—
103C22×C3⋊Dic3—21no—
104#3830—22no—
105#3830—22no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237D414yescomplemented
115C3×D3×D4—22no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124D3×#67—28no—
125D3×#67—44no—
126C2×#627—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#625—21no—
130C2×#625—21no—
131C2×#624D411yescharacteristic
132#3805—28no—
133#3804—28no—
134C2×D3×Dic3—28no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137C2×D3×Dic3—21no—
138C2×D3×Dic3—21no—
139C2×D3×Dic3D411yescharacteristic
140C2×D3×Dic3D411yescharacteristic
141C4×D32—22no—
142C4×D32—22no—
143#3796—22no—
144#3796—22no—
145#3795—22no—
146#3795D414yescomplemented
147D3×Dic6—22no—
148D3×Dic6—22no—
149C32×D8—22no—
150C2×C32×C8C2311yescharacteristic
151#3757—21no—
152#3754—22no—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#214—22no—
157C3×#213—22no—
158C3×#213—22no—
159C3×C4⋊Dic3C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162C3×#204—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—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×#67—61no—
175C22×#67—61no—
176C23×Dic3—61no—
177D3×#41—64no—
178D3×#41—64no—
179C2×#239—31no—
180C2×D3×Q8—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237—61no—
190C2×#237—64no—
191C2×#237C2×D311yescharacteristic
192C2×D3×D4—61no—
193C2×D3×D4—61no—
194C2×D3×D4C2×D311yescharacteristic, complemented
195C2×D3×D4C2×D311yescharacteristic, complemented
196C2×#235—31no—
197C2×#235—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×Dic6—31no—
202C3×AGL(1,ℤ/8)—64no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×D8—21no—
206C2×C3×D8—31no—
207C2×C3×D8—31no—
208C2×C3×D8C2×D311yescharacteristic, complemented
209C2×C3×D8C2×D311yescharacteristic, complemented
210C2×C3×M16—31no—
211C3×#121—31no—
212C2×#217—61no—
213#939—61no—
214#938—31no—
215#938—31no—
216#938—31no—
217#938—31no—
218#938—61no—
219#938—61no—
220#938—61no—
221#938C2×D311yescharacteristic
222C2×#214—31no—
223C2×#214—31no—
224C2×#214—31no—
225C2×#214—61no—
226C2×#214C2×D311yescharacteristic, complemented
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#911—24no—
236#911—64no—
237C2×#204—31no—
238C2×#204C2×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×#102—31no—
246C3×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—61no—
254#832C2×D311yescharacteristic, complemented
255#830—31no—
256#821—31no—
257#821C2×D311yescharacteristic, complemented
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—61no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#816—31no—
267#816—31no—
268#816—31no—
269#816—61no—
270#810—31no—
271#810—31no—
272C23×C32—21no—
273C23×C32—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—24no—
276C22×C3×D3—21no—
277C22×C3×D3—21no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3—42no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—22no—
286C2×D32—22no—
287C2×D32—41no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4—21no—
291C32×D4C2×D412yescomplemented
292C2×C32×C4C2411yescharacteristic
293#638—24no—
294#638—42no—
295C2×C3⋊Dic3—24no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3C2×D411yescharacteristic
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—24no—
305C3×#67—42no—
306C3×#67—42no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—24no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D411yescharacteristic
311C2×C3×Dic3C2×D411yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D412yescomplemented
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—21no—
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#626—42no—
325#625—24no—
326#625—42no—
327#624—22no—
328D3×Dic3—24no—
329D3×Dic3—24no—
330D3×Dic3—22no—
331D3×Dic3—24no—
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—91no—
347#448—91no—
348#447—31no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—91no—
353C24×C3—61no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—21no—
357C23×D3—31no—
358C23×D3—31no—
359C3×#41—34no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—62no—
373C2×C3×D4—61no—
374C2×C3×D4C22×D311yescharacteristic
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C2×#67—21no—
382C2×#67—21no—
383C2×#67—21no—
384C2×#67—21no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—68no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—121no—
397C2×#67—121no—
398C2×#67—124no—
399C22×Dic3—21no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—68no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3—121no—
410#239—62no—
411#239—62no—
412D3×Q8—62no—
413D3×Q8—62no—
414#237—22no—
415#237—34no—
416#237—62no—
417#237—62no—
418#237—62no—
419#237—68no—
420#237—68no—
421#237—68no—
422#237—62no—
423#237—62no—
424#237—62no—
425#237—62no—
426#237—122no—
427#237—122no—
428#237#6714yescomplemented
429D3×D4—22no—
430D3×D4—22no—
431D3×D4—22no—
432D3×D4—22no—
433D3×D4—68no—
434D3×D4—124no—
435#235—34no—
436#235—62no—
437#235—68no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—61no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—68no—
454C2×C4×D3—61no—
455C2×C4×D3—62no—
456C2×C4×D3—62no—
457C2×C4×D3—61no—
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—61no—
463C2×Dic6—62no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6—62no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×SD16—62no—
470C3×D8—22no—
471C3×D8—22no—
472C3×D8—42no—
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#214—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
512#204—22no—
513#204—62no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32C22×D411yescharacteristic
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—48no—
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—
539C2×C3×D3AGL(1,ℤ/8)12yescomplemented
540D32—44no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—21no—
544C3⋊Dic3—22no—
545C3⋊Dic3—41no—
546C3×Dic3—22no—
547C3×Dic3—21no—
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—91no—
559C22×D4—31no—
560C22×D4—31no—
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×SD16—91no—
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—91no—
574C2×D8D3211yescharacteristic, complemented
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—91no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—31no—
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—21no—
600C23×C3—21no—
601C23×C3—31no—
602C23×C3—31no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—64no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—122no—
609C23×C3—122no—
610C23×C3—122no—
611C23×C3—122no—
612C23×C3—122no—
613C22×D3—24no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—31no—
617C22×D3—31no—
618C22×D3—42no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—42no—
622C22×D3—42no—
623C22×D3—61no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—22no—
641C3×D4—32no—
642C3×D4—41no—
643C3×D4—41no—
644C3×D4—41no—
645C3×D4—64no—
646C3×D4—64no—
647C3×D4—61no—
648C3×D4—61no—
649C3×D4—61no—
650C3×D4—122no—
651C3×D4—122no—
652C3×D4D3×D412yescomplemented
653C3×D4C2×#6712yescomplemented
654C2×C3×C4—21no—
655C2×C3×C4—31no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—31no—
659C2×C3×C4—64no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666#67—24no—
667#67—24no—
668#67—42no—
669#67—42no—
670#67—64no—
671#67—64no—
672#67—64no—
673#67—64no—
674#67—64no—
675#67—124no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—122no—
680#67—122no—
681#67—242no—
682C2×Dic3—21no—
683C2×Dic3—24no—
684C2×Dic3—21no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—61no—
688C2×Dic3—62no—
689C2×Dic3—64no—
690C2×Dic3—64no—
691C2×Dic3—64no—
692C2×Dic3—64no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—62no—
696C2×Dic3—64no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—121no—
700C2×Dic3—124no—
701C2×Dic3—121no—
702C2×Dic3—122no—
703C2×Dic3D3×D411yescharacteristic
704C2×Dic3D3×D411yescharacteristic
705D12—21no—
706D12—21no—
707D12—21no—
708D12—64no—
709D12—122no—
710D12D3×D412yescomplemented
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—62no—
714C4×D3—62no—
715C4×D3—64no—
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—122no—
727C4×D3D3×D412yes—
728C4×D3C2×#6712yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6C2×#6712yescomplemented
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—42no—
750C2×C32—81no—
751C2×C32C2×#12011yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C2×C32#57511yescharacteristic
754C3⋊D3—41no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—61no—
760C24—61no—
761C24—91no—
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—91no—
774C2×Q8—181no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—61no—
785C2×D4—62no—
786C2×D4—61no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—188no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—364no—
795C2×D4C2×D3211yescharacteristic
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—91no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—182no—
805C22×C4—182no—
806C22×C4—181no—
807C22×C4—181no—
808C22×C4—181no—
809C22×C4—188no—
810C22×C4—181no—
811C22×C4—181no—
812SD16—62no—
813SD16—62no—
814SD16—182no—
815SD16—182no—
816D8—22no—
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—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—32no—
837C22×C3—32no—
838C22×C3—42no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—62no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—128no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—244no—
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—22no—
873C2×D3—48no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—84no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—124no—
890C2×D3—124no—
891C2×D3#91112yescomplemented
892C2×D3#93712yes—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—32no—
896C3×C4—61no—
897C3×C4—62no—
898C3×C4—121no—
899C3×C4C2×D3×D411yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902C3×C4C22×#6711yescharacteristic
903Dic3—22no—
904Dic3—21no—
905Dic3—41no—
906Dic3—62no—
907Dic3—61no—
908Dic3—62no—
909Dic3—61no—
910Dic3—122no—
911Dic3—121no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#93712yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—21no—
919C23—31no—
920C23—31no—
921C23—64no—
922C23—61no—
923C23—61no—
924C23—91no—
925C23—122no—
926C23—122no—
927C23—122no—
928C23—122no—
929C23—122no—
930C23—182no—
931C23—182no—
932C23—361no—
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—21no—
939D4—21no—
940D4—21no—
941D4—32no—
942D4—64no—
943D4—64no—
944D4—61no—
945D4—61no—
946D4—61no—
947D4—122no—
948D4—122no—
949D4—184no—
950D4—184no—
951D4—184no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4D3×#6712yescomplemented
956C2×C4—31no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—31no—
960C2×C4—64no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—91no—
966C2×C4—182no—
967C2×C4—182no—
968C2×C4—184no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—184no—
972C2×C4—184no—
973C2×C4—181no—
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—42no—
987C2×C3—42no—
988C2×C3—62no—
989C2×C3—62no—
990C2×C3—82no—
991C2×C3—81no—
992C2×C3—81no—
993C2×C3—122no—
994C2×C3—161no—
995C2×C3—241no—
996C2×C3D3×#12011yescharacteristic
997C2×C3C2×#91111yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999C2×C3#577311yescharacteristic
1000C2×C3#577311yescharacteristic
1001C2×C3C2×#93711yescharacteristic
1002D3—22no—
1003D3—22no—
1004D3—42no—
1005D3—81no—
1006D3—121no—
1007D3—121no—
1008D3—241no—
1009C22—22no—
1010C22—32no—
1011C22—32no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—61no—
1018C22—61no—
1019C22—61no—
1020C22—61no—
1021C22—62no—
1022C22—128no—
1023C22—121no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—181no—
1029C22—181no—
1030C22—181no—
1031C22—244no—
1032C22—364no—
1033C22D32×D411yescharacteristic
1034C4—32no—
1035C4—61no—
1036C4—62no—
1037C4—121no—
1038C4—181no—
1039C4—182no—
1040C4—361no—
1041C4D32×D411yescharacteristic
1042C4C2×D3×#6711yescharacteristic
1043C3—21no—
1044C3#8000311yescharacteristic, complemented
1045C3#8394611yescharacteristic, complemented
1046C2—42no—
1047C2—62no—
1048C2—62no—
1049C2—81no—
1050C2—122no—
1051C2—241no—
1052C2—361no—
1053C2D3×#91111yescharacteristic
1054C2#1059472811yescharacteristic
1055C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×C3×#911C2semidirect
3. D3×#938C2semidirect
4. C2×#63932C2semidirect
5. #10592857C2semidirect
6. C3×#5156C2semidirect
7. #10591520C2semidirect
8. #10591517C2semidirect
9. #10591457C2semidirect
10. #10591447C2semidirect
11. #10591414C2semidirect
12. #10590964C2semidirect
13. #10590936C2semidirect
14. #10590822C2semidirect
15. #10590670C2semidirect
18. C2×#3830C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C2×C3×D3×D4C22semidirect
30. C2×#3796C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×C32×D8C22semidirect
34. #64147C22semidirect
35. C2×#3754C22semidirect
37. C2×C3×#214C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
41. C2×C3×#204C22semidirect
42. C2×C3×ΓL(1,𝔽25)C22semidirect
47. #63916C22semidirect
49. D3×C4⋊Dic3C22semidirect
50. C2×#3716C22semidirect
51. C2×#3713C22semidirect
52. C2×#3711C22semidirect
53. #63659C22semidirect
54. #63647C22semidirect
55. #63643C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63563C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#911D3semidirect
86. #5156D3semidirect
114. C3×#237D4semidirect
146. #3795D4semidirect
194. C2×D3×D4C2×D3semidirect
195. C2×D3×D4C2×D3semidirect
208. C2×C3×D8C2×D3semidirect
209. C2×C3×D8C2×D3semidirect
226. C2×#214C2×D3semidirect
230. C2×#213C2×D3semidirect
231. C2×#213C2×D3semidirect
238. C2×#204C2×D3semidirect
240. C2×ΓL(1,𝔽25)C2×D3semidirect
254. #832C2×D3semidirect
257. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
291. C32×D4C2×D4semidirect
302. #634C2×D4semidirect
315. C3×D12C2×D4semidirect
321. C3×Dic6C2×D4semidirect
428. #237#67semidirect
539. C2×C3×D3AGL(1,ℤ/8)semidirect
574. C2×D8D32semidirect
652. C3×D4D3×D4semidirect
653. C3×D4C2×#67semidirect
710. D12D3×D4semidirect
738. Dic6C2×#67semidirect
891. C2×D3#911semidirect
916. C32#3006semidirect
955. D4D3×#67semidirect
1044. C3#80003semidirect
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×#2372
C2×C3×#9112
D3×#9382
C2×#639322
#105928572
C3×#51562
#105915202
#105915172
#105914572
#105914472
#105914142
#105909642
#105909362
#105908222
#105906702
#839463
#800033