Finite Group Databasebeta

← #11864125

Subgroups — #11864125

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×#64120C211yesmaximal, characteristic, complemented
3#10595282C211yesmaximal, characteristic, complemented
4C2×#63937C211yesmaximal, characteristic, complemented
5C3×#5158C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic, complemented
7#10591519C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591418C211yesmaximal, characteristic, complemented
12#10590968C211yesmaximal, characteristic, complemented
13#10590957C211yesmaximal, characteristic, complemented
14#10590951C211yesmaximal, characteristic, complemented
15#10590937C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#80003—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×#3811—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
31C2×#3795C2211yescharacteristic, complemented
32C2×D3×Dic6C2211yescharacteristic, complemented
33C2×C32×D8C2211yescharacteristic, complemented
34C2×#3754C2211yescharacteristic, complemented
35C2×#3753C2211yescharacteristic, complemented
36#64120—24no—
37C2×#3744C2211yescharacteristic, complemented
38C2×#3743C2211yescharacteristic, complemented
39C3×#938C2211yescharacteristic
40C3×#938C2211yescharacteristic, complemented
41C2×C3×#214C2211yescharacteristic, complemented
42C2×C3×#213C2211yescharacteristic, complemented
43#63974—21no—
44#63971—21no—
45#63971—21no—
46#63937—24no—
47#63909C2211yescharacteristic
48#63909C2211yescharacteristic, complemented
49#63900C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×#3712C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#914—31no—
68C2×#911—31no—
69C2×#911—31no—
70C2×#911—31no—
71C2×#911—61no—
72D3×#121—31no—
73D3×#121—31no—
74C3×#449—31no—
75C3×#447—31no—
76#5238—31no—
77#5217—31no—
78#5170—31no—
79#5158—31no—
80#5158D311yescharacteristic, complemented
81#5156D311yescharacteristic, complemented
82#5040—31no—
83#5037—31no—
84#4806—31no—
85#4803—31no—
86#4781—31no—
87#4781—31no—
88#4773—31no—
89#4771—31no—
90#4771—31no—
91#4771—31no—
92#4738—31no—
93#4734—31no—
94#4726—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#3830D414yescomplemented
106D4×C3⋊D3—22no—
107D4×C3⋊D3—22no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×#634C2311yescharacteristic
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C22×C3×Dic3—21no—
116C3×#237—22no—
117C3×#237—22no—
118C3×D3×D4—22no—
119C3×D3×D4—22no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124#3811—44no—
125D3×#67—28no—
126C2×#627—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#624—21no—
132C2×#624D411yescharacteristic
133#3805—28no—
134#3804—28no—
135C2×D3×Dic3—28no—
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#3796D414yescomplemented
145#3795—22no—
146#3795—22no—
147D3×Dic6—22no—
148D3×Dic6—22no—
149C32×D8—22no—
150C2×C32×C8C2311yescharacteristic
151#3754—22no—
152#3753—22no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3744—22no—
155#3743—22no—
156C3×#217—21no—
157C3×#217—21no—
158C3×#214—22no—
159C3×#213—22no—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163C2×C3×C3⋊C8C2311yescharacteristic
164#3724—21no—
165#3722—21no—
166#3722—21no—
167#3717—22no—
168#3714—22no—
169#3712—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C23×Dic3—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—61no—
185C2×#237—61no—
186C2×#237—64no—
187C2×#237—64no—
188C2×#237—61no—
189C2×#237C2×D311yescharacteristic, complemented
190C2×D3×D4—31no—
191C2×D3×D4—31no—
192C2×D3×D4—61no—
193C2×D3×D4—61no—
194C2×D3×D4—61no—
195C2×D3×D4—61no—
196C2×D3×D4C2×D311yescharacteristic, complemented
197C2×#235—31no—
198C2×#235—61no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C22×C4×D3—61no—
202C22×Dic6—31no—
203C2×C3×SD16—31no—
204C2×C3×D8—21no—
205C2×C3×D8—31no—
206C2×C3×D8C2×D311yescharacteristic, complemented
207C2×C3×D8C2×D311yescharacteristic, complemented
208C3×#121—31no—
209C3×#121—31no—
210C2×#215—31no—
211#939—61no—
212#939—61no—
213#938C2×D311yescharacteristic
214#938C2×D311yescharacteristic, complemented
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—61no—
218C2×#214C2×D311yescharacteristic, complemented
219C2×#213—31no—
220C2×#213—31no—
221C2×#213—31no—
222C2×#213—61no—
223C2×#213C2×D311yescharacteristic, complemented
224#930—31no—
225#930—31no—
226#914—64no—
227#911—64no—
228#911—64no—
229#911—64no—
230#911—68no—
231C2×D24—31no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—61no—
236C2×ΓL(1,𝔽25)—31no—
237C2×ΓL(1,𝔽25)—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)—61no—
241#895—31no—
242#895—31no—
243D3×C4⋊C4—31no—
244D3×C4⋊C4—31no—
245#884—61no—
246#884—61no—
247D3×C22⋊C4—61no—
248D3×C22⋊C4—61no—
249C3×#103—31no—
250C3×#102—31no—
251C3×#102—31no—
252C3×#102—31no—
253C3×C22⋊C8—31no—
254C3×C22⋊C8—31no—
255#835—31no—
256#832—31no—
257#832C2×D311yescharacteristic, complemented
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#816—31no—
267#816—31no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#810—31no—
271#810—31no—
272#809—31no—
273C23×C32—21no—
274C23×C32—21no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3—42no—
279C22×C3⋊D3C2×D411yescharacteristic
280C22×C3×D3—24no—
281C22×C3×D3—21no—
282C22×C3×D3—42no—
283C22×C3×D3—42no—
284C22×C3×D3C2×D411yescharacteristic
285C22×C3×D3C2×D411yescharacteristic
286C2×D32—22no—
287C2×D32—22no—
288C2×D32—41no—
289C32×D4—21no—
290C32×D4—21no—
291C32×D4—21no—
292C32×D4C2×D412yescomplemented
293C2×C32×C4C2411yescharacteristic
294#638—24no—
295#638—42no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—24no—
298C2×C3⋊Dic3C2×D411yescharacteristic
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301C4×C3⋊D3C2×D412yes—
302C4×C3⋊D3C2×D412yes—
303#634—21no—
304#634C2×D412yescomplemented
305C3×#67—24no—
306C3×#67—24no—
307C3×#67—42no—
308C3×#67—42no—
309C2×C3×Dic3—24no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3C2×D411yescharacteristic
314C2×C3×Dic3C2×D411yescharacteristic
315C3×D12—21no—
316C3×D12C2×D412yescomplemented
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#627—24no—
324#626—24no—
325#626—42no—
326#626—42no—
327#625—24no—
328#624—22no—
329#624—42no—
330D3×Dic3—24no—
331D3×Dic3—24no—
332D3×Dic3—24no—
333D3×Dic3—22no—
334D3×Dic3—22no—
335C32×C8—21no—
336C3⋊(C3⋊C8)—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C22×#41—91no—
340C2×AGL(1,ℤ/8)—91no—
341C2×AGL(1,ℤ/8)—91no—
342C2×#121—91no—
343#449—31no—
344#449—91no—
345#449—91no—
346#449—91no—
347#448—91no—
348#448—91no—
349#447—31no—
350#447—91no—
351#417—91no—
352#417—91no—
353#407—91no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—121no—
361C3×#41—62no—
362C3×#41—62no—
363C2×C3×Q8—31no—
364C2×C3×D4—21no—
365C2×C3×D4—21no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C2×C3×D4—62no—
369C2×C3×D4—61no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D311yescharacteristic
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—61no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—21no—
383C2×#67—21no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—68no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—121no—
395C2×#67—121no—
396C22×Dic3—21no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—68no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3—121no—
406#239—34no—
407#239—62no—
408D3×Q8—62no—
409D3×Q8—62no—
410#237—22no—
411#237—22no—
412#237—34no—
413#237—34no—
414#237—34no—
415#237—64no—
416#237—62no—
417#237—62no—
418#237—62no—
419#237—62no—
420#237—62no—
421#237—68no—
422#237—68no—
423#237—68no—
424#237—122no—
425D3×D4—22no—
426D3×D4—22no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—68no—
432D3×D4—64no—
433D3×D4—122no—
434D3×D4—124no—
435D3×D4—124no—
436#235—62no—
437#235—68no—
438#235—62no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—61no—
442C2×D12—61no—
443C2×D12—61no—
444C2×D12—61no—
445C2×D12C22×D311yescharacteristic
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—61no—
453C2×C4×D3—62no—
454C2×C4×D3—62no—
455C2×C4×D3—62no—
456C2×C4×D3—62no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—68no—
460C2×C4×D3—61no—
461C2×C4×D3—61no—
462C2×C4×D3—61no—
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—61no—
468C2×Dic6—62no—
469C2×Dic6—61no—
470C2×Dic6—61no—
471C2×Dic6—62no—
472C2×Dic6C22×D311yescharacteristic
473C3×SD16—62no—
474C3×D8—24no—
475C3×D8—22no—
476C3×D8—22no—
477C3×D8—62no—
478C2×C3×C8—21no—
479C2×C3×C8—31no—
480C2×C3×C8—31no—
481C2×C3×C8C22×D311yescharacteristic
482C2×C3×C8C22×D311yescharacteristic
483C3×C4⋊C4—31no—
484C3×C4⋊C4—31no—
485C3×C22⋊C4—61no—
486C3×C22⋊C4—61no—
487#217—21no—
488#217—21no—
489#215—62no—
490#214—22no—
491#214—62no—
492#214—62no—
493#214—64no—
494#213—22no—
495#213—62no—
496#213—64no—
497#213—62no—
498#213—62no—
499(C2×D3)⋊C4—61no—
500(C2×D3)⋊C4—61no—
501(C2×D3)⋊C4—61no—
502(C2×D3)⋊C4—61no—
503C4⋊Dic3C22×D311yescharacteristic
504C4⋊Dic3C22×D311yescharacteristic
505Dic3⋊C4—61no—
506Dic3⋊C4—61no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—31no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—62no—
514#204—62no—
515#204—64no—
516#204—62no—
517ΓL(1,𝔽25)—62no—
518ΓL(1,𝔽25)—62no—
519ΓL(1,𝔽25)—62no—
520ΓL(1,𝔽25)—62no—
521ΓL(1,𝔽25)—64no—
522C22×C32—22no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32C22×D411yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D3—41no—
532C2×C3⋊D3—41no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3—84no—
535C2×C3⋊D3#12012yes—
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—22no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—48no—
543C2×C3×D3—41no—
544C2×C3×D3—41no—
545C2×C3×D3AGL(1,ℤ/8)12yescomplemented
546D32—44no—
547C32×C4C22×D411yescharacteristic
548C32×C4C22×D411yescharacteristic
549C3⋊Dic3—22no—
550C3⋊Dic3#12012yes—
551C3×Dic3—21no—
552C3×Dic3—22no—
553C3×Dic3—21no—
554C3×Dic3—41no—
555C3×Dic3—41no—
556C2×#41—31no—
557C2×#41—91no—
558C2×#41—91no—
559C2×#41—91no—
560C2×#41—181no—
561C2×#41—181no—
562C2×#41—184no—
563C2×#41—184no—
564C22×Q8—91no—
565C22×D4—31no—
566C22×D4—91no—
567C22×D4—181no—
568C22×D4—181no—
569C23×C4—91no—
570C23×C4—181no—
571AGL(1,ℤ/8)—184no—
572AGL(1,ℤ/8)—184no—
573C2×SD16—31no—
574C2×SD16—91no—
575C2×SD16—91no—
576C2×SD16—91no—
577C2×D8—31no—
578C2×D8—91no—
579C2×D8—91no—
580C2×D8D3211yescharacteristic, complemented
581C2×M16—91no—
582C2×M16—91no—
583#121—31no—
584#121—31no—
585#121—91no—
586#121—91no—
587#121—181no—
588#121—181no—
589C2×C4⋊C4—91no—
590C2×C22⋊C4—181no—
591#103—31no—
592#103—91no—
593#103—91no—
594#103—91no—
595#102—31no—
596#102—31no—
597#102—31no—
598#102—91no—
599C22⋊C8—31no—
600C22⋊C8—31no—
601C22⋊C8—91no—
602C22⋊C8—91no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—31no—
608C23×C3—31no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—64no—
612C23×C3—61no—
613C23×C3—122no—
614C23×C3—122no—
615C22×D3—24no—
616C22×D3—21no—
617C22×D3—31no—
618C22×D3—31no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—61no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3—124no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—122no—
637C22×D3—122no—
638C22×D3—242no—
639C22×D3—242no—
640C22×D3D3×D411yescharacteristic
641C22×D3D3×D411yescharacteristic
642C3×Q8—32no—
643C3×Q8—61no—
644C3×D4—22no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—22no—
652C3×D4—32no—
653C3×D4—41no—
654C3×D4—41no—
655C3×D4—64no—
656C3×D4—64no—
657C3×D4—61no—
658C3×D4—122no—
659C3×D4—122no—
660C3×D4D3×D412yescomplemented
661C3×D4D3×D412yescomplemented
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—64no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675#67—24no—
676#67—24no—
677#67—42no—
678#67—42no—
679#67—64no—
680#67—64no—
681#67—64no—
682#67—64no—
683#67—64no—
684#67—124no—
685#67—122no—
686#67—122no—
687#67—122no—
688#67—122no—
689#67—124no—
690C2×Dic3—24no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—61no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—64no—
700C2×Dic3—64no—
701C2×Dic3—64no—
702C2×Dic3—64no—
703C2×Dic3—64no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—124no—
707C2×Dic3—121no—
708C2×Dic3D3×D411yescharacteristic
709C2×Dic3D3×D411yescharacteristic
710D12—21no—
711D12—62no—
712D12—64no—
713D12—61no—
714D12—61no—
715D12—61no—
716D12—61no—
717D12—121no—
718D12—122no—
719D12—122no—
720D12D3×D412yescomplemented
721C4×D3—21no—
722C4×D3—21no—
723C4×D3—21no—
724C4×D3—21no—
725C4×D3—32no—
726C4×D3—32no—
727C4×D3—32no—
728C4×D3—32no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—62no—
735C4×D3—64no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—122no—
739C4×D3—122no—
740Dic6—21no—
741Dic6—32no—
742Dic6—32no—
743Dic6—62no—
744Dic6—64no—
745Dic6—64no—
746Dic6—61no—
747Dic6—61no—
748Dic6—121no—
749Dic6D3×D412yescomplemented
750C3×C8—22no—
751C3×C8—21no—
752C3×C8—21no—
753C3×C8—61no—
754C3×C8—61no—
755C3⋊C8—21no—
756C3⋊C8—21no—
757C3⋊C8—62no—
758C3⋊C8—61no—
759C3⋊C8—61no—
760C2×C32—42no—
761C2×C32—81no—
762C2×C32C2×#12011yescharacteristic
763C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
764C2×C32#57511yescharacteristic
765C3⋊D3—22no—
766C3⋊D3—81no—
767C3×D3—22no—
768C3×D3—41no—
769C3×D3—42no—
770C24—61no—
771C24—91no—
772C24—181no—
773#41—62no—
774#41—62no—
775#41—94no—
776#41—94no—
777#41—182no—
778#41—182no—
779#41—188no—
780#41—182no—
781#41—182no—
782#41—188no—
783C2×Q8—31no—
784C2×Q8—91no—
785C2×Q8—181no—
786C2×Q8—182no—
787C2×Q8—182no—
788C2×D4—31no—
789C2×D4—61no—
790C2×D4—62no—
791C2×D4—61no—
792C2×D4—62no—
793C2×D4—61no—
794C2×D4—61no—
795C2×D4—91no—
796C2×D4—181no—
797C2×D4—181no—
798C2×D4—181no—
799C2×D4—182no—
800C2×D4—182no—
801C2×D4—181no—
802C2×D4—188no—
803C2×D4—181no—
804C2×D4—181no—
805C2×D4—364no—
806C2×D4C2×D3211yescharacteristic
807C2×D4C2×D3211yescharacteristic
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—61no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—181no—
816C22×C4—182no—
817C22×C4—182no—
818C22×C4—181no—
819C22×C4—181no—
820C22×C4—181no—
821C22×C4—188no—
822C22×C4—181no—
823SD16—62no—
824SD16—182no—
825SD16—182no—
826SD16—182no—
827D8—22no—
828D8—62no—
829D8—182no—
830D8—182no—
831M16—182no—
832M16—182no—
833C2×C8—31no—
834C2×C8—31no—
835C2×C8—91no—
836C2×C8C2×D3211yescharacteristic
837C4⋊C4—31no—
838C4⋊C4—31no—
839C4⋊C4—181no—
840C22⋊C4—61no—
841C22⋊C4—61no—
842C22⋊C4—181no—
843C22⋊C4—181no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—21no—
847C22×C3—32no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—62no—
865C22×C3—61no—
866C22×C3—81no—
867C22×C3—81no—
868C22×C3—81no—
869C22×C3—81no—
870C22×C3—128no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3C2×D3×D411yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C2×D3—21no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—22no—
881C2×D3—32no—
882C2×D3—32no—
883C2×D3—48no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—62no—
887C2×D3—61no—
888C2×D3—61no—
889C2×D3—61no—
890C2×D3—61no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—124no—
894C2×D3—124no—
895C2×D3—122no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—241no—
903C2×D3—241no—
904C2×D3—244no—
905C2×D3—244no—
906C2×D3—248no—
907C2×D3#91112yescomplemented
908C3×C4—21no—
909C3×C4—21no—
910C3×C4—61no—
911C3×C4—62no—
912C3×C4—61no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4C2×D3×D411yescharacteristic
916C3×C4C2×D3×D411yescharacteristic
917C3×C4C2×D3×D411yescharacteristic
918C3×C4C2×D3×D411yescharacteristic
919Dic3—22no—
920Dic3—21no—
921Dic3—21no—
922Dic3—32no—
923Dic3—32no—
924Dic3—41no—
925Dic3—41no—
926Dic3—62no—
927Dic3—62no—
928Dic3—62no—
929Dic3—122no—
930C32#300611yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—31no—
934C23—31no—
935C23—64no—
936C23—61no—
937C23—91no—
938C23—122no—
939C23—122no—
940C23—182no—
941C23—182no—
942C23—181no—
943C23—362no—
944C23—362no—
945C23—362no—
946C23—361no—
947Q8—32no—
948Q8—61no—
949Q8—92no—
950Q8—184no—
951Q8—181no—
952D4—21no—
953D4—21no—
954D4—21no—
955D4—32no—
956D4—64no—
957D4—64no—
958D4—61no—
959D4—122no—
960D4—122no—
961D4—184no—
962D4—184no—
963D4—184no—
964D4—181no—
965D4—181no—
966D4—362no—
967D4—362no—
968D4—362no—
969D4#381112yescomplemented
970C2×C4—31no—
971C2×C4—31no—
972C2×C4—64no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—91no—
981C2×C4—92no—
982C2×C4—92no—
983C2×C4—182no—
984C2×C4—182no—
985C2×C4—182no—
986C2×C4—184no—
987C2×C4—184no—
988C2×C4—184no—
989C2×C4—184no—
990C2×C4—181no—
991C2×C4—362no—
992C2×C4C22×D3211yescharacteristic
993C8—21no—
994C8—61no—
995C8—61no—
996C8—181no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—42no—
1001C2×C3—42no—
1002C2×C3—62no—
1003C2×C3—82no—
1004C2×C3—82no—
1005C2×C3—81no—
1006C2×C3—81no—
1007C2×C3—121no—
1008C2×C3—122no—
1009C2×C3D3×#12011yescharacteristic
1010C2×C3D3×#12011yescharacteristic
1011C2×C3C2×#91111yescharacteristic
1012C2×C3#576811yescharacteristic
1013C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1014C2×C3#577311yescharacteristic
1015D3—22no—
1016D3—42no—
1017D3—41no—
1018D3—62no—
1019D3—62no—
1020D3—122no—
1021D3—242no—
1022D3—241no—
1023D3—241no—
1024C22—22no—
1025C22—32no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—61no—
1032C22—61no—
1033C22—61no—
1034C22—61no—
1035C22—61no—
1036C22—62no—
1037C22—92no—
1038C22—128no—
1039C22—121no—
1040C22—121no—
1041C22—181no—
1042C22—181no—
1043C22—364no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22—724no—
1048C22D32×D411yescharacteristic
1049C4—61no—
1050C4—61no—
1051C4—62no—
1052C4—92no—
1053C4—121no—
1054C4—121no—
1055C4—182no—
1056C4D32×D411yescharacteristic
1057C4C2×#381111yescharacteristic
1058C3—21no—
1059C3#8000311yescharacteristic, complemented
1060C3#8008411yescharacteristic, complemented
1061C2—42no—
1062C2—62no—
1063C2—81no—
1064C2—121no—
1065C2—122no—
1066C2—182no—
1067C2—721no—
1068C2D3×#91111yescharacteristic
1069C2#1059472911yescharacteristic
1070C2#1059527811yescharacteristic
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×#64120C2semidirect
3. #10595282C2semidirect
4. C2×#63937C2semidirect
5. C3×#5158C2semidirect
6. C3×#5156C2semidirect
7. #10591519C2semidirect
8. #10591517C2semidirect
9. #10591452C2semidirect
10. #10591448C2semidirect
11. #10591418C2semidirect
12. #10590968C2semidirect
13. #10590957C2semidirect
14. #10590951C2semidirect
15. #10590937C2semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C2×C3×#237C22semidirect
21. C2×C3×D3×D4C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×C32×D8C22semidirect
34. C2×#3754C22semidirect
35. C2×#3753C22semidirect
37. C2×#3744C22semidirect
38. C2×#3743C22semidirect
40. C3×#938C22semidirect
41. C2×C3×#214C22semidirect
42. C2×C3×#213C22semidirect
48. #63909C22semidirect
49. #63900C22semidirect
50. C2×#3717C22semidirect
51. C2×#3714C22semidirect
52. C2×#3712C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
80. #5158D3semidirect
81. #5156D3semidirect
105. #3830D4semidirect
144. #3796D4semidirect
189. C2×#237C2×D3semidirect
196. C2×D3×D4C2×D3semidirect
206. C2×C3×D8C2×D3semidirect
207. C2×C3×D8C2×D3semidirect
214. #938C2×D3semidirect
218. C2×#214C2×D3semidirect
223. C2×#213C2×D3semidirect
257. #832C2×D3semidirect
258. #832C2×D3semidirect
261. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
292. C32×D4C2×D4semidirect
304. #634C2×D4semidirect
316. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
545. C2×C3×D3AGL(1,ℤ/8)semidirect
580. C2×D8D32semidirect
660. C3×D4D3×D4semidirect
661. C3×D4D3×D4semidirect
720. D12D3×D4semidirect
749. Dic6D3×D4semidirect
907. C2×D3#911semidirect
930. C32#3006semidirect
969. D4#3811semidirect
1059. C3#80003semidirect
1060. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#641202
#105952822
C2×#639372
C3×#51582
C3×#51562
#105915192
#105915172
#105914522
#105914482
#105914182
#105909682
#105909572
#105909512
#105909372
#800843
#800033