Finite Group Databasebeta

← #11864154

Subgroups — #11864154

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×#239C211yesmaximal, characteristic, complemented
2C2×#64123C211yesmaximal, characteristic, complemented
3#10595282C211yesmaximal, characteristic, complemented
4C2×#63937C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6C3×#5170C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591554C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591515C211yesmaximal, characteristic, complemented
12#10590967C211yesmaximal, characteristic, complemented
13#10590957C211yesmaximal, characteristic, complemented
14#10590947C211yesmaximal, characteristic, complemented
15#10590937C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#80040—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22C2×#3811—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, complemented
31C2×#3796—21no—
32C2×#3796C2211yescharacteristic
33C2×C32×SD16C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C2×#3753C2211yescharacteristic, complemented
36#64123—24no—
37C2×#3745C2211yescharacteristic, 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×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#914—31no—
68C2×#914—31no—
69C2×#914—31no—
70C2×#914—61no—
71C2×#911—31no—
72D3×#121—31no—
73D3×#121—31no—
74C3×#449—31no—
75C3×#448—31no—
76#5238—31no—
77#5227—31no—
78#5172—31no—
79#5172D311yescharacteristic, complemented
80#5170D311yescharacteristic, complemented
81#5156—31no—
82#5037—31no—
83#5036—31no—
84#4810—31no—
85#4810—31no—
86#4806—31no—
87#4803—31no—
88#4803—31no—
89#4803—31no—
90#4773—31no—
91#4771—31no—
92#4734—31no—
93#4732—31no—
94#4726—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#3832D414yescomplemented
104D4×C3⋊D3—22no—
105D4×C3⋊D3—22no—
106C2×C4⋊(C3⋊D3)—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C3×#239—22no—
114C3×#239—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C2×C3×D12—21no—
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
125#3811—44no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626—21no—
131C2×#624—21no—
132C2×#624—21no—
133C2×#624D411yescharacteristic
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#3799—22no—
146#3796—28no—
147#3796—22no—
148#3796D414yescomplemented
149C32×SD16—22no—
150C2×C32×C8C2311yescharacteristic
151#3755—22no—
152#3753—22no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3745—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×Q8—31no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic, complemented
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4—61no—
194C2×D3×D4—61no—
195C2×#235—31no—
196C2×#235—61no—
197C22×D12—31no—
198C22×D12—61no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C22×C4×D3—61no—
202C22×C4×D3—61no—
203C2×C3×SD16—21no—
204C2×C3×SD16—31no—
205C2×C3×SD16C2×D311yescharacteristic, complemented
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×D8—31no—
208C3×#121—31no—
209C3×#121—31no—
210C2×#215—31no—
211C2×#215—31no—
212C2×#215—31no—
213C2×#215—61no—
214#939—61no—
215#939—61no—
216#938C2×D311yescharacteristic
217#938C2×D311yescharacteristic, complemented
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#914—64no—
228#914—64no—
229#914—68no—
230#911—64no—
231C2×D24—31no—
232C2×D24—31no—
233C2×D24—31no—
234C2×D24—61no—
235C2×#204—31no—
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×#103—31no—
251C3×#103—31no—
252C3×#102—31no—
253C3×C22⋊C8—31no—
254C3×C22⋊C8—31no—
255#835—31no—
256#835C2×D311yescharacteristic, complemented
257#835C2×D311yescharacteristic, complemented
258#832—31no—
259#830—31no—
260#830—31no—
261#821—31no—
262#821—31no—
263#821C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267(C2×D3)⋊C8C2×D311yescharacteristic, complemented
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
271#809—31no—
272#809—31no—
273C23×C32—21no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3—42no—
279C22×C3⋊D3C2×D411yescharacteristic
280C22×C3×D3—21no—
281C22×C3×D3C2×D411yescharacteristic
282C22×C3×D3C2×D411yescharacteristic
283C2×D32—24no—
284C2×D32—22no—
285C2×D32—22no—
286C2×D32—41no—
287C2×D32—42no—
288C2×D32—42no—
289C32×Q8—21no—
290C32×Q8C2×D412yescomplemented
291C32×D4—21no—
292C32×D4—21no—
293C2×C32×C4—21no—
294C2×C32×C4C2411yescharacteristic
295#638—42no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—24no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)C2×D412yescomplemented
302C4×C3⋊D3—24no—
303C4×C3⋊D3C2×D412yes—
304C4×C3⋊D3C2×D412yes—
305C3×#67—42no—
306C3×#67—42no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D411yescharacteristic
311C2×C3×Dic3C2×D411yescharacteristic
312C3×D12—24no—
313C3×D12—21no—
314C3×D12C2×D412yescomplemented
315C3×C4×D3—24no—
316C3×C4×D3—24no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×Dic6—24no—
322C3×Dic6—21no—
323C3×Dic6C2×D412yescomplemented
324#626—24no—
325#626—24no—
326#626—24no—
327#626—42no—
328#626—42no—
329#624—24no—
330#624—22no—
331#624—42no—
332D3×Dic3—22no—
333D3×Dic3—24no—
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—31no—
348#448—91no—
349#447—91no—
350#447—91no—
351#417—91no—
352#417—91no—
353#407—91no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—121no—
361C3×#41—62no—
362C3×#41—62no—
363C2×C3×Q8—21no—
364C2×C3×Q8—31no—
365C2×C3×Q8—61no—
366C2×C3×Q8—62no—
367C2×C3×Q8—62no—
368C2×C3×Q8C22×D311yescharacteristic
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—61no—
380C22×C3×C4—61no—
381C2×#67—21no—
382C2×#67—21no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—121no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—61no—
394#239—22no—
395#239—22no—
396#239—34no—
397#239—34no—
398#239—34no—
399#239—64no—
400#239—62no—
401#239—62no—
402#239—68no—
403#239—62no—
404#239—62no—
405#239—62no—
406#239—68no—
407#239—122no—
408D3×Q8—22no—
409D3×Q8—22no—
410#237—34no—
411#237—62no—
412#237—68no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—68no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4—64no—
421D3×D4—122no—
422D3×D4—124no—
423D3×D4—124no—
424#235—62no—
425#235—68no—
426#235—62no—
427C2×D12—21no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—68no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—62no—
442C2×D12—61no—
443C2×D12—61no—
444C2×D12—121no—
445C2×D12C22×D311yescharacteristic
446C2×C4×D3—21no—
447C2×C4×D3—21no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—61no—
455C2×C4×D3—62no—
456C2×C4×D3—62no—
457C2×C4×D3—62no—
458C2×C4×D3—62no—
459C2×C4×D3—68no—
460C2×C4×D3—68no—
461C2×C4×D3—61no—
462C2×C4×D3—61no—
463C2×C4×D3—61no—
464C2×C4×D3—61no—
465C2×C4×D3—61no—
466C2×C4×D3—61no—
467C2×C4×D3—61no—
468C2×C4×D3—121no—
469C2×C4×D3C22×D311yescharacteristic
470C2×C4×D3C22×D311yescharacteristic
471C2×Dic6—21no—
472C2×Dic6C22×D311yescharacteristic
473C3×SD16—24no—
474C3×SD16—22no—
475C3×SD16—22no—
476C3×SD16—62no—
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#215—64no—
491#215—62no—
492#215—62no—
493#214—22no—
494#213—22no—
495#213—62no—
496#213—62no—
497#213—62no—
498#213—64no—
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—
513D24—62no—
514D24—64no—
515D24—62no—
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—41no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32C22×D411yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3⋊D3—21no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—41no—
530C2×C3⋊D3—41no—
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—21no—
539C2×C3×D3—22no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—41no—
543C2×C3×D3—41no—
544C2×C3×D3AGL(1,ℤ/8)12yescomplemented
545D32—44no—
546D32—48no—
547C32×C4—22no—
548C32×C4C22×D411yescharacteristic
549C32×C4C22×D411yescharacteristic
550C3⋊Dic3#12012yes—
551C3×Dic3—21no—
552C3×Dic3—21no—
553C3×Dic3—22no—
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—31no—
565C22×D4—91no—
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×SD16D3211yescharacteristic, complemented
577C2×D8—31no—
578C2×D8—91no—
579C2×D8—91no—
580C2×D8—91no—
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—31no—
593#103—31no—
594#103—91no—
595#102—31no—
596#102—91no—
597#102—91no—
598#102—91no—
599C22⋊C8—31no—
600C22⋊C8—31no—
601C22⋊C8—91no—
602C22⋊C8—91no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—31no—
606C23×C3—31no—
607C23×C3—41no—
608C23×C3—61no—
609C22×D3—21no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—61no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—64no—
617C22×D3—64no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—62no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—124no—
633C22×D3—122no—
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—21no—
643C3×Q8—21no—
644C3×Q8—22no—
645C3×Q8—32no—
646C3×Q8—41no—
647C3×Q8—64no—
648C3×Q8—61no—
649C3×Q8D3×D412yescomplemented
650C3×Q8D3×D412yescomplemented
651C3×D4—22no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—32no—
657C3×D4—41no—
658C3×D4—64no—
659C3×D4—61no—
660C3×D4—122no—
661C3×D4—122no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—41no—
668C2×C3×C4—64no—
669C2×C3×C4—64no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679#67—42no—
680#67—42no—
681#67—64no—
682#67—64no—
683#67—64no—
684#67—122no—
685#67—122no—
686#67—122no—
687#67—122no—
688#67—124no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—61no—
695C2×Dic3—62no—
696C2×Dic3—64no—
697C2×Dic3—62no—
698C2×Dic3D3×D411yescharacteristic
699C2×Dic3D3×D411yescharacteristic
700D12—24no—
701D12—21no—
702D12—32no—
703D12—32no—
704D12—62no—
705D12—64no—
706D12—64no—
707D12—62no—
708D12—64no—
709D12—64no—
710D12—64no—
711D12—61no—
712D12—61no—
713D12—61no—
714D12—61no—
715D12—61no—
716D12—61no—
717D12—121no—
718D12—121no—
719D12—124no—
720D12—122no—
721D12—122no—
722D12D3×D412yescomplemented
723C4×D3—24no—
724C4×D3—24no—
725C4×D3—21no—
726C4×D3—21no—
727C4×D3—21no—
728C4×D3—21no—
729C4×D3—32no—
730C4×D3—32no—
731C4×D3—32no—
732C4×D3—32no—
733C4×D3—62no—
734C4×D3—62no—
735C4×D3—62no—
736C4×D3—62no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—64no—
741C4×D3—62no—
742C4×D3—62no—
743C4×D3—64no—
744C4×D3—124no—
745C4×D3—122no—
746C4×D3—122no—
747Dic6—24no—
748Dic6—21no—
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—81no—
761C2×C32C2×#12011yescharacteristic
762C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
763C2×C32#57511yescharacteristic
764C3⋊D3—22no—
765C3⋊D3—42no—
766C3⋊D3—81no—
767C3×D3—22no—
768C3×D3—41no—
769C3×D3—42no—
770C24—91no—
771C24—181no—
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—61no—
785C2×Q8—62no—
786C2×Q8—62no—
787C2×Q8C2×D3211yescharacteristic
788C2×D4—31no—
789C2×D4—61no—
790C2×D4—61no—
791C2×D4—61no—
792C2×D4—91no—
793C2×D4—91no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—182no—
797C2×D4—182no—
798C2×D4—188no—
799C2×D4—181no—
800C2×D4—181no—
801C2×D4—181no—
802C2×D4—181no—
803C2×D4—182no—
804C2×D4—182no—
805C2×D4—181no—
806C2×D4—364no—
807C2×D4C2×D3211yescharacteristic
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—91no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—91no—
816C22×C4—181no—
817C22×C4—181no—
818C22×C4—182no—
819C22×C4—182no—
820C22×C4—188no—
821C22×C4—181no—
822C22×C4—181no—
823SD16—22no—
824SD16—62no—
825SD16—182no—
826SD16—182no—
827D8—62no—
828D8—182no—
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—21no—
845C22×C3—32no—
846C22×C3—42no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—62no—
858C22×C3—61no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3C2×D3×D411yescharacteristic
864C22×C3C2×D3×D411yescharacteristic
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—22no—
871C2×D3—32no—
872C2×D3—32no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—62no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—122no—
885C2×D3—124no—
886C2×D3—128no—
887C2×D3—124no—
888C2×D3—128no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—122no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—241no—
901C2×D3—241no—
902C2×D3—241no—
903C2×D3—241no—
904C2×D3—244no—
905C2×D3—244no—
906C2×D3—248no—
907C2×D3#91412yescomplemented
908C3×C4—22no—
909C3×C4—22no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—42no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—62no—
916C3×C4—121no—
917C3×C4—121no—
918C3×C4C2×D3×D411yescharacteristic
919C3×C4C2×D3×D411yescharacteristic
920C3×C4C2×D3×D411yescharacteristic
921C3×C4C2×D3×D411yescharacteristic
922Dic3—21no—
923Dic3—22no—
924Dic3—21no—
925Dic3—32no—
926Dic3—32no—
927Dic3—41no—
928Dic3—41no—
929Dic3—62no—
930C32#300611yescharacteristic, complemented, Sylow
931C23—21no—
932C23—31no—
933C23—31no—
934C23—61no—
935C23—91no—
936C23—182no—
937C23—182no—
938C23—184no—
939C23—181no—
940C23—181no—
941C23—362no—
942C23—362no—
943C23—362no—
944C23—362no—
945C23—361no—
946C23—362no—
947Q8—21no—
948Q8—32no—
949Q8—64no—
950Q8—61no—
951Q8#381112yescomplemented
952D4—21no—
953D4—21no—
954D4—32no—
955D4—64no—
956D4—61no—
957D4—92no—
958D4—122no—
959D4—122no—
960D4—184no—
961D4—184no—
962D4—184no—
963D4—184no—
964D4—181no—
965D4—181no—
966D4—181no—
967D4—362no—
968D4—362no—
969D4—362no—
970C2×C4—21no—
971C2×C4—31no—
972C2×C4—31no—
973C2×C4—64no—
974C2×C4—64no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—91no—
983C2×C4—92no—
984C2×C4—92no—
985C2×C4—184no—
986C2×C4—182no—
987C2×C4—184no—
988C2×C4—182no—
989C2×C4—182no—
990C2×C4—184no—
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—62no—
1001C2×C3—82no—
1002C2×C3—81no—
1003C2×C3—81no—
1004C2×C3—121no—
1005C2×C3—122no—
1006C2×C3D3×#12011yescharacteristic
1007C2×C3D3×#12011yescharacteristic
1008C2×C3C2×#91411yescharacteristic
1009C2×C3#576811yescharacteristic
1010C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1011C2×C3#577711yescharacteristic
1012D3—22no—
1013D3—41no—
1014D3—42no—
1015D3—62no—
1016D3—62no—
1017D3—122no—
1018D3—122no—
1019D3—122no—
1020D3—242no—
1021D3—242no—
1022D3—241no—
1023D3—241no—
1024C22—32no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—61no—
1029C22—61no—
1030C22—61no—
1031C22—61no—
1032C22—62no—
1033C22—61no—
1034C22—92no—
1035C22—121no—
1036C22—121no—
1037C22—181no—
1038C22—181no—
1039C22—182no—
1040C22—364no—
1041C22—368no—
1042C22—361no—
1043C22—361no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22—724no—
1048C22D32×D411yescharacteristic
1049C4—22no—
1050C4—61no—
1051C4—61no—
1052C4—62no—
1053C4—92no—
1054C4—121no—
1055C4—121no—
1056C4D32×D411yescharacteristic
1057C4C2×#381111yescharacteristic
1058C3—21no—
1059C3#8004011yescharacteristic, complemented
1060C3#8008411yescharacteristic, complemented
1061C2—62no—
1062C2—81no—
1063C2—121no—
1064C2—122no—
1065C2—182no—
1066C2—362no—
1067C2—721no—
1068C2D3×#91411yescharacteristic
1069C2#1059474611yescharacteristic
1070C2#1059527811yescharacteristic
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×#64123C2semidirect
3. #10595282C2semidirect
4. C2×#63937C2semidirect
5. C3×#5172C2semidirect
6. C3×#5170C2semidirect
7. #10591588C2semidirect
8. #10591584C2semidirect
9. #10591554C2semidirect
10. #10591521C2semidirect
11. #10591515C2semidirect
12. #10590967C2semidirect
13. #10590957C2semidirect
14. #10590947C2semidirect
15. #10590937C2semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C2×C3×#239C22semidirect
21. C2×C3×D3×Q8C22semidirect
26. C2×D3×D12C22semidirect
30. C2×#3799C22semidirect
33. C2×C32×SD16C22semidirect
34. C2×#3755C22semidirect
35. C2×#3753C22semidirect
37. C2×#3745C22semidirect
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×#835C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #5172D3semidirect
80. #5170D3semidirect
103. #3832D4semidirect
148. #3796D4semidirect
184. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
205. C2×C3×SD16C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
217. #938C2×D3semidirect
218. C2×#214C2×D3semidirect
223. C2×#213C2×D3semidirect
256. #835C2×D3semidirect
257. #835C2×D3semidirect
263. #821C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
267. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
290. C32×Q8C2×D4semidirect
301. C4⋊(C3⋊D3)C2×D4semidirect
314. C3×D12C2×D4semidirect
323. C3×Dic6C2×D4semidirect
544. C2×C3×D3AGL(1,ℤ/8)semidirect
576. C2×SD16D32semidirect
649. C3×Q8D3×D4semidirect
650. C3×Q8D3×D4semidirect
722. D12D3×D4semidirect
749. Dic6D3×D4semidirect
907. C2×D3#914semidirect
930. C32#3006semidirect
951. Q8#3811semidirect
1059. C3#80040semidirect
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×#2392
C2×#641232
#105952822
C2×#639372
C3×#51722
C3×#51702
#105915882
#105915842
#105915542
#105915212
#105915152
#105909672
#105909572
#105909472
#105909372
#800843
#800403