Finite Group Databasebeta

← #11864159

Subgroups — #11864159

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×#235C211yesmaximal, characteristic, complemented
2C3×D3×#121C211yesmaximal, characteristic, complemented
3C2×#63934C211yesmaximal, characteristic, complemented
4C2×#63932C211yesmaximal, characteristic, complemented
5#10592736C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591517C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591154C211yesmaximal, characteristic, complemented
12#10590609C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590603C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#82624—31nomaximal
17#80084—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×C3×#235C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic
23C2×D3×#67—21no—
24C2×#3804—21no—
25D3×#235—24no—
26D3×#235—24no—
27C2×D3×D12C2211yescharacteristic, complemented
28C2×C4×D32—21no—
29C2×#3799C2211yescharacteristic
30C2×#3798—21no—
31C2×#3795C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic, complemented
33C32×#121C2211yescharacteristic, complemented
34C2×#3754C2211yescharacteristic, complemented
35C2×#3753C2211yescharacteristic, complemented
36C3×#939—21no—
37C3×#938C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#930C2211yescharacteristic, complemented
41C3×#895C2211yescharacteristic
42C3×D3×C4⋊C4C2211yescharacteristic, complemented
43C3×#884—21no—
44C3×D3×C22⋊C4—21no—
45#63934—24no—
46#63932—24no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, 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×#235—31no—
67C2×C3×#121—31no—
68C2×#932—31no—
69C2×#932—31no—
70C2×#914—31no—
71C2×#911—31no—
72D3×#121D311yescharacteristic, complemented
73C3×#449—31no—
74#5238—31no—
75#5207—31no—
76#5170—31no—
77#5156—31no—
78#5040—31no—
79#5040—31no—
80#5037—31no—
81#5037—31no—
82#5037—31no—
83#5037—31no—
84#5037—61no—
85#5037D311yescharacteristic, complemented
86#5036—31no—
87#5036—31no—
88#4966—31no—
89#4966—31no—
90#4806—31no—
91#4803—31no—
92#4773—31no—
93#4771—31no—
94#4734—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C23×C3×D3D411yescharacteristic
98C22×D32—21no—
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103#3828—22no—
104#3828—22no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C22×C3×Dic3D411yescharacteristic
113C3×D3×D4—22no—
114C3×D3×D4—22no—
115C3×D3×D4—44no—
116C3×#235—22no—
117C3×#235—22no—
118C2×C3×D12—21no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3D411yescharacteristic
126C2×C3×C4×D3D411yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130D3×#67—28no—
131C2×#627—21no—
132C2×#626—21no—
133C2×#626—21no—
134C2×#625—21no—
135C2×#624—21no—
136#3804—28no—
137C2×D3×Dic3—21no—
138C2×D3×Dic3—21no—
139D3×D12—22no—
140D3×D12—22no—
141C4×D32—28no—
142#3799—22no—
143#3799D414yescomplemented
144#3798—28no—
145#3795—22no—
146#3795D414yescomplemented
147D3×Dic6—22no—
148D3×Dic6—22no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4—21no—
151#3754—22no—
152#3753—22no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#214—22no—
157C3×#213—22no—
158C3×(C2×D3)⋊C4—21no—
159C3×(C2×D3)⋊C4—21no—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4—21no—
162C2×C3×C3⋊C8C2311yescharacteristic
163C2×C3×C3⋊C8C2311yescharacteristic
164#3716—22no—
165#3715—22no—
166#3714—22no—
167#3713—22no—
168#3711—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×C3×D4—61no—
174C23×C3×C4—31no—
175C22×#67—61no—
176D3×#41—64no—
177D3×#41—64no—
178C2×#239—31no—
179C2×D3×Q8—31no—
180C2×#237—31no—
181C2×#237—61no—
182C2×D3×D4—21no—
183C2×D3×D4—31no—
184C2×D3×D4—61no—
185C2×D3×D4C2×D311yescharacteristic, complemented
186C2×#235—31no—
187C2×#235—31no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—61no—
191C2×#235—61no—
192C2×#235—64no—
193C2×#235—64no—
194C2×#235—61no—
195C2×#235—61no—
196C2×#235C2×D311yescharacteristic, complemented
197C22×D12—31no—
198C22×C4×D3—61no—
199C22×C4×D3—61no—
200C22×C4×D3C2×D311yescharacteristic
201C22×Dic6—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C3×#121—21no—
205C3×#121—31no—
206C3×#121—31no—
207C3×#121—31no—
208C3×#121—61no—
209C3×#121—61no—
210C3×#121C2×D311yescharacteristic, complemented
211C3×#121C2×D311yescharacteristic, complemented
212C2×C3×C4⋊C4—31no—
213C2×C3×C22⋊C4—61no—
214C2×#215—31no—
215#939—21no—
216#938C2×D311yescharacteristic
217C2×#214—31no—
218C2×#214—31no—
219C2×#214—31no—
220C2×#214—31no—
221C2×#214—61no—
222C2×#214C2×D311yescharacteristic, complemented
223#932—64no—
224#932—64no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—31no—
230C2×#213—61no—
231C2×#213C2×D311yescharacteristic, complemented
232#930C2×D311yescharacteristic, complemented
233C2×#208—31no—
234C2×#208—31no—
235#914—64no—
236#911—64no—
237C2×D24—31no—
238C2×#204—31no—
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)—31no—
241#895C2×D311yescharacteristic
242D3×C4⋊C4C2×D311yescharacteristic, complemented
243#884—21no—
244D3×C22⋊C4—21no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#832—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—31no—
254#830—61no—
255#830C2×D311yescharacteristic, complemented
256#821—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259#816—31no—
260#810—31no—
261#810—31no—
262#810—31no—
263#810—31no—
264#810—61no—
265#810C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272C23×C32—21no—
273C23×C32C2×D411yescharacteristic
274C22×C3⋊D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—21no—
279C22×C3×D3—41no—
280C22×C3×D3—42no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—24no—
286C2×D32—42no—
287C2×D32—42no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4—42no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4C2×D411yescharacteristic
295C2×C32×C4C2411yescharacteristic
296#638—24no—
297C2×C3⋊Dic3—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—42no—
305C3×#67—42no—
306C3×#67—42no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D411yescharacteristic
311C2×C3×Dic3C2×D411yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—42no—
316C3×D12C2×D412yescomplemented
317C3×C4×D3—24no—
318C3×C4×D3—22no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—22no—
322C3×C4×D3—42no—
323C3×C4×D3C2×D412yes—
324C3×C4×D3C2×D412yes—
325C3×Dic6—21no—
326C3×Dic6C2×D412yescomplemented
327#627—24no—
328#626—24no—
329#626—24no—
330#625—24no—
331#624—24no—
332D3×Dic3—24no—
333D3×Dic3—24no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—91no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—31no—
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—31no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3#6711yescharacteristic
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4—21no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—41no—
368C2×C3×D4—61no—
369C2×C3×D4—62no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—124no—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—62no—
385C22×C3×C4—62no—
386C22×C3×C4—61no—
387C22×C3×C4—61no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C2×#67—21no—
391C2×#67—21no—
392C2×#67—21no—
393C2×#67—21no—
394C2×#67—61no—
395C2×#67—68no—
396C2×#67—61no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—61no—
400C2×#67—61no—
401C2×#67—121no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3#6711yescharacteristic
405#239—34no—
406#239—62no—
407D3×Q8—62no—
408D3×Q8—62no—
409#237—34no—
410#237—68no—
411#237—62no—
412D3×D4—22no—
413D3×D4—22no—
414D3×D4—44no—
415D3×D4—62no—
416D3×D4—62no—
417D3×D4—68no—
418#235—22no—
419#235—22no—
420#235—34no—
421#235—34no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—68no—
426#235—68no—
427#235—62no—
428#235—62no—
429#235—62no—
430#235—68no—
431#235—122no—
432#235—122no—
433C2×D12—21no—
434C2×D12—31no—
435C2×D12—31no—
436C2×D12—61no—
437C2×D12—62no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—62no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×C4×D3—21no—
444C2×C4×D3—22no—
445C2×C4×D3—22no—
446C2×C4×D3—21no—
447C2×C4×D3—68no—
448C2×C4×D3—68no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—121no—
456C2×C4×D3#6711yescharacteristic
457C2×C4×D3#6711yescharacteristic
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×D8—62no—
470C2×C3×C8—31no—
471C2×C3×C8—31no—
472C3×C4⋊C4—21no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—61no—
475C3×C4⋊C4C22×D311yescharacteristic
476C3×C4⋊C4C22×D311yescharacteristic
477C3×C22⋊C4—21no—
478C3×C22⋊C4—21no—
479C3×C22⋊C4—41no—
480C3×C22⋊C4—61no—
481C3×C22⋊C4—61no—
482C3×C22⋊C4—61no—
483#217—21no—
484#215—62no—
485#214—22no—
486#214—62no—
487#214—62no—
488#214—62no—
489#214—62no—
490#214—122no—
491#213—22no—
492#213—62no—
493#213—62no—
494#213—62no—
495#213—62no—
496#213—62no—
497#213—122no—
498(C2×D3)⋊C4—21no—
499(C2×D3)⋊C4—21no—
500C4⋊Dic3C22×D311yescharacteristic
501Dic3⋊C4—21no—
502#208—62no—
503#208—62no—
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—31no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—62no—
514ΓL(1,𝔽25)—62no—
515ΓL(1,𝔽25)—62no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32C22×D411yescharacteristic
523C2×C3⋊D3—22no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—44no—
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—48no—
541C32×C4—21no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—22no—
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—61no—
561C22×D4—91no—
562C22×D4—181no—
563C23×C4—31no—
564C23×C4—181no—
565AGL(1,ℤ/8)—184no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—91no—
576C2×M16—91no—
577#121—31no—
578#121—31no—
579#121—31no—
580#121—61no—
581#121—61no—
582#121D3211yescharacteristic, complemented
583C2×C4⋊C4—31no—
584C2×C22⋊C4—61no—
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—21no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—41no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—121no—
608C23×C3—122no—
609C23×C3—122no—
610C23×C3—122no—
611C23×C3D3×D411yescharacteristic
612C23×C3C2×#6711yescharacteristic
613C22×D3—21no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—21no—
617C22×D3—41no—
618C22×D3—42no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—64no—
622C22×D3—64no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3C2×#6711yescharacteristic
631C22×D3C2×#6711yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—32no—
639C3×D4—41no—
640C3×D4—41no—
641C3×D4—42no—
642C3×D4—42no—
643C3×D4—64no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—82no—
648C3×D4—122no—
649C3×D4—122no—
650C3×D4—122no—
651C3×D4—122no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—31no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—31no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—64no—
670C2×C3×C4—62no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—122no—
676C2×C3×C4D3×D411yescharacteristic
677C2×C3×C4C2×#6711yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680#67—24no—
681#67—42no—
682#67—42no—
683#67—42no—
684#67—64no—
685#67—64no—
686#67—64no—
687#67—64no—
688#67—64no—
689#67—64no—
690#67—124no—
691C2×Dic3—21no—
692C2×Dic3—22no—
693C2×Dic3—21no—
694C2×Dic3—64no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—64no—
698C2×Dic3—121no—
699C2×Dic3C2×#6711yescharacteristic
700C2×Dic3C2×#6711yescharacteristic
701D12—21no—
702D12—21no—
703D12—21no—
704D12—32no—
705D12—32no—
706D12—42no—
707D12—62no—
708D12—64no—
709D12—64no—
710D12—61no—
711D12—61no—
712D12—121no—
713D12D3×D412yescomplemented
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—21no—
717C4×D3—21no—
718C4×D3—22no—
719C4×D3—42no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—124no—
727C4×D3D3×D412yes—
728C4×D3D3×D412yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6D3×D412yescomplemented
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—61no—
744C3⋊C8—61no—
745C3⋊C8—61no—
746C3⋊C8—61no—
747C3⋊C8—121no—
748C3⋊C8—121no—
749C2×C32—41no—
750C2×C32—81no—
751C2×C32C2×#12011yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C2×C32#57511yescharacteristic
754C3⋊D3—42no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—31no—
760C24—61no—
761C24—181no—
762#41—62no—
763#41—62no—
764#41—94no—
765#41—94no—
766#41—182no—
767#41—182no—
768#41—182no—
769#41—182no—
770#41—188no—
771#41—188no—
772C2×Q8—31no—
773C2×Q8—91no—
774C2×Q8—181no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—21no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—61no—
787C2×D4—91no—
788C2×D4—124no—
789C2×D4—181no—
790C2×D4—182no—
791C2×D4—182no—
792C2×D4—181no—
793C2×D4—188no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—181no—
807C22×C4—181no—
808C22×C4—188no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4C2×D3211yescharacteristic
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820M16—182no—
821M16—182no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8—91no—
825C2×C8—91no—
826C4⋊C4—31no—
827C4⋊C4—61no—
828C4⋊C4C2×D3211yescharacteristic
829C22⋊C4—21no—
830C22⋊C4—61no—
831C22⋊C4—61no—
832C22⋊C4—61no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—32no—
841C22×C3—32no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—62no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—124no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—244no—
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C22×#6711yescharacteristic
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—22no—
873C2×D3—44no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—84no—
882C2×D3—122no—
883C2×D3—128no—
884C2×D3—128no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—241no—
890C2×D3—241no—
891C2×D3#93212yescomplemented
892C2×D3#93712yes—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—62no—
902C3×C4—61no—
903C3×C4—81no—
904C3×C4—121no—
905C3×C4C2×D3×D411yescharacteristic
906C3×C4C2×D3×D411yescharacteristic
907C3×C4C2×D3×D411yescharacteristic
908C3×C4C2×D3×D411yescharacteristic
909Dic3—21no—
910Dic3—22no—
911Dic3—41no—
912Dic3—62no—
913Dic3—62no—
914Dic3—122no—
915Dic3#93712yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—62no—
921C23—62no—
922C23—61no—
923C23—61no—
924C23—121no—
925C23—122no—
926C23—122no—
927C23—122no—
928C23—184no—
929C23—181no—
930C23—362no—
931C23—362no—
932C23D3×#6711yescharacteristic
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—21no—
939D4—21no—
940D4—32no—
941D4—42no—
942D4—64no—
943D4—61no—
944D4—61no—
945D4—61no—
946D4—92no—
947D4—122no—
948D4—122no—
949D4—122no—
950D4—122no—
951D4—184no—
952D4—184no—
953D4—184no—
954D4—184no—
955D4—181no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—31no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—31no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—64no—
966C2×C4—62no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—122no—
972C2×C4—184no—
973C2×C4—184no—
974C2×C4—184no—
975C2×C4—184no—
976C2×C4—181no—
977C2×C4D3×#6711yescharacteristic
978C2×C4C22×D3211yescharacteristic
979C8—61no—
980C8—61no—
981C8—181no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—41no—
988C2×C3—62no—
989C2×C3—62no—
990C2×C3—81no—
991C2×C3—81no—
992C2×C3—81no—
993C2×C3—122no—
994C2×C3—161no—
995C2×C3—241no—
996C2×C3D3×#12011yescharacteristic
997C2×C3#576811yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999C2×C3C2×#93211yescharacteristic
1000C2×C3C2×#93711yescharacteristic
1001C2×C3#582211yescharacteristic
1002D3—22no—
1003D3—22no—
1004D3—42no—
1005D3—81no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—32no—
1013C22—32no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—61no—
1018C22—61no—
1019C22—61no—
1020C22—61no—
1021C22—62no—
1022C22—124no—
1023C22—121no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—182no—
1029C22—244no—
1030C22—368no—
1031C22—361no—
1032C22—361no—
1033C22C2×D3×#6711yescharacteristic
1034C4—21no—
1035C4—32no—
1036C4—41no—
1037C4—61no—
1038C4—62no—
1039C4—121no—
1040C4—182no—
1041C4D32×D411yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3#8008411yescharacteristic, complemented
1045C3#8262411yescharacteristic, complemented
1046C2—41no—
1047C2—62no—
1048C2—62no—
1049C2—81no—
1050C2—122no—
1051C2—241no—
1052C2—362no—
1053C2D3×#93211yescharacteristic
1054C2D3×#93711yescharacteristic
1055C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C3×D3×#121C2semidirect
3. C2×#63934C2semidirect
4. C2×#63932C2semidirect
5. #10592736C2semidirect
6. C3×#5037C2semidirect
7. #10591517C2semidirect
8. #10591515C2semidirect
9. #10591182C2semidirect
10. #10591161C2semidirect
11. #10591154C2semidirect
12. #10590609C2semidirect
13. #10590607C2semidirect
14. #10590603C2semidirect
15. #10590595C2semidirect
18. C2×#3828C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C2×C3×#235C22semidirect
27. C2×D3×D12C22semidirect
32. C2×D3×Dic6C22semidirect
33. C32×#121C22semidirect
34. C2×#3754C22semidirect
35. C2×#3753C22semidirect
38. C2×C3×#214C22semidirect
39. C2×C3×#213C22semidirect
40. C3×#930C22semidirect
42. C3×D3×C4⋊C4C22semidirect
47. C2×#3716C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×#3711C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
72. D3×#121D3semidirect
85. #5037D3semidirect
143. #3799D4semidirect
146. #3795D4semidirect
185. C2×D3×D4C2×D3semidirect
196. C2×#235C2×D3semidirect
210. C3×#121C2×D3semidirect
211. C3×#121C2×D3semidirect
222. C2×#214C2×D3semidirect
231. C2×#213C2×D3semidirect
232. #930C2×D3semidirect
242. D3×C4⋊C4C2×D3semidirect
255. #830C2×D3semidirect
265. #810C2×D3semidirect
271. #809C2×D3semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
302. #634C2×D4semidirect
316. C3×D12C2×D4semidirect
326. C3×Dic6C2×D4semidirect
539. C2×C3×D3AGL(1,ℤ/8)semidirect
582. #121D32semidirect
713. D12D3×D4semidirect
738. Dic6D3×D4semidirect
891. C2×D3#932semidirect
916. C32#3006semidirect
1044. C3#80084semidirect
1045. C3#82624semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C3×D3×#1212
C2×#639342
C2×#639322
#105927362
C3×#50372
#105915172
#105915152
#105911822
#105911612
#105911542
#105906092
#105906072
#105906032
#105905952
#826243
#800843