Finite Group Databasebeta

← #11883993

Subgroups — #11883993

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5633C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3#10595074C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10592745C211yesmaximal, characteristic, complemented
6C3×#5049C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80834—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×D12C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C2×#3755C2211yescharacteristic, complemented
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#930C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic, complemented
31C3×#896—21no—
32C3×#895C2211yescharacteristic, complemented
33C3×#893—21no—
34C3×#887C2211yescharacteristic, complemented
35C3×#885—21no—
36C3×#884—21no—
37#63981—21no—
38D3×#215—24no—
39#63923—21no—
40#63911C2211yescharacteristic
41#63910—21no—
42#63909C2211yescharacteristic
43#63894C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47#63825—24no—
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65C22×#215—31no—
66C2×D3×SD16—31no—
67C2×#908—31no—
68#5633D311yescharacteristic, complemented
69#5609—31no—
70D4×D12—31no—
71C3×#468—31no—
72#5238—31no—
73#5227—31no—
74#5176—31no—
75#5127—31no—
76#5058—31no—
77#5057—31no—
78#5049D311yescharacteristic, complemented
79#5046—31no—
80#5046—31no—
81#5046—61no—
82#5038—31no—
83#5037—31no—
84#5036—31no—
85#5027—31no—
86#5026—31no—
87#5011—31no—
88#4889—31no—
89#4883—31no—
90#4819—31no—
91#4806—31no—
92#4773—31no—
93#4762—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×D3×Q8—22no—
107C3×D3×Q8—41no—
108C3×#235—22no—
109C3×#235—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118#3811—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#624—21no—
124D3×D12—22no—
125D3×D12—41no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129#3755—22no—
130#3755—41no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217D411yescharacteristic
134C3×#215—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3—21no—
144C3×C4×Dic3C2311yescharacteristic
145C3×#208—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3722—21no—
149#3722—21no—
150#3717—22no—
151#3717D414yescomplemented
152#3715—22no—
153#3714—22no—
154#3714—22no—
155#3713—41no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×D3×D4—61no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—61no—
169C2×C3×SD16—31no—
170C2×C3×M16—31no—
171C3×#124—31no—
172C3×#124—61no—
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8—61no—
175C3×C22⋊Q8C2×D311yescharacteristic, complemented
176C3×C22⋊Q8C2×D311yescharacteristic, complemented
177C3×#121—31no—
178C3×#121—31no—
179C3×#121—61no—
180C3×C4×Q8—31no—
181C3×C4×D4—31no—
182C3×C4×D4—61no—
183#949—64no—
184#947C2×D311yescharacteristic, complemented
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215—61no—
194C2×#215—64no—
195C2×#215C2×D311yescharacteristic, complemented
196#940—31no—
197#937—61no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203#930—31no—
204#930C2×D311yescharacteristic
205C4×#67C2×D311yescharacteristic
206C2×#208C2×D311yescharacteristic, complemented
207C22×C3⋊C8—31no—
208D3×SD16—64no—
209#908—64no—
210C2×D24—31no—
211C2×D24—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×D3×C8—31no—
215#896—21no—
216#895—31no—
217#895—61no—
218#895C2×D311yescharacteristic, complemented
219#893—21no—
220#893—31no—
221#887C2×D311yescharacteristic, complemented
222#885—21no—
223#884—21no—
224#884—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—31no—
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#830—31no—
237#830—31no—
238#830—31no—
239#830—61no—
240(C2×D3)⋊C8—31no—
241#815—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809—61no—
251#809C2×D311yescharacteristic, complemented
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)C2×D412yes—
280C3×#67—22no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C3×Dic6C2×D412yescomplemented
300#626—42no—
301#626—42no—
302#626—42no—
303#626—81no—
304#624—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C3×#41—62no—
330C3×#41—121no—
331C2×C3×Q8—21no—
332C2×C3×Q8—31no—
333C2×C3×Q8—61no—
334C2×C3×Q8—62no—
335C2×C3×Q8—121no—
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67#6711yescharacteristic
357D3×Q8—22no—
358D3×Q8—41no—
359D3×D4—62no—
360D3×D4—121no—
361D3×D4—124no—
362D3×D4—124no—
363#235—22no—
364#235—41no—
365C2×D12—21no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—62no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—122no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12—121no—
385C2×D12—121no—
386C2×D12—122no—
387C2×D12C22×D311yescharacteristic
388C2×D12C22×D311yescharacteristic
389C2×C4×D3—21no—
390C2×C4×D3—21no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—21no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—62no—
397C3×M16—62no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—41no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4C22×D311yescharacteristic
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—41no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C42—31no—
419C3×C42—61no—
420#217#6711yescharacteristic
421#215—22no—
422#215—34no—
423#215—62no—
424#215—62no—
425#215—62no—
426#215—62no—
427#215—122no—
428#215—121no—
429#215—121no—
430#215—122no—
431#214—62no—
432#213—62no—
433#213—62no—
434#213—121no—
435#213—121no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4#6711yescharacteristic
445C4⋊Dic3C22×D311yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4#6711yescharacteristic
448C4×Dic3—21no—
449C4×Dic3C22×D311yescharacteristic
450#208—22no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460D24—62no—
461D24—62no—
462#204—34no—
463#204—62no—
464D3×C8—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—22no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—84no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3×Dic3—21no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8—31no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—91no—
515#124—31no—
516#124—61no—
517C22⋊Q8—61no—
518C22⋊Q8D3211yescharacteristic, complemented
519#121—31no—
520#121—31no—
521#121—61no—
522#121—91no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—61no—
529C4×D4—91no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3D3×D411yescharacteristic
546C23×C3C2×#6711yescharacteristic
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—122no—
564C22×D3—242no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—242no—
570C22×D3C2×#6711yescharacteristic
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—32no—
576C3×Q8—41no—
577C3×Q8—41no—
578C3×Q8—61no—
579C3×Q8—122no—
580C3×D4—62no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—31no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4C2×#6711yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615#67—22no—
616#67—42no—
617#67—42no—
618#67—122no—
619#67—122no—
620#67—122no—
621#67—241no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3C2×#6711yescharacteristic
625C2×Dic3C2×#6711yescharacteristic
626C2×Dic3C2×#6711yescharacteristic
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—32no—
632D12—32no—
633D12—42no—
634D12—62no—
635D12—62no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—61no—
642D12—121no—
643D12—121no—
644D12—122no—
645D12—122no—
646D12—124no—
647D12—122no—
648D12—122no—
649D12—122no—
650D12—241no—
651C4×D3—21no—
652C4×D3—21no—
653C4×D3—42no—
654C4×D3—42no—
655C4×D3—122no—
656C4×D3—122no—
657Dic6—21no—
658Dic6—42no—
659Dic6D3×D412yescomplemented
660C3×C8—32no—
661C3×C8—61no—
662C3⋊C8—21no—
663C3⋊C8—61no—
664C3⋊C8—61no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8—121no—
669C3⋊C8D3×D412yescomplemented
670C2×C32—41no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—42no—
675C3⋊D3—81no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—181no—
680C24—181no—
681#41—62no—
682#41—121no—
683C2×Q8—31no—
684C2×Q8—61no—
685C2×Q8—62no—
686C2×Q8—121no—
687C2×Q8C2×D3211yescharacteristic
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—91no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—182no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—361no—
704C2×D4—361no—
705C2×D4—364no—
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—181no—
710C22×C4C2×D3211yescharacteristic
711SD16—62no—
712SD16—94no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
717D8—182no—
718D8—182no—
719D8—361no—
720M16—62no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—91no—
724C2×C8—91no—
725C2×C8—182no—
726C4⋊C4—21no—
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—61no—
730C4⋊C4C2×D3211yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—31no—
733C22⋊C4—31no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—61no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—32no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C22×#6711yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—122no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—122no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#94912yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—61no—
807C3×C4—62no—
808C3×C4—81no—
809C3×C4—81no—
810C3×C4—121no—
811C3×C4C2×D3×D411yescharacteristic
812C3×C4C2×D3×D411yescharacteristic
813C3×C4#100411yescharacteristic
814C3×C4#100911yescharacteristic
815Dic3—22no—
816Dic3—21no—
817Dic3—21no—
818Dic3—21no—
819Dic3—41no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—31no—
822C23—61no—
823C23—61no—
824C23—181no—
825C23—181no—
826C23—362no—
827C23—362no—
828C23—362no—
829C23—362no—
830C23—721no—
831C23—721no—
832C23D3×#6711yescharacteristic
833Q8—21no—
834Q8—21no—
835Q8—32no—
836Q8—61no—
837Q8—122no—
838D4—62no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—92no—
844D4—122no—
845D4—122no—
846D4—122no—
847D4—181no—
848D4—181no—
849D4—181no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—721no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—362no—
869C2×C4D3×#6711yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C8—32no—
872C8—61no—
873C8—181no—
874C8—181no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—62no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#560911yescharacteristic
885C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
886C2×C3#577811yescharacteristic
887C2×C3D4×#6711yescharacteristic
888C2×C3C2×#94911yescharacteristic
889C2×C3#583711yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—122no—
895D3—242no—
896D3—242no—
897D3—241no—
898D3—241no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—32no—
903C22—61no—
904C22—61no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—182no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22—724no—
918C22—724no—
919C22C2×D3×#6711yescharacteristic
920C4—21no—
921C4—41no—
922C4—41no—
923C4—61no—
924C4—61no—
925C4—62no—
926C4—61no—
927C4—121no—
928C4D32×D411yescharacteristic
929C4#6431411yescharacteristic
930C3—21no—
931C3#8083411yescharacteristic, complemented
932C3#8354211yescharacteristic, complemented
933C2—41no—
934C2—62no—
935C2—241no—
936C2—241no—
937C2—362no—
938C2—721no—
939C2#1059529111yescharacteristic
940C2#1059531911yescharacteristic
941C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5633C2semidirect
2. C2×D3×#215C2semidirect
3. #10595074C2semidirect
4. C2×#63825C2semidirect
5. #10592745C2semidirect
6. C3×#5049C2semidirect
7. #10591619C2semidirect
8. #10591584C2semidirect
9. #10591568C2semidirect
10. #10591161C2semidirect
11. #10591147C2semidirect
12. #10590595C2semidirect
13. #10590576C2semidirect
14. #10590549C2semidirect
15. #10590457C2semidirect
19. C2×C3×D3×Q8C22semidirect
20. C2×C3×#235C22semidirect
23. C32×C22⋊Q8C22semidirect
25. C2×#3755C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
30. C2×C3×#208C22semidirect
32. C3×#895C22semidirect
34. C3×#887C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63657C22semidirect
54. #63636C22semidirect
55. C3×#835C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. #5633D3semidirect
78. #5049D3semidirect
151. #3717D4semidirect
160. C2×D3×Q8C2×D3semidirect
164. C2×#235C2×D3semidirect
175. C3×C22⋊Q8C2×D3semidirect
176. C3×C22⋊Q8C2×D3semidirect
184. #947C2×D3semidirect
195. C2×#215C2×D3semidirect
206. C2×#208C2×D3semidirect
218. #895C2×D3semidirect
221. #887C2×D3semidirect
234. #835C2×D3semidirect
251. #809C2×D3semidirect
252. #807C2×D3semidirect
299. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
518. C22⋊Q8D32semidirect
659. Dic6D3×D4semidirect
669. C3⋊C8D3×D4semidirect
794. C2×D3#949semidirect
820. C32#3265semidirect
931. C3#80834semidirect
932. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#56332
C2×D3×#2152
#105950742
C2×#638252
#105927452
C3×#50492
#105916192
#105915842
#105915682
#105911612
#105911472
#105905952
#105905762
#105905492
#105904572
#835423
#808343