Finite Group Databasebeta

← #11883943

Subgroups — #11883943

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5831C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4D12×#67C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591583C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591515C211yesmaximal, characteristic, complemented
10#10591498C211yesmaximal, characteristic, complemented
11#10591483C211yesmaximal, characteristic, complemented
12#10591431C211yesmaximal, characteristic, complemented
13#10591178C211yesmaximal, characteristic, complemented
14#10591169C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83953—31nomaximal
17#83542—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25#64139C2211yescharacteristic
26C3×#949—24no—
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#938—21no—
31C3×#938C2211yescharacteristic, complemented
32C3×#936—21no—
33C3×#936C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic, complemented
36C3×C4×#67—21no—
37C3×C4×#67C2211yescharacteristic
38C3×#924—21no—
39C3×#924C2211yescharacteristic, complemented
40C2×C3×#208C2211yescharacteristic, complemented
41#63977—21no—
42D3×#215—24no—
43#63922—21no—
44#63911C2211yescharacteristic
45#63908C2211yescharacteristic
46Dic3×D12C2211yescharacteristic
47#63886—21no—
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×#548—31no—
65#5831D311yescharacteristic, complemented
66C2×#949D311yescharacteristic, complemented
67C22×#215—31no—
68D4×#67—31no—
69C2×D3×SD16—31no—
70D4×D12—31no—
71#5238—31no—
72#5238—31no—
73#5238—61no—
74#5227—31no—
75#5218—31no—
76#5170—31no—
77#5164—31no—
78#5163—31no—
79#5157—31no—
80#5156—31no—
81#5154—31no—
82#5153—31no—
83#5134—31no—
84#5127—31no—
85#5058—31no—
86#5057—31no—
87#5049—31no—
88#5046—31no—
89#5038—31no—
90#5036—31no—
91#5027—31no—
92#5026—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C3×D3×Q8—22no—
108C3×D3×Q8—41no—
109C2×C3×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124D3×D12—22no—
125D3×D12—41no—
126#3755—22no—
127#3753—41no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#215—22no—
138C3×#215D414yescomplemented
139C3×#213—22no—
140C3×#213—22no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4D411yescharacteristic
146C3×C4×Dic3—21no—
147C3×C4×Dic3C2311yescharacteristic
148C3×#208—22no—
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153#3717—22no—
154#3715—22no—
155#3715—41no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—21no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C22×C3×Q8—31no—
162C22×C3×D4—31no—
163C22×#67—61no—
164C2×D3×Q8C2×D311yescharacteristic, complemented
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C22×D12—31no—
168C22×D12C2×D311yescharacteristic
169C3×AGL(1,ℤ/8)—64no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×#124—31no—
176C3×#124—61no—
177C3×C22⋊Q8—31no—
178C3×C22⋊Q8—61no—
179C3×#121—31no—
180C3×#121—61no—
181C3×C4×Q8—31no—
182C3×C4×D4—31no—
183C3×C4×D4—61no—
184#953—61no—
185#949—24no—
186Q8×Dic3C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215—64no—
194C2×#215C2×D311yescharacteristic
195C2×#215C2×D311yescharacteristic, complemented
196#940—31no—
197#939—61no—
198#938—21no—
199#938—31no—
200#938C2×D311yescharacteristic, complemented
201#937—61no—
202#936—21no—
203#936C2×D311yescharacteristic, complemented
204D4×Dic3—31no—
205C2×#214—31no—
206C2×#214—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—61no—
210C2×#213C2×D311yescharacteristic
211C2×#213C2×D311yescharacteristic, complemented
212#930—31no—
213#930—31no—
214#930—31no—
215#930—61no—
216C4×#67—21no—
217C4×#67C2×D311yescharacteristic
218#924—21no—
219#924C2×D311yescharacteristic, complemented
220C2×#208C2×D311yescharacteristic, complemented
221C22×C3⋊C8—31no—
222D3×SD16—64no—
223C2×#204—31no—
224C2×D3×C8—31no—
225#895—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#830—31no—
241#830—31no—
242#830—61no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245#818—31no—
246#816—31no—
247#815—31no—
248Dic3⋊C8—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—42no—
279C2×C3⋊Dic3—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)—21no—
282C3×#67—22no—
283C3×#67—42no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—91no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—91no—
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—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—22no—
329C3×#41—22no—
330C3×#41—42no—
331C3×#41—41no—
332C3×#41—41no—
333C3×#41—42no—
334C2×C3×Q8—21no—
335C2×C3×Q8—31no—
336C2×C3×Q8—61no—
337C2×C3×Q8—62no—
338C2×C3×Q8—121no—
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—41no—
348C2×C3×D4—62no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—121no—
352C2×C3×D4C22×D311yescharacteristic
353C2×C3×D4C22×D311yescharacteristic
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—41no—
359C22×C3×C4—61no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C2×#67—21no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—121no—
371C2×#67—124no—
372C2×#67#6711yescharacteristic
373C22×Dic3—61no—
374D3×Q8—22no—
375D3×Q8—41no—
376D3×D4—62no—
377D3×D4—121no—
378D3×D4—124no—
379C2×D12—22no—
380C2×D12—21no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—41no—
384C2×D12—61no—
385C2×D12—62no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—121no—
390C2×D12C22×D311yescharacteristic
391C2×D12C22×D311yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—61no—
394C2×C4×D3C22×D311yescharacteristic
395C2×Dic6—21no—
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—34no—
398C3×SD16—62no—
399C3×D8—62no—
400C3×D8—62no—
401C3×M16—62no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C42—31no—
415C3×C42—61no—
416#217—21no—
417#217—21no—
418#217—21no—
419#217—21no—
420#217—61no—
421#217—61no—
422#217#6711yescharacteristic
423#215—22no—
424#215—62no—
425#215—62no—
426#215—62no—
427#215—62no—
428#215—122no—
429#215—121no—
430#215#6714yescomplemented
431#214—62no—
432#214—121no—
433#213—22no—
434#213—22no—
435#213—121no—
436#213—121no—
437#213—122no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4#6711yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3C22×D311yescharacteristic
449Dic3⋊C4—21no—
450Dic3⋊C4#6711yescharacteristic
451C4×Dic3—21no—
452C4×Dic3C22×D311yescharacteristic
453#208—22no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—31no—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—61no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8—62no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463#204—62no—
464D3×C8—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32C22×D411yescharacteristic
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—22no—
487C32×C4—21no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—41no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41D3211yescharacteristic, complemented
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—64no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—91no—
514#127—91no—
515#124—31no—
516#124—61no—
517C22⋊Q8—31no—
518C22⋊Q8—61no—
519#121—31no—
520#121—61no—
521#121—91no—
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—91no—
531C4⋊C8—91no—
532#103—91no—
533#103—91no—
534#102—91no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3D3×D411yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3C2×#6711yescharacteristic
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—22no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8—122no—
575C3×Q8D3×D412yescomplemented
576C3×Q8C2×#6712yescomplemented
577C3×D4—22no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—32no—
583C3×D4—41no—
584C3×D4—42no—
585C3×D4—42no—
586C3×D4—44no—
587C3×D4—62no—
588C3×D4—61no—
589C3×D4—61no—
590C3×D4—61no—
591C3×D4—122no—
592C3×D4—122no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—44no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—122no—
615C2×C3×C4D3×D411yescharacteristic
616C2×C3×C4C2×#6711yescharacteristic
617C2×C3×C4C23×D311yescharacteristic
618C2×C3×C4C23×D311yescharacteristic
619#67—22no—
620#67—42no—
621#67—122no—
622#67—122no—
623#67—122no—
624#67—122no—
625#67—122no—
626#67—122no—
627#67—242no—
628#67—241no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—121no—
634C2×Dic3—122no—
635C2×Dic3C2×#6711yescharacteristic
636C2×Dic3C2×#6711yescharacteristic
637C2×Dic3C2×#6711yescharacteristic
638D12—21no—
639D12—21no—
640D12—21no—
641D12—42no—
642D12—61no—
643D12—61no—
644D12—61no—
645D12—61no—
646D12—121no—
647D12—121no—
648D12—122no—
649D12—122no—
650D12—241no—
651D12C2×#6712yes—
652C4×D3—21no—
653C4×D3—21no—
654C4×D3—42no—
655C4×D3—122no—
656Dic6—21no—
657Dic6—21no—
658Dic6—42no—
659C3×C8—32no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—61no—
663C3⋊C8—61no—
664C3⋊C8—61no—
665C3⋊C8—61no—
666C3⋊C8—121no—
667C3⋊C8—121no—
668C3⋊C8C2×#6712yescomplemented
669C2×C32—41no—
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—81no—
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—22no—
681#41—41no—
682C2×Q8—31no—
683C2×Q8—61no—
684C2×Q8—62no—
685C2×Q8—121no—
686C2×Q8C2×D3211yescharacteristic
687C2×D4—21no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4—364no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—21no—
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710SD16—34no—
711SD16—62no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—62no—
718D8—361no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—91no—
723C2×C8—91no—
724C2×C8—182no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4—91no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—32no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—42no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—62no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—244no—
770C22×C3C2×D3×D411yescharacteristic
771C22×C3C22×#6711yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—22no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—84no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3#94912yescomplemented
793C3×C4—22no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—22no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—42no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—61no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100411yescharacteristic
809C3×C4C22×#6711yescharacteristic
810Dic3—21no—
811Dic3—21no—
812Dic3—21no—
813Dic3—41no—
814Dic3—41no—
815Dic3—121no—
816Dic3—121no—
817Dic3—241no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—21no—
820C23—31no—
821C23—61no—
822C23—61no—
823C23—122no—
824C23—122no—
825C23—181no—
826C23—241no—
827C23—362no—
828C23—362no—
829C23—721no—
830C23D3×#6711yescharacteristic
831Q8—21no—
832Q8—61no—
833Q8—61no—
834Q8—122no—
835Q8D3×#6712yescomplemented
836D4—21no—
837D4—21no—
838D4—32no—
839D4—42no—
840D4—62no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—122no—
845D4—122no—
846D4—181no—
847D4—181no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—721no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—42no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—122no—
865C2×C4—181no—
866C2×C4—362no—
867C2×C4D3×#6711yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C8—32no—
870C8—61no—
871C8—181no—
872C8—181no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—62no—
879C2×C3—81no—
880C2×C3—82no—
881C2×C3—81no—
882C2×C3—81no—
883C2×C3—122no—
884C2×C3—241no—
885C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
886C2×C3#577511yescharacteristic
887C2×C3D4×#6711yescharacteristic
888C2×C3D4×#6711yescharacteristic
889C2×C3C2×#94911yescharacteristic
890C2×C3#583711yescharacteristic
891D3—22no—
892D3—42no—
893D3—81no—
894D3—241no—
895D3—241no—
896D3—481no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—32no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—61no—
905C22—61no—
906C22—62no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—244no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—724no—
917C22C2×D3×#6711yescharacteristic
918C4—21no—
919C4—22no—
920C4—61no—
921C4—61no—
922C4—61no—
923C4—121no—
924C4—121no—
925C4—361no—
926C4C2×D3×#6711yescharacteristic
927C4#6433011yescharacteristic
928C3—21no—
929C3#8354211yescharacteristic, complemented
930C3#8395311yescharacteristic, complemented
931C2—41no—
932C2—62no—
933C2—81no—
934C2—122no—
935C2—241no—
936C2—721no—
937C2D3×#94911yescharacteristic
938C2#1059545511yescharacteristic
939C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5831C2semidirect
2. C2×C3×#949C2semidirect
3. C2×D3×#215C2semidirect
4. D12×#67C2semidirect
5. #10592937C2semidirect
6. #10591617C2semidirect
7. #10591583C2semidirect
8. #10591566C2semidirect
9. #10591515C2semidirect
10. #10591498C2semidirect
11. #10591483C2semidirect
12. #10591431C2semidirect
13. #10591178C2semidirect
14. #10591169C2semidirect
15. #10591147C2semidirect
18. C2×C32×#41C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C2×#3755C22semidirect
24. C2×#3753C22semidirect
27. C3×Q8×Dic3C22semidirect
29. C2×C3×#215C22semidirect
31. C3×#938C22semidirect
33. C3×#936C22semidirect
35. C2×C3×#213C22semidirect
39. C3×#924C22semidirect
40. C2×C3×#208C22semidirect
48. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5831D3semidirect
66. C2×#949D3semidirect
138. C3×#215D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
164. C2×D3×Q8C2×D3semidirect
186. Q8×Dic3C2×D3semidirect
195. C2×#215C2×D3semidirect
200. #938C2×D3semidirect
203. #936C2×D3semidirect
211. C2×#213C2×D3semidirect
219. #924C2×D3semidirect
220. C2×#208C2×D3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
430. #215#67semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
496. C2×#41D32semidirect
575. C3×Q8D3×D4semidirect
576. C3×Q8C2×#67semidirect
668. C3⋊C8C2×#67semidirect
792. C2×D3#949semidirect
818. C32#3265semidirect
835. Q8D3×#67semidirect
929. C3#83542semidirect
930. C3#83953semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C2×C3×#9492
C2×D3×#2152
D12×#672
#105929372
#105916172
#105915832
#105915662
#105915152
#105914982
#105914832
#105914312
#105911782
#105911692
#105911472
#839533
#835423