Finite Group Databasebeta

← #11883942

Subgroups — #11883942

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic, complemented
2C3×#5831C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10595074C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591515C211yesmaximal, characteristic, complemented
10#10591483C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591432C211yesmaximal, characteristic, complemented
13#10591183C211yesmaximal, characteristic, complemented
14#10591180C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80121—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×D12C2211yescharacteristic
23#64158—24no—
24C2×#3755C2211yescharacteristic
25C2×#3755C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic
27C2×#3753C2211yescharacteristic, complemented
28C2×#3748C2211yescharacteristic, complemented
29C3×Q8×Dic3C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C3×#938—21no—
32C3×#938C2211yescharacteristic, complemented
33C3×#936—21no—
34C3×#936C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C3×#930C2211yescharacteristic
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C3×#924—21no—
40C3×#924C2211yescharacteristic, complemented
41#63981—21no—
42D3×#215—24no—
43#63923—21no—
44#63911C2211yescharacteristic
45#63910—21no—
46#63909C2211yescharacteristic
47#63894C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#548—31no—
64#5831D311yescharacteristic, complemented
65C2×#949—31no—
66C2×#949—31no—
67C2×#949—61no—
68C22×#215—31no—
69C2×D3×SD16—31no—
70#5609—31no—
71D4×D12—31no—
72C3×#449—31no—
73#5238D311yescharacteristic, complemented
74#5227—31no—
75#5163—31no—
76#5156—31no—
77#5154—31no—
78#5058—31no—
79#5057—31no—
80#5049—31no—
81#5046—31no—
82#5042—31no—
83#5038—31no—
84#5036—31no—
85#5027—31no—
86#5026—31no—
87#5011—31no—
88#4817—31no—
89#4806—31no—
90#4787—31no—
91#4775—31no—
92#4731—31no—
93#4728—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×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C3×D3×Q8—22no—
112C3×D3×Q8—41no—
113C2×C3×D12C2311yescharacteristic
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—
126#3755—22no—
127#3755D414yescomplemented
128#3753—22no—
129#3753—22no—
130#3748—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217—21no—
137C3×#217D411yescharacteristic
138C3×#215—22no—
139C3×#213—41no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4D411yescharacteristic
147C3×C4×Dic3—21no—
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151#3722—21no—
152#3722—21no—
153#3717—22no—
154#3717—41no—
155#3715—22no—
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—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—61no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C3×#124—31no—
173C3×#124—61no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—61no—
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—61no—
179C3×C4×Q8—31no—
180C3×C4×D4—31no—
181C3×C4×D4—61no—
182#949—64no—
183#949—64no—
184#949—68no—
185Q8×Dic3C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215—61no—
195C2×#215—64no—
196C2×#215C2×D311yescharacteristic, complemented
197#940—31no—
198#938—21no—
199#938C2×D311yescharacteristic, complemented
200#937—61no—
201#936—21no—
202#936C2×D311yescharacteristic, complemented
203C2×#214—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213—61no—
210C2×#213C2×D311yescharacteristic, complemented
211#930—31no—
212#930C2×D311yescharacteristic
213C4×#67—21no—
214C4×#67C2×D311yescharacteristic
215#924—21no—
216#924C2×D311yescharacteristic, complemented
217C2×#208—31no—
218C2×#208—31no—
219C2×#208—61no—
220C22×C3⋊C8—31no—
221D3×SD16—64no—
222C2×#204—31no—
223C2×#204—31no—
224C2×D3×C8—31no—
225#895—31no—
226#895—61no—
227#893—31no—
228#884—61no—
229#882—61no—
230#882—61no—
231#882—61no—
232#874—31no—
233C4×D12—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×C22⋊C8—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#832—31no—
240#832C2×D311yescharacteristic, complemented
241#830—31no—
242#830C2×D311yescharacteristic, complemented
243#821—31no—
244#821—31no—
245(C2×D3)⋊C8—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C4⋊(C3⋊C8)—31no—
255#803—31no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3⋊D3—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—81no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—81no—
268C32×Q8—21no—
269C32×Q8C2×D412yescomplemented
270C32×D4—21no—
271C32×D4—21no—
272C32×D4—42no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—42no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—42no—
283C4⋊(C3⋊D3)C2×D412yes—
284C3×#67—22no—
285C3×#67—42no—
286C3×#67—42no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—42no—
301#626—42no—
302#626—42no—
303#626—42no—
304#626—81no—
305#624—42no—
306C3⋊(C3⋊C8)—21no—
307C3⋊(C3⋊C8)C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)—91no—
311C22×SD16—91no—
312#548—31no—
313D42—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#463—91no—
318#460—91no—
319#450—91no—
320#449—31no—
321#448—91no—
322#447—91no—
323#440—91no—
324#435—91no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—121no—
330C3×#41—24no—
331C3×#41—22no—
332C3×#41—22no—
333C3×#41—41no—
334C3×#41—41no—
335C3×#41—42no—
336C2×C3×Q8—21no—
337C2×C3×Q8—31no—
338C2×C3×Q8—61no—
339C2×C3×Q8—62no—
340C2×C3×Q8—121no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—41no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C22×D311yescharacteristic
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—41no—
358C22×C3×C4—61no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67#6711yescharacteristic
368D3×Q8—22no—
369D3×Q8—41no—
370D3×D4—62no—
371D3×D4—121no—
372D3×D4—124no—
373D3×D4—124no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—62no—
381C2×D12—62no—
382C2×D12—62no—
383C2×D12—64no—
384C2×D12—61no—
385C2×D12—61no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—121no—
391C2×D12—121no—
392C2×D12—121no—
393C2×D12—121no—
394C2×D12—122no—
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—21no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3C22×D311yescharacteristic
400C2×Dic6—21no—
401C2×Dic6C22×D311yescharacteristic
402C3×SD16—62no—
403C3×D8—121no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C42—31no—
419C3×C42—61no—
420#217—21no—
421#217—21no—
422#217—21no—
423#217—21no—
424#217#6711yescharacteristic
425#215—22no—
426#215—34no—
427#215—34no—
428#215—64no—
429#215—62no—
430#215—62no—
431#215—64no—
432#215—62no—
433#215—62no—
434#215—121no—
435#214—62no—
436#213—41no—
437#213—62no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—64no—
442#213—64no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4#6711yescharacteristic
449C4⋊Dic3—21no—
450C4⋊Dic3C22×D311yescharacteristic
451C4⋊Dic3C22×D311yescharacteristic
452Dic3⋊C4—21no—
453Dic3⋊C4#6711yescharacteristic
454C4×Dic3—21no—
455C4×Dic3C22×D311yescharacteristic
456#208—62no—
457#208—62no—
458#208—64no—
459C2×C3⋊C8—31no—
460C2×C3⋊C8—31no—
461C2×C3⋊C8—31no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—61no—
464C2×C3⋊C8—61no—
465C2×C3⋊C8—62no—
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468#204—62no—
469#204—121no—
470D3×C8—62no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—22no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—84no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3AGL(1,ℤ/8)12yescomplemented
491D32—84no—
492C32×C4—21no—
493C32×C4—22no—
494C32×C4C22×D411yescharacteristic
495C32×C4H(5,𝔽2)11yescharacteristic
496C3×Dic3—21no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41D3211yescharacteristic, complemented
503C22×Q8—31no—
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—181no—
507AGL(1,ℤ/8)—184no—
508C2×SD16—31no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×SD16—184no—
515C2×D8—31no—
516C2×D8—91no—
517C2×D8—91no—
518C2×M16—91no—
519C22×C8—91no—
520#127—91no—
521#124—31no—
522#124—61no—
523C22⋊Q8—31no—
524C22⋊Q8—61no—
525#121—31no—
526#121—31no—
527#121—61no—
528#121—91no—
529#121—181no—
530#120—181no—
531#120—181no—
532C4×Q8—31no—
533C4×D4—31no—
534C4×D4—61no—
535C4×D4—91no—
536#107—91no—
537C4⋊C8—91no—
538#103—31no—
539#103—91no—
540#102—31no—
541#102—91no—
542#102—91no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—91no—
546#97—91no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—31no—
551C23×C3—41no—
552C23×C3—61no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—21no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—124no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—242no—
572C22×D3—241no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—241no—
576C22×D3—242no—
577C22×D3C2×#6711yescharacteristic
578C3×Q8—21no—
579C3×Q8—21no—
580C3×Q8—22no—
581C3×Q8—41no—
582C3×Q8—61no—
583C3×Q8—61no—
584C3×Q8—122no—
585C3×Q8D3×D412yescomplemented
586C3×Q8D3×D412yescomplemented
587C3×D4—22no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—21no—
592C3×D4—41no—
593C3×D4—42no—
594C3×D4—42no—
595C3×D4—44no—
596C3×D4—62no—
597C3×D4—61no—
598C3×D4—61no—
599C3×D4—122no—
600C3×D4—122no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—31no—
614C2×C3×C4—41no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—44no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—122no—
624C2×C3×C4D3×D411yescharacteristic
625C2×C3×C4C2×#6711yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628#67—22no—
629#67—42no—
630#67—42no—
631#67—122no—
632#67—122no—
633#67—122no—
634#67—241no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3C2×#6711yescharacteristic
639C2×Dic3C2×#6711yescharacteristic
640C2×Dic3C2×#6711yescharacteristic
641D12—21no—
642D12—21no—
643D12—32no—
644D12—32no—
645D12—62no—
646D12—62no—
647D12—61no—
648D12—61no—
649D12—61no—
650D12—61no—
651D12—61no—
652D12—61no—
653D12—121no—
654D12—121no—
655D12—122no—
656D12—122no—
657D12—124no—
658D12—122no—
659D12—122no—
660D12—122no—
661D12—241no—
662C4×D3—21no—
663C4×D3—21no—
664C4×D3—42no—
665C4×D3—122no—
666C4×D3—122no—
667Dic6—21no—
668Dic6—21no—
669Dic6—42no—
670C3×C8—61no—
671C3×C8—61no—
672C3⋊C8—21no—
673C3⋊C8—21no—
674C3⋊C8—32no—
675C3⋊C8—32no—
676C3⋊C8—62no—
677C3⋊C8—62no—
678C3⋊C8—61no—
679C3⋊C8—61no—
680C2×C32—41no—
681C2×C32—81no—
682C2×C32D4211yescharacteristic
683C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
684C2×C32#57711yescharacteristic
685C3⋊D3—42no—
686C3⋊D3—81no—
687C3×D3—22no—
688C3×D3—81no—
689C24—181no—
690C24—181no—
691#41—22no—
692#41—41no—
693C2×Q8—31no—
694C2×Q8—61no—
695C2×Q8—62no—
696C2×Q8—121no—
697C2×Q8C2×D3211yescharacteristic
698C2×D4—21no—
699C2×D4—31no—
700C2×D4—31no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—91no—
704C2×D4—91no—
705C2×D4—182no—
706C2×D4—181no—
707C2×D4—181no—
708C2×D4—181no—
709C2×D4—182no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—361no—
713C2×D4—361no—
714C2×D4—364no—
715C2×D4C2×D3211yescharacteristic
716C22×C4—21no—
717C22×C4—31no—
718C22×C4—61no—
719C22×C4—181no—
720C22×C4C2×D3211yescharacteristic
721SD16—62no—
722SD16—94no—
723SD16—182no—
724SD16—182no—
725SD16—182no—
726SD16—361no—
727D8—121no—
728D8—182no—
729D8—182no—
730M16—182no—
731C2×C8—31no—
732C2×C8—31no—
733C2×C8—91no—
734C2×C8—91no—
735C2×C8—182no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—61no—
740C4⋊C4—61no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C42—31no—
751C42—61no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—32no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—42no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3C2×D3×D411yescharacteristic
778C22×C3C22×#6711yescharacteristic
779C2×D3—21no—
780C2×D3—21no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—122no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—122no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—241no—
801C2×D3—241no—
802C2×D3—244no—
803C2×D3—244no—
804C2×D3—244no—
805C2×D3—244no—
806C2×D3—248no—
807C2×D3#94912yescomplemented
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—22no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—42no—
816C3×C4—61no—
817C3×C4—61no—
818C3×C4—61no—
819C3×C4—121no—
820C3×C4—121no—
821C3×C4—121no—
822C3×C4C2×D3×D411yescharacteristic
823C3×C4C2×D3×D411yescharacteristic
824C3×C4#100411yescharacteristic
825C3×C4#100411yescharacteristic
826Dic3—21no—
827Dic3—21no—
828Dic3—21no—
829Dic3—41no—
830Dic3—41no—
831Dic3—41no—
832C32#326511yescharacteristic, complemented, Sylow
833C23—21no—
834C23—31no—
835C23—61no—
836C23—181no—
837C23—181no—
838C23—362no—
839C23—362no—
840C23—362no—
841C23—362no—
842C23—721no—
843C23—721no—
844C23D3×#6711yescharacteristic
845Q8—21no—
846Q8—61no—
847Q8—61no—
848Q8—122no—
849Q8#381112yescomplemented
850D4—21no—
851D4—21no—
852D4—42no—
853D4—62no—
854D4—61no—
855D4—61no—
856D4—92no—
857D4—122no—
858D4—122no—
859D4—181no—
860D4—181no—
861D4—181no—
862D4—362no—
863D4—362no—
864D4—362no—
865D4—362no—
866D4—721no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—42no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—122no—
880C2×C4—362no—
881C2×C4D3×#6711yescharacteristic
882C2×C4C22×D3211yescharacteristic
883C8—61no—
884C8—61no—
885C8—92no—
886C8—181no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—41no—
892C2×C3—41no—
893C2×C3—62no—
894C2×C3—82no—
895C2×C3—81no—
896C2×C3—81no—
897C2×C3—241no—
898C2×C3#559011yescharacteristic
899C2×C3#577011yescharacteristic
900C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
901C2×C3D4×#6711yescharacteristic
902C2×C3C2×#94911yescharacteristic
903C2×C3#583711yescharacteristic
904D3—22no—
905D3—81no—
906D3—122no—
907D3—122no—
908D3—242no—
909D3—242no—
910D3—241no—
911D3—241no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—32no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—61no—
920C22—61no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—182no—
925C22—361no—
926C22—361no—
927C22—361no—
928C22—361no—
929C22—361no—
930C22—724no—
931C22—724no—
932C22C2×D3×#6711yescharacteristic
933C4—21no—
934C4—22no—
935C4—61no—
936C4—61no—
937C4—61no—
938C4—121no—
939C4—121no—
940C4—121no—
941C4C2×#381111yescharacteristic
942C4#6433011yescharacteristic
943C3—21no—
944C3#8012111yescharacteristic, complemented
945C3#8354211yescharacteristic, complemented
946C2—41no—
947C2—62no—
948C2—81no—
949C2—241no—
950C2—362no—
951C2—721no—
952C2D3×#94911yescharacteristic
953C2#1059545711yescharacteristic
954C2#1059552611yescharacteristic
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. C2×#64158C2semidirect
2. C3×#5831C2semidirect
3. C2×D3×#215C2semidirect
4. #10595074C2semidirect
5. C3×#5238C2semidirect
6. #10591617C2semidirect
7. #10591584C2semidirect
8. #10591540C2semidirect
9. #10591515C2semidirect
10. #10591483C2semidirect
11. #10591449C2semidirect
12. #10591432C2semidirect
13. #10591183C2semidirect
14. #10591180C2semidirect
15. #10591151C2semidirect
18. C2×C32×#41C22semidirect
20. C2×C3×D3×Q8C22semidirect
25. C2×#3755C22semidirect
27. C2×#3753C22semidirect
28. C2×#3748C22semidirect
29. C3×Q8×Dic3C22semidirect
30. C2×C3×#215C22semidirect
32. C3×#938C22semidirect
34. C3×#936C22semidirect
35. C2×C3×#213C22semidirect
40. C3×#924C22semidirect
49. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
64. #5831D3semidirect
73. #5238D3semidirect
127. #3755D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
162. C2×D3×Q8C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
196. C2×#215C2×D3semidirect
199. #938C2×D3semidirect
202. #936C2×D3semidirect
210. C2×#213C2×D3semidirect
216. #924C2×D3semidirect
238. #835C2×D3semidirect
240. #832C2×D3semidirect
242. #830C2×D3semidirect
269. C32×Q8C2×D4semidirect
307. C3⋊(C3⋊C8)C2×D4semidirect
490. C2×C3×D3AGL(1,ℤ/8)semidirect
502. C2×#41D32semidirect
585. C3×Q8D3×D4semidirect
586. C3×Q8D3×D4semidirect
807. C2×D3#949semidirect
832. C32#3265semidirect
849. Q8#3811semidirect
944. C3#80121semidirect
945. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58312
C2×D3×#2152
#105950742
C3×#52382
#105916172
#105915842
#105915402
#105915152
#105914832
#105914492
#105914322
#105911832
#105911802
#105911512
#835423
#801213