Finite Group Databasebeta

← #11883951

Subgroups — #11883951

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C3×#5817C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10595074C211yesmaximal, characteristic, complemented
5C3×#5227C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10591589C211yesmaximal, characteristic, complemented
10#10591588C211yesmaximal, characteristic, complemented
11#10591568C211yesmaximal, characteristic, complemented
12#10591540C211yesmaximal, characteristic, complemented
13#10591168C211yesmaximal, characteristic, complemented
14#10591166C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80060—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×D12C2211yescharacteristic
23C2×#3755—24no—
24C2×#3755C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic, complemented
27C2×#3755C2211yescharacteristic, complemented
28C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
29C3×#947—21no—
30C3×#947C2211yescharacteristic, complemented
31C3×#946—21no—
32C3×#946C2211yescharacteristic, complemented
33C3×Q8×Dic3C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C3×#930—21no—
37C3×#930C2211yescharacteristic
38C3×#930C2211yescharacteristic, complemented
39C3×C4×#67—21no—
40C3×C4×#67C2211yescharacteristic
41#63981—21no—
42#63939—24no—
43#63923—21no—
44#63911C2211yescharacteristic
45#63910—21no—
46#63909C2211yescharacteristic
47#63894C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65#5817D311yescharacteristic, complemented
66C22×#215—31no—
67C22×#215—31no—
68C22×#215—61no—
69C2×#914—31no—
70#5609—31no—
71D4×D12—31no—
72C3×#448—31no—
73#5238—31no—
74#5227D311yescharacteristic, complemented
75#5176—31no—
76#5169—31no—
77#5163—31no—
78#5058—31no—
79#5057—31no—
80#5049—31no—
81#5046—31no—
82#5038—31no—
83#5038—31no—
84#5036—31no—
85#5027—31no—
86#5026—31no—
87#5011—31no—
88#4819—31no—
89#4817—31no—
90#4812—31no—
91#4810—31no—
92#4732—31no—
93#4730—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—22no—
98C2×C32×Q8—41no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
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×#239—22no—
112C3×#239—41no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
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#3755—22no—
128#3755—22no—
129#3755D414yescomplemented
130C2×C3⋊(C3⋊C8)—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217D411yescharacteristic
134C3×#215—22no—
135C3×#215—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
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#3714—22no—
154#3714—41no—
155#3713—22no—
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—21no—
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C22×C3×Q8C2×D311yescharacteristic, complemented
162C2×#239C2×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×SD16—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#947—21no—
184#947C2×D311yescharacteristic, complemented
185#946—21no—
186#946C2×D311yescharacteristic, complemented
187Q8×Dic3C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—61no—
197C2×#215—61no—
198C2×#215—61no—
199C2×#215—61no—
200C2×#215—64no—
201C2×#215—64no—
202C2×#215—68no—
203C2×#215C2×D311yescharacteristic, complemented
204C2×#215C2×D311yescharacteristic, complemented
205#940—31no—
206#937—61no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—31no—
210C2×#213—31no—
211#930—21no—
212#930—31no—
213#930C2×D311yescharacteristic
214#930C2×D311yescharacteristic, complemented
215C4×#67—21no—
216C4×#67C2×D311yescharacteristic
217C2×#208—31no—
218C22×C3⋊C8—31no—
219C22×C3⋊C8—31no—
220C22×C3⋊C8—61no—
221#914—64no—
222C2×D24—31no—
223C2×D24—31no—
224C2×ΓL(1,𝔽25)—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×#103—31no—
236C3×C22⋊C8—31no—
237#835C2×D311yescharacteristic, complemented
238#835C2×D311yescharacteristic, complemented
239#832—31no—
240#832—31no—
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#809—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C4⋊(C3⋊C8)—31no—
255#803—31no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—81no—
268C32×Q8—21no—
269C32×Q8—21no—
270C32×Q8—21no—
271C32×Q8—42no—
272C32×Q8C2×D412yescomplemented
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—42no—
278C2×C32×C4C2×D411yescharacteristic
279C2×C32×C4C2411yescharacteristic
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—42no—
284C4⋊(C3⋊D3)C2×D412yes—
285C3×#67—22no—
286C3×#67—42no—
287C3×#67—42no—
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×D12—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—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—91no—
321#448—31no—
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—62no—
331C3×#41—121no—
332C2×C3×Q8—21no—
333C2×C3×Q8—21no—
334C2×C3×Q8—24no—
335C2×C3×Q8—22no—
336C2×C3×Q8—22no—
337C2×C3×Q8—21no—
338C2×C3×Q8—21no—
339C2×C3×Q8—41no—
340C2×C3×Q8—41no—
341C2×C3×Q8—41no—
342C2×C3×Q8—42no—
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×Q8C22×D311yescharacteristic
346C2×C3×Q8C22×D311yescharacteristic
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
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
368#239—22no—
369#239—41no—
370D3×D4—62no—
371D3×D4—121no—
372D3×D4—124no—
373D3×D4—124no—
374C2×D12—21no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—62no—
382C2×D12—62no—
383C2×D12—62no—
384C2×D12—64no—
385C2×D12—61no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—61no—
391C2×D12—121no—
392C2×D12—121no—
393C2×D12—121no—
394C2×D12—121no—
395C2×D12—122no—
396C2×D12C22×D311yescharacteristic
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3C22×D311yescharacteristic
402C3×SD16—62no—
403C3×SD16—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#6711yescharacteristic
421#215—22no—
422#215—34no—
423#215—34no—
424#215—41no—
425#215—64no—
426#215—62no—
427#215—62no—
428#215—62no—
429#215—62no—
430#215—64no—
431#215—64no—
432#215—64no—
433#215—62no—
434#215—62no—
435#213—62no—
436#213—62no—
437#213—62no—
438#213—121no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
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—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—31no—
459C2×C3⋊C8—31no—
460C2×C3⋊C8—31no—
461C2×C3⋊C8—61no—
462C2×C3⋊C8—61no—
463C2×C3⋊C8—62no—
464C2×C3⋊C8—62no—
465C2×C3⋊C8—64no—
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468D24—62no—
469D24—121no—
470ΓL(1,𝔽25)—62no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32AGL(1,ℤ/8)12yescomplemented
474C22×C32C22×D411yescharacteristic
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—84no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491D32—84no—
492C32×C4—21no—
493C32×C4—22no—
494C32×C4—41no—
495C32×C4C22×D411yescharacteristic
496C32×C4H(5,𝔽2)11yescharacteristic
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—31no—
503C22×Q8D3211yescharacteristic, complemented
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—181no—
507AGL(1,ℤ/8)—184no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×SD16—184no—
515C2×D8—91no—
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—31no—
540#102—91no—
541#102—91no—
542#102—91no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—91no—
546#97—91no—
547C23×C3—21no—
548C23×C3—31no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3D3×D411yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—122no—
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—242no—
571C22×D3—241no—
572C22×D3—241no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—242no—
576C22×D3C2×#6711yescharacteristic
577C3×Q8—21no—
578C3×Q8—21no—
579C3×Q8—22no—
580C3×Q8—21no—
581C3×Q8—21no—
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—22no—
585C3×Q8—41no—
586C3×Q8—41no—
587C3×Q8—42no—
588C3×Q8—42no—
589C3×Q8—44no—
590C3×Q8D3×D412yescomplemented
591C3×Q8D3×D412yescomplemented
592C3×D4—62no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—61no—
596C3×D4—61no—
597C3×D4—122no—
598C3×D4—122no—
599C3×D4—122no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—21no—
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—21no—
612C2×C3×C4—31no—
613C2×C3×C4—31no—
614C2×C3×C4—31no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—44no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—122no—
625C2×C3×C4D3×D411yescharacteristic
626C2×C3×C4C2×#6711yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628C2×C3×C4C23×D311yescharacteristic
629#67—22no—
630#67—42no—
631#67—42no—
632#67—122no—
633#67—122no—
634#67—122no—
635#67—241no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3C2×#6711yescharacteristic
639C2×Dic3C2×#6711yescharacteristic
640C2×Dic3C2×#6711yescharacteristic
641D12—21no—
642D12—21no—
643D12—21no—
644D12—21no—
645D12—32no—
646D12—32no—
647D12—42no—
648D12—62no—
649D12—62no—
650D12—61no—
651D12—61no—
652D12—61no—
653D12—61no—
654D12—61no—
655D12—61no—
656D12—121no—
657D12—121no—
658D12—122no—
659D12—122no—
660D12—124no—
661D12—122no—
662D12—122no—
663D12—122no—
664D12—241no—
665C4×D3—21no—
666C4×D3—21no—
667C4×D3—42no—
668C4×D3—122no—
669C4×D3—122no—
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—22no—
681C2×C32D4211yescharacteristic
682C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
683C2×C32#57711yescharacteristic
684C3⋊D3—42no—
685C3⋊D3—81no—
686C3×D3—41no—
687C3×D3—81no—
688C3×D3—81no—
689C24—181no—
690C24—181no—
691#41—62no—
692#41—121no—
693C2×Q8—21no—
694C2×Q8—22no—
695C2×Q8—41no—
696C2×Q8C2×D3211yescharacteristic
697C2×Q8C2×D3211yescharacteristic
698C2×D4—31no—
699C2×D4—31no—
700C2×D4—31no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—182no—
707C2×D4—181no—
708C2×D4—181no—
709C2×D4—181no—
710C2×D4—182no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—361no—
714C2×D4—361no—
715C2×D4—364no—
716C22×C4—21no—
717C22×C4—31no—
718C22×C4—61no—
719C22×C4—181no—
720C22×C4C2×D3211yescharacteristic
721SD16—62no—
722SD16—94no—
723SD16—121no—
724SD16—182no—
725SD16—182no—
726SD16—182no—
727D8—182no—
728D8—182no—
729D8—361no—
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—22no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3#91412yescomplemented
770C22×C3#94912yescomplemented
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C22×#6711yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—122no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—122no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—241no—
797C2×D3—241no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—244no—
801C2×D3—244no—
802C2×D3—244no—
803C2×D3—244no—
804C2×D3—248no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—22no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—61no—
817C3×C4—61no—
818C3×C4—61no—
819C3×C4—121no—
820C3×C4—121no—
821C3×C4C2×D3×D411yescharacteristic
822C3×C4C2×D3×D411yescharacteristic
823C3×C4#100411yescharacteristic
824C3×C4#100411yescharacteristic
825Dic3—21no—
826Dic3—21no—
827Dic3—21no—
828Dic3—41no—
829Dic3—41no—
830C32#326511yescharacteristic, complemented, Sylow
831C23—31no—
832C23—61no—
833C23—61no—
834C23—181no—
835C23—181no—
836C23—362no—
837C23—362no—
838C23—362no—
839C23—362no—
840C23—721no—
841C23—721no—
842C23D3×#6711yescharacteristic
843Q8—21no—
844Q8—21no—
845Q8—21no—
846Q8—42no—
847Q8#381112yescomplemented
848D4—62no—
849D4—61no—
850D4—61no—
851D4—61no—
852D4—61no—
853D4—92no—
854D4—122no—
855D4—122no—
856D4—122no—
857D4—181no—
858D4—181no—
859D4—181no—
860D4—362no—
861D4—362no—
862D4—362no—
863D4—362no—
864D4—721no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—31no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—42no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—122no—
878C2×C4—362no—
879C2×C4D3×#6711yescharacteristic
880C2×C4C22×D3211yescharacteristic
881C8—61no—
882C8—61no—
883C8—92no—
884C8—181no—
885C2×C3—24no—
886C2×C3—22no—
887C2×C3—22no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—121no—
892C2×C3—241no—
893C2×C3—241no—
894C2×C3#559011yescharacteristic
895C2×C3C2×#91411yescharacteristic
896C2×C3#577811yescharacteristic
897C2×C3D4×#6711yescharacteristic
898C2×C3C2×#94911yescharacteristic
899C2×C3#583711yescharacteristic
900D3—41no—
901D3—81no—
902D3—81no—
903D3—122no—
904D3—122no—
905D3—242no—
906D3—242no—
907D3—241no—
908D3—241no—
909C22—21no—
910C22—21no—
911C22—61no—
912C22—61no—
913C22—61no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—182no—
921C22—361no—
922C22—361no—
923C22—361no—
924C22—361no—
925C22—361no—
926C22—724no—
927C22—724no—
928C22#6393912yescomplemented
929C22C2×D3×#6711yescharacteristic
930C4—21no—
931C4—22no—
932C4—41no—
933C4—61no—
934C4—61no—
935C4—61no—
936C4—121no—
937C4—121no—
938C4C2×#381111yescharacteristic
939C4#6433011yescharacteristic
940C3—21no—
941C3#8006011yescharacteristic, complemented
942C3#8354211yescharacteristic, complemented
943C2—22no—
944C2—121no—
945C2—241no—
946C2—241no—
947C2—362no—
948C2—721no—
949C2C2×#6393911yescharacteristic
950C2#1059531911yescharacteristic
951C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×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. C22×#3755C2semidirect
2. C3×#5817C2semidirect
3. C2×#63939C2semidirect
4. #10595074C2semidirect
5. C3×#5227C2semidirect
6. #10591651C2semidirect
7. #10591619C2semidirect
8. #10591617C2semidirect
9. #10591589C2semidirect
10. #10591588C2semidirect
11. #10591568C2semidirect
12. #10591540C2semidirect
13. #10591168C2semidirect
14. #10591166C2semidirect
15. #10591158C2semidirect
18. C22×C32×Q8C22semidirect
20. C2×C3×#239C22semidirect
26. C2×#3755C22semidirect
27. C2×#3755C22semidirect
28. C22×C3⋊(C3⋊C8)C22semidirect
30. C3×#947C22semidirect
32. C3×#946C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C2×C3×#215C22semidirect
35. C2×C3×#215C22semidirect
38. C3×#930C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63564C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5817D3semidirect
74. #5227D3semidirect
129. #3755D4semidirect
160. C22×C3×Q8C2×D3semidirect
161. C22×C3×Q8C2×D3semidirect
162. C2×#239C2×D3semidirect
184. #947C2×D3semidirect
186. #946C2×D3semidirect
187. Q8×Dic3C2×D3semidirect
203. C2×#215C2×D3semidirect
204. C2×#215C2×D3semidirect
214. #930C2×D3semidirect
237. #835C2×D3semidirect
238. #835C2×D3semidirect
242. #830C2×D3semidirect
272. C32×Q8C2×D4semidirect
307. C3⋊(C3⋊C8)C2×D4semidirect
473. C22×C32AGL(1,ℤ/8)semidirect
503. C22×Q8D32semidirect
590. C3×Q8D3×D4semidirect
591. C3×Q8D3×D4semidirect
769. C22×C3#914semidirect
770. C22×C3#949semidirect
830. C32#3265semidirect
847. Q8#3811semidirect
928. C22#63939semidirect
941. C3#80060semidirect
942. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C3×#58172
C2×#639392
#105950742
C3×#52272
#105916512
#105916192
#105916172
#105915892
#105915882
#105915682
#105915402
#105911682
#105911662
#105911582
#835423
#800603