Finite Group Databasebeta

← #11885741

Subgroups — #11885741

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4756C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590945C211yesmaximal, characteristic, complemented
11#10590880C211yesmaximal, characteristic, complemented
12#10590721C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80024—31nomaximal
17D8×D12—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic, complemented
20C22×#626—21no—
21C2×#3802C2211yescharacteristic, complemented
22C2×D3×D12—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26#64104C2211yescharacteristic, complemented
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic, complemented
32C3×#893C2211yescharacteristic, complemented
33#63981—21no—
34#63978—21no—
35#63977—21no—
36#63926—24no—
37D3×#213—24no—
38#63923—21no—
39#63922—21no—
40#63916C2211yescharacteristic, complemented
41#63911C2211yescharacteristic, complemented
42#63911C2211yescharacteristic, complemented
43#63909C2211yescharacteristic, complemented
44#63906—21no—
45C4×#626C2211yescharacteristic
46C2×#3714C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3710C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×C8×Dic3C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68#5609—31no—
69D4×D12—31no—
70D4×D12—31no—
71C3×#447—31no—
72C3×C4×D8—31no—
73#5156—31no—
74#5151—31no—
75#5150—31no—
76#5038—31no—
77#5015—31no—
78#5015—31no—
79#4883—31no—
80#4883—31no—
81#4786—31no—
82#4775—31no—
83#4773—31no—
84#4773—31no—
85#4773—31no—
86#4773—31no—
87#4773—61no—
88#4773D311yescharacteristic, complemented
89#4756D311yescharacteristic, complemented
90#4732—31no—
91#67⋊C8—31no—
92#4695—31no—
93C8×D12—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C22×D32—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—41no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C3×D3×D4—22no—
109C3×D3×D4—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—44no—
124C2×#626D411yescharacteristic
125C2×#625—21no—
126#3802—22no—
127#3802—41no—
128D3×D12—22no—
129D3×D12—41no—
130D3×D12—44no—
131C2×C32×C8C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133#3753—22no—
134#3752—21no—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3745—41no—
137C3×#217—21no—
138C3×#213—22no—
139C3×#213D414yescomplemented
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—41no—
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3714—22no—
153#3714—22no—
154#3714—22no—
155#3713—22no—
156#3710—22no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4C2×D311yescharacteristic, complemented
169C22×D12—31no—
170C22×D12—61no—
171C22×D12—61no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C3×#121—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178#953—61no—
179#940—31no—
180#940—31no—
181#939—61no—
182#938—31no—
183#937—61no—
184#937—61no—
185D4×Dic3C2×D311yescharacteristic, complemented
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—61no—
194C2×#213—64no—
195C2×#213C2×D311yescharacteristic
196C2×#213C2×D311yescharacteristic, complemented
197#930—31no—
198#930—61no—
199#930—61no—
200C4×#67—31no—
201C22×C3⋊C8—31no—
202D3×D8—64no—
203D3×D8—64no—
204D3×D8—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—61no—
211C2×D24C2×D311yescharacteristic, complemented
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214C2×D3×C8—31no—
215#895—31no—
216#895—31no—
217#895—31no—
218#895—31no—
219#895—61no—
220#895C2×D311yescharacteristic, complemented
221#893C2×D311yescharacteristic, complemented
222#884—61no—
223#882—61no—
224#882—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229#874—31no—
230C4×D12—31no—
231C3×#107—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102C2×D311yescharacteristic, complemented
236C3×#102C2×D311yescharacteristic, complemented
237C3×C22⋊C8—31no—
238C3×C4×C8—31no—
239#832—31no—
240#821—31no—
241#821C2×D311yescharacteristic, complemented
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—61no—
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246Dic3⋊C8—31no—
247C8×Dic3C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#809—61no—
253#809C2×D311yescharacteristic, complemented
254#807C2×D311yescharacteristic, complemented
255C4⋊(C3⋊C8)—31no—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—81no—
269C22×C3×D3C2×D411yescharacteristic
270C2×D32—42no—
271C2×D32—42no—
272C2×D32—42no—
273C2×D32—42no—
274C2×D32—81no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4C2×D412yescomplemented
278C2×C32×C4—21no—
279C2×C32×C4C2411yescharacteristic
280#638—42no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—42no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C3×#67—42no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—42no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—42no—
301C3×D12C2×D412yescomplemented
302C3×C4×D3—21no—
303C3×C4×D3—21no—
304C3×C4×D3—42no—
305#626—42no—
306#626—42no—
307#626—42no—
308#626—42no—
309#626—42no—
310#626—81no—
311#626—81no—
312#626D814yescomplemented
313#625—42no—
314C32×C8—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—91no—
319C22×D8—91no—
320D42—91no—
321D42—91no—
322#493—91no—
323#466—91no—
324#466—91no—
325#459—91no—
326#459—91no—
327#447—31no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—31no—
332C8×D4—91no—
333C24×C3—61no—
334C23×D3—21no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—121no—
342C2×C3×D4—21no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—62no—
349C2×C3×D4—121no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C2×#67—21no—
356C2×#67—31no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—121no—
369C2×#67—124no—
370C22×Dic3—21no—
371D3×D4—22no—
372D3×D4—41no—
373D3×D4—62no—
374D3×D4—62no—
375D3×D4—62no—
376D3×D4—62no—
377D3×D4—62no—
378D3×D4—122no—
379D3×D4—121no—
380D3×D4—124no—
381D3×D4—121no—
382D3×D4—121no—
383D3×D4—121no—
384D3×D4—121no—
385D3×D4—122no—
386C2×D12—21no—
387C2×D12—31no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—62no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—124no—
407C2×D12—124no—
408C2×D12C22×D311yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×D12C22×D311yescharacteristic
411C2×C4×D3—21no—
412C2×C4×D3—31no—
413C2×C4×D3—31no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—34no—
417C3×D8—62no—
418C3×D8—121no—
419C2×C3×C8—21no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8C22×D311yescharacteristic
423C2×C3×C8C22×D311yescharacteristic
424C3×C4⋊C4—21no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4C22×D311yescharacteristic
427C3×C4⋊C4C22×D311yescharacteristic
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C42—31no—
432#217—21no—
433#217—31no—
434#217—61no—
435#213—22no—
436#213—62no—
437#213—62no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—62no—
442#213—62no—
443#213—122no—
444#213D1214yescomplemented
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—121no—
456C4⋊Dic3—31no—
457C4⋊Dic3C22×D311yescharacteristic
458Dic3⋊C4—31no—
459C4×Dic3C22×D311yescharacteristic
460C2×C3⋊C8—31no—
461C2×C3⋊C8—31no—
462C2×C3⋊C8—61no—
463C2×C3⋊C8—62no—
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466D24—41no—
467D24—62no—
468D24—62no—
469D24—62no—
470D24—121no—
471D24—121no—
472D24—122no—
473D3×C8—62no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—22no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—84no—
489C2×C3⋊D3C2×D812yescomplemented
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—84no—
502C2×C3×D3C2×D812yescomplemented
503D32—84no—
504D32—84no—
505C32×C4—41no—
506C32×C4C22×D411yescharacteristic
507C32×C4H(5,𝔽2)11yescharacteristic
508C3⋊Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—41no—
512C3×Dic3C2×D812yescomplemented
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—181no—
518C22×D4—181no—
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—31no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—184no—
529C2×D8—184no—
530C22×C8—91no—
531C22×C8—91no—
532#127—91no—
533#127—91no—
534#121—31no—
535#121—91no—
536#121—91no—
537#121—91no—
538#121—181no—
539#121—181no—
540#120—181no—
541#120—181no—
542#120—181no—
543#120—181no—
544C4×D4—31no—
545C4×D4—31no—
546C4×D4—91no—
547#107—31no—
548C4⋊C8—91no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102D3211yescharacteristic, complemented
555C22⋊C8—31no—
556C22⋊C8—91no—
557C4×C8—31no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—31no—
561C23×C3—41no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—122no—
566C23×C3—122no—
567C23×C3—241no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—31no—
572C22×D3—31no—
573C22×D3—42no—
574C22×D3—42no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—81no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—124no—
595C22×D3—122no—
596C22×D3—242no—
597C22×D3—241no—
598C22×D3—241no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—242no—
604C22×D3D3×D411yescharacteristic
605C3×D4—21no—
606C3×D4—21no—
607C3×D4—22no—
608C3×D4—32no—
609C3×D4—41no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—122no—
616C3×D4—122no—
617C3×D4C2×D1212yescomplemented
618C3×D4D3×D412yescomplemented
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—31no—
625C2×C3×C4—41no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—122no—
630C2×C3×C4—122no—
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633#67—34no—
634#67—42no—
635#67—122no—
636#67—122no—
637#67—122no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—124no—
643#67—122no—
644#67—122no—
645#67—241no—
646#67—241no—
647C2×Dic3—21no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—42no—
651C2×Dic3—61no—
652C2×Dic3D3×D411yescharacteristic
653C2×Dic3D3×D411yescharacteristic
654C2×Dic3D3×D411yescharacteristic
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—34no—
661D12—42no—
662D12—62no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—121no—
672D12—121no—
673D12—121no—
674D12—122no—
675D12—122no—
676D12—122no—
677D12—122no—
678D12—122no—
679D12—122no—
680D12—122no—
681D12—242no—
682D12—241no—
683D12—241no—
684D12C2×D1212yescomplemented
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—42no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—121no—
693C4×D3—121no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—32no—
697C3×C8—41no—
698C3×C8—61no—
699C3⋊C8—21no—
700C3⋊C8—61no—
701C3⋊C8—61no—
702C3⋊C8—121no—
703C3⋊C8C2×D1212yescomplemented
704C2×C32—42no—
705C2×C32D4211yescharacteristic
706C2×C32C22×D811yescharacteristic
707C2×C32#57611yescharacteristic
708C3⋊D3—22no—
709C3⋊D3—81no—
710C3⋊D3—81no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—61no—
716C24—181no—
717C24—181no—
718C24—181no—
719C2×D4—31no—
720C2×D4—31no—
721C2×D4—31no—
722C2×D4—61no—
723C2×D4—61no—
724C2×D4—62no—
725C2×D4—91no—
726C2×D4—91no—
727C2×D4—91no—
728C2×D4—121no—
729C2×D4—181no—
730C2×D4—181no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—182no—
736C2×D4—181no—
737C2×D4—181no—
738C2×D4—181no—
739C2×D4—181no—
740C2×D4—182no—
741C2×D4—182no—
742C2×D4—361no—
743C2×D4—364no—
744C2×D4—364no—
745C2×D4—361no—
746C2×D4—361no—
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—91no—
752D8—34no—
753D8—62no—
754D8—121no—
755D8—182no—
756D8—182no—
757D8—182no—
758D8—182no—
759D8—182no—
760D8—361no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—91no—
764C2×C8—182no—
765C2×C8—182no—
766C2×C8C2×D3211yescharacteristic
767C4⋊C4—31no—
768C4⋊C4—91no—
769C4⋊C4C2×D3211yescharacteristic
770C22⋊C4—61no—
771C22⋊C4—61no—
772C22⋊C4—61no—
773C22⋊C4—91no—
774C22⋊C4—91no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—21no—
782C22×C3—32no—
783C22×C3—42no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—61no—
789C22×C3—61no—
790C22×C3—62no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—244no—
802C22×C3C2×D3×D411yescharacteristic
803C22×C3C2×D3×D411yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—22no—
807C2×D3—32no—
808C2×D3—32no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—62no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—84no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—122no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C2×D3—241no—
843C2×D3—244no—
844C2×D3—244no—
845C2×D3—244no—
846C2×D3—244no—
847C2×D3—244no—
848C2×D3—244no—
849C2×D3—248no—
850C2×D3D3×D812yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—32no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—81no—
859C3×C4—121no—
860C3×C4C22×D1211yescharacteristic
861C3×C4C2×D3×D411yescharacteristic
862C3×C4#100411yescharacteristic
863C3×C4#100911yescharacteristic
864Dic3—21no—
865Dic3—21no—
866Dic3—41no—
867Dic3—61no—
868Dic3—61no—
869Dic3—121no—
870Dic3D3×D812yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—31no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—91no—
878C23—122no—
879C23—122no—
880C23—181no—
881C23—181no—
882C23—241no—
883C23—362no—
884C23—362no—
885C23—362no—
886C23—362no—
887C23—362no—
888C23—362no—
889C23—721no—
890C23—721no—
891C23—721no—
892D4—21no—
893D4—32no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—94no—
900D4—122no—
901D4—122no—
902D4—181no—
903D4—181no—
904D4—181no—
905D4—181no—
906D4—362no—
907D4—362no—
908D4—362no—
909D4—362no—
910D4—362no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—721no—
915D4—721no—
916D4D3×D1212yescomplemented
917C2×C4—21no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—91no—
925C2×C4—122no—
926C2×C4—122no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4C22×D3211yescharacteristic
930C8—21no—
931C8—32no—
932C8—61no—
933C8—181no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—62no—
940C2×C3—82no—
941C2×C3—122no—
942C2×C3—241no—
943C2×C3—241no—
944C2×C3D4×D1211yescharacteristic
945C2×C3#559011yescharacteristic
946C2×C3C2×D3×D811yescharacteristic
947C2×C3C2×D3×D811yescharacteristic
948C2×C3#576911yescharacteristic
949C2×C3#577411yescharacteristic
950D3—22no—
951D3—42no—
952D3—62no—
953D3—62no—
954D3—81no—
955D3—81no—
956D3—122no—
957D3—242no—
958D3—241no—
959D3—241no—
960D3—241no—
961D3—241no—
962D3—481no—
963C22—22no—
964C22—32no—
965C22—41no—
966C22—41no—
967C22—61no—
968C22—61no—
969C22—62no—
970C22—92no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—181no—
980C22—181no—
981C22—244no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22—361no—
988C22—724no—
989C22—724no—
990C22—724no—
991C22D32×D411yescharacteristic
992C4—32no—
993C4—41no—
994C4—61no—
995C4—61no—
996C4—121no—
997C4—181no—
998C4C2×D3×D1211yescharacteristic
999C4#6431411yescharacteristic
1000C3—21no—
1001C3D8×D1211yescharacteristic, complemented
1002C3#8002411yescharacteristic, complemented
1003C2—42no—
1004C2—62no—
1005C2—122no—
1006C2—182no—
1007C2—241no—
1008C2—241no—
1009C2—721no—
1010C2—721no—
1011C2#1059427711yescharacteristic
1012C2D32×D811yescharacteristic
1013C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#626C2semidirect
2. C2×#63926C2semidirect
3. C2×D3×#213C2semidirect
4. #10594621C2semidirect
5. #10592472C2semidirect
6. C3×#4773C2semidirect
7. C3×#4756C2semidirect
8. #10591481C2semidirect
9. #10590947C2semidirect
10. #10590945C2semidirect
11. #10590880C2semidirect
12. #10590721C2semidirect
13. #10590576C2semidirect
14. #10590547C2semidirect
15. #10590509C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×C3×D3×D4C22semidirect
21. C2×#3802C22semidirect
23. C2×D3×D12C22semidirect
24. C2×#3753C22semidirect
25. C2×#3745C22semidirect
26. #64104C22semidirect
27. C3×D4×Dic3C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×D24C22semidirect
31. C3×#895C22semidirect
32. C3×#893C22semidirect
40. #63916C22semidirect
41. #63911C22semidirect
42. #63911C22semidirect
43. #63909C22semidirect
46. C2×#3714C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3710C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
53. #63647C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×C8×Dic3C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
88. #4773D3semidirect
89. #4756D3semidirect
139. C3×#213D4semidirect
168. C2×D3×D4C2×D3semidirect
185. D4×Dic3C2×D3semidirect
196. C2×#213C2×D3semidirect
211. C2×D24C2×D3semidirect
220. #895C2×D3semidirect
221. #893C2×D3semidirect
235. C3×#102C2×D3semidirect
236. C3×#102C2×D3semidirect
241. #821C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
247. C8×Dic3C2×D3semidirect
253. #809C2×D3semidirect
254. #807C2×D3semidirect
277. C32×D4C2×D4semidirect
301. C3×D12C2×D4semidirect
312. #626D8semidirect
317. C3×C3⋊C8C2×D4semidirect
444. #213D12semidirect
489. C2×C3⋊D3C2×D8semidirect
502. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
554. #102D32semidirect
617. C3×D4C2×D12semidirect
618. C3×D4D3×D4semidirect
684. D12C2×D12semidirect
703. C3⋊C8C2×D12semidirect
850. C2×D3D3×D8semidirect
870. Dic3D3×D8semidirect
871. C32D4×D8semidirect
916. D4D3×D12semidirect
1001. C3D8×D12semidirect
1002. C3#80024semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
C2×#639262
C2×D3×#2132
#105946212
#105924722
C3×#47732
C3×#47562
#105914812
#105909472
#105909452
#105908802
#105907212
#105905762
#105905472
#105905092
#800243
D8×D123