Finite Group Databasebeta

← #11885764

Subgroups — #11885764

Order 1152.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594618C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4775C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591484C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#80729—31nomaximal
17#80024—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic, complemented
19C2×D3×#67—21no—
20C2×#3802—21no—
21C2×D3×D12C2211yescharacteristic, complemented
22C2×D3×D12C2211yescharacteristic, complemented
23C2×D3×D12C2211yescharacteristic, complemented
24#64149C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C2×#3745C2211yescharacteristic, complemented
27#64102C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic, complemented
34C3×#895C2211yescharacteristic, complemented
35#63983—21no—
36#63977—21no—
37#63971—21no—
38D3×#213—24no—
39#63922—21no—
40#63922—21no—
41#63914C2211yescharacteristic, complemented
42#63912—21no—
43#63909C2211yescharacteristic, complemented
44C4×#625C2211yescharacteristic
45#63898C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51D3×D24—24no—
52C32×#102C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68#5609—31no—
69#5609—31no—
70#5609—31no—
71C3×#466—31no—
72C3×#447—31no—
73#5156—31no—
74#5151—31no—
75#5151—31no—
76#5150—31no—
77C8×#67—31no—
78#5038—31no—
79#5036—31no—
80#5036—31no—
81#4883—31no—
82#4872—31no—
83#4786—31no—
84#4786—31no—
85#4786—31no—
86#4786—61no—
87#4775D311yescharacteristic, complemented
88#4773—31no—
89#4773—31no—
90#4773D311yescharacteristic, complemented
91#4756—31no—
92#4732—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×D32—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115D3×#67—44no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#625—21no—
121C2×#625—21no—
122C2×#625D411yescharacteristic
123C2×D3×Dic3—21no—
124#3802—44no—
125D3×D12—22no—
126D3×D12—22no—
127D3×D12—22no—
128D3×D12—41no—
129D3×D12—41no—
130D3×D12—41no—
131C2×C32×C8C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133#3753—22no—
134#3752—21no—
135C4×C3⋊Dic3C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137#3745—22no—
138C3×#217—21no—
139C3×#213—22no—
140C3×#213—41no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—22no—
147C3×D3×C8—22no—
148#3724D411yescharacteristic
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152(C2×D3)⋊Dic3D411yescharacteristic
153#3714—22no—
154#3714—41no—
155#3714D414yescomplemented
156#3713—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—61no—
165C2×D3×D4—61no—
166C2×D3×D4—61no—
167C2×D3×D4C2×D311yescharacteristic, complemented
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—31no—
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#121—31no—
176C3×#121—31no—
177C3×#121—31no—
178#953—61no—
179#940—31no—
180#940—31no—
181#940—31no—
182#940—31no—
183#940—61no—
184#939—61no—
185#938C2×D311yescharacteristic, complemented
186#937—61no—
187#937—61no—
188#937—61no—
189#937—61no—
190D4×Dic3—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—61no—
199C2×#213—64no—
200C2×#213C2×D311yescharacteristic, complemented
201C2×#213C2×D311yescharacteristic, complemented
202#930—31no—
203C4×#67—31no—
204C4×#67—31no—
205C22×C3⋊C8—31no—
206D3×D8—64no—
207D3×D8—64no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—31no—
211C2×D24—31no—
212C2×D24—31no—
213C2×D24—61no—
214C2×D24—64no—
215C2×D24C2×D311yescharacteristic, complemented
216C2×D3×C8—31no—
217C2×D3×C8C2×D311yescharacteristic, complemented
218#895—31no—
219#895C2×D311yescharacteristic, complemented
220#895C2×D311yescharacteristic, complemented
221#893—31no—
222#893—31no—
223#893—31no—
224#893—61no—
225#884—61no—
226#884—61no—
227#884—61no—
228#882—61no—
229#882—61no—
230#882—61no—
231C3×#107—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102C2×D311yescharacteristic, complemented
236C3×#102C2×D311yescharacteristic, complemented
237C3×C22⋊C8—31no—
238#832—31no—
239#830—31no—
240#821—31no—
241#821C2×D311yescharacteristic, complemented
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247C8×Dic3—31no—
248C8×Dic3—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#809—31no—
253#809—61no—
254#809C2×D311yescharacteristic, complemented
255#807C2×D311yescharacteristic, complemented
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C2×D32—42no—
268C2×D32—42no—
269C2×D32—42no—
270C2×D32—42no—
271C2×D32—42no—
272C2×D32—42no—
273C2×D32—81no—
274C2×D32—81no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4—21no—
278C2×C32×C4—21no—
279C2×C32×C4C2411yescharacteristic
280#638—42no—
281#638—81no—
282C2×C3⋊Dic3C2×D411yescharacteristic
283C2×C3⋊Dic3C2×D411yescharacteristic
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)C2×D412yescomplemented
288C4×C3⋊D3—42no—
289C3×#67—42no—
290C3×#67—42no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—42no—
300C3×D12—42no—
301C3×D12C2×D412yescomplemented
302C3×C4×D3—21no—
303C3×C4×D3—21no—
304C3×C4×D3—21no—
305C3×C4×D3—21no—
306#626—42no—
307#626—42no—
308#626—42no—
309#626—42no—
310#625—42no—
311#625—81no—
312#625D814yescomplemented
313D3×Dic3—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—31no—
324#466—91no—
325#459—91no—
326#459—91no—
327#447—31no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
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—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—62no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C22×D311yescharacteristic
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—31no—
358C2×#67—31no—
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—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—121no—
372C2×#67—121no—
373C2×#67—124no—
374C22×Dic3—61no—
375D3×D4—22no—
376D3×D4—41no—
377D3×D4—62no—
378D3×D4—62no—
379D3×D4—62no—
380D3×D4—121no—
381D3×D4—121no—
382D3×D4—121no—
383D3×D4—124no—
384D3×D4—124no—
385D3×D4—124no—
386C2×D12—21no—
387C2×D12—21no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—62no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—121no—
402C2×D12—121no—
403C2×D12—121no—
404C2×D12C22×D311yescharacteristic
405C2×D12C22×D311yescharacteristic
406C2×D12C22×D311yescharacteristic
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—121no—
411C2×C4×D3C22×D311yescharacteristic
412C2×C4×D3C22×D311yescharacteristic
413C3×D8—62no—
414C3×D8—62no—
415C3×D8—121no—
416C2×C3×C8—21no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—62no—
420C2×C3×C8C22×D311yescharacteristic
421C2×C3×C8C22×D311yescharacteristic
422C3×C4⋊C4—21no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4C22×D311yescharacteristic
425C3×C4⋊C4C22×D311yescharacteristic
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429#217—21no—
430#217—31no—
431#217—31no—
432#217—61no—
433#213—22no—
434#213—34no—
435#213—41no—
436#213—62no—
437#213—62no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—122no—
442#213—121no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—121no—
453C4⋊Dic3C22×D311yescharacteristic
454Dic3⋊C4—31no—
455Dic3⋊C4—31no—
456C4×Dic3—31no—
457C4×Dic3—31no—
458C4×Dic3—61no—
459C2×C3⋊C8—31no—
460C2×C3⋊C8—31no—
461C2×C3⋊C8—61no—
462C2×C3⋊C8—62no—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465D24—22no—
466D24—34no—
467D24—62no—
468D24—62no—
469D24—62no—
470D24—122no—
471D24—121no—
472D3×C8—22no—
473D3×C8—62no—
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—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—22no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—84no—
498C2×C3×D3C2×D812yescomplemented
499C2×C3×D3C2×D812yescomplemented
500D32—84no—
501D32—84no—
502D32—84no—
503C32×C4—41no—
504C32×C4C22×D411yescharacteristic
505C32×C4H(5,𝔽2)11yescharacteristic
506C3⋊Dic3—21no—
507C3⋊Dic3C2×D812yescomplemented
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—41no—
511C22×D4—31no—
512C22×D4—91no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—181no—
516C22×D4—181no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—31no—
520C2×D8—91no—
521C2×D8—91no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—184no—
527C2×D8—184no—
528C22×C8—31no—
529C22×C8—91no—
530#127—91no—
531#127—91no—
532#121—31no—
533#121—31no—
534#121—31no—
535#121—91no—
536#121—181no—
537#121—181no—
538#120—181no—
539#120—181no—
540#120—181no—
541#120—181no—
542C4×D4—91no—
543C4×D4—91no—
544C4×D4—91no—
545#107—31no—
546C4⋊C8—91no—
547#102—31no—
548#102—31no—
549#102—91no—
550#102—91no—
551#102—91no—
552#102D3211yescharacteristic, complemented
553C22⋊C8—31no—
554C22⋊C8—91no—
555C4×C8—91no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—31no—
559C23×C3—31no—
560C23×C3—41no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—122no—
565C23×C3—122no—
566C23×C3—241no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—42no—
571C22×D3—42no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—81no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
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—241no—
592C22×D3—241no—
593C22×D3—241no—
594C22×D3—241no—
595C22×D3—241no—
596C22×D3—241no—
597C22×D3D3×D411yescharacteristic
598C22×D3D3×D411yescharacteristic
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—32no—
604C3×D4—41no—
605C3×D4—41no—
606C3×D4—61no—
607C3×D4—61no—
608C3×D4—61no—
609C3×D4—61no—
610C3×D4—61no—
611C3×D4—122no—
612C3×D4—122no—
613C3×D4—122no—
614C3×D4—122no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—41no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628#67—34no—
629#67—34no—
630#67—42no—
631#67—42no—
632#67—122no—
633#67—122no—
634#67—122no—
635#67—122no—
636#67—122no—
637#67—122no—
638#67—122no—
639#67—122no—
640#67—242no—
641#67—241no—
642#67—241no—
643#67—241no—
644#67—241no—
645#67—242no—
646C2×Dic3—21no—
647C2×Dic3—31no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—122no—
654C2×Dic3D3×D411yescharacteristic
655C2×Dic3D3×D411yescharacteristic
656D12—21no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—21no—
661D12—32no—
662D12—32no—
663D12—42no—
664D12—42no—
665D12—62no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—61no—
672D12—121no—
673D12—121no—
674D12—121no—
675D12—122no—
676D12—122no—
677D12—122no—
678D12—122no—
679D12D3×D412yescomplemented
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—21no—
684C4×D3—122no—
685C4×D3—122no—
686C4×D3—122no—
687C4×D3—242no—
688C3×C8—21no—
689C3×C8—21no—
690C3×C8—32no—
691C3×C8—41no—
692C3×C8—61no—
693C3⋊C8—21no—
694C3⋊C8—61no—
695C3⋊C8—61no—
696C3⋊C8—121no—
697C3⋊C8D3×D412yescomplemented
698C2×C32—81no—
699C2×C32D4211yescharacteristic
700C2×C32C22×D811yescharacteristic
701C2×C32#57611yescharacteristic
702C3⋊D3—42no—
703C3⋊D3—81no—
704C3×D3—22no—
705C3×D3—22no—
706C3×D3—42no—
707C3×D3—81no—
708C3×D3—81no—
709C24—61no—
710C24—181no—
711C24—181no—
712C24—181no—
713C2×D4—31no—
714C2×D4—31no—
715C2×D4—31no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—61no—
719C2×D4—62no—
720C2×D4—61no—
721C2×D4—91no—
722C2×D4—91no—
723C2×D4—91no—
724C2×D4—121no—
725C2×D4—181no—
726C2×D4—181no—
727C2×D4—181no—
728C2×D4—182no—
729C2×D4—182no—
730C2×D4—182no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—361no—
737C2×D4—361no—
738C2×D4—361no—
739C2×D4—364no—
740C2×D4—364no—
741C2×D4C2×D3211yescharacteristic
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—181no—
745C22×C4—181no—
746D8—62no—
747D8—62no—
748D8—94no—
749D8—121no—
750D8—182no—
751D8—182no—
752D8—182no—
753D8—182no—
754D8—361no—
755C2×C8—31no—
756C2×C8—31no—
757C2×C8—62no—
758C2×C8—91no—
759C2×C8—182no—
760C2×C8C2×D3211yescharacteristic
761C4⋊C4—31no—
762C4⋊C4—91no—
763C4⋊C4C2×D3211yescharacteristic
764C22⋊C4—61no—
765C22⋊C4—61no—
766C22⋊C4—61no—
767C22⋊C4—91no—
768C22⋊C4—91no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C22⋊C4—181no—
772C42—91no—
773C22×C3—21no—
774C22×C3—32no—
775C22×C3—32no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—62no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—244no—
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C2×D3—21no—
802C2×D3—21no—
803C2×D3—21no—
804C2×D3—21no—
805C2×D3—22no—
806C2×D3—41no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—84no—
817C2×D3—122no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—241no—
829C2×D3—241no—
830C2×D3—241no—
831C2×D3—241no—
832C2×D3—241no—
833C2×D3—244no—
834C2×D3—244no—
835C2×D3—244no—
836C2×D3—244no—
837C2×D3—244no—
838C2×D3—244no—
839C2×D3D3×D812yescomplemented
840C2×D3D3×D812yescomplemented
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—81no—
848C3×C4—121no—
849C3×C4C2×D3×D411yescharacteristic
850C3×C4C2×D3×D411yescharacteristic
851C3×C4#100411yescharacteristic
852C3×C4#100911yescharacteristic
853Dic3—21no—
854Dic3—21no—
855Dic3—32no—
856Dic3—32no—
857Dic3—41no—
858Dic3—62no—
859Dic3—61no—
860Dic3—61no—
861Dic3—121no—
862C32D4×D811yescharacteristic, complemented, Sylow
863C23—21no—
864C23—31no—
865C23—31no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—122no—
870C23—122no—
871C23—181no—
872C23—181no—
873C23—241no—
874C23—362no—
875C23—362no—
876C23—362no—
877C23—362no—
878C23—362no—
879C23—362no—
880C23—721no—
881C23—721no—
882C23—721no—
883D4—21no—
884D4—21no—
885D4—32no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—94no—
892D4—92no—
893D4—122no—
894D4—122no—
895D4—122no—
896D4—122no—
897D4—181no—
898D4—181no—
899D4—181no—
900D4—362no—
901D4—362no—
902D4—362no—
903D4—362no—
904D4—362no—
905D4—362no—
906D4—721no—
907D4—721no—
908C2×C4—21no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—362no—
919C2×C4—362no—
920C2×C4C22×D3211yescharacteristic
921C8—21no—
922C8—32no—
923C8—61no—
924C8—181no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—62no—
929C2×C3—62no—
930C2×C3—81no—
931C2×C3—81no—
932C2×C3—122no—
933C2×C3—161no—
934C2×C3—241no—
935C2×C3—241no—
936C2×C3#559011yescharacteristic
937C2×C3#560911yescharacteristic
938C2×C3C2×D3×D811yescharacteristic
939C2×C3C2×D3×D811yescharacteristic
940C2×C3#576911yescharacteristic
941C2×C3#577411yescharacteristic
942D3—22no—
943D3—22no—
944D3—42no—
945D3—81no—
946D3—81no—
947D3—122no—
948D3—122no—
949D3—242no—
950D3—241no—
951D3—241no—
952D3—481no—
953C22—32no—
954C22—32no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—61no—
962C22—62no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—182no—
972C22—244no—
973C22—361no—
974C22—361no—
975C22—361no—
976C22—361no—
977C22—361no—
978C22—724no—
979C22—724no—
980C22—724no—
981C22D32×D411yescharacteristic
982C4—41no—
983C4—61no—
984C4—61no—
985C4—92no—
986C4—121no—
987C4—181no—
988C4#6430711yescharacteristic
989C4D32×D411yescharacteristic
990C3—21no—
991C3#8002411yescharacteristic, complemented
992C3#8072911yescharacteristic, complemented
993C2—62no—
994C2—62no—
995C2—81no—
996C2—122no—
997C2—241no—
998C2—241no—
999C2—362no—
1000C2—721no—
1001C2#1059427511yescharacteristic
1002C2D32×D811yescharacteristic
1003C2#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. #10595288C2semidirect
2. C2×D3×#213C2semidirect
3. C2×D3×D24C2semidirect
4. #10594618C2semidirect
5. #10592485C2semidirect
6. C3×#4775C2semidirect
7. C3×#4773C2semidirect
8. #10591515C2semidirect
9. #10591484C2semidirect
10. #10590947C2semidirect
11. #10590749C2semidirect
12. #10590717C2semidirect
13. #10590595C2semidirect
14. #10590576C2semidirect
15. #10590459C2semidirect
18. C2×C3×D3×D4C22semidirect
21. C2×D3×D12C22semidirect
22. C2×D3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. #64149C22semidirect
25. C2×#3753C22semidirect
26. C2×#3745C22semidirect
27. #64102C22semidirect
28. C3×#938C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×D24C22semidirect
32. C2×C3×D3×C8C22semidirect
33. C3×#895C22semidirect
34. C3×#895C22semidirect
41. #63914C22semidirect
43. #63909C22semidirect
45. #63898C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
53. #63641C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63553C22semidirect
87. #4775D3semidirect
90. #4773D3semidirect
155. #3714D4semidirect
167. C2×D3×D4C2×D3semidirect
185. #938C2×D3semidirect
200. C2×#213C2×D3semidirect
201. C2×#213C2×D3semidirect
215. C2×D24C2×D3semidirect
217. C2×D3×C8C2×D3semidirect
219. #895C2×D3semidirect
220. #895C2×D3semidirect
235. C3×#102C2×D3semidirect
236. C3×#102C2×D3semidirect
241. #821C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
254. #809C2×D3semidirect
255. #807C2×D3semidirect
287. C4⋊(C3⋊D3)C2×D4semidirect
301. C3×D12C2×D4semidirect
312. #625D8semidirect
317. C3×C3⋊C8C2×D4semidirect
498. C2×C3×D3C2×D8semidirect
499. C2×C3×D3C2×D8semidirect
507. C3⋊Dic3C2×D8semidirect
552. #102D32semidirect
679. D12D3×D4semidirect
697. C3⋊C8D3×D4semidirect
839. C2×D3D3×D8semidirect
840. C2×D3D3×D8semidirect
862. C32D4×D8semidirect
991. C3#80024semidirect
992. C3#80729semidirect

Maximal subgroups

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

subgroupindex
#105952882
C2×D3×#2132
C2×D3×D242
#105946182
#105924852
C3×#47752
C3×#47732
#105915152
#105914842
#105909472
#105907492
#105907172
#105905952
#105905762
#105904592
#807293
#800243