Finite Group Databasebeta

← #11885765

Subgroups — #11885765

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×#63797C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592474C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591516C211yesmaximal, characteristic, complemented
9#10591482C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590906C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80350—31nomaximal
17#80024—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic, complemented
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic, complemented
21C2×#3802C2211yescharacteristic, complemented
22C2×D3×D12—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24#64147C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C2×C8×C3⋊D3C2211yescharacteristic, complemented
27#64104C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×D24C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic, complemented
34C3×#893C2211yescharacteristic, complemented
35#63983—21no—
36#63976—21no—
37#63970—21no—
38D3×#213—24no—
39#63923—21no—
40#63922—21no—
41#63911C2211yescharacteristic, complemented
42#63908C2211yescharacteristic, complemented
43#63906—21no—
44C4×#626C2211yescharacteristic
45Dic3×D12C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63797—24no—
52C32×#102C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68#5717—31no—
69#5609—31no—
70D4×D12—31no—
71C3×#459—31no—
72C3×#447—31no—
73#5156—31no—
74#5156—31no—
75#5156—31no—
76#5151—31no—
77#5150—31no—
78#5073—31no—
79#5038—31no—
80C4×#213—31no—
81#4843—31no—
82#4834—31no—
83#4786D311yescharacteristic, complemented
84#4775—31no—
85#4775—31no—
86#4775—31no—
87#4775—61no—
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×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115D3×#67—44no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626D411yescharacteristic
120C2×#625—21no—
121C2×#625—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124#3802—22no—
125#3802—22no—
126#3802—41no—
127#3802—41no—
128D3×D12—22no—
129D3×D12—41no—
130D3×D12—44no—
131C2×C32×C8C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133#3757—21no—
134#3753—22no—
135#3752—21no—
136C4⋊(C3⋊Dic3)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C8×C3⋊D3—22no—
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×D24—22no—
148Dic3⋊Dic3D411yescharacteristic
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3714—22no—
154#3714—41no—
155#3713—22no—
156#3713D414yescomplemented
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—
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C3×#127—31no—
176C3×#121—31no—
177C3×C4×D4—31no—
178#953—61no—
179#940—31no—
180#940C2×D311yescharacteristic, complemented
181#939—61no—
182#938—31no—
183#938—31no—
184#938—31no—
185#938—61no—
186#938—61no—
187#937—61no—
188#937—61no—
189#937—61no—
190#937—61no—
191D4×Dic3—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213—64no—
202C2×#213C2×D311yescharacteristic, complemented
203C2×#213C2×D311yescharacteristic, complemented
204#930—31no—
205#930—61no—
206C4×#67—31no—
207C22×C3⋊C8—31no—
208D3×D8—64no—
209D3×D8—64no—
210D3×D8—64no—
211C2×D24—31no—
212C2×D24—31no—
213C2×D24C2×D311yescharacteristic, complemented
214C2×D24C2×D311yescharacteristic, complemented
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217C2×D3×C8—31no—
218C2×D3×C8—61no—
219#895—31no—
220#895—31no—
221#895—61no—
222#895C2×D311yescharacteristic, complemented
223#893C2×D311yescharacteristic, complemented
224#884—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230C4×D12—31no—
231C3×C4⋊C8—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#832—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248Dic3⋊C8C2×D311yescharacteristic, complemented
249C8×Dic3—31no—
250#809C2×D311yescharacteristic, complemented
251#809C2×D311yescharacteristic, complemented
252#807—31no—
253#807—31no—
254#807—61no—
255C4×C3⋊C8—31no—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3C2×D411yescharacteristic
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
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—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3C2×D411yescharacteristic
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—42no—
286C4×C3⋊D3—21no—
287C4×C3⋊D3—21no—
288C3×#67—42no—
289C3×#67—42no—
290C3×#67—81no—
291C2×C3×Dic3C2×D411yescharacteristic
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—21no—
300C3×D12—42no—
301C3×D12C2×D412yescomplemented
302C3×D12C2×D412yescomplemented
303C3×C4×D3—21no—
304C3×C4×D3—21no—
305C3×C4×D3—42no—
306#626—42no—
307#626—42no—
308#626—81no—
309#626D814yescomplemented
310#625—42no—
311#625—42no—
312#625—42no—
313D3×Dic3—42no—
314C32×C8—21no—
315C3⋊(C3⋊C8)C2×D412yescomplemented
316C3×C3⋊C8—21no—
317C3×C3⋊C8—21no—
318C22×D8—91no—
319C22×D8—91no—
320D42—91no—
321D42—91no—
322#493—91no—
323#466—91no—
324#466—91no—
325#459—31no—
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—31no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
352C2×C3×D4C22×D311yescharacteristic
353C2×C3×D4C22×D311yescharacteristic
354C22×C3×C4—31no—
355C22×C3×C4—61no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—31no—
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—124no—
373C22×Dic3—61no—
374D3×D4—22no—
375D3×D4—41no—
376D3×D4—62no—
377D3×D4—62no—
378D3×D4—62no—
379D3×D4—62no—
380D3×D4—62no—
381D3×D4—121no—
382D3×D4—124no—
383D3×D4—121no—
384D3×D4—121no—
385D3×D4—121no—
386D3×D4—121no—
387D3×D4—124no—
388C2×D12—21no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—61no—
393C2×D12—62no—
394C2×D12—61no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—121no—
400C2×D12—121no—
401C2×D12—124no—
402C2×D12C22×D311yescharacteristic
403C2×D12C22×D311yescharacteristic
404C2×D12C22×D311yescharacteristic
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C3×D8—62no—
413C3×D8—62no—
414C3×D8—62no—
415C3×D8—121no—
416C2×C3×C8—21no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8C22×D311yescharacteristic
420C2×C3×C8C22×D311yescharacteristic
421C3×C4⋊C4—21no—
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C42—31no—
427#217—31no—
428#217—61no—
429#217—61no—
430#217—61no—
431#217—61no—
432#217—121no—
433#213—22no—
434#213—34no—
435#213—34no—
436#213—41no—
437#213—62no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—62no—
442#213—122no—
443#213—121no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—121no—
454C4⋊Dic3—31no—
455C4⋊Dic3—31no—
456C4⋊Dic3—31no—
457C4⋊Dic3—61no—
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—22no—
467D24—22no—
468D24—62no—
469D24—121no—
470D3×C8—62no—
471D3×C8—62no—
472D3×C8—62no—
473D3×C8—122no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3C2×D812yescomplemented
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—41no—
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—41no—
498C2×C3×D3—84no—
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⋊Dic3—41no—
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3C2×D812yescomplemented
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—31no—
521C2×D8—91no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—184no—
527C2×D8—184no—
528C22×C8—91no—
529C22×C8—91no—
530#127—31no—
531#127—91no—
532#121—31no—
533#121—91no—
534#121—91no—
535#121—91no—
536#121—181no—
537#121—181no—
538#120—181no—
539#120—181no—
540#120—181no—
541#120—181no—
542C4×D4—31no—
543C4×D4—91no—
544C4×D4—91no—
545#107—91no—
546C4⋊C8—31no—
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—41no—
560C23×C3—61no—
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—21no—
571C22×D3—31no—
572C22×D3—31no—
573C22×D3—42no—
574C22×D3—42no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—81no—
579C22×D3—121no—
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—122no—
592C22×D3—241no—
593C22×D3—241no—
594C22×D3—241no—
595C22×D3—241no—
596C22×D3—241no—
597C22×D3—241no—
598C22×D3D3×D411yescharacteristic
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—32no—
604C3×D4—32no—
605C3×D4—41no—
606C3×D4—41no—
607C3×D4—61no—
608C3×D4—61no—
609C3×D4—61no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—122no—
614C3×D4—122no—
615C3×D4—122no—
616C3×D4—241no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—31no—
621C2×C3×C4—31no—
622C2×C3×C4—31no—
623C2×C3×C4—41no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—122no—
627C2×C3×C4C23×D311yescharacteristic
628C2×C3×C4C23×D311yescharacteristic
629#67—34no—
630#67—42no—
631#67—42no—
632#67—81no—
633#67—122no—
634#67—122no—
635#67—122no—
636#67—122no—
637#67—122no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—122no—
643#67—242no—
644#67—241no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—121no—
651C2×Dic3—122no—
652C2×Dic3D3×D411yescharacteristic
653C2×Dic3D3×D411yescharacteristic
654C2×Dic3D3×D411yescharacteristic
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—21no—
661D12—34no—
662D12—42no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—61no—
667D12—121no—
668D12—121no—
669D12—122no—
670D12—122no—
671D12—122no—
672D12—122no—
673D12—242no—
674D12—241no—
675D12D3×D412yescomplemented
676D12D3×D412yescomplemented
677C4×D3—21no—
678C4×D3—21no—
679C4×D3—42no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—121no—
685C4×D3—121no—
686C4×D3—122no—
687C3×C8—21no—
688C3×C8—21no—
689C3×C8—41no—
690C3×C8—61no—
691C3×C8—61no—
692C3⋊C8—21no—
693C3⋊C8—21no—
694C3⋊C8—32no—
695C3⋊C8—32no—
696C3⋊C8—62no—
697C2×C32—81no—
698C2×C32D4211yescharacteristic
699C2×C32C22×D811yescharacteristic
700C2×C32#57611yescharacteristic
701C3⋊D3—22no—
702C3⋊D3—81no—
703C3×D3—22no—
704C3×D3—42no—
705C3×D3—42no—
706C3×D3—81no—
707C3×D3—81no—
708C24—61no—
709C24—181no—
710C24—181no—
711C24—181no—
712C2×D4—31no—
713C2×D4—31no—
714C2×D4—31no—
715C2×D4—31no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—61no—
719C2×D4—61no—
720C2×D4—62no—
721C2×D4—91no—
722C2×D4—91no—
723C2×D4—121no—
724C2×D4—181no—
725C2×D4—181no—
726C2×D4—181no—
727C2×D4—181no—
728C2×D4—182no—
729C2×D4—181no—
730C2×D4—181no—
731C2×D4—182no—
732C2×D4—182no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—361no—
736C2×D4—364no—
737C2×D4—361no—
738C2×D4—361no—
739C2×D4—364no—
740C2×D4C2×D3211yescharacteristic
741C22×C4—31no—
742C22×C4—61no—
743C22×C4—91no—
744C22×C4—181no—
745D8—62no—
746D8—62no—
747D8—62no—
748D8—94no—
749D8—121no—
750D8—182no—
751D8—182no—
752D8—182no—
753D8—361no—
754C2×C8—31no—
755C2×C8—31no—
756C2×C8—91no—
757C2×C8—182no—
758C2×C8—182no—
759C2×C8C2×D3211yescharacteristic
760C4⋊C4—91no—
761C4⋊C4—91no—
762C4⋊C4C2×D3211yescharacteristic
763C22⋊C4—61no—
764C22⋊C4—61no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—181no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C42—31no—
772C22×C3—21no—
773C22×C3—32no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—244no—
798C22×C3C2×D3×D411yescharacteristic
799C22×C3C2×D3×D411yescharacteristic
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—32no—
805C2×D3—32no—
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—41no—
815C2×D3—41no—
816C2×D3—62no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—84no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
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
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—32no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—81no—
848C3×C4C2×D3×D411yescharacteristic
849C3×C4C2×D3×D411yescharacteristic
850C3×C4#100411yescharacteristic
851C3×C4#100911yescharacteristic
852Dic3—21no—
853Dic3—21no—
854Dic3—61no—
855Dic3—61no—
856Dic3—121no—
857Dic3—121no—
858Dic3—121no—
859Dic3—241no—
860Dic3D3×D812yescomplemented
861C32D4×D811yescharacteristic, complemented, Sylow
862C23—21no—
863C23—31no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—91no—
869C23—122no—
870C23—122no—
871C23—181no—
872C23—241no—
873C23—362no—
874C23—362no—
875C23—362no—
876C23—362no—
877C23—362no—
878C23—362no—
879C23—721no—
880C23—721no—
881C23—721no—
882D4—21no—
883D4—21no—
884D4—32no—
885D4—32no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—61no—
892D4—94no—
893D4—122no—
894D4—122no—
895D4—122no—
896D4—181no—
897D4—181no—
898D4—241no—
899D4—362no—
900D4—362no—
901D4—362no—
902D4—362no—
903D4—362no—
904D4—362no—
905D4—362no—
906D4—721no—
907C2×C4—21no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—91no—
914C2×C4—122no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—362no—
919C2×C4C22×D3211yescharacteristic
920C8—21no—
921C8—61no—
922C8—61no—
923C8—92no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—62no—
928C2×C3—81no—
929C2×C3—81no—
930C2×C3—122no—
931C2×C3—122no—
932C2×C3—161no—
933C2×C3—241no—
934C2×C3—241no—
935C2×C3#559011yescharacteristic
936C2×C3#560911yescharacteristic
937C2×C3C2×D3×D811yescharacteristic
938C2×C3C2×D3×D811yescharacteristic
939C2×C3#577411yescharacteristic
940C2×C3#577411yescharacteristic
941D3—22no—
942D3—42no—
943D3—42no—
944D3—62no—
945D3—62no—
946D3—81no—
947D3—81no—
948D3—122no—
949D3—241no—
950D3—241no—
951D3—481no—
952C22—32no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—61no—
957C22—61no—
958C22—62no—
959C22—62no—
960C22—92no—
961C22—121no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—181no—
972C22—181no—
973C22—244no—
974C22—361no—
975C22—361no—
976C22—361no—
977C22—724no—
978C22—724no—
979C22—724no—
980C22D32×D411yescharacteristic
981C4—32no—
982C4—41no—
983C4—61no—
984C4—61no—
985C4—181no—
986C4—361no—
987C4#6430711yescharacteristic
988C4D32×D411yescharacteristic
989C3—21no—
990C3#8002411yescharacteristic, complemented
991C3#8035011yescharacteristic, complemented
992C2—62no—
993C2—81no—
994C2—122no—
995C2—122no—
996C2—182no—
997C2—241no—
998C2—241no—
999C2—721no—
1000C2#1059427511yescharacteristic
1001C2D32×D811yescharacteristic
1002C2#1059475011yescharacteristic
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. #10595293C2semidirect
2. C2×D3×#213C2semidirect
3. C2×#63797C2semidirect
4. #10594621C2semidirect
5. #10592474C2semidirect
6. C3×#4786C2semidirect
7. C3×#4773C2semidirect
8. #10591516C2semidirect
9. #10591482C2semidirect
10. #10590944C2semidirect
11. #10590906C2semidirect
12. #10590753C2semidirect
13. #10590598C2semidirect
14. #10590499C2semidirect
15. #10590452C2semidirect
18. C2×C3×D3×D4C22semidirect
20. C2×#3802C22semidirect
21. C2×#3802C22semidirect
23. C2×D3×D12C22semidirect
24. #64147C22semidirect
25. C2×#3753C22semidirect
26. C2×C8×C3⋊D3C22semidirect
27. #64104C22semidirect
28. C3×#940C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×D24C22semidirect
32. C2×C3×D24C22semidirect
33. C3×#895C22semidirect
34. C3×#893C22semidirect
41. #63911C22semidirect
42. #63908C22semidirect
45. Dic3×D12C22semidirect
46. C2×#3714C22semidirect
47. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
53. #63648C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. Dic3×C3⋊C8C22semidirect
83. #4786D3semidirect
90. #4773D3semidirect
156. #3713D4semidirect
168. C2×D3×D4C2×D3semidirect
180. #940C2×D3semidirect
202. C2×#213C2×D3semidirect
203. C2×#213C2×D3semidirect
213. C2×D24C2×D3semidirect
214. C2×D24C2×D3semidirect
222. #895C2×D3semidirect
223. #893C2×D3semidirect
235. C3×#102C2×D3semidirect
236. C3×#102C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
250. #809C2×D3semidirect
251. #809C2×D3semidirect
301. C3×D12C2×D4semidirect
302. C3×D12C2×D4semidirect
309. #626D8semidirect
315. C3⋊(C3⋊C8)C2×D4semidirect
483. C2×C3⋊D3C2×D8semidirect
499. C2×C3×D3C2×D8semidirect
510. C3×Dic3C2×D8semidirect
552. #102D32semidirect
675. D12D3×D4semidirect
676. D12D3×D4semidirect
839. C2×D3D3×D8semidirect
860. Dic3D3×D8semidirect
861. C32D4×D8semidirect
990. C3#80024semidirect
991. C3#80350semidirect

Maximal subgroups

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

subgroupindex
#105952932
C2×D3×#2132
C2×#637972
#105946212
#105924742
C3×#47862
C3×#47732
#105915162
#105914822
#105909442
#105909062
#105907532
#105905982
#105904992
#105904522
#803503
#800243