Finite Group Databasebeta

← #11884010

Subgroups — #11884010

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592774C211yesmaximal, characteristic, complemented
6C3×#5074C211yesmaximal, characteristic, complemented
7#10591519C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591502C211yesmaximal, characteristic, complemented
10#10591498C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10591447C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#81857—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×#127C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic, complemented
26C4×#634C2211yescharacteristic, complemented
27C3×#938—21no—
28C3×#938C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C3×#937—21no—
31C3×#937—21no—
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C3×#875C2211yescharacteristic, complemented
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39#63932—24no—
40D3×#214—24no—
41#63915—21no—
42#63908C2211yescharacteristic, complemented
43#63902—21no—
44#63899—21no—
45#63885—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D42—31no—
64C22×#214—31no—
65C2×#932—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5717D311yescharacteristic, complemented
69#5677—31no—
70#5552—31no—
71C3×#496—31no—
72#5218—31no—
73#5217—31no—
74#5174—31no—
75#5170—31no—
76#5169—31no—
77#5158—31no—
78#5157—31no—
79#5156—31no—
80#5075—31no—
81#5075—31no—
82#5075—61no—
83#5074D311yescharacteristic, complemented
84#5057—31no—
85#5042—31no—
86#5040—31no—
87#5038—31no—
88#5037—31no—
89#5018—31no—
90#5016—31no—
91#5011—31no—
92#4710—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C3×D3×D4—41no—
109C3×D3×D4—44no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×C42C2311yescharacteristic
127#3754—22no—
128#3754—22no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131C4×C3⋊Dic3—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#217—21no—
135C3×#217—21no—
136C3×#214—22no—
137C3×#214—41no—
138C3×#213—22no—
139C3×#213—41no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×C4⋊Dic3D411yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149#3724—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3716D414yescomplemented
153#3715—22no—
154#3713—22no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×D3×Q8—31no—
162C2×#237—31no—
163C2×D3×D4—21no—
164C2×D3×D4C2×D311yescharacteristic
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C3×#127—21no—
173C3×#127C2×D311yescharacteristic
174C3×#127C2×D311yescharacteristic
175C3×#124—31no—
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—61no—
179C3×#120—61no—
180C3×#120—61no—
181C3×C4×D4—31no—
182C3×C4×D4—31no—
183#946—31no—
184C2×#215—31no—
185#939—61no—
186#938—21no—
187#938—31no—
188#938C2×D311yescharacteristic
189#938C2×D311yescharacteristic
190#937—21no—
191#937—21no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—61no—
199C2×#214—61no—
200C2×#214—64no—
201C2×#214C2×D311yescharacteristic, complemented
202C2×#214C2×D311yescharacteristic, complemented
203#932—64no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213C2×D311yescharacteristic, complemented
207C2×#213C2×D311yescharacteristic, complemented
208#930—31no—
209#924—31no—
210C2×#208—31no—
211C22×C3⋊C8—31no—
212D3×SD16—64no—
213#911—64no—
214C2×#204—31no—
215C2×ΓL(1,𝔽25)—31no—
216C2×D3×C8—31no—
217#896—61no—
218#885—61no—
219#885—61no—
220#884—61no—
221#67⋊C4—61no—
222#67⋊C4—61no—
223#878—61no—
224#875C2×D311yescharacteristic, complemented
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227C4×Dic6—31no—
228C4×Dic6—31no—
229C4×Dic6—61no—
230C3×#97—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832—61no—
240#830—31no—
241#830—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#818—31no—
246#816—31no—
247#810—31no—
248#810—31no—
249#809—31no—
250#807—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—31no—
253C4⋊(C3⋊C8)—61no—
254#803C2×D311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4—81no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278#634—21no—
279#634C2×D412yescomplemented
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—22no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300#627—42no—
301#625—42no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—31no—
313#496—31no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—41no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C2×C3×D4—124no—
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C22×D311yescharacteristic
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—61no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366D3×Q8—62no—
367D3×Q8—121no—
368#237—62no—
369#237—121no—
370D3×D4—22no—
371D3×D4—22no—
372D3×D4—41no—
373D3×D4—41no—
374D3×D4—44no—
375#235—62no—
376#235—121no—
377C2×D12#6711yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6—31no—
386C2×Dic6—31no—
387C2×Dic6—61no—
388C2×Dic6—62no—
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6—121no—
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—62no—
394C3×SD16—121no—
395C3×D8—62no—
396C3×D8—121no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—21no—
409C3×C42C22×D311yescharacteristic
410C3×C42C22×D311yescharacteristic
411#217—21no—
412#217—21no—
413#217—61no—
414#217—61no—
415#215—62no—
416#214—22no—
417#214—34no—
418#214—41no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—62no—
423#214—62no—
424#214—122no—
425#214—122no—
426#213—22no—
427#213—41no—
428#213—62no—
429#213—62no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4#6711yescharacteristic
436(C2×D3)⋊C4#6711yescharacteristic
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3#6711yescharacteristic
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—121no—
447C4×Dic3—61no—
448C4×Dic3—61no—
449C4×Dic3—121no—
450#208—62no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460#204—34no—
461ΓL(1,𝔽25)—62no—
462D3×C8—62no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
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—84no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484C32×C4—21no—
485C32×C4—21no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—22no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—61no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127D3211yescharacteristic
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—61no—
520#121—91no—
521#121—181no—
522#120—61no—
523#120—61no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—31no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—241no—
554C23×C3—241no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—81no—
562C22×D3—81no—
563C22×D3C2×#6711yescharacteristic
564C22×D3C2×#6711yescharacteristic
565C3×Q8—61no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—32no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—62no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—82no—
587C3×D4—81no—
588C3×D4—81no—
589C3×D4—82no—
590C3×D4—122no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—122no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C2×#6711yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612#67—42no—
613#67—42no—
614#67—42no—
615#67—42no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—122no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—122no—
629C2×Dic3—122no—
630C2×Dic3C2×#6711yescharacteristic
631C2×Dic3C2×#6711yescharacteristic
632D12—22no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12D3×D412yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—122no—
643C4×D3—122no—
644Dic6—21no—
645Dic6—21no—
646Dic6—32no—
647Dic6—32no—
648Dic6—62no—
649Dic6—61no—
650Dic6—61no—
651Dic6—121no—
652Dic6—122no—
653Dic6—122no—
654C3×C8—32no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C3⋊C8—121no—
663C3⋊C8D3×D412yescomplemented
664C2×C32—81no—
665C2×C32—81no—
666C2×C32D4211yescharacteristic
667C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
668C2×C32#57711yescharacteristic
669C3×D3—22no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—61no—
674C24—61no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—91no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—31no—
685C2×D4—31no—
686C2×D4—31no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—62no—
690C2×D4—62no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—121no—
694C2×D4—121no—
695C2×D4—124no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4C2×D3211yescharacteristic
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—181no—
704C22×C4—181no—
705SD16—62no—
706SD16—94no—
707SD16—121no—
708SD16—182no—
709SD16—182no—
710SD16—182no—
711D8—62no—
712D8—121no—
713D8—182no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—91no—
719C2×C8—182no—
720C4⋊C4—31no—
721C4⋊C4—31no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C4⋊C4—181no—
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—181no—
735C42C2×D3211yescharacteristic
736C22×C3—21no—
737C22×C3—32no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—62no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—244no—
768C22×C3—244no—
769C22×C3C2×D3×D411yescharacteristic
770C22×C3C22×#6711yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—22no—
776C2×D3—21no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—84no—
783C2×D3—84no—
784C2×D3#93212yescomplemented
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—41no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4C2×D3×D411yescharacteristic
798C3×C4C2×D3×D411yescharacteristic
799C3×C4#100411yescharacteristic
800C3×C4#100411yescharacteristic
801Dic3—21no—
802Dic3—21no—
803Dic3—41no—
804Dic3—41no—
805Dic3—62no—
806Dic3—62no—
807Dic3—122no—
808Dic3—121no—
809Dic3—121no—
810Dic3—241no—
811C32#326511yescharacteristic, complemented, Sylow
812C23—21no—
813C23—21no—
814C23—31no—
815C23—31no—
816C23—61no—
817C23—61no—
818C23—122no—
819C23—122no—
820C23—122no—
821C23—122no—
822C23—241no—
823C23—241no—
824Q8—61no—
825Q8—61no—
826Q8—92no—
827Q8—181no—
828Q8—362no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—32no—
834D4—42no—
835D4—62no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—81no—
840D4—122no—
841D4—122no—
842D4—122no—
843D4—122no—
844D4—362no—
845D4—362no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—122no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4D3×#6711yescharacteristic
860C2×C4D3×#6711yescharacteristic
861C2×C4C22×D3211yescharacteristic
862C8—32no—
863C8—61no—
864C8—181no—
865C8—181no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—62no—
870C2×C3—81no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—81no—
874C2×C3—121no—
875C2×C3—122no—
876C2×C3—161no—
877C2×C3—161no—
878C2×C3—241no—
879C2×C3#571711yescharacteristic
880C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
881C2×C3#577511yescharacteristic
882C2×C3C2×#93211yescharacteristic
883C2×C3D4×#6711yescharacteristic
884C2×C3#583611yescharacteristic
885D3—22no—
886D3—41no—
887D3—42no—
888D3—81no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—61no—
901C22—62no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—244no—
908C22—244no—
909C22C2×D3×#6711yescharacteristic
910C4—21no—
911C4—21no—
912C4—61no—
913C4—61no—
914C4—121no—
915C4—121no—
916C4—182no—
917C4—361no—
918C4D32×D411yescharacteristic
919C4#6431311yescharacteristic
920C3—21no—
921C3#8185711yescharacteristic, complemented
922C3#8349111yescharacteristic, complemented
923C2—62no—
924C2—81no—
925C2—81no—
926C2—121no—
927C2—122no—
928C2—241no—
929C2D3×#93211yescharacteristic
930C2#1059510611yescharacteristic
931C2#1059529311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5717C2semidirect
2. C2×#63932C2semidirect
3. C2×D3×#214C2semidirect
4. #10593905C2semidirect
5. #10592774C2semidirect
6. C3×#5074C2semidirect
7. #10591519C2semidirect
8. #10591517C2semidirect
9. #10591502C2semidirect
10. #10591498C2semidirect
11. #10591458C2semidirect
12. #10591447C2semidirect
13. #10590360C2semidirect
14. #10590348C2semidirect
15. #10590326C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. C2×#3754C22semidirect
26. C4×#634C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#213C22semidirect
35. C2×C3×#213C22semidirect
36. C3×#875C22semidirect
42. #63908C22semidirect
46. #63856C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63659C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5717D3semidirect
83. #5074D3semidirect
152. #3716D4semidirect
201. C2×#214C2×D3semidirect
202. C2×#214C2×D3semidirect
206. C2×#213C2×D3semidirect
207. C2×#213C2×D3semidirect
224. #875C2×D3semidirect
254. #803C2×D3semidirect
279. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
663. C3⋊C8D3×D4semidirect
784. C2×D3#932semidirect
811. C32#3265semidirect
921. C3#81857semidirect
922. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
C2×#639322
C2×D3×#2142
#105939052
#105927742
C3×#50742
#105915192
#105915172
#105915022
#105914982
#105914582
#105914472
#105903602
#105903482
#105903262
#834913
#818573