Finite Group Databasebeta

← #11884039

Subgroups — #11884039

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
1C2×#63795C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3D122C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592547C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590968C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590942C211yesmaximal, characteristic, complemented
12#10590850C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590351C211yesmaximal, characteristic, complemented
16#80553—31nomaximal
17#79494—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25#64083C2211yescharacteristic
26C4×#634C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic, complemented
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34#63923—21no—
35#63923—21no—
36#63915—21no—
37#63909—21no—
38#63909C2211yescharacteristic
39#63909C2211yescharacteristic
40#63908C2211yescharacteristic, complemented
41#63902—21no—
42#63899—21no—
43#63885—21no—
44#63856C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63795—24no—
51D3×#204—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63C2×D3×SD16—31no—
64C2×#911—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5677—31no—
68#5552—31no—
69D4×D12—31no—
70D4×D12—31no—
71C3×#463—31no—
72C3×#435—31no—
73#5169—31no—
74#5156—31no—
75#5134—31no—
76#5115—31no—
77#5058—31no—
78#5018—31no—
79#4848—31no—
80#4848—31no—
81#4848—61no—
82#4844D311yescharacteristic, complemented
83#4836D311yescharacteristic, complemented
84#4812—31no—
85#4806—31no—
86#4781—31no—
87#4775—31no—
88#4738—31no—
89#4734—31no—
90#4732—31no—
91#4731—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—22no—
119D3×D12—41no—
120D3×D12—41no—
121D3×D12—44no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C42C2311yescharacteristic
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131C4×C3⋊Dic3—21no—
132#3744—22no—
133#3744—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×#204—22no—
145C3×ΓL(1,𝔽25)—22no—
146C3×D3×C8—22no—
147#3724—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3717—22no—
153#3717—41no—
154#3716D414yescomplemented
155#3714—22no—
156#3714—41no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C22×C3×C8—31no—
172C3×#124—31no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175#946—31no—
176C2×#215—31no—
177C2×#215—31no—
178#939—61no—
179#938—31no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183#930—31no—
184#930—31no—
185#930—31no—
186#930—61no—
187#924—31no—
188D3×SD16—64no—
189#911—64no—
190#908—64no—
191C2×D24—31no—
192C2×D24—31no—
193C2×D24C2×D311yescharacteristic
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—61no—
202C2×#204—61no—
203C2×#204—64no—
204C2×#204C2×D311yescharacteristic
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
206C2×D3×C8C2×D311yescharacteristic, complemented
207#896—61no—
208#895—31no—
209#895—31no—
210#895—61no—
211#885—61no—
212#885—61no—
213#884—61no—
214#882—61no—
215#882—61no—
216#882—61no—
217#882—61no—
218#67⋊C4—61no—
219#67⋊C4—61no—
220#878—61no—
221#875C2×D311yescharacteristic, complemented
222#874—31no—
223#874—31no—
224#874—61no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227C4×Dic6—31no—
228C4×Dic6—31no—
229C4×Dic6—61no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C2×D311yescharacteristic, complemented
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8—31no—
237C3×#97—31no—
238#832—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245#821—61no—
246#821C2×D311yescharacteristic, complemented
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248(C2×D3)⋊C8C2×D311yescharacteristic, complemented
249#818—31no—
250#816—31no—
251#816C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254#803C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4⋊(C3⋊D3)—81no—
278#634—21no—
279#634C2×D412yescomplemented
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—22no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#625—42no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—31no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—31no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345D3×Q8—62no—
346D3×Q8—121no—
347#237—62no—
348#237—121no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—121no—
353D3×D4—124no—
354#235—62no—
355#235—121no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—121no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—124no—
377C2×D12D1211yescharacteristic
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×D8—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—21no—
413C3×C42C22×D311yescharacteristic
414C3×C42C22×D311yescharacteristic
415#217—61no—
416#217—61no—
417#215—62no—
418#215—121no—
419#214—34no—
420#213—62no—
421#213—121no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4D1211yescharacteristic
432(C2×D3)⋊C4D1211yescharacteristic
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3D1211yescharacteristic
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443C4×Dic3—61no—
444C4×Dic3—61no—
445C4×Dic3—121no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448D24—22no—
449D24—62no—
450D24—121no—
451#204—22no—
452#204—34no—
453#204—62no—
454#204—62no—
455#204—62no—
456#204—62no—
457#204—62no—
458#204—122no—
459#204—122no—
460#204—121no—
461ΓL(1,𝔽25)—22no—
462D3×C8—22no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
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×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
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—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—31no—
511C22×C8—31no—
512#127—91no—
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—31no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8D3211yescharacteristic, complemented
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—31no—
538#97—31no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3C2×D1211yescharacteristic
564C22×D3C2×D1211yescharacteristic
565C3×Q8—61no—
566C3×Q8—61no—
567C3×D4—32no—
568C3×D4—62no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4C2×D1211yescharacteristic
585C2×C3×C4C2×D1211yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610D12—22no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—121no—
623D12—121no—
624D12—121no—
625D12—121no—
626D12—122no—
627D12—122no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—242no—
633D12—241no—
634D12—241no—
635D12—242no—
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—21no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—21no—
658C3×C8—32no—
659C3×C8—41no—
660C3×C8—41no—
661C3×C8—61no—
662C3⋊C8—21no—
663C3⋊C8D3×D412yescomplemented
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3⋊D3—81no—
669C3×D3—22no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—181no—
674C24—181no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—91no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—91no—
686C2×D4—91no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—361no—
699C2×D4—364no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—181no—
704C22×C4—181no—
705SD16—62no—
706SD16—94no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—361no—
711D8—62no—
712D8—182no—
713D8—361no—
714M16—62no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C2×C8C2×D3211yescharacteristic
719C2×C8C2×D3211yescharacteristic
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—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—181no—
735C42C2×D3211yescharacteristic
736C22×C3—21no—
737C22×C3—32no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—61no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C22×D1211yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—22no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3#90812yescomplemented
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#100911yescharacteristic
800C3×C4#100911yescharacteristic
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—31no—
813C23—31no—
814C23—61no—
815C23—61no—
816C23—181no—
817C23—181no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—362no—
822C23—721no—
823C23—721no—
824Q8—61no—
825Q8—61no—
826Q8—92no—
827Q8—181no—
828Q8—362no—
829D4—32no—
830D4—62no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—181no—
835D4—181no—
836D4—181no—
837D4—181no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—721no—
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×D1211yescharacteristic
860C2×C4D3×D1211yescharacteristic
861C2×C4C22×D3211yescharacteristic
862C8—21no—
863C8—21no—
864C8—32no—
865C8—61no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—62no—
870C2×C3—122no—
871C2×C3—121no—
872C2×C3—241no—
873C2×C3D4×D1211yescharacteristic
874C2×C3#560911yescharacteristic
875C2×C3C2×#90811yescharacteristic
876C2×C3#575111yescharacteristic
877C2×C3#577011yescharacteristic
878C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
879D3—22no—
880D3—41no—
881D3—42no—
882D3—81no—
883D3—241no—
884D3—241no—
885D3—241no—
886D3—241no—
887D3—481no—
888D3—481no—
889C22—32no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—62no—
894C22—61no—
895C22—61no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—724no—
908C22—724no—
909C22C2×D3×D1211yescharacteristic
910C4—21no—
911C4—21no—
912C4—61no—
913C4—61no—
914C4—121no—
915C4—121no—
916C4—182no—
917C4—361no—
918C4D32×D411yescharacteristic
919C4#6432011yescharacteristic
920C3—21no—
921C3#7949411yescharacteristic, complemented
922C3#8055311yescharacteristic, complemented
923C2—62no—
924C2—121no—
925C2—122no—
926C2—241no—
927C2—721no—
928C2—721no—
929C2#1059462111yescharacteristic
930C2#1059467911yescharacteristic
931C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×D3×#204C2semidirect
3. D122C2semidirect
4. #10593905C2semidirect
5. #10592547C2semidirect
6. C3×#4844C2semidirect
7. C3×#4836C2semidirect
8. #10590968C2semidirect
9. #10590951C2semidirect
10. #10590944C2semidirect
11. #10590942C2semidirect
12. #10590850C2semidirect
13. #10590826C2semidirect
14. #10590360C2semidirect
15. #10590351C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×#3744C22semidirect
24. C2×#3744C22semidirect
26. C4×#634C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C2×C3×D3×C8C22semidirect
31. C3×#875C22semidirect
40. #63908C22semidirect
44. #63856C22semidirect
45. C2×#3717C22semidirect
46. C2×#3717C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
52. C32×C4⋊C8C22semidirect
53. #63648C22semidirect
54. #63648C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#803C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
82. #4844D3semidirect
83. #4836D3semidirect
154. #3716D4semidirect
205. C2×ΓL(1,𝔽25)C2×D3semidirect
206. C2×D3×C8C2×D3semidirect
221. #875C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C2×D3semidirect
246. #821C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
248. (C2×D3)⋊C8C2×D3semidirect
251. #816C2×D3semidirect
254. #803C2×D3semidirect
279. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
529. C4⋊C8D32semidirect
663. C3⋊C8D3×D4semidirect
784. C2×D3#908semidirect
811. C32#3265semidirect
921. C3#79494semidirect
922. C3#80553semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×D3×#2042
D1222
#105939052
#105925472
C3×#48442
C3×#48362
#105909682
#105909512
#105909442
#105909422
#105908502
#105908262
#105903602
#105903512
#805533
#794943