Finite Group Databasebeta

← #11883980

Subgroups — #11883980

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595401C211yesmaximal, characteristic, complemented
3D4×#626C211yesmaximal, characteristic, complemented
4C2×#63937C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591584C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591440C211yesmaximal, characteristic, complemented
12#10590964C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590799C211yesmaximal, characteristic, complemented
15#10590727C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#80553—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C22×#626—21no—
22C2×#3796C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24#64155C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×D3×SD16—24no—
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63981—21no—
35#63978—21no—
36#63977—21no—
37#63937—24no—
38#63916C2211yescharacteristic
39#63911C2211yescharacteristic
40#63909C2211yescharacteristic
41#63908C2211yescharacteristic, complemented
42#63907—21no—
43#63906—21no—
44C4×#626C2211yescharacteristic
45#63887—21no—
46#63879—21no—
47Dic3×Dic6C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5817—31no—
65D4×#67—31no—
66C2×#914—31no—
67C2×D3×SD16D311yescharacteristic, complemented
68C2×#911—31no—
69#5677—31no—
70D4×D12—31no—
71C3×#463—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5174—31no—
76#5172—31no—
77#5169—31no—
78#5169—31no—
79#5169—61no—
80#5165D311yescharacteristic, complemented
81#5164—31no—
82#5163—31no—
83#5156—31no—
84#5115—31no—
85#5111—31no—
86#5058—31no—
87#5018—31no—
88#4848—31no—
89#4836—31no—
90#4812—31no—
91#4806—31no—
92#4781—31no—
93#4775—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×Q8—22no—
106C3×D3×Q8—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—44no—
121C2×#626D411yescharacteristic
122C2×#625—21no—
123C2×D3×Dic3—21no—
124#3796—22no—
125#3796—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3755—41no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#215—22no—
135C3×#214D414yescomplemented
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3D411yescharacteristic
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152Dic32—21no—
153#3717—22no—
154#3714—22no—
155#3713—41no—
156#3712—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#237—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4C2×D311yescharacteristic
168C22×D12—61no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×D8—31no—
177C22×C3×C8—31no—
178C3×#124—31no—
179C3×C4×D4—31no—
180#953—61no—
181#947—61no—
182#947C2×D311yescharacteristic, complemented
183#946—31no—
184#946—31no—
185#946—61no—
186#946—61no—
187Q8×Dic3—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—61no—
192C2×#215C2×D311yescharacteristic, complemented
193#940—31no—
194#939—61no—
195#938—31no—
196#938—31no—
197#937—61no—
198D4×Dic3C2×D311yescharacteristic
199C2×#214C2×D311yescharacteristic
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213C2×D311yescharacteristic
204#930—31no—
205#930—31no—
206#930—61no—
207#930—61no—
208C4×#67—31no—
209C4×#67—61no—
210#914—64no—
211D3×SD16—24no—
212#911—64no—
213C2×D24—31no—
214C2×#204—31no—
215C2×#204C2×D311yescharacteristic, complemented
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×D3×C8C2×D311yescharacteristic, complemented
219#895—31no—
220#895—31no—
221#885—61no—
222#884—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#878—61no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#102—31no—
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—61no—
249#818—31no—
250#815—31no—
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6C2×D412yescomplemented
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—31no—
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—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8—61no—
332C2×C3×Q8—62no—
333C2×C3×Q8—121no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—121no—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—31no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—124no—
360C22×Dic3—21no—
361C22×Dic3—61no—
362#239—62no—
363#239—121no—
364D3×Q8—22no—
365D3×Q8—41no—
366#237—62no—
367#237—121no—
368D3×D4—22no—
369D3×D4—41no—
370D3×D4—62no—
371D3×D4—62no—
372D3×D4—122no—
373D3×D4—121no—
374D3×D4—121no—
375D3×D4—122no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—124no—
386C2×D12C22×D311yescharacteristic
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—31no—
390C2×C4×D3—31no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—21no—
395C2×Dic6C22×D311yescharacteristic
396C3×SD16—22no—
397C3×SD16—22no—
398C3×SD16—34no—
399C3×SD16—42no—
400C3×SD16—62no—
401C3×SD16—62no—
402C3×D8—62no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—62no—
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C3×C4⋊C4—31no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414#217—21no—
415#217—31no—
416#217—61no—
417#217—61no—
418#215—22no—
419#215—62no—
420#215—121no—
421#215—121no—
422#215—122no—
423#214#6714yescomplemented
424#213—22no—
425#213—62no—
426#213—121no—
427#213—121no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—121no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444C4⋊Dic3—61no—
445C4⋊Dic3C22×D311yescharacteristic
446Dic3⋊C4—31no—
447Dic3⋊C4—61no—
448Dic3⋊C4—61no—
449Dic3⋊C4—61no—
450Dic3⋊C4—121no—
451C4×Dic3—61no—
452C4×Dic3—61no—
453C4×Dic3C22×D311yescharacteristic
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459D24—62no—
460#204—22no—
461#204—62no—
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—84no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—64no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16D3211yescharacteristic
509C2×D8—31no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—91no—
515#124—31no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—124no—
566C22×D3—242no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—242no—
570C22×D3D3×D411yescharacteristic
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—32no—
576C3×Q8—41no—
577C3×Q8—41no—
578C3×Q8—61no—
579C3×Q8—122no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—22no—
583C3×D4—41no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—61no—
587C3×D4—61no—
588C3×D4—122no—
589C3×D4D3×D412yes—
590C3×D4C2×#6712yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—41no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—122no—
603C2×C3×C4—122no—
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606#67—42no—
607#67—62no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—122no—
615#67—124no—
616#67—122no—
617#67—241no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—42no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—121no—
627C2×Dic3—122no—
628C2×Dic3D3×D411yescharacteristic
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—62no—
636D12—62no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—122no—
645D12—122no—
646D12—241no—
647C4×D3—21no—
648C4×D3—21no—
649C4×D3—42no—
650C4×D3—61no—
651C4×D3—61no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—121no—
655C4×D3—121no—
656C4×D3—122no—
657Dic6—21no—
658Dic6—42no—
659Dic6C2×#6712yescomplemented
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—32no—
663C3×C8—41no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C3⋊C8—121no—
669C3⋊C8C2×#6712yescomplemented
670C2×C32—42no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—81no—
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—61no—
680C24—181no—
681#41—182no—
682#41—361no—
683C2×Q8—31no—
684C2×Q8—61no—
685C2×Q8—62no—
686C2×Q8—121no—
687C2×Q8C2×D3211yescharacteristic
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—62no—
692C2×D4—91no—
693C2×D4—91no—
694C2×D4—121no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—182no—
702C2×D4—181no—
703C2×D4—364no—
704C2×D4—361no—
705C2×D4C2×D3211yescharacteristic
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—91no—
710C22×C4—181no—
711SD16—22no—
712SD16—34no—
713SD16—62no—
714SD16—62no—
715SD16—182no—
716SD16—361no—
717D8—62no—
718D8—182no—
719D8—361no—
720M16—182no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—62no—
724C2×C8—91no—
725C2×C8C2×D3211yescharacteristic
726C4⋊C4—31no—
727C4⋊C4—91no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C4⋊C4—181no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—91no—
735C22⋊C4—91no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—31no—
741C42—181no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—42no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—244no—
762C22×C3C2×D3×D411yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—62no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—84no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—244no—
792C2×D3—244no—
793C2×D3—248no—
794C2×D3#91412yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—62no—
802C3×C4—61no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4#100411yescharacteristic
807C3×C4#100911yescharacteristic
808C3×C4C22×#6711yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—22no—
812Dic3—21no—
813Dic3—41no—
814Dic3—61no—
815Dic3—61no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—241no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—21no—
822C23—31no—
823C23—61no—
824C23—61no—
825C23—91no—
826C23—122no—
827C23—122no—
828C23—181no—
829C23—241no—
830C23—362no—
831C23—362no—
832C23—721no—
833Q8—21no—
834Q8—21no—
835Q8—32no—
836Q8—61no—
837Q8—122no—
838D4—21no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—122no—
844D4—182no—
845D4—181no—
846D4—181no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—721no—
854D4D3×#6712yes—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—91no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—362no—
870C2×C4C22×D3211yescharacteristic
871C8—21no—
872C8—32no—
873C8—61no—
874C8—181no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3—42no—
880C2×C3—62no—
881C2×C3—82no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#560911yescharacteristic
885C2×C3C2×#91411yescharacteristic
886C2×C3#576211yescharacteristic
887C2×C3#577011yescharacteristic
888C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
889C2×C3D4×#6711yescharacteristic
890D3—22no—
891D3—81no—
892D3—81no—
893D3—122no—
894D3—121no—
895D3—121no—
896D3—242no—
897D3—241no—
898D3—241no—
899C22—22no—
900C22—32no—
901C22—41no—
902C22—41no—
903C22—61no—
904C22—61no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—181no—
912C22—181no—
913C22—181no—
914C22—244no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22—724no—
919C22D32×D411yescharacteristic
920C4—41no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—62no—
925C4—121no—
926C4—181no—
927C4—361no—
928C4#6431411yescharacteristic
929C4C2×D3×#6711yescharacteristic
930C3—21no—
931C3#8055311yescharacteristic, complemented
932C3#8386411yescharacteristic, complemented
933C2—42no—
934C2—62no—
935C2—241no—
936C2—241no—
937C2—361no—
938C2—721no—
939C2D3×#91411yescharacteristic
940C2#1059475311yescharacteristic
941C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. #10595401C2semidirect
3. D4×#626C2semidirect
4. C2×#63937C2semidirect
5. #10592868C2semidirect
6. C3×#5165C2semidirect
7. #10591619C2semidirect
8. #10591590C2semidirect
9. #10591584C2semidirect
10. #10591447C2semidirect
11. #10591440C2semidirect
12. #10590964C2semidirect
13. #10590826C2semidirect
14. #10590799C2semidirect
15. #10590727C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C2×#3796C22semidirect
24. #64155C22semidirect
25. C2×#3755C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
41. #63908C22semidirect
47. Dic3×Dic6C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3712C22semidirect
53. #63648C22semidirect
54. #63647C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63565C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
67. C2×D3×SD16D3semidirect
80. #5165D3semidirect
135. C3×#214D4semidirect
162. C2×D3×Q8C2×D3semidirect
182. #947C2×D3semidirect
192. C2×#215C2×D3semidirect
215. C2×#204C2×D3semidirect
218. C2×D3×C8C2×D3semidirect
234. #835C2×D3semidirect
244. #821C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
296. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
423. #214#67semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
659. Dic6C2×#67semidirect
669. C3⋊C8C2×#67semidirect
794. C2×D3#914semidirect
820. C32#3265semidirect
931. C3#80553semidirect
932. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105954012
D4×#6262
C2×#639372
#105928682
C3×#51652
#105916192
#105915902
#105915842
#105914472
#105914402
#105909642
#105908262
#105907992
#105907272
#838643
#805533