Finite Group Databasebeta

← #11863934

Subgroups — #11863934

Order 1152.

2087 conjugacy classes of subgroups.

The subgroup lattice has 1119 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3#10595301C211yesmaximal, characteristic, complemented
4C2×#63925C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic, complemented
7#10591516C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591467C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14#10590939C211yesmaximal, characteristic, complemented
15#10590936C211yesmaximal, characteristic, complemented
16#83944—31nomaximal
17#80002—31nomaximal
18C23×D32—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C3×D3×D4C2211yescharacteristic
23C2×#3811—21no—
24C2×D3×#67—21no—
25C2×D3×#67—21no—
26D32×D4—24no—
27D32×D4—24no—
28C2×#3802C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×D3×D12C2211yescharacteristic
31C2×C4×D32C2211yescharacteristic
32C2×C32×D8C2211yescharacteristic, complemented
33#64147C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35C3×#938C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#911—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63983—21no—
43Dic3×#67—21no—
44#63969—21no—
45#63952—21no—
46#63925—24no—
47#63871C2211yescharacteristic, complemented
48#63856C2211yescharacteristic, complemented
49#63841C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68#5828—31no—
69C2×#949—31no—
70C2×#911—31no—
71C2×#911D311yescharacteristic, complemented
72#5606—31no—
73C3×#447—31no—
74#5218—31no—
75#5215—31no—
76#5169—31no—
77#5169—31no—
78#5169—31no—
79#5169—31no—
80#5156—31no—
81#5156—31no—
82#5156—31no—
83#5156—31no—
84#5156—31no—
85#5156—61no—
86#5156D311yescharacteristic, complemented
87#5131—31no—
88#5126—31no—
89#5036—31no—
90#4776—31no—
91#4776—31no—
92#4770—31no—
93#4770—31no—
94#4731—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C22×D32—28no—
100C22×D32—21no—
101C22×D32—21no—
102C22×D32—21no—
103C22×D32—44no—
104C22×D32—44no—
105C22×D32D411yescharacteristic
106C2×C32×D4C2311yescharacteristic
107C2×C32×D4C2311yescharacteristic, complemented
108C2×#638—21no—
109C2×#638—21no—
110D4×C3⋊D3—22no—
111D4×C3⋊D3—22no—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×#67—21no—
115C2×C3×#67—21no—
116C2×C3×#67—21no—
117C2×C3×#67—21no—
118C22×C3×Dic3—21no—
119C3×#237—22no—
120C3×#237—22no—
121C3×D3×D4—22no—
122C3×D3×D4—22no—
123C3×D3×D4—22no—
124C3×D3×D4D414yescomplemented
125C2×C3×D12C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic, complemented
130#3811—28no—
131D3×#67—28no—
132D3×#67—28no—
133C2×#626—21no—
134C2×#626—21no—
135C2×#625—21no—
136C2×#624D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138C2×D3×Dic3D411yescharacteristic
139#3802—22no—
140#3802—22no—
141D3×D12—22no—
142D3×D12—22no—
143D3×D12—22no—
144D3×D12D414yescomplemented
145C4×D32—22no—
146C4×D32—22no—
147C32×D8—22no—
148C2×C32×C8C2311yescharacteristic, complemented
149#3757—21no—
150#3753—22no—
151C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
152C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
153C3×#217—21no—
154C3×#214—22no—
155C3×#213—22no—
156C3×#213—22no—
157C3×C4⋊Dic3C2311yescharacteristic, complemented
158C2×C3×C3⋊C8C2311yescharacteristic, complemented
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C3×#204—22no—
161C3×ΓL(1,𝔽25)—22no—
162#3724—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166(C2×D3)⋊Dic3—21no—
167Dic32—21no—
168#3717—22no—
169#3715—22no—
170#3711—22no—
171#3003—91noSylow
172C24×D3—61no—
173C24×D3—61no—
174C2×C3×#41—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×#67—61no—
178C22×#67—61no—
179C2×#237C2×D311yescharacteristic, complemented
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C2×D3×D4—64no—
194C2×D3×D4—64no—
195C2×D3×D4C2×D311yescharacteristic
196C2×D3×D4C2×D311yescharacteristic
197C22×D12—31no—
198C22×D12—31no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C3×AGL(1,ℤ/8)—64no—
202C2×C3×SD16—31no—
203C2×C3×SD16—31no—
204C2×C3×D8—21no—
205C2×C3×D8—31no—
206C2×C3×D8—31no—
207C2×C3×D8C2×D311yescharacteristic, complemented
208C2×C3×D8C2×D311yescharacteristic, complemented
209C2×C3×M16—31no—
210C3×#121—31no—
211#949—64no—
212#946—31no—
213#946—31no—
214C2×#215—31no—
215C2×#215—31no—
216#938—31no—
217#938—31no—
218#938—61no—
219#938C2×D311yescharacteristic, complemented
220#937—61no—
221#937—61no—
222#935—61no—
223D4×Dic3—61no—
224C2×#214—31no—
225C2×#214C2×D311yescharacteristic, complemented
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—61no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#213C2×D311yescharacteristic, complemented
231C4×#67—61no—
232C4×#67—61no—
233#926—31no—
234#924—31no—
235C2×#208—31no—
236#911—24no—
237#911—64no—
238C2×#204—31no—
239C2×#204C2×D311yescharacteristic, complemented
240C2×ΓL(1,𝔽25)—31no—
241C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
242#897—31no—
243#892—31no—
244#883—61no—
245#67⋊C4—61no—
246C3×#102—31no—
247C3×#102—31no—
248C3×C22⋊C8—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#832C2×D311yescharacteristic, complemented
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—31no—
262#821—61no—
263#821C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269(C2×D3)⋊C8—61no—
270(C2×D3)⋊C8C2×D311yescharacteristic, complemented
271#809—31no—
272#809—31no—
273C23×C32—21no—
274C23×C32—21no—
275C22×C3⋊D3—24no—
276C22×C3⋊D3—21no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3—42no—
279C22×C3⋊D3C2×D411yescharacteristic
280C22×C3×D3—24no—
281C22×C3×D3—21no—
282C22×C3×D3—21no—
283C22×C3×D3—24no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3—42no—
288C22×C3×D3C2×D411yescharacteristic
289C22×C3×D3C2×D411yescharacteristic
290C2×D32—22no—
291C2×D32—22no—
292C2×D32—22no—
293C2×D32—24no—
294C2×D32—24no—
295C2×D32—24no—
296C2×D32—432no—
297C2×D32—42no—
298C2×D32—42no—
299C2×D32—42no—
300C2×D32—42no—
301C2×D32—42no—
302C2×D32—42no—
303C32×D4—21no—
304C32×D4—21no—
305C32×D4—21no—
306C32×D4C2×D412yes—
307C2×C32×C4C2411yescharacteristic
308#638—24no—
309#638—42no—
310C2×C3⋊Dic3—21no—
311C2×C3⋊Dic3C2×D411yescharacteristic
312C4⋊(C3⋊D3)—21no—
313C4⋊(C3⋊D3)C2×D412yes—
314C4×C3⋊D3—21no—
315C4×C3⋊D3—21no—
316C3×#67—24no—
317C3×#67—24no—
318C3×#67—42no—
319C3×#67—42no—
320C2×C3×Dic3—21no—
321C2×C3×Dic3—21no—
322C2×C3×Dic3—42no—
323C2×C3×Dic3C2×D411yescharacteristic
324C2×C3×Dic3C2×D411yescharacteristic
325C3×D12—21no—
326C3×D12—21no—
327C3×D12C2×D412yes—
328C3×D12C2×D412yes—
329C3×C4×D3—21no—
330C3×C4×D3—21no—
331C3×C4×D3C2×D412yes—
332C3×C4×D3C2×D412yes—
333C3×Dic6—21no—
334C3×Dic6—21no—
335#626—24no—
336#626—24no—
337#625—24no—
338#624—22no—
339D3×Dic3—22no—
340D3×Dic3—22no—
341C32×C8—21no—
342C3⋊(C3⋊C8)—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8—21no—
345C23×D4—91no—
346C2×AGL(1,ℤ/8)—31no—
347C2×AGL(1,ℤ/8)—91no—
348#525—91no—
349#450—91no—
350#450—91no—
351#450—91no—
352#450—91no—
353#447—31no—
354#447—91no—
355#447—91no—
356#447—91no—
357#418—91no—
358#418—91no—
359#407—91no—
360C24×C3—61no—
361C24×C3—61no—
362C23×D3—21no—
363C23×D3—21no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3—61no—
367C23×D3—61no—
368C23×D3—61no—
369C23×D3—61no—
370C23×D3—68no—
371C23×D3—68no—
372C23×D3—61no—
373C23×D3—61no—
374C23×D3—61no—
375C23×D3—61no—
376C23×D3—121no—
377C23×D3—124no—
378C23×D3—124no—
379C23×D3—124no—
380C23×D3—124no—
381C3×#41—62no—
382C3×#41—62no—
383C2×C3×Q8—31no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—34no—
387C2×C3×D4—31no—
388C2×C3×D4—31no—
389C2×C3×D4—62no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—62no—
394C2×C3×D4—61no—
395C2×C3×D4—61no—
396C2×C3×D4C22×D311yescharacteristic
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic, complemented
399C2×C3×D4C22×D311yescharacteristic, complemented
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—61no—
403C2×#67—21no—
404C2×#67—21no—
405C2×#67—21no—
406C2×#67—21no—
407C2×#67—61no—
408C2×#67—61no—
409C2×#67—61no—
410C2×#67—61no—
411C2×#67—68no—
412C2×#67—68no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—61no—
416C2×#67—61no—
417C2×#67—121no—
418C2×#67—121no—
419C22×Dic3—21no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422#237—22no—
423#237—22no—
424D3×D4—22no—
425D3×D4—22no—
426D3×D4—22no—
427D3×D4—34no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—62no—
434D3×D4—68no—
435D3×D4—68no—
436D3×D4—68no—
437D3×D4—68no—
438D3×D4—62no—
439D3×D4—62no—
440D3×D4—62no—
441D3×D4—62no—
442D3×D4—62no—
443D3×D4—122no—
444D3×D4—122no—
445D3×D4#6714yescomplemented
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—34no—
449C2×D12—61no—
450C2×D12—62no—
451C2×D12—62no—
452C2×D12—61no—
453C2×D12—61no—
454C2×D12—62no—
455C2×D12C22×D311yescharacteristic
456C2×D12C22×D311yescharacteristic
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—61no—
464C2×C4×D3—62no—
465C2×C4×D3—62no—
466C2×C4×D3—62no—
467C2×C4×D3—62no—
468C2×C4×D3C22×D311yescharacteristic
469C2×C4×D3C22×D311yescharacteristic
470C2×Dic6C22×D311yescharacteristic, complemented
471C3×SD16—62no—
472C3×SD16—62no—
473C3×D8—22no—
474C3×D8—22no—
475C3×D8—42no—
476C3×D8—62no—
477C3×D8—62no—
478C3×M16—62no—
479C2×C3×C8—21no—
480C2×C3×C8—31no—
481C2×C3×C8—31no—
482C2×C3×C8C22×D311yescharacteristic, complemented
483C2×C3×C8C22×D311yescharacteristic, complemented
484C3×C4⋊C4—31no—
485C3×C22⋊C4—61no—
486#217—21no—
487#217—61no—
488#217—61no—
489#217—61no—
490#217—61no—
491#217—121no—
492#215—62no—
493#215—62no—
494#214—22no—
495#214—62no—
496#213—22no—
497#213—22no—
498#213—62no—
499#213—62no—
500#213—122no—
501(C2×D3)⋊C4—61no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—61no—
504(C2×D3)⋊C4—61no—
505C4⋊Dic3—31no—
506C4⋊Dic3—31no—
507C4⋊Dic3—61no—
508C4⋊Dic3—61no—
509C4⋊Dic3C22×D311yescharacteristic, complemented
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513C4×Dic3—61no—
514C4×Dic3—61no—
515#208—62no—
516C2×C3⋊C8—31no—
517C2×C3⋊C8—31no—
518C2×C3⋊C8—61no—
519C2×C3⋊C8C22×D311yescharacteristic, complemented
520C2×C3⋊C8C22×D311yescharacteristic, complemented
521#204—22no—
522#204—62no—
523ΓL(1,𝔽25)—22no—
524ΓL(1,𝔽25)—62no—
525C22×C32—22no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—41no—
530C22×C32—41no—
531C22×C32C22×D411yescharacteristic
532C2×C3⋊D3—21no—
533C2×C3⋊D3—21no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—48no—
536C2×C3⋊D3—41no—
537C2×C3⋊D3—41no—
538C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—48no—
546C2×C3×D3—48no—
547C2×C3×D3—41no—
548C2×C3×D3—41no—
549C2×C3×D3—41no—
550C2×C3×D3—41no—
551C2×C3×D3#12012yes—
552C2×C3×D3AGL(1,ℤ/8)12yescomplemented
553D32—28no—
554D32—48no—
555D32—48no—
556D32—48no—
557C32×C4C22×D411yescharacteristic
558C32×C4C22×D411yescharacteristic
559C3⋊Dic3—21no—
560C3⋊Dic3—41no—
561C3×Dic3—21no—
562C3×Dic3—41no—
563C3×Dic3—41no—
564C3×Dic3#12012yes—
565C25—181no—
566C2×#41—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C22×D4—181no—
574C22×D4—181no—
575C22×D4—181no—
576C22×D4—184no—
577C22×D4—184no—
578C23×C4—91no—
579AGL(1,ℤ/8)—64no—
580AGL(1,ℤ/8)—184no—
581C2×SD16—31no—
582C2×SD16—31no—
583C2×SD16—91no—
584C2×SD16—91no—
585C2×D8—31no—
586C2×D8—31no—
587C2×D8—91no—
588C2×D8D3211yescharacteristic, complemented
589C2×M16—31no—
590C2×M16—91no—
591#123—181no—
592C22⋊Q8—91no—
593C22⋊Q8—91no—
594#121—31no—
595#121—91no—
596#120—181no—
597C4×D4—181no—
598C4×D4—181no—
599#117—91no—
600#102—31no—
601#102—31no—
602#102—91no—
603#102—91no—
604#102—91no—
605#102—91no—
606#102—91no—
607#102—91no—
608C22⋊C8—31no—
609C22⋊C8—91no—
610C22⋊C8—91no—
611C22⋊C8—91no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—31no—
617C23×C3—31no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—64no—
621C23×C3—64no—
622C23×C3—61no—
623C23×C3—61no—
624C23×C3—122no—
625C23×C3—122no—
626C23×C3—122no—
627C23×C3—122no—
628C22×D3—24no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—24no—
632C22×D3—31no—
633C22×D3—31no—
634C22×D3—42no—
635C22×D3—42no—
636C22×D3—42no—
637C22×D3—42no—
638C22×D3—61no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—62no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—64no—
651C22×D3—64no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—64no—
655C22×D3—121no—
656C22×D3—124no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—1232no—
665C22×D3—1232no—
666C22×D3—122no—
667C22×D3—122no—
668C22×D3—122no—
669C22×D3—122no—
670C22×D3—122no—
671C22×D3—122no—
672C22×D3—122no—
673C22×D3—122no—
674C22×D3—122no—
675C22×D3—242no—
676C22×D3—242no—
677C22×D3D3×D411yescharacteristic
678C22×D3D3×D411yescharacteristic
679C3×Q8—61no—
680C3×Q8—61no—
681C3×D4—21no—
682C3×D4—21no—
683C3×D4—21no—
684C3×D4—21no—
685C3×D4—21no—
686C3×D4—21no—
687C3×D4—22no—
688C3×D4—32no—
689C3×D4—32no—
690C3×D4—41no—
691C3×D4—41no—
692C3×D4—41no—
693C3×D4—64no—
694C3×D4—64no—
695C3×D4—61no—
696C3×D4—61no—
697C3×D4—122no—
698C3×D4—122no—
699C3×D4D3×D412yes—
700C3×D4C2×#6712yes—
701C2×C3×C4—21no—
702C2×C3×C4—31no—
703C2×C3×C4—32no—
704C2×C3×C4—32no—
705C2×C3×C4—31no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—122no—
711C2×C3×C4C23×D311yescharacteristic
712C2×C3×C4C23×D311yescharacteristic
713#67—24no—
714#67—24no—
715#67—42no—
716#67—42no—
717#67—64no—
718#67—64no—
719#67—64no—
720#67—64no—
721#67—64no—
722#67—64no—
723#67—124no—
724#67—122no—
725#67—122no—
726#67—242no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—42no—
732C2×Dic3—61no—
733C2×Dic3—62no—
734C2×Dic3—62no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—121no—
738C2×Dic3D3×D411yescharacteristic
739C2×Dic3D3×D411yescharacteristic
740D12—21no—
741D12—21no—
742D12—32no—
743D12—32no—
744D12—62no—
745D12—64no—
746D12—64no—
747D12—61no—
748D12—61no—
749D12—121no—
750D12D3×D412yes—
751D12C2×#6712yes—
752C4×D3—21no—
753C4×D3—21no—
754C4×D3—62no—
755C4×D3—62no—
756C4×D3—62no—
757C4×D3—61no—
758C4×D3—61no—
759C4×D3—61no—
760C4×D3—61no—
761C4×D3—62no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3D3×D412yes—
765C4×D3C2×#6712yes—
766Dic6—21no—
767Dic6—21no—
768C3×C8—21no—
769C3×C8—21no—
770C3×C8—41no—
771C3×C8—61no—
772C3×C8—61no—
773C3⋊C8—21no—
774C3⋊C8—21no—
775C3⋊C8—61no—
776C3⋊C8—61no—
777C3⋊C8—121no—
778C2×C32—42no—
779C2×C32—81no—
780C2×C32C2×#12011yescharacteristic
781C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
782C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
783C3⋊D3—22no—
784C3⋊D3—42no—
785C3×D3—22no—
786C3×D3—22no—
787C3×D3—42no—
788C3×D3—42no—
789C24—61no—
790C24—61no—
791C24—91no—
792C24—181no—
793C24—181no—
794C24—181no—
795C24—181no—
796C24—188no—
797C24—364no—
798C24—364no—
799#41—62no—
800#41—62no—
801C2×Q8—31no—
802C2×D4—34no—
803C2×D4—31no—
804C2×D4—31no—
805C2×D4—62no—
806C2×D4—61no—
807C2×D4—61no—
808C2×D4—62no—
809C2×D4—62no—
810C2×D4—61no—
811C2×D4—61no—
812C2×D4—94no—
813C2×D4—91no—
814C2×D4—182no—
815C2×D4—181no—
816C2×D4—181no—
817C2×D4—182no—
818C2×D4—182no—
819C2×D4—181no—
820C2×D4—181no—
821C2×D4—182no—
822C2×D4—182no—
823C2×D4—182no—
824C2×D4—188no—
825C2×D4—188no—
826C2×D4—188no—
827C2×D4—182no—
828C2×D4—181no—
829C2×D4C2×D3211yescharacteristic
830C2×D4C2×D3211yescharacteristic, complemented
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—61no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—91no—
837C22×C4—91no—
838C22×C4—182no—
839C22×C4—182no—
840SD16—62no—
841SD16—62no—
842SD16—182no—
843SD16—182no—
844D8—22no—
845D8—62no—
846D8—62no—
847D8—182no—
848M16—62no—
849M16—182no—
850C2×C8—31no—
851C2×C8—31no—
852C2×C8—91no—
853C2×C8C2×D3211yescharacteristic, complemented
854C4⋊C4—31no—
855C4⋊C4—91no—
856C4⋊C4—181no—
857C4⋊C4—181no—
858C22⋊C4—61no—
859C22⋊C4—181no—
860C22⋊C4—181no—
861C22⋊C4—181no—
862C22⋊C4—181no—
863C42—181no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—21no—
867C22×C3—32no—
868C22×C3—32no—
869C22×C3—42no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—61no—
881C22×C3—61no—
882C22×C3—61no—
883C22×C3—61no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—81no—
887C22×C3—81no—
888C22×C3—81no—
889C22×C3—81no—
890C22×C3—81no—
891C22×C3—128no—
892C22×C3—128no—
893C22×C3—121no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—121no—
897C22×C3C2×D3×D411yescharacteristic
898C22×C3C2×D3×D411yescharacteristic
899C2×D3—21no—
900C2×D3—21no—
901C2×D3—21no—
902C2×D3—21no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—32no—
906C2×D3—32no—
907C2×D3—48no—
908C2×D3—48no—
909C2×D3—41no—
910C2×D3—41no—
911C2×D3—41no—
912C2×D3—41no—
913C2×D3—62no—
914C2×D3—68no—
915C2×D3—68no—
916C2×D3—61no—
917C2×D3—61no—
918C2×D3—61no—
919C2×D3—61no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—122no—
925C2×D3—128no—
926C2×D3—128no—
927C2×D3—128no—
928C2×D3—128no—
929C2×D3—128no—
930C2×D3—128no—
931C2×D3—128no—
932C2×D3—128no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—248no—
938C2×D3—241no—
939C2×D3—241no—
940C2×D3#91112yescomplemented
941C2×D3#93712yes—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—32no—
945C3×C4—61no—
946C3×C4—121no—
947C3×C4—121no—
948C3×C4C2×D3×D411yescharacteristic
949C3×C4C2×D3×D411yescharacteristic
950C3×C4C2×D3×D411yescharacteristic
951C3×C4C22×#6711yescharacteristic
952Dic3—21no—
953Dic3—41no—
954Dic3—41no—
955Dic3—61no—
956Dic3—61no—
957Dic3—121no—
958Dic3—121no—
959Dic3—121no—
960Dic3—241no—
961Dic3#93712yes—
962C32#300311yescharacteristic, complemented, Sylow
963C23—21no—
964C23—21no—
965C23—31no—
966C23—31no—
967C23—64no—
968C23—64no—
969C23—61no—
970C23—61no—
971C23—91no—
972C23—122no—
973C23—122no—
974C23—122no—
975C23—122no—
976C23—184no—
977C23—182no—
978C23—182no—
979C23—184no—
980C23—182no—
981C23—184no—
982C23—184no—
983C23—181no—
984C23—362no—
985C23—362no—
986C23—362no—
987C23—362no—
988C23—362no—
989C23—362no—
990C23—362no—
991C23—3632no—
992C23—362no—
993Q8—61no—
994Q8—61no—
995D4—21no—
996D4—21no—
997D4—21no—
998D4—32no—
999D4—32no—
1000D4—64no—
1001D4—64no—
1002D4—61no—
1003D4—61no—
1004D4—92no—
1005D4—122no—
1006D4—122no—
1007D4—184no—
1008D4—184no—
1009D4—184no—
1010D4—184no—
1011D4—181no—
1012D4—362no—
1013D4D3×#6712yes—
1014C2×C4—31no—
1015C2×C4—32no—
1016C2×C4—32no—
1017C2×C4—31no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—91no—
1023C2×C4—122no—
1024C2×C4—182no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—181no—
1028C2×C4—181no—
1029C2×C4—181no—
1030C2×C4C22×D3211yescharacteristic
1031C8—21no—
1032C8—61no—
1033C8—61no—
1034C8—181no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—42no—
1039C2×C3—42no—
1040C2×C3—62no—
1041C2×C3—62no—
1042C2×C3—82no—
1043C2×C3—81no—
1044C2×C3—81no—
1045C2×C3—122no—
1046C2×C3—122no—
1047C2×C3—161no—
1048C2×C3D3×#12011yescharacteristic
1049C2×C3C2×#91111yescharacteristic
1050C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1051C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1052C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1053C2×C3C2×#93711yescharacteristic
1054D3—22no—
1055D3—22no—
1056D3—42no—
1057D3—42no—
1058D3—62no—
1059D3—62no—
1060D3—122no—
1061D3—122no—
1062D3—122no—
1063D3—242no—
1064C22—22no—
1065C22—32no—
1066C22—32no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—61no—
1073C22—61no—
1074C22—61no—
1075C22—61no—
1076C22—62no—
1077C22—62no—
1078C22—92no—
1079C22—128no—
1080C22—128no—
1081C22—121no—
1082C22—121no—
1083C22—121no—
1084C22—121no—
1085C22—188no—
1086C22—181no—
1087C22—181no—
1088C22—182no—
1089C22—368no—
1090C22—368no—
1091C22—368no—
1092C22—368no—
1093C22—361no—
1094C22—361no—
1095C22D32×D411yescharacteristic
1096C4—32no—
1097C4—61no—
1098C4—121no—
1099C4—121no—
1100C4—181no—
1101C4—361no—
1102C4D32×D411yescharacteristic
1103C4C2×D3×#6711yescharacteristic
1104C3—21no—
1105C3#8000211yescharacteristic, complemented
1106C3#8394411yescharacteristic, complemented
1107C2—42no—
1108C2—62no—
1109C2—62no—
1110C2—81no—
1111C2—122no—
1112C2—122no—
1113C2—182no—
1114C2—362no—
1115C2D3×#91111yescharacteristic
1116C2#1059472611yescharacteristic
1117C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D32×D4C2semidirect
2. C2×C3×#911C2semidirect
3. #10595301C2semidirect
4. C2×#63925C2semidirect
5. #10592855C2semidirect
6. C3×#5156C2semidirect
7. #10591516C2semidirect
8. #10591515C2semidirect
9. #10591467C2semidirect
10. #10591458C2semidirect
11. #10591421C2semidirect
12. #10590943C2semidirect
13. #10590942C2semidirect
14. #10590939C2semidirect
15. #10590936C2semidirect
20. C2×C3×#237C22semidirect
32. C2×C32×D8C22semidirect
33. #64147C22semidirect
34. C2×#3753C22semidirect
35. C3×#938C22semidirect
36. C2×C3×#214C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
47. #63871C22semidirect
48. #63856C22semidirect
49. #63841C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
52. C2×#3711C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#911D3semidirect
86. #5156D3semidirect
107. C2×C32×D4C23semidirect
124. C3×D3×D4D4semidirect
129. C2×C3×Dic6C23semidirect
144. D3×D12D4semidirect
148. C2×C32×C8C23semidirect
151. C4⋊(C3⋊Dic3)C23semidirect
152. C2×C3⋊(C3⋊C8)C23semidirect
157. C3×C4⋊Dic3C23semidirect
158. C2×C3×C3⋊C8C23semidirect
159. C2×C3×C3⋊C8C23semidirect
179. C2×#237C2×D3semidirect
207. C2×C3×D8C2×D3semidirect
208. C2×C3×D8C2×D3semidirect
219. #938C2×D3semidirect
225. C2×#214C2×D3semidirect
229. C2×#213C2×D3semidirect
230. C2×#213C2×D3semidirect
239. C2×#204C2×D3semidirect
241. C2×ΓL(1,𝔽25)C2×D3semidirect
255. #832C2×D3semidirect
263. #821C2×D3semidirect
270. (C2×D3)⋊C8C2×D3semidirect
398. C2×C3×D4C22×D3semidirect
399. C2×C3×D4C22×D3semidirect
445. D3×D4#67semidirect
470. C2×Dic6C22×D3semidirect
482. C2×C3×C8C22×D3semidirect
483. C2×C3×C8C22×D3semidirect
509. C4⋊Dic3C22×D3semidirect
519. C2×C3⋊C8C22×D3semidirect
520. C2×C3⋊C8C22×D3semidirect
538. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C2×C3×D3AGL(1,ℤ/8)semidirect
588. C2×D8D32semidirect
830. C2×D4C2×D32semidirect
853. C2×C8C2×D32semidirect
940. C2×D3#911semidirect
962. C32#3003semidirect
1105. C3#80002semidirect
1106. C3#83944semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×C3×#9112
#105953012
C2×#639252
#105928552
C3×#51562
#105915162
#105915152
#105914672
#105914582
#105914212
#105909432
#105909422
#105909392
#105909362
#839443
#800023