Finite Group Databasebeta

← #11863936

Subgroups — #11863936

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×#63934C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590943C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80146—31nomaximal
17#78926—31nomaximal
18C23×D32—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×#3811—21no—
23C2×D3×#67—21no—
24C2×D3×#67—21no—
25D32×D4—24no—
26D32×D4—24no—
27C2×#3802C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×C4×D32C2211yescharacteristic
31C2×#3799C2211yescharacteristic, complemented
32C2×#3753C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63934—24no—
41#63923—21no—
42#63909C2211yescharacteristic, complemented
43#63894—21no—
44#63890—21no—
45#63880—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63794—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C2×#932—31no—
68C2×#914—31no—
69C2×#914—31no—
70C2×#908—31no—
71#5627—31no—
72#5524—31no—
73C3×#450—31no—
74C3×#418—31no—
75#5217—31no—
76#5169—31no—
77#5169—31no—
78#5126—31no—
79#5046—31no—
80#5001—31no—
81#4776—31no—
82#4776—31no—
83#4776—31no—
84#4776D311yescharacteristic, complemented
85#4773—31no—
86#4773—31no—
87#4773—31no—
88#4773—31no—
89#4773—31no—
90#4773—31no—
91#4773—61no—
92#4770—31no—
93#4770D311yescharacteristic, complemented
94#4732—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×#638—21no—
108D4×C3⋊D3—22no—
109D4×C3⋊D3—22no—
110C2×C4⋊(C3⋊D3)—21no—
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×#67—21no—
115C2×C3×#67—21no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C3×D3×D4D414yescomplemented
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic, complemented
125#3811—28no—
126D3×#67—28no—
127D3×#67—28no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#624—21no—
134C2×#624D411yescharacteristic
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137#3802—22no—
138#3802—22no—
139D3×D12—22no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12D414yescomplemented
143C4×D32—22no—
144C4×D32—22no—
145#3799—22no—
146#3799—22no—
147C2×C32×C8C2311yescharacteristic, complemented
148C32×C4⋊C4C2311yescharacteristic, complemented
149#3753—22no—
150#3752—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
152#3745—22no—
153C3×#214—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C3×C4⋊Dic3C2311yescharacteristic, complemented
158C3×C4×Dic3—21no—
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C2×C3×C3⋊C8C2311yescharacteristic, complemented
161C3×#204—22no—
162C3×ΓL(1,𝔽25)—22no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165#3722—21no—
166#3717—22no—
167#3715—22no—
168#3714—22no—
169#3714—22no—
170#3711—22no—
171#3003—91noSylow
172C24×D3—61no—
173C24×D3—61no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×#67—61no—
177C22×#67—61no—
178C2×#239—31no—
179C2×D3×D4—31no—
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—64no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C2×D3×D4—64no—
194C2×D3×D4C2×D311yescharacteristic
195C2×D3×D4C2×D311yescharacteristic
196C2×#235—31no—
197C22×D12—31no—
198C22×D12—31no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C2×C3×M16—31no—
204C3×C22⋊Q8—31no—
205C3×#117—31no—
206#946—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#214—31no—
210C2×#214C2×D311yescharacteristic, complemented
211#932—64no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—61no—
217#930—31no—
218C2×#208—31no—
219#914—64no—
220#914—64no—
221#908—64no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—31no—
226C2×D24—61no—
227C2×#204—31no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
231#897—31no—
232#897C2×D311yescharacteristic, complemented
233#895—31no—
234#895—31no—
235#895—31no—
236#895—61no—
237#894—61no—
238#893—61no—
239#892C2×D311yescharacteristic, complemented
240#886—61no—
241#882—61no—
242#882—61no—
243#67⋊C4—61no—
244C4×D12—61no—
245C4×D12—61no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×#102C2×D311yescharacteristic, complemented
252C3×#102C2×D311yescharacteristic, complemented
253C3×C22⋊C8—31no—
254#832—31no—
255#832C2×D311yescharacteristic, complemented
256#830—31no—
257#821—31no—
258#821C2×D311yescharacteristic, complemented
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272#809C2×D311yescharacteristic, complemented
273C23×C32—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—21no—
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×D4C2×D412yes—
305C2×C32×C4—21no—
306C2×C32×C4C2411yescharacteristic
307#638—24no—
308C2×C3⋊Dic3C2×D411yescharacteristic
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)—21no—
311C4⋊(C3⋊D3)—21no—
312C4⋊(C3⋊D3)—42no—
313C4⋊(C3⋊D3)C2×D412yes—
314C4×C3⋊D3—21no—
315C4×C3⋊D3—21no—
316C3×#67—24no—
317C3×#67—24no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3C2×D411yescharacteristic
321C2×C3×Dic3C2×D411yescharacteristic
322C3×D12—21no—
323C3×D12—21no—
324C3×D12C2×D412yes—
325C3×D12C2×D412yes—
326C3×C4×D3—21no—
327C3×C4×D3—21no—
328C3×C4×D3C2×D412yes—
329C3×C4×D3C2×D412yes—
330C3×Dic6—21no—
331C3×Dic6—21no—
332#626—24no—
333#626—24no—
334#626—42no—
335#626—42no—
336#625—24no—
337#624—22no—
338#624—42no—
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)—91no—
347C2×AGL(1,ℤ/8)—91no—
348#525—91no—
349#450—31no—
350#450—91no—
351#450—91no—
352#450—91no—
353#447—91no—
354#447—91no—
355#447—91no—
356#447—91no—
357#418—31no—
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—
381C2×C3×Q8—31no—
382C2×C3×D4—21no—
383C2×C3×D4—34no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—62no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—62no—
390C2×C3×D4—62no—
391C2×C3×D4C22×D311yescharacteristic
392C2×C3×D4C22×D311yescharacteristic
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C2×#67—21no—
396C2×#67—21no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—61no—
400C2×#67—61no—
401C2×#67—61no—
402C2×#67—61no—
403C2×#67—68no—
404C2×#67—68no—
405C2×#67—61no—
406C2×#67—61no—
407C2×#67—121no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410#239—62no—
411#239—62no—
412D3×D4—22no—
413D3×D4—22no—
414D3×D4—22no—
415D3×D4—34no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—68no—
423D3×D4—68no—
424D3×D4—68no—
425D3×D4—68no—
426D3×D4—62no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—122no—
432D3×D4—122no—
433D3×D4D1214yescomplemented
434#235—62no—
435#235—62no—
436C2×D12—31no—
437C2×D12—31no—
438C2×D12—34no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—61no—
442C2×D12—61no—
443C2×D12—62no—
444C2×D12—62no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12—62no—
448C2×D12—61no—
449C2×D12—61no—
450C2×D12—61no—
451C2×D12—61no—
452C2×D12—121no—
453C2×D12C22×D311yescharacteristic
454C2×D12C22×D311yescharacteristic
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—61no—
462C2×C4×D3—62no—
463C2×C4×D3—62no—
464C2×C4×D3—62no—
465C2×C4×D3—62no—
466C2×C4×D3—61no—
467C2×C4×D3—61no—
468C2×C4×D3C22×D311yescharacteristic
469C2×C4×D3C22×D311yescharacteristic
470C2×Dic6C22×D311yescharacteristic, complemented
471C3×SD16—62no—
472C3×SD16—62no—
473C3×M16—62no—
474C2×C3×C8—21no—
475C2×C3×C8—31no—
476C2×C3×C8—31no—
477C2×C3×C8C22×D311yescharacteristic, complemented
478C2×C3×C8C22×D311yescharacteristic, complemented
479C3×C4⋊C4—21no—
480C3×C4⋊C4—31no—
481C3×C4⋊C4—61no—
482C3×C4⋊C4C22×D311yescharacteristic, complemented
483C3×C4⋊C4C22×D311yescharacteristic, complemented
484C3×C22⋊C4—61no—
485C3×C22⋊C4—61no—
486C3×C42—61no—
487#215—62no—
488#215—62no—
489#214—22no—
490#214—62no—
491#213—62no—
492#213—62no—
493#213—62no—
494#213—62no—
495#213—122no—
496(C2×D3)⋊C4—21no—
497(C2×D3)⋊C4—21no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—61no—
500(C2×D3)⋊C4—61no—
501(C2×D3)⋊C4—61no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—61no—
504(C2×D3)⋊C4—121no—
505C4⋊Dic3—21no—
506C4⋊Dic3—61no—
507C4⋊Dic3C22×D311yescharacteristic, complemented
508Dic3⋊C4—61no—
509C4×Dic3—21no—
510#208—62no—
511C2×C3⋊C8—31no—
512C2×C3⋊C8—31no—
513C2×C3⋊C8—61no—
514C2×C3⋊C8C22×D311yescharacteristic, complemented
515C2×C3⋊C8C22×D311yescharacteristic, complemented
516D24—62no—
517D24—62no—
518D24—62no—
519D24—62no—
520D24—122no—
521#204—22no—
522#204—62no—
523ΓL(1,𝔽25)—22no—
524ΓL(1,𝔽25)—62no—
525C22×C32—22no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32C22×D411yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D3—22no—
532C2×C3⋊D3—48no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3—41no—
535C2×C3⋊D3—41no—
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×C4—41no—
558C32×C4C22×D411yescharacteristic
559C32×C4C22×D411yescharacteristic
560C3⋊Dic3—21no—
561C3×Dic3—21no—
562C3×Dic3—41no—
563C3×Dic3—41no—
564C3×Dic3#12012yes—
565C25—181no—
566C2×#41—91no—
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)—184no—
580AGL(1,ℤ/8)—184no—
581C2×SD16—31no—
582C2×SD16—31no—
583C2×SD16—91no—
584C2×SD16—91no—
585C2×D8—91no—
586C2×D8—91no—
587C2×D8—91no—
588C2×D8—91no—
589C2×M16—31no—
590C2×M16—91no—
591#123—181no—
592C22⋊Q8—31no—
593C22⋊Q8—91no—
594#121—91no—
595#121—91no—
596#120—181no—
597C4×D4—181no—
598C4×D4—181no—
599#117—31no—
600#102—31no—
601#102—31no—
602#102—31no—
603#102—31no—
604#102—91no—
605#102—91no—
606#102—91no—
607#102D3211yescharacteristic, complemented
608C22⋊C8—31no—
609C22⋊C8—91no—
610C22⋊C8—91no—
611C22⋊C8—91no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—31no—
615C23×C3—31no—
616C23×C3—41no—
617C23×C3—64no—
618C23×C3—64no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—122no—
622C23×C3—122no—
623C23×C3—122no—
624C23×C3—122no—
625C22×D3—24no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—24no—
629C22×D3—31no—
630C22×D3—31no—
631C22×D3—42no—
632C22×D3—42no—
633C22×D3—42no—
634C22×D3—42no—
635C22×D3—61no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—64no—
641C22×D3—64no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—64no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—121no—
655C22×D3—124no—
656C22×D3—121no—
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—22no—
684C3×D4—32no—
685C3×D4—32no—
686C3×D4—41no—
687C3×D4—64no—
688C3×D4—64no—
689C3×D4—61no—
690C3×D4—61no—
691C3×D4C2×D1212yes—
692C3×D4D3×D412yes—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—31no—
697C2×C3×C4—32no—
698C2×C3×C4—32no—
699C2×C3×C4—31no—
700C2×C3×C4—41no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4C23×D311yescharacteristic
706C2×C3×C4C23×D311yescharacteristic
707#67—24no—
708#67—24no—
709#67—64no—
710#67—64no—
711#67—64no—
712#67—64no—
713#67—64no—
714#67—64no—
715#67—124no—
716#67—122no—
717#67—122no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—61no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3D3×D411yescharacteristic
726C2×Dic3D3×D411yescharacteristic
727D12—21no—
728D12—21no—
729D12—32no—
730D12—32no—
731D12—62no—
732D12—64no—
733D12—64no—
734D12—61no—
735D12—61no—
736D12—61no—
737D12—61no—
738D12—61no—
739D12—61no—
740D12—121no—
741D12—121no—
742D12—121no—
743D12—122no—
744D12—122no—
745D12—122no—
746D12—122no—
747D12—242no—
748D12C2×D1212yes—
749D12D3×D412yes—
750C4×D3—21no—
751C4×D3—21no—
752C4×D3—62no—
753C4×D3—62no—
754C4×D3—62no—
755C4×D3—61no—
756C4×D3—61no—
757C4×D3—61no—
758C4×D3—61no—
759C4×D3—62no—
760C4×D3—121no—
761C4×D3—121no—
762C4×D3—122no—
763C4×D3—122no—
764C4×D3C2×D1212yes—
765C4×D3D3×D412yes—
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×C32C2×#12011yescharacteristic
780C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
781C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
782C3⋊D3—22no—
783C3⋊D3—42no—
784C3⋊D3—81no—
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—182no—
800#41—182no—
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—94no—
811C2×D4—91no—
812C2×D4—91no—
813C2×D4—181no—
814C2×D4—182no—
815C2×D4—181no—
816C2×D4—181no—
817C2×D4—182no—
818C2×D4—182no—
819C2×D4—181no—
820C2×D4—181no—
821C2×D4—181no—
822C2×D4—181no—
823C2×D4—182no—
824C2×D4—182no—
825C2×D4—182no—
826C2×D4—188no—
827C2×D4—188no—
828C2×D4—188no—
829C2×D4—182no—
830C2×D4C2×D3211yescharacteristic
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—91no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—91no—
837C22×C4—182no—
838C22×C4—182no—
839C22×C4—181no—
840SD16—62no—
841SD16—62no—
842SD16—182no—
843SD16—182no—
844D8—182no—
845D8—182no—
846D8—182no—
847D8—182no—
848M16—62no—
849M16—182no—
850C2×C8—31no—
851C2×C8—31no—
852C2×C8—91no—
853C2×C8C2×D3211yescharacteristic, complemented
854C4⋊C4—31no—
855C4⋊C4—61no—
856C4⋊C4—181no—
857C4⋊C4C2×D3211yescharacteristic, complemented
858C22⋊C4—61no—
859C22⋊C4—61no—
860C22⋊C4—181no—
861C22⋊C4—181no—
862C22⋊C4—181no—
863C42—61no—
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—61no—
875C22×C3—61no—
876C22×C3—61no—
877C22×C3—61no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—81no—
881C22×C3—81no—
882C22×C3—128no—
883C22×C3—128no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3C2×D3×D411yescharacteristic
889C22×C3C2×D3×D411yescharacteristic
890C2×D3—21no—
891C2×D3—21no—
892C2×D3—21no—
893C2×D3—21no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—32no—
897C2×D3—32no—
898C2×D3—48no—
899C2×D3—48no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—62no—
905C2×D3—68no—
906C2×D3—68no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—122no—
916C2×D3—128no—
917C2×D3—128no—
918C2×D3—128no—
919C2×D3—128no—
920C2×D3—128no—
921C2×D3—128no—
922C2×D3—128no—
923C2×D3—128no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—248no—
935C2×D3—241no—
936C2×D3—241no—
937C2×D3—241no—
938C2×D3—241no—
939C2×D3—241no—
940C2×D3#88212yes—
941C2×D3#91412yescomplemented
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—32no—
945C3×C4—41no—
946C3×C4—41no—
947C3×C4—61no—
948C3×C4—81no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4C22×D1211yescharacteristic
952C3×C4C2×D3×D411yescharacteristic
953C3×C4C2×D3×D411yescharacteristic
954C3×C4C2×D3×D411yescharacteristic
955Dic3—21no—
956Dic3—41no—
957Dic3—41no—
958Dic3—61no—
959Dic3—61no—
960Dic3—121no—
961Dic3#88212yes—
962C32#300311yescharacteristic, complemented, Sylow
963C23—21no—
964C23—31no—
965C23—31no—
966C23—64no—
967C23—64no—
968C23—61no—
969C23—61no—
970C23—91no—
971C23—122no—
972C23—122no—
973C23—122no—
974C23—122no—
975C23—184no—
976C23—182no—
977C23—182no—
978C23—184no—
979C23—182no—
980C23—184no—
981C23—184no—
982C23—181no—
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—32no—
997D4—32no—
998D4—64no—
999D4—64no—
1000D4—61no—
1001D4—61no—
1002D4—92no—
1003D4—184no—
1004D4—184no—
1005D4—184no—
1006D4—184no—
1007D4—181no—
1008D4—181no—
1009D4—181no—
1010D4—362no—
1011D4—362no—
1012D4—362no—
1013D4D3×D1212yes—
1014C2×C4—21no—
1015C2×C4—31no—
1016C2×C4—32no—
1017C2×C4—32no—
1018C2×C4—31no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—91no—
1024C2×C4—182no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—181no—
1028C2×C4—181no—
1029C2×C4—362no—
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—122no—
1044C2×C3—122no—
1045C2×C3C2×#88211yescharacteristic
1046C2×C3D3×#12011yescharacteristic
1047C2×C3C2×#91411yescharacteristic
1048C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1049C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1050C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1051D3—22no—
1052D3—22no—
1053D3—42no—
1054D3—42no—
1055D3—62no—
1056D3—62no—
1057D3—122no—
1058D3—122no—
1059D3—122no—
1060D3—242no—
1061D3—241no—
1062D3—241no—
1063D3—481no—
1064C22—22no—
1065C22—32no—
1066C22—32no—
1067C22—41no—
1068C22—41no—
1069C22—61no—
1070C22—61no—
1071C22—61no—
1072C22—61no—
1073C22—62no—
1074C22—62no—
1075C22—92no—
1076C22—128no—
1077C22—128no—
1078C22—121no—
1079C22—121no—
1080C22—121no—
1081C22—121no—
1082C22—188no—
1083C22—181no—
1084C22—181no—
1085C22—182no—
1086C22—368no—
1087C22—368no—
1088C22—368no—
1089C22—368no—
1090C22—361no—
1091C22—361no—
1092C22—361no—
1093C22—361no—
1094C22—361no—
1095C22D32×D411yescharacteristic
1096C4—32no—
1097C4—41no—
1098C4—61no—
1099C4—121no—
1100C4—121no—
1101C4—181no—
1102C4C2×D3×D1211yescharacteristic
1103C4D32×D411yescharacteristic
1104C3—21no—
1105C3#7892611yescharacteristic, complemented
1106C3#8014611yescharacteristic, complemented
1107C2—42no—
1108C2—62no—
1109C2—62no—
1110C2—122no—
1111C2—122no—
1112C2—182no—
1113C2—362no—
1114C2—721no—
1115C2D3×#88211yescharacteristic
1116C2#1059472611yescharacteristic
1117C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3003
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. C2×D32×D4C2semidirect
2. C2×#63934C2semidirect
3. C2×#63794C2semidirect
4. #10594627C2semidirect
5. #10592472C2semidirect
6. C3×#4776C2semidirect
7. C3×#4770C2semidirect
8. #10591467C2semidirect
9. #10591448C2semidirect
10. #10590947C2semidirect
11. #10590943C2semidirect
12. #10590936C2semidirect
13. #10590598C2semidirect
14. #10590596C2semidirect
15. #10590592C2semidirect
31. C2×#3799C22semidirect
32. C2×#3753C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#897C22semidirect
39. C3×#892C22semidirect
42. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4776D3semidirect
93. #4770D3semidirect
112. C2×C4⋊(C3⋊D3)C23semidirect
119. C3×D3×D4D4semidirect
124. C2×C3×Dic6C23semidirect
142. D3×D12D4semidirect
147. C2×C32×C8C23semidirect
148. C32×C4⋊C4C23semidirect
151. C2×C3⋊(C3⋊C8)C23semidirect
157. C3×C4⋊Dic3C23semidirect
159. C2×C3×C3⋊C8C23semidirect
160. C2×C3×C3⋊C8C23semidirect
210. C2×#214C2×D3semidirect
228. C2×#204C2×D3semidirect
230. C2×ΓL(1,𝔽25)C2×D3semidirect
232. #897C2×D3semidirect
239. #892C2×D3semidirect
251. C3×#102C2×D3semidirect
252. C3×#102C2×D3semidirect
255. #832C2×D3semidirect
258. #821C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
271. #809C2×D3semidirect
272. #809C2×D3semidirect
433. D3×D4D12semidirect
470. C2×Dic6C22×D3semidirect
477. C2×C3×C8C22×D3semidirect
478. C2×C3×C8C22×D3semidirect
482. C3×C4⋊C4C22×D3semidirect
483. C3×C4⋊C4C22×D3semidirect
507. C4⋊Dic3C22×D3semidirect
514. C2×C3⋊C8C22×D3semidirect
515. C2×C3⋊C8C22×D3semidirect
538. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C2×C3×D3AGL(1,ℤ/8)semidirect
607. #102D32semidirect
853. C2×C8C2×D32semidirect
857. C4⋊C4C2×D32semidirect
941. C2×D3#914semidirect
962. C32#3003semidirect
1105. C3#78926semidirect
1106. C3#80146semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×#639342
C2×#637942
#105946272
#105924722
C3×#47762
C3×#47702
#105914672
#105914482
#105909472
#105909432
#105909362
#105905982
#105905962
#105905922
#801463
#789263