Finite Group Databasebeta

← #11863938

Subgroups — #11863938

Order 1152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594626C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590945C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80002—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×#3795C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63932—24no—
41#63922—21no—
42#63916C2211yescharacteristic, complemented
43Dic3×D12—21no—
44#63891—21no—
45#63880—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63795—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×#911—31no—
69C2×#911—31no—
70C2×#908—31no—
71#5606—31no—
72#5524—31no—
73C3×#447—31no—
74C3×#418—31no—
75#5218—31no—
76#5156—31no—
77#5156—31no—
78#5126—31no—
79#5036—31no—
80#5001—31no—
81#4776—31no—
82#4776—31no—
83#4776—31no—
84#4776—31no—
85#4776—31no—
86#4776—31no—
87#4776—61no—
88#4773—31no—
89#4773—31no—
90#4773—31no—
91#4773D311yescharacteristic, complemented
92#4770—31no—
93#4770D311yescharacteristic, complemented
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×#638—21no—
108D4×C3⋊D3—22no—
109D4×C3⋊D3—22no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×#634C2311yescharacteristic, complemented
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C3×D3×D4—22no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C3×D3×D4D414yescomplemented
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic, complemented
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125#3811—28no—
126D3×#67—28no—
127D3×#67—28no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626—21no—
131C2×#625—21no—
132C2×#625—21no—
133C2×#624D411yescharacteristic
134C2×D3×Dic3—21no—
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#3795—22no—
146#3795—22no—
147C2×C32×C8C2311yescharacteristic, complemented
148C32×C4⋊C4C2311yescharacteristic, complemented
149#3754—22no—
150#3752—21no—
151C4⋊(C3⋊Dic3)—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
153#3744—22no—
154C3×#213—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic, complemented
158C3×C4×Dic3—21no—
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C2×C3×C3⋊C8C2311yescharacteristic, complemented
161C3×D24—22no—
162C3×ΓL(1,𝔽25)—22no—
163Dic3⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3716—22no—
167#3716—22no—
168#3714—22no—
169#3713—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×#237—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×D8—31no—
202C2×C3×D8—31no—
203C2×C3×M16—31no—
204C3×#121—31no—
205C3×#117—31no—
206#938—31no—
207#937—61no—
208D4×Dic3—61no—
209C2×#214—31no—
210C2×#214—31no—
211C2×#214—31no—
212C2×#214—31no—
213C2×#214—61no—
214#932—64no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213C2×D311yescharacteristic, complemented
219#924—31no—
220C2×#208—31no—
221#911—64no—
222#911—64no—
223#908—64no—
224C2×D24—31no—
225C2×D24C2×D311yescharacteristic, complemented
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—61no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
233#897—31no—
234#897—31no—
235#897—31no—
236#897—61no—
237#895—31no—
238#895C2×D311yescharacteristic, complemented
239#892C2×D311yescharacteristic, complemented
240#886—61no—
241#883—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—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—21no—
282C22×C3×D3—24no—
283C22×C3×D3—21no—
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⋊Dic3—21no—
309C2×C3⋊Dic3C2×D411yescharacteristic
310C4⋊(C3⋊D3)—21no—
311C4⋊(C3⋊D3)C2×D412yes—
312C4×C3⋊D3—21no—
313C4×C3⋊D3—21no—
314#634—21no—
315#634—21no—
316C3×#67—24no—
317C3×#67—24no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C2×D411yescharacteristic
320C2×C3×Dic3C2×D411yescharacteristic
321C3×D12—21no—
322C3×D12—21no—
323C3×D12—21no—
324C3×D12—21no—
325C3×D12—42no—
326C3×D12C2×D412yes—
327C3×D12C2×D412yes—
328C3×C4×D3—21no—
329C3×C4×D3—21no—
330C3×C4×D3C2×D412yes—
331C3×C4×D3C2×D412yes—
332#626—24no—
333#626—24no—
334#626—42no—
335#625—24no—
336#625—42no—
337#624—22no—
338D3×Dic3—22no—
339D3×Dic3—22no—
340D3×Dic3—42no—
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—91no—
350#450—91no—
351#450—91no—
352#450—91no—
353#447—31no—
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×D4—21no—
382C2×C3×D4—34no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—61no—
387C2×C3×D4—62no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—62no—
391C2×C3×D4—62no—
392C2×C3×D4C22×D311yescharacteristic
393C2×C3×D4C22×D311yescharacteristic
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C2×#67—21no—
397C2×#67—21no—
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—61no—
408C2×#67—61no—
409C2×#67—121no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—61no—
413#237—62no—
414#237—62no—
415D3×D4—22no—
416D3×D4—22no—
417D3×D4—22no—
418D3×D4—34no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—62no—
423D3×D4—62no—
424D3×D4—62no—
425D3×D4—68no—
426D3×D4—68no—
427D3×D4—68no—
428D3×D4—68no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—62no—
434D3×D4—122no—
435D3×D4—122no—
436D3×D4D1214yescomplemented
437#235—62no—
438#235—62no—
439C2×D12—21no—
440C2×D12—31no—
441C2×D12—31no—
442C2×D12—34no—
443C2×D12—61no—
444C2×D12—62no—
445C2×D12—62no—
446C2×D12—61no—
447C2×D12—61no—
448C2×D12—62no—
449C2×D12—61no—
450C2×D12C22×D311yescharacteristic
451C2×D12C22×D311yescharacteristic
452C2×D12C22×D311yescharacteristic, complemented
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—61no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3—62no—
463C2×C4×D3—62no—
464C2×C4×D3—61no—
465C2×C4×D3C22×D311yescharacteristic
466C2×C4×D3C22×D311yescharacteristic
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6—61no—
470C3×D8—62no—
471C3×D8—62no—
472C3×M16—62no—
473C2×C3×C8—21no—
474C2×C3×C8—31no—
475C2×C3×C8—31no—
476C2×C3×C8C22×D311yescharacteristic, complemented
477C2×C3×C8C22×D311yescharacteristic, complemented
478C3×C4⋊C4—21no—
479C3×C4⋊C4—31no—
480C3×C4⋊C4C22×D311yescharacteristic, complemented
481C3×C4⋊C4C22×D311yescharacteristic, complemented
482C3×C22⋊C4—61no—
483C3×C22⋊C4—61no—
484C3×C42—61no—
485#217—61no—
486#217—61no—
487#214—62no—
488#214—62no—
489#214—62no—
490#214—62no—
491#214—122no—
492#213—22no—
493#213—62no—
494#213—62no—
495#213—62no—
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—121no—
503C4⋊Dic3—61no—
504C4⋊Dic3—61no—
505C4⋊Dic3—61no—
506C4⋊Dic3—121no—
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—22no—
517D24—62no—
518#204—62no—
519#204—62no—
520#204—62no—
521#204—62no—
522#204—122no—
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⋊D3AGL(1,ℤ/8)12yescomplemented
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—48no—
543C2×C3×D3—48no—
544C2×C3×D3—41no—
545C2×C3×D3—41no—
546C2×C3×D3—41no—
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—41no—
562C3×Dic3—21no—
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—91no—
582C2×SD16—91no—
583C2×SD16—91no—
584C2×SD16—91no—
585C2×D8—31no—
586C2×D8—31no—
587C2×D8—91no—
588C2×D8—91no—
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—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—61no—
622C23×C3—122no—
623C23×C3—122no—
624C23×C3—122no—
625C23×C3—122no—
626C22×D3—24no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—24no—
630C22×D3—21no—
631C22×D3—31no—
632C22×D3—31no—
633C22×D3—42no—
634C22×D3—42no—
635C22×D3—42no—
636C22×D3—42no—
637C22×D3—61no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—64no—
650C22×D3—64no—
651C22×D3—61no—
652C22×D3—61no—
653C22×D3—64no—
654C22×D3—121no—
655C22×D3—124no—
656C22×D3—122no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—1232no—
664C22×D3—1232no—
665C22×D3—122no—
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—242no—
675C22×D3—242no—
676C22×D3D3×D411yescharacteristic
677C22×D3D3×D411yescharacteristic
678C3×D4—21no—
679C3×D4—21no—
680C3×D4—22no—
681C3×D4—32no—
682C3×D4—32no—
683C3×D4—41no—
684C3×D4—64no—
685C3×D4—64no—
686C3×D4—61no—
687C3×D4—61no—
688C3×D4—61no—
689C3×D4—61no—
690C3×D4—122no—
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×C4C23×D311yescharacteristic
705C2×C3×C4C23×D311yescharacteristic
706#67—24no—
707#67—24no—
708#67—64no—
709#67—64no—
710#67—64no—
711#67—64no—
712#67—64no—
713#67—64no—
714#67—124no—
715#67—122no—
716#67—122no—
717#67—122no—
718C2×Dic3—21no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—61no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—121no—
727C2×Dic3—122no—
728C2×Dic3D3×D411yescharacteristic
729C2×Dic3D3×D411yescharacteristic
730D12—21no—
731D12—21no—
732D12—21no—
733D12—21no—
734D12—32no—
735D12—32no—
736D12—42no—
737D12—62no—
738D12—64no—
739D12—64no—
740D12—61no—
741D12—61no—
742D12—121no—
743D12—122no—
744D12C2×D1212yes—
745D12D3×D412yes—
746C4×D3—21no—
747C4×D3—21no—
748C4×D3—62no—
749C4×D3—62no—
750C4×D3—62no—
751C4×D3—61no—
752C4×D3—61no—
753C4×D3—61no—
754C4×D3—61no—
755C4×D3—62no—
756C4×D3—121no—
757C4×D3—121no—
758C4×D3—122no—
759C4×D3C2×D1212yes—
760C4×D3D3×D412yes—
761Dic6—61no—
762Dic6—61no—
763Dic6—61no—
764Dic6—61no—
765Dic6—121no—
766Dic6—121no—
767C3×C8—21no—
768C3×C8—21no—
769C3×C8—41no—
770C3×C8—61no—
771C3×C8—61no—
772C3⋊C8—21no—
773C3⋊C8—21no—
774C3⋊C8—61no—
775C3⋊C8—61no—
776C3⋊C8—121no—
777C2×C32—42no—
778C2×C32C2×#12011yescharacteristic
779C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
780C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
781C3⋊D3—22no—
782C3⋊D3—42no—
783C3×D3—22no—
784C3×D3—22no—
785C3×D3—42no—
786C3×D3—42no—
787C3×D3—81no—
788C24—61no—
789C24—61no—
790C24—91no—
791C24—181no—
792C24—181no—
793C24—181no—
794C24—181no—
795C24—188no—
796C24—364no—
797C24—364no—
798#41—182no—
799#41—182no—
800C2×Q8—91no—
801C2×D4—34no—
802C2×D4—31no—
803C2×D4—31no—
804C2×D4—31no—
805C2×D4—61no—
806C2×D4—62no—
807C2×D4—61no—
808C2×D4—61no—
809C2×D4—62no—
810C2×D4—62no—
811C2×D4—94no—
812C2×D4—91no—
813C2×D4—182no—
814C2×D4—181no—
815C2×D4—181no—
816C2×D4—182no—
817C2×D4—182no—
818C2×D4—181no—
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
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—91no—
833C22×C4—91no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—182no—
837C22×C4—182no—
838C22×C4—181no—
839SD16—182no—
840SD16—182no—
841SD16—182no—
842SD16—182no—
843D8—62no—
844D8—62no—
845D8—182no—
846D8—182no—
847M16—62no—
848M16—182no—
849C2×C8—31no—
850C2×C8—31no—
851C2×C8—91no—
852C2×C8C2×D3211yescharacteristic, complemented
853C4⋊C4—31no—
854C4⋊C4—181no—
855C4⋊C4—181no—
856C4⋊C4C2×D3211yescharacteristic, complemented
857C22⋊C4—61no—
858C22⋊C4—61no—
859C22⋊C4—181no—
860C22⋊C4—181no—
861C22⋊C4—181no—
862C42—61no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—21no—
866C22×C3—32no—
867C22×C3—32no—
868C22×C3—42no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—61no—
874C22×C3—61no—
875C22×C3—61no—
876C22×C3—61no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—81no—
880C22×C3—81no—
881C22×C3—128no—
882C22×C3—128no—
883C22×C3—121no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3—121no—
889C22×C3—121no—
890C22×C3C2×D3×D411yescharacteristic
891C22×C3C2×D3×D411yescharacteristic
892C2×D3—21no—
893C2×D3—21no—
894C2×D3—21no—
895C2×D3—21no—
896C2×D3—22no—
897C2×D3—22no—
898C2×D3—32no—
899C2×D3—32no—
900C2×D3—48no—
901C2×D3—48no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—41no—
907C2×D3—41no—
908C2×D3—41no—
909C2×D3—62no—
910C2×D3—68no—
911C2×D3—68no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—122no—
921C2×D3—128no—
922C2×D3—128no—
923C2×D3—128no—
924C2×D3—128no—
925C2×D3—128no—
926C2×D3—128no—
927C2×D3—128no—
928C2×D3—128no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—248no—
934C2×D3—241no—
935C2×D3—241no—
936C2×D3#88212yes—
937C2×D3#91112yescomplemented
938C3×C4—21no—
939C3×C4—21no—
940C3×C4—32no—
941C3×C4—41no—
942C3×C4—41no—
943C3×C4—61no—
944C3×C4—81no—
945C3×C4—121no—
946C3×C4C22×D1211yescharacteristic
947C3×C4C2×D3×D411yescharacteristic
948C3×C4C2×D3×D411yescharacteristic
949C3×C4C2×D3×D411yescharacteristic
950Dic3—21no—
951Dic3—41no—
952Dic3—61no—
953Dic3—61no—
954Dic3—121no—
955Dic3—121no—
956Dic3—121no—
957Dic3—241no—
958Dic3#88212yes—
959C32#300311yescharacteristic, complemented, Sylow
960C23—21no—
961C23—31no—
962C23—31no—
963C23—64no—
964C23—64no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—91no—
969C23—122no—
970C23—122no—
971C23—122no—
972C23—122no—
973C23—184no—
974C23—182no—
975C23—182no—
976C23—184no—
977C23—182no—
978C23—184no—
979C23—184no—
980C23—181no—
981C23—362no—
982C23—362no—
983C23—362no—
984C23—362no—
985C23—362no—
986C23—362no—
987C23—362no—
988C23—3632no—
989C23—362no—
990Q8—181no—
991Q8—181no—
992D4—21no—
993D4—32no—
994D4—32no—
995D4—64no—
996D4—64no—
997D4—61no—
998D4—61no—
999D4—61no—
1000D4—61no—
1001D4—92no—
1002D4—122no—
1003D4—184no—
1004D4—184no—
1005D4—184no—
1006D4—184no—
1007D4—181no—
1008D4—362no—
1009D4—362no—
1010D4D3×D1212yes—
1011C2×C4—21no—
1012C2×C4—31no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—31no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—91no—
1020C2×C4—182no—
1021C2×C4—182no—
1022C2×C4—182no—
1023C2×C4—181no—
1024C2×C4—181no—
1025C2×C4—181no—
1026C2×C4—362no—
1027C2×C4C22×D3211yescharacteristic
1028C8—21no—
1029C8—61no—
1030C8—61no—
1031C8—181no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—42no—
1036C2×C3—42no—
1037C2×C3—62no—
1038C2×C3—62no—
1039C2×C3—82no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3—241no—
1043C2×C3C2×#88211yescharacteristic
1044C2×C3D3×#12011yescharacteristic
1045C2×C3C2×#91111yescharacteristic
1046C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1047C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1048C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1049D3—22no—
1050D3—22no—
1051D3—42no—
1052D3—42no—
1053D3—62no—
1054D3—62no—
1055D3—81no—
1056D3—122no—
1057D3—122no—
1058D3—122no—
1059D3—242no—
1060C22—22no—
1061C22—32no—
1062C22—32no—
1063C22—41no—
1064C22—41no—
1065C22—61no—
1066C22—61no—
1067C22—61no—
1068C22—61no—
1069C22—62no—
1070C22—62no—
1071C22—92no—
1072C22—128no—
1073C22—128no—
1074C22—121no—
1075C22—121no—
1076C22—121no—
1077C22—121no—
1078C22—121no—
1079C22—121no—
1080C22—121no—
1081C22—188no—
1082C22—181no—
1083C22—181no—
1084C22—182no—
1085C22—368no—
1086C22—368no—
1087C22—368no—
1088C22—368no—
1089C22—361no—
1090C22—361no—
1091C22D32×D411yescharacteristic
1092C4—32no—
1093C4—41no—
1094C4—61no—
1095C4—121no—
1096C4—181no—
1097C4—361no—
1098C4C2×D3×D1211yescharacteristic
1099C4D32×D411yescharacteristic
1100C3—21no—
1101C3#7892611yescharacteristic, complemented
1102C3#8000211yescharacteristic, complemented
1103C2—42no—
1104C2—62no—
1105C2—62no—
1106C2—122no—
1107C2—122no—
1108C2—182no—
1109C2—241no—
1110C2—362no—
1111C2D3×#88211yescharacteristic
1112C2D3×#91111yescharacteristic
1113C2#1059474011yescharacteristic
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×#63932C2semidirect
3. C2×#63795C2semidirect
4. #10594626C2semidirect
5. #10592475C2semidirect
6. C3×#4773C2semidirect
7. C3×#4770C2semidirect
8. #10591459C2semidirect
9. #10591456C2semidirect
10. #10590946C2semidirect
11. #10590945C2semidirect
12. #10590936C2semidirect
13. #10590597C2semidirect
14. #10590595C2semidirect
15. #10590592C2semidirect
31. C2×#3795C22semidirect
32. C2×#3754C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#895C22semidirect
39. C3×#892C22semidirect
42. #63916C22semidirect
46. #63857C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
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
91. #4773D3semidirect
93. #4770D3semidirect
112. C2×#634C23semidirect
118. C3×D3×D4D4semidirect
122. C2×C3×D12C23semidirect
142. D3×D12D4semidirect
147. C2×C32×C8C23semidirect
148. C32×C4⋊C4C23semidirect
152. C2×C3⋊(C3⋊C8)C23semidirect
157. C3×C4⋊Dic3C23semidirect
159. C2×C3×C3⋊C8C23semidirect
160. C2×C3×C3⋊C8C23semidirect
218. C2×#213C2×D3semidirect
225. C2×D24C2×D3semidirect
232. C2×ΓL(1,𝔽25)C2×D3semidirect
238. #895C2×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
436. D3×D4D12semidirect
452. C2×D12C22×D3semidirect
476. C2×C3×C8C22×D3semidirect
477. C2×C3×C8C22×D3semidirect
480. C3×C4⋊C4C22×D3semidirect
481. C3×C4⋊C4C22×D3semidirect
507. C4⋊Dic3C22×D3semidirect
514. C2×C3⋊C8C22×D3semidirect
515. C2×C3⋊C8C22×D3semidirect
535. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C2×C3×D3AGL(1,ℤ/8)semidirect
607. #102D32semidirect
852. C2×C8C2×D32semidirect
856. C4⋊C4C2×D32semidirect
937. C2×D3#911semidirect
959. C32#3003semidirect
1101. C3#78926semidirect
1102. C3#80002semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×#639322
C2×#637952
#105946262
#105924752
C3×#47732
C3×#47702
#105914592
#105914562
#105909462
#105909452
#105909362
#105905972
#105905952
#105905922
#800023
#789263