Finite Group Databasebeta

← #11863937

Subgroups — #11863937

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594632C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590942C211yesmaximal, characteristic, complemented
12#10590937C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15#10590594C211yesmaximal, characteristic, complemented
16#80146—31nomaximal
17#80002—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×#3796C2211yescharacteristic, complemented
32C2×#3743C2211yescharacteristic, complemented
33#64101C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63937—24no—
41#63922—21no—
42#63908C2211yescharacteristic, complemented
43#63902—21no—
44#63898—21no—
45#63856C2211yescharacteristic, complemented
46#63854—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63798—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C2×#914—31no—
68C2×#914—31no—
69C2×#911—31no—
70C2×#911—31no—
71#5627—31no—
72#5606—31no—
73C3×#450—31no—
74C3×#447—31no—
75#5218—31no—
76#5217—31no—
77#5169—31no—
78#5169—31no—
79#5156—31no—
80#5156—31no—
81#5046—31no—
82#5036—31no—
83#4776—31no—
84#4776D311yescharacteristic, complemented
85#4773—31no—
86#4773D311yescharacteristic, complemented
87#4770—31no—
88#4770—31no—
89#4770—31no—
90#4770—31no—
91#4770—61no—
92#4732—31no—
93#4731—31no—
94#4726—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⋊D3D414yescomplemented
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C3×D3×D4—22no—
115C3×D3×D4—22no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C2×C3×D12—21no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic, complemented
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×#625—21no—
132C2×#625—21no—
133C2×#624D411yescharacteristic
134C2×D3×Dic3—21no—
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137#3802—22no—
138#3802D414yescomplemented
139D3×D12—22no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12—22no—
143C4×D32—22no—
144C4×D32—22no—
145#3796—22no—
146#3796—22no—
147C2×C32×C8C2311yescharacteristic, complemented
148C32×C4⋊C4C2311yescharacteristic, complemented
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
151C4×C3⋊Dic3—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
153#3743—22no—
154C3×#214—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3—21no—
159C2×C3×C3⋊C8C2311yescharacteristic, complemented
160C2×C3×C3⋊C8C2311yescharacteristic, complemented
161C3×D24—22no—
162C3×#204—22no—
163#3724—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3717—22no—
167#3715—22no—
168#3714—22no—
169#3713—22no—
170#3712—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×#237—31no—
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—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C2×C3×D8—31no—
205C3×C22⋊Q8—31no—
206C3×#121—31no—
207#946—31no—
208C2×#215—31no—
209C2×#215—31no—
210#938—31no—
211#937—61no—
212D4×Dic3—61no—
213C2×#214—31no—
214C2×#214C2×D311yescharacteristic, complemented
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220#924—31no—
221#914—64no—
222#914—64no—
223#911—64no—
224#911—64no—
225C2×D24—31no—
226C2×D24C2×D311yescharacteristic, complemented
227C2×#204—31no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)—61no—
234#897C2×D311yescharacteristic, complemented
235#895C2×D311yescharacteristic, complemented
236#894—61no—
237#893—61no—
238#892—31no—
239#892—31no—
240#892—61no—
241#883—61no—
242#882—61no—
243#67⋊C4—61no—
244#67⋊C4—61no—
245C3×#102—21no—
246C3×#102—31no—
247C3×#102—31no—
248C3×#102C2×D311yescharacteristic, complemented
249C3×#102C2×D311yescharacteristic, complemented
250C3×C22⋊C8—31no—
251C3×C22⋊C8—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—31no—
256#832—61no—
257#830—31no—
258#830—31no—
259#821—31no—
260#821—31no—
261#821—31no—
262#821—31no—
263#821—61no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267(C2×D3)⋊C8C2×D311yescharacteristic, complemented
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272#809C2×D311yescharacteristic, complemented
273C23×C32—21no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—24no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—24no—
280C22×C3×D3—24no—
281C22×C3×D3—21no—
282C22×C3×D3—21no—
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⋊D3C2×D412yes—
313C4×C3⋊D3C2×D412yes—
314C3×#67—24no—
315C3×#67—24no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3C2×D411yescharacteristic
318C2×C3×Dic3C2×D411yescharacteristic
319C3×D12—21no—
320C3×D12—21no—
321C3×D12—21no—
322C3×D12—21no—
323C3×D12—42no—
324C3×D12C2×D412yes—
325C3×D12C2×D412yes—
326C3×C4×D3—21no—
327C3×C4×D3—21no—
328C3×C4×D3—21no—
329C3×C4×D3—21no—
330C3×Dic6—21no—
331C3×Dic6—21no—
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—31no—
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—
381C2×C3×Q8—31no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—62no—
390C2×C3×D4—62no—
391C2×C3×D4—62no—
392C2×C3×D4—62no—
393C2×C3×D4C22×D311yescharacteristic
394C2×C3×D4C22×D311yescharacteristic
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C2×#67—21no—
398C2×#67—21no—
399C2×#67—61no—
400C2×#67—61no—
401C2×#67—61no—
402C2×#67—61no—
403C2×#67—61no—
404C2×#67—68no—
405C2×#67—68no—
406C2×#67—61no—
407C2×#67—61no—
408C2×#67—61no—
409C2×#67—61no—
410C2×#67—121no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—61no—
414#239—62no—
415#239—62no—
416#237—62no—
417#237—62no—
418D3×D4—22no—
419D3×D4—22no—
420D3×D4—22no—
421D3×D4—22no—
422D3×D4—34no—
423D3×D4—34no—
424D3×D4—34no—
425D3×D4—34no—
426D3×D4—64no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—62no—
434D3×D4—62no—
435D3×D4—68no—
436D3×D4—68no—
437D3×D4—68no—
438D3×D4—68no—
439D3×D4—122no—
440C2×D12—21no—
441C2×D12—31no—
442C2×D12—31no—
443C2×D12—61no—
444C2×D12—62no—
445C2×D12—62no—
446C2×D12—61no—
447C2×D12—61no—
448C2×D12—62no—
449C2×D12—62no—
450C2×D12—61no—
451C2×D12C22×D311yescharacteristic
452C2×D12C22×D311yescharacteristic
453C2×D12C22×D311yescharacteristic, complemented
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—61no—
461C2×C4×D3—62no—
462C2×C4×D3—62no—
463C2×C4×D3—62no—
464C2×C4×D3—62no—
465C2×C4×D3—61no—
466C2×C4×D3C22×D311yescharacteristic
467C2×C4×D3C22×D311yescharacteristic
468C2×Dic6C22×D311yescharacteristic, complemented
469C3×SD16—62no—
470C3×SD16—62no—
471C3×D8—62no—
472C3×D8—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—61no—
480C3×C4⋊C4C22×D311yescharacteristic, complemented
481C3×C4⋊C4C22×D311yescharacteristic, complemented
482C3×C22⋊C4—61no—
483C3×C22⋊C4—61no—
484#217—61no—
485#217—61no—
486#215—62no—
487#215—62no—
488#214—22no—
489#214—62no—
490#213—22no—
491#213—62no—
492#213—62no—
493#213—62no—
494(C2×D3)⋊C4—21no—
495(C2×D3)⋊C4—21no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—61no—
500(C2×D3)⋊C4—121no—
501C4⋊Dic3—21no—
502C4⋊Dic3—31no—
503C4⋊Dic3—31no—
504C4⋊Dic3—61no—
505Dic3⋊C4—61no—
506Dic3⋊C4—61no—
507C4×Dic3—61no—
508C4×Dic3—61no—
509C4×Dic3—121no—
510C2×C3⋊C8—31no—
511C2×C3⋊C8—31no—
512C2×C3⋊C8—61no—
513C2×C3⋊C8C22×D311yescharacteristic, complemented
514C2×C3⋊C8C22×D311yescharacteristic, complemented
515D24—22no—
516D24—62no—
517#204—22no—
518#204—62no—
519ΓL(1,𝔽25)—62no—
520ΓL(1,𝔽25)—62no—
521ΓL(1,𝔽25)—62no—
522ΓL(1,𝔽25)—62no—
523ΓL(1,𝔽25)—122no—
524C22×C32—22no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32C22×D411yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3⋊D3—21no—
530C2×C3⋊D3—22no—
531C2×C3⋊D3—48no—
532C2×C3⋊D3—41no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3#12012yes—
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—48no—
542C2×C3×D3—48no—
543C2×C3×D3—41no—
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×D3AGL(1,ℤ/8)12yescomplemented
551C2×C3×D3AGL(1,ℤ/8)12yescomplemented
552D32—28no—
553D32—48no—
554D32—48no—
555D32—48no—
556C32×C4—41no—
557C32×C4C22×D411yescharacteristic
558C32×C4C22×D411yescharacteristic
559C3⋊Dic3—41no—
560C3⋊Dic3#12012yes—
561C3×Dic3—21no—
562C3×Dic3—21no—
563C3×Dic3—41no—
564C25—181no—
565C2×#41—91no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—181no—
573C22×D4—181no—
574C22×D4—181no—
575C22×D4—184no—
576C22×D4—184no—
577C23×C4—91no—
578AGL(1,ℤ/8)—184no—
579AGL(1,ℤ/8)—184no—
580C2×SD16—31no—
581C2×SD16—31no—
582C2×SD16—91no—
583C2×SD16—91no—
584C2×D8—31no—
585C2×D8—31no—
586C2×D8—91no—
587C2×D8—91no—
588C2×M16—91no—
589C2×M16—91no—
590#123—181no—
591C22⋊Q8—31no—
592C22⋊Q8—91no—
593#121—31no—
594#121—91no—
595#120—181no—
596C4×D4—181no—
597C4×D4—181no—
598#117—91no—
599#102—31no—
600#102—31no—
601#102—91no—
602#102—91no—
603#102—91no—
604#102—91no—
605#102—91no—
606#102D3211yescharacteristic, complemented
607C22⋊C8—31no—
608C22⋊C8—31no—
609C22⋊C8—91no—
610C22⋊C8—91no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—31no—
614C23×C3—31no—
615C23×C3—41no—
616C23×C3—64no—
617C23×C3—64no—
618C23×C3—61no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—122no—
622C23×C3—122no—
623C23×C3—122no—
624C23×C3—122no—
625C22×D3—24no—
626C22×D3—24no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—31no—
631C22×D3—31no—
632C22×D3—42no—
633C22×D3—42no—
634C22×D3—42no—
635C22×D3—42no—
636C22×D3—61no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—64no—
640C22×D3—64no—
641C22×D3—62no—
642C22×D3—62no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—61no—
652C22×D3—61no—
653C22×D3—124no—
654C22×D3—121no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—1232no—
658C22×D3—1232no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
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—242no—
674C22×D3—242no—
675C22×D3D3×D411yescharacteristic
676C22×D3D3×D411yescharacteristic
677C3×Q8—61no—
678C3×Q8—61no—
679C3×D4—21no—
680C3×D4—21no—
681C3×D4—22no—
682C3×D4—32no—
683C3×D4—32no—
684C3×D4—41no—
685C3×D4—64no—
686C3×D4—64no—
687C3×D4—61no—
688C3×D4—61no—
689C3×D4—61no—
690C3×D4—61no—
691C3×D4—122no—
692C3×D4D3×D412yes—
693C3×D4D3×D412yes—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—41no—
700C2×C3×C4—61no—
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—
718#67—122no—
719C2×Dic3—21no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—61no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—121no—
728C2×Dic3—122no—
729C2×Dic3D3×D411yescharacteristic
730C2×Dic3D3×D411yescharacteristic
731D12—21no—
732D12—21no—
733D12—21no—
734D12—21no—
735D12—32no—
736D12—32no—
737D12—42no—
738D12—62no—
739D12—64no—
740D12—64no—
741D12—61no—
742D12—61no—
743D12—121no—
744D12—122no—
745D12D3×D412yes—
746D12D3×D412yes—
747C4×D3—21no—
748C4×D3—21no—
749C4×D3—21no—
750C4×D3—21no—
751C4×D3—32no—
752C4×D3—32no—
753C4×D3—32no—
754C4×D3—32no—
755C4×D3—62no—
756C4×D3—62no—
757C4×D3—62no—
758C4×D3—62no—
759C4×D3—62no—
760C4×D3—62no—
761C4×D3—122no—
762Dic6—21no—
763Dic6—21no—
764C3×C8—21no—
765C3×C8—21no—
766C3×C8—41no—
767C3×C8—61no—
768C3×C8—61no—
769C3⋊C8—21no—
770C3⋊C8—21no—
771C3⋊C8—61no—
772C3⋊C8—61no—
773C3⋊C8—121no—
774C2×C32—42no—
775C2×C32C2×#12011yescharacteristic
776C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
777C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
778C3⋊D3—22no—
779C3⋊D3—42no—
780C3×D3—22no—
781C3×D3—22no—
782C3×D3—42no—
783C3×D3—42no—
784C3×D3—81no—
785C24—61no—
786C24—61no—
787C24—91no—
788C24—181no—
789C24—181no—
790C24—181no—
791C24—181no—
792C24—188no—
793C24—364no—
794C24—364no—
795#41—182no—
796#41—182no—
797C2×Q8—31no—
798C2×D4—31no—
799C2×D4—31no—
800C2×D4—31no—
801C2×D4—61no—
802C2×D4—61no—
803C2×D4—61no—
804C2×D4—62no—
805C2×D4—62no—
806C2×D4—62no—
807C2×D4—62no—
808C2×D4—94no—
809C2×D4—94no—
810C2×D4—91no—
811C2×D4—181no—
812C2×D4—181no—
813C2×D4—182no—
814C2×D4—182no—
815C2×D4—182no—
816C2×D4—182no—
817C2×D4—181no—
818C2×D4—182no—
819C2×D4—182no—
820C2×D4—181no—
821C2×D4—181no—
822C2×D4—188no—
823C2×D4—188no—
824C2×D4—188no—
825C2×D4—181no—
826C2×D4C2×D3211yescharacteristic
827C22×C4—31no—
828C22×C4—31no—
829C22×C4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—182no—
834C22×C4—182no—
835C22×C4—181no—
836SD16—62no—
837SD16—62no—
838SD16—182no—
839SD16—182no—
840D8—62no—
841D8—62no—
842D8—182no—
843D8—182no—
844M16—182no—
845M16—182no—
846C2×C8—31no—
847C2×C8—31no—
848C2×C8—91no—
849C2×C8C2×D3211yescharacteristic, complemented
850C4⋊C4—61no—
851C4⋊C4—91no—
852C4⋊C4—181no—
853C4⋊C4C2×D3211yescharacteristic, complemented
854C22⋊C4—61no—
855C22⋊C4—61no—
856C22⋊C4—181no—
857C22⋊C4—181no—
858C22⋊C4—181no—
859C42—181no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—21no—
863C22×C3—32no—
864C22×C3—32no—
865C22×C3—42no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—61no—
873C22×C3—61no—
874C22×C3—62no—
875C22×C3—62no—
876C22×C3—81no—
877C22×C3—81no—
878C22×C3—128no—
879C22×C3—128no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3—121no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3C2×D3×D411yescharacteristic
888C22×C3C2×D3×D411yescharacteristic
889C2×D3—21no—
890C2×D3—21no—
891C2×D3—21no—
892C2×D3—21no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—32no—
896C2×D3—32no—
897C2×D3—48no—
898C2×D3—48no—
899C2×D3—41no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—62no—
907C2×D3—68no—
908C2×D3—68no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—121no—
916C2×D3—121no—
917C2×D3—122no—
918C2×D3—128no—
919C2×D3—128no—
920C2×D3—128no—
921C2×D3—128no—
922C2×D3—128no—
923C2×D3—128no—
924C2×D3—128no—
925C2×D3—128no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—248no—
931C2×D3—241no—
932C2×D3—241no—
933C2×D3#91112yescomplemented
934C2×D3#91412yescomplemented
935C3×C4—21no—
936C3×C4—21no—
937C3×C4—41no—
938C3×C4—41no—
939C3×C4—61no—
940C3×C4—61no—
941C3×C4—81no—
942C3×C4—121no—
943C3×C4C2×D3×D411yescharacteristic
944C3×C4C2×D3×D411yescharacteristic
945C3×C4C2×D3×D411yescharacteristic
946C3×C4C2×D3×D411yescharacteristic
947Dic3—21no—
948Dic3—21no—
949Dic3—32no—
950Dic3—32no—
951Dic3—41no—
952Dic3—62no—
953Dic3—121no—
954Dic3—121no—
955Dic3—241no—
956C32#300311yescharacteristic, complemented, Sylow
957C23—21no—
958C23—31no—
959C23—31no—
960C23—64no—
961C23—64no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—91no—
966C23—122no—
967C23—122no—
968C23—122no—
969C23—122no—
970C23—184no—
971C23—182no—
972C23—182no—
973C23—182no—
974C23—184no—
975C23—184no—
976C23—184no—
977C23—181no—
978C23—362no—
979C23—362no—
980C23—362no—
981C23—362no—
982C23—362no—
983C23—362no—
984C23—3632no—
985C23—362no—
986C23—362no—
987Q8—61no—
988Q8—61no—
989D4—21no—
990D4—32no—
991D4—32no—
992D4—64no—
993D4—64no—
994D4—61no—
995D4—61no—
996D4—61no—
997D4—61no—
998D4—92no—
999D4—122no—
1000D4—184no—
1001D4—184no—
1002D4—184no—
1003D4—184no—
1004D4—181no—
1005D4—362no—
1006D4—362no—
1007D4#380212yes—
1008C2×C4—21no—
1009C2×C4—31no—
1010C2×C4—31no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—91no—
1017C2×C4—92no—
1018C2×C4—92no—
1019C2×C4—182no—
1020C2×C4—182no—
1021C2×C4—182no—
1022C2×C4—181no—
1023C2×C4—362no—
1024C2×C4C22×D3211yescharacteristic
1025C8—21no—
1026C8—61no—
1027C8—61no—
1028C8—181no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—42no—
1033C2×C3—42no—
1034C2×C3—62no—
1035C2×C3—62no—
1036C2×C3—82no—
1037C2×C3—122no—
1038C2×C3—122no—
1039C2×C3—241no—
1040C2×C3D3×#12011yescharacteristic
1041C2×C3D3×#12011yescharacteristic
1042C2×C3C2×#91111yescharacteristic
1043C2×C3C2×#91411yescharacteristic
1044C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1045C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1046D3—22no—
1047D3—22no—
1048D3—42no—
1049D3—42no—
1050D3—62no—
1051D3—62no—
1052D3—81no—
1053D3—122no—
1054D3—122no—
1055D3—122no—
1056D3—242no—
1057C22—22no—
1058C22—32no—
1059C22—32no—
1060C22—41no—
1061C22—41no—
1062C22—61no—
1063C22—61no—
1064C22—61no—
1065C22—61no—
1066C22—62no—
1067C22—62no—
1068C22—92no—
1069C22—128no—
1070C22—128no—
1071C22—121no—
1072C22—121no—
1073C22—121no—
1074C22—121no—
1075C22—121no—
1076C22—121no—
1077C22—121no—
1078C22—188no—
1079C22—181no—
1080C22—181no—
1081C22—182no—
1082C22—368no—
1083C22—368no—
1084C22—368no—
1085C22—368no—
1086C22—361no—
1087C22—361no—
1088C22D32×D411yescharacteristic
1089C4—41no—
1090C4—61no—
1091C4—61no—
1092C4—92no—
1093C4—121no—
1094C4—361no—
1095C4C2×#380211yescharacteristic
1096C4D32×D411yescharacteristic
1097C3—21no—
1098C3#8000211yescharacteristic, complemented
1099C3#8014611yescharacteristic, complemented
1100C2—42no—
1101C2—62no—
1102C2—62no—
1103C2—122no—
1104C2—122no—
1105C2—182no—
1106C2—241no—
1107C2—362no—
1108C2#1059425811yescharacteristic
1109C2D3×#91111yescharacteristic
1110C2D3×#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×#63937C2semidirect
3. C2×#63798C2semidirect
4. #10594632C2semidirect
5. #10592469C2semidirect
6. C3×#4776C2semidirect
7. C3×#4773C2semidirect
8. #10591458C2semidirect
9. #10591447C2semidirect
10. #10590944C2semidirect
11. #10590942C2semidirect
12. #10590937C2semidirect
13. #10590596C2semidirect
14. #10590595C2semidirect
15. #10590594C2semidirect
31. C2×#3796C22semidirect
32. C2×#3743C22semidirect
33. #64101C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
42. #63908C22semidirect
45. #63856C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3712C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4776D3semidirect
86. #4773D3semidirect
109. D4×C3⋊D3D4semidirect
121. C2×C3×D12C23semidirect
124. C2×C3×Dic6C23semidirect
138. #3802D4semidirect
147. C2×C32×C8C23semidirect
148. C32×C4⋊C4C23semidirect
150. C4⋊(C3⋊Dic3)C23semidirect
152. C2×C3⋊(C3⋊C8)C23semidirect
159. C2×C3×C3⋊C8C23semidirect
160. C2×C3×C3⋊C8C23semidirect
214. C2×#214C2×D3semidirect
218. C2×#213C2×D3semidirect
226. C2×D24C2×D3semidirect
228. C2×#204C2×D3semidirect
234. #897C2×D3semidirect
235. #895C2×D3semidirect
248. C3×#102C2×D3semidirect
249. C3×#102C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
267. (C2×D3)⋊C8C2×D3semidirect
271. #809C2×D3semidirect
272. #809C2×D3semidirect
453. C2×D12C22×D3semidirect
468. C2×Dic6C22×D3semidirect
476. C2×C3×C8C22×D3semidirect
477. C2×C3×C8C22×D3semidirect
480. C3×C4⋊C4C22×D3semidirect
481. C3×C4⋊C4C22×D3semidirect
513. C2×C3⋊C8C22×D3semidirect
514. C2×C3⋊C8C22×D3semidirect
550. C2×C3×D3AGL(1,ℤ/8)semidirect
551. C2×C3×D3AGL(1,ℤ/8)semidirect
606. #102D32semidirect
849. C2×C8C2×D32semidirect
853. C4⋊C4C2×D32semidirect
933. C2×D3#911semidirect
934. C2×D3#914semidirect
956. C32#3003semidirect
1098. C3#80002semidirect
1099. 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×#639372
C2×#637982
#105946322
#105924692
C3×#47762
C3×#47732
#105914582
#105914472
#105909442
#105909422
#105909372
#105905962
#105905952
#105905942
#801463
#800023