Finite Group Databasebeta

← #11865891

Subgroups — #11865891

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic, complemented
2C2×#63794C211yesmaximal, characteristic, complemented
3C4×D3×D12C211yesmaximal, characteristic, complemented
4#10593969C211yesmaximal, characteristic, complemented
5#10592543C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4837C211yesmaximal, characteristic, complemented
8#10590765C211yesmaximal, characteristic, complemented
9#10590760C211yesmaximal, characteristic, complemented
10#10590753C211yesmaximal, characteristic, complemented
11#10590752C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590670C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590356C211yesmaximal, characteristic, complemented
16#80534—31nomaximal
17#79055—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3799C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64084C2211yescharacteristic, complemented
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C3×#875C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×C42×D3C2211yescharacteristic
33D3×(C2×D3)⋊C4—21no—
34#63911C2211yescharacteristic, complemented
35#63906—21no—
36#63906—21no—
37C4×#626—21no—
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41#63880—21no—
42#63880—21no—
43#63880—21no—
44#63866C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49#63795—24no—
50#63794—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×#908—31no—
66C2×#908—31no—
67#5668—31no—
68C4×D3×D4—31no—
69#5477—31no—
70C2×C4×D12—31no—
71C3×#463—31no—
72C3×#423—31no—
73#5162—31no—
74#5150—31no—
75#5133—31no—
76#5133—31no—
77#5057—31no—
78#5016—31no—
79#4844—31no—
80#4844—31no—
81#4844—31no—
82#4844—31no—
83#4844—61no—
84#4844D311yescharacteristic, complemented
85#4843—31no—
86#4843—31no—
87#4841—31no—
88#4841—31no—
89#4837D311yescharacteristic, complemented
90#4818—31no—
91#4803—31no—
92#4786—31no—
93#4771—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×#624—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116D3×D12—22no—
117D3×D12D414yescomplemented
118C4×D32—44no—
119#3799—22no—
120#3799—22no—
121#3795—22no—
122#3795—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C42C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—22no—
131#3744—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×#204—22no—
143C3×ΓL(1,𝔽25)—22no—
144C3×ΓL(1,𝔽25)—22no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150#3717—22no—
151#3716—22no—
152#3714—22no—
153#3714—22no—
154#3036—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×#235—31no—
159C2×#235—31no—
160C22×D12—31no—
161C22×C4×D3—61no—
162C22×C4×D3—61no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C2×C3×M16—31no—
166C2×C3×M16—31no—
167C3×#124—31no—
168C3×C4×D4—31no—
169C2×C3×C42—31no—
170#944—31no—
171C2×#215—31no—
172#940—31no—
173D4×Dic3—31no—
174C2×#214—31no—
175C2×#213—31no—
176C2×#213—31no—
177#930—61no—
178#930—61no—
179C4×#67—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×C4⋊Dic3—31no—
182#914—64no—
183#911—64no—
184#908—64no—
185#908—64no—
186C2×D24—31no—
187C2×D24—31no—
188C2×D24—31no—
189C2×D24—31no—
190C2×D24—61no—
191C2×D24C2×D311yescharacteristic
192C2×#204—31no—
193C2×#204—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—61no—
197C2×#204C2×D311yescharacteristic
198C2×ΓL(1,𝔽25)C2×D311yescharacteristic
199C2×ΓL(1,𝔽25)C2×D311yescharacteristic
200#893—31no—
201D3×C4⋊C4—31no—
202#884—61no—
203#884—61no—
204#67⋊C4—61no—
205#67⋊C4—61no—
206#67⋊C4—61no—
207D3×C22⋊C4—61no—
208#875—31no—
209#875—31no—
210#875—61no—
211#875C2×D311yescharacteristic, complemented
212#874—31no—
213C4×D12—31no—
214C4×D12—31no—
215C4×D12—31no—
216C4×D12—31no—
217C4×D12—61no—
218C4×D12—61no—
219C4×D12—61no—
220C4×D12—61no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic
223C42×D3C2×D311yescharacteristic
224#869—31no—
225C3×C4⋊C8—21no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8—31no—
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×#103—31no—
232C3×#102—31no—
233#835—31no—
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#816—31no—
242#816—31no—
243#816—31no—
244#816—31no—
245#816—61no—
246#816C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#810—31no—
250#809—31no—
251C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—42no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)C2×D412yes—
269C4×C3⋊D3—42no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—22no—
282C3×C4×D3—41no—
283C3×C4×D3—42no—
284C3×C4×D3C2×D412yes—
285C3×C4×D3#4112yes—
286C3×Dic6—21no—
287C3×Dic6—21no—
288#626—24no—
289#626—42no—
290#626—42no—
291#626—42no—
292#625—42no—
293#624—42no—
294#624—42no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—91no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—31no—
315#417—91no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335#239—62no—
336#239—62no—
337#237—62no—
338#237—62no—
339D3×D4—34no—
340D3×D4—62no—
341#235—62no—
342#235—62no—
343#235—62no—
344#235—62no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—34no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—121no—
370C2×C4×D3—124no—
371C2×C4×D3—124no—
372C2×C4×D3D1211yescharacteristic
373C2×C4×D3D1211yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×D8—62no—
381C3×M16—62no—
382C3×M16—62no—
383C2×C3×C8—21no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42—31no—
397C3×C42—31no—
398C3×C42—31no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—61no—
402#215—62no—
403#214—62no—
404#213—62no—
405#213—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431C4×Dic3D1211yescharacteristic
432C4×Dic3D1211yescharacteristic
433C4×Dic3C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436D24—22no—
437D24—62no—
438D24—62no—
439D24—62no—
440D24—62no—
441D24—122no—
442#204—22no—
443#204—62no—
444#204—62no—
445#204—62no—
446#204—62no—
447#204—122no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—22no—
450C22×C32C22×D411yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#12112yes—
466D32—48no—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—91no—
479C2×#41—91no—
480C22×D4—91no—
481C23×C4—181no—
482AGL(1,ℤ/8)—184no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C4⋊Q8—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500C4×D4—31no—
501C4×D4—91no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—181no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C2×C4⋊C4—91no—
509C2×C22⋊C4—181no—
510C2×C42—31no—
511C4⋊C8—31no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8D3211yescharacteristic, complemented
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—64no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—64no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—121no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3C2×D1211yescharacteristic
541C3×Q8—61no—
542C3×Q8—61no—
543C3×D4—32no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—31no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—121no—
559C2×C3×C4—122no—
560C2×C3×C4C2×D1211yescharacteristic
561C2×C3×C4C2×D1211yescharacteristic
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—64no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—122no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—122no—
583C2×Dic3C2×D1211yescharacteristic
584C2×Dic3C2×D1211yescharacteristic
585C2×Dic3C2×D1211yescharacteristic
586D12—21no—
587D12—21no—
588D12—21no—
589D12—32no—
590D12—32no—
591D12—62no—
592D12—64no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—121no—
600D12—121no—
601D12—121no—
602D12—122no—
603D12—122no—
604D12—122no—
605D12D3×D412yes—
606C4×D3—22no—
607C4×D3—41no—
608C4×D3—42no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—242no—
619C4×D3D3×D412yes—
620C4×D3#23912yes—
621Dic6—21no—
622Dic6—21no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—41no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C2×C32C2×#12111yescharacteristic
640C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
641C2×C32#57511yescharacteristic
642C3⋊D3—42no—
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—181no—
648#41—182no—
649#41—182no—
650#41—182no—
651#41—182no—
652C2×Q8—31no—
653C2×Q8—91no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—94no—
657C2×D4—91no—
658C2×D4—91no—
659C2×D4—182no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4—181no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4—181no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—364no—
676SD16—62no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—182no—
682D8—182no—
683D8—182no—
684M16—62no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8C2×D3211yescharacteristic
689C2×C8C2×D3211yescharacteristic
690C4⋊C4—31no—
691C4⋊C4—91no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42C2×D3211yescharacteristic
707C22×C3—21no—
708C22×C3—32no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3C22×D1211yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—22no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—122no—
730C2×D3—128no—
731C2×D3—128no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#89512yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4C2×#23911yescharacteristic
764C3×C4D3×#4111yescharacteristic
765Dic3—21no—
766Dic3—41no—
767Dic3—41no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—241no—
773Dic3—241no—
774Dic3#89512yes—
775Dic3#90812yescomplemented
776C32#303611yescharacteristic, complemented, Sylow
777C23—31no—
778C23—61no—
779C23—61no—
780C23—184no—
781C23—181no—
782C23—181no—
783C23—362no—
784C23—362no—
785Q8—61no—
786Q8—61no—
787Q8—181no—
788Q8—181no—
789D4—32no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—92no—
794D4—184no—
795D4—181no—
796D4—181no—
797D4—181no—
798D4—362no—
799D4—362no—
800D4—362no—
801D4—362no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—31no—
807C2×C4—62no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—121no—
811C2×C4—122no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—362no—
815C2×C4—362no—
816C2×C4—362no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4D3×D1211yescharacteristic
821C2×C4D3×D1211yescharacteristic
822C2×C4C22×D3211yescharacteristic
823C8—21no—
824C8—21no—
825C8—61no—
826C8—61no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—62no—
831C2×C3—122no—
832C2×C3—241no—
833C2×C3C2×#89511yescharacteristic
834C2×C3D3×#12111yescharacteristic
835C2×C3C2×#90811yescharacteristic
836C2×C3#574811yescharacteristic
837C2×C3#576811yescharacteristic
838C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
839D3—22no—
840D3—42no—
841D3—81no—
842D3—122no—
843D3—122no—
844D3—242no—
845D3—241no—
846D3—241no—
847D3—481no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—182no—
858C22—368no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22C2×D3×D1211yescharacteristic
865C4—21no—
866C4—21no—
867C4—32no—
868C4—32no—
869C4—61no—
870C4—121no—
871C4—121no—
872C4—361no—
873C4—361no—
874C4D32×D411yescharacteristic
875C4D3×#23911yescharacteristic
876C3—21no—
877C3#7905511yescharacteristic, complemented
878C3#8053411yescharacteristic, complemented
879C2—62no—
880C2—122no—
881C2—241no—
882C2—362no—
883C2—721no—
884C2D3×#89511yescharacteristic
885C2#1059467611yescharacteristic
886C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×#63794C2semidirect
3. C4×D3×D12C2semidirect
4. #10593969C2semidirect
5. #10592543C2semidirect
6. C3×#4844C2semidirect
7. C3×#4837C2semidirect
8. #10590765C2semidirect
9. #10590760C2semidirect
10. #10590753C2semidirect
11. #10590752C2semidirect
12. #10590671C2semidirect
13. #10590670C2semidirect
14. #10590366C2semidirect
15. #10590356C2semidirect
24. #64084C22semidirect
30. C3×#875C22semidirect
34. #63911C22semidirect
44. #63866C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63648C22semidirect
53. #63643C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
84. #4844D3semidirect
89. #4837D3semidirect
117. D3×D12D4semidirect
211. #875C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
240. #821C2×D3semidirect
246. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
514. C4⋊C8D32semidirect
775. Dic3#908semidirect
776. C32#3036semidirect
877. C3#79055semidirect
878. C3#80534semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×#637942
C4×D3×D122
#105939692
#105925432
C3×#48442
C3×#48372
#105907652
#105907602
#105907532
#105907522
#105906712
#105906702
#105903662
#105903562
#805343
#790553