Finite Group Databasebeta

← #11866184

Subgroups — #11866184

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic, complemented
2C2×#63797C211yesmaximal, characteristic, complemented
3#10594010C211yesmaximal, characteristic, complemented
4#10593996C211yesmaximal, characteristic, complemented
5#10592538C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4843C211yesmaximal, characteristic, complemented
8#10590956C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10#10590751C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590749C211yesmaximal, characteristic, complemented
13#10590749C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590347C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#80334—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64081C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic, complemented
28C3×#875C2211yescharacteristic, complemented
29C3×#874C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic, complemented
32#63922—21no—
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63914C2211yescharacteristic, complemented
37#63898C2211yescharacteristic, complemented
38#63898C2211yescharacteristic, complemented
39#63885—21no—
40#63885—21no—
41#63879—21no—
42#63879—21no—
43#63863C2211yescharacteristic, complemented
44#63849C2211yescharacteristic
45C2×#3715C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic
47C2×#3713C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49#63798—24no—
50#63797—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67#5715—31no—
68#5674—31no—
69#5545—31no—
70#5545—31no—
71C3×#463—31no—
72C3×#459—31no—
73#5165—31no—
74#5153—31no—
75#5150—31no—
76#5150—31no—
77#5072—31no—
78#5057—31no—
79#5016—31no—
80#5015—31no—
81#4844D311yescharacteristic, complemented
82#4843D311yescharacteristic, complemented
83#4839—31no—
84#4839—31no—
85#4839—61no—
86#4819—31no—
87#4804—31no—
88#4787—31no—
89#4786—31no—
90#4786—31no—
91#4772—31no—
92#4770—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115#3802—22no—
116#3802—22no—
117#3802—22no—
118#3802D414yescomplemented
119#3796—22no—
120#3796—22no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3752D411yescharacteristic
125#3752D411yescharacteristic
126#3750D411yescharacteristic
127#3750D411yescharacteristic
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3743—22no—
132C8×C3⋊D3—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×D24—22no—
140C3×D24—22no—
141C3×D24—22no—
142C3×#204—22no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3715—22no—
150#3713—22no—
151#3713—22no—
152#3713—22no—
153#3041—91noSylow
154C2×#239—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C3×#127—31no—
165C3×#124—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168#947—31no—
169C2×#215—31no—
170#940—31no—
171#940—31no—
172#939—61no—
173#939—61no—
174#937—61no—
175#937—61no—
176#936—31no—
177D4×Dic3—31no—
178D4×Dic3—31no—
179C2×#214—31no—
180C2×#213—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C4×#67—61no—
187C4×#67—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190#914—64no—
191#911—64no—
192D3×D8—64no—
193D3×D8—64no—
194C2×D24C2×D311yescharacteristic
195C2×D24C2×D311yescharacteristic
196C2×D24C2×D311yescharacteristic, complemented
197C2×#204C2×D311yescharacteristic, complemented
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—61no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—61no—
204#893—31no—
205#893—31no—
206#892—31no—
207#892—31no—
208#884—61no—
209#884—61no—
210#882—61no—
211#882—61no—
212#67⋊C4—61no—
213#67⋊C4—61no—
214D3×C22⋊C4—61no—
215D3×C22⋊C4—61no—
216#875C2×D311yescharacteristic, complemented
217#874C2×D311yescharacteristic, complemented
218C4×D12C2×D311yescharacteristic, complemented
219C4×D12C2×D311yescharacteristic, complemented
220#872—31no—
221#872—31no—
222#872—61no—
223C3×C4⋊C8—21no—
224C3×C4⋊C8C2×D311yescharacteristic, complemented
225C3×C4⋊C8C2×D311yescharacteristic, complemented
226C3×#103—31no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#821C2×D311yescharacteristic, complemented
235#821C2×D311yescharacteristic, complemented
236#821C2×D311yescharacteristic, complemented
237#816C2×D311yescharacteristic, complemented
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8—61no—
244#810—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—81no—
260C2×D32—81no—
261C2×D32—81no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3C2×D412yes—
270C4×C3⋊D3#4112yes—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—81no—
283C3×D12—81no—
284C3×D12C2×D412yes—
285C3×D12C2×D412yes—
286C3×C4×D3—81no—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290#626—42no—
291#625—24no—
292#625—42no—
293#625—81no—
294#625—81no—
295D3×Dic3—42no—
296D3×Dic3—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—31no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—91no—
316#416—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343#239—62no—
344#239—62no—
345#237—62no—
346#237—62no—
347D3×D4—34no—
348D3×D4—34no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—62no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—61no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×Dic6C22×D311yescharacteristic
372C3×SD16—62no—
373C3×D8—62no—
374C3×D8—62no—
375C3×D8—62no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C42—21no—
389C3×C42C22×D311yescharacteristic
390C3×C42C22×D311yescharacteristic
391#217—61no—
392#217—61no—
393#217—61no—
394#217—61no—
395#215—62no—
396#214—62no—
397#213—62no—
398#213—62no—
399#213—62no—
400#213—62no—
401#213—62no—
402#213—62no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
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—61no—
419C4⋊Dic3C22×D311yescharacteristic
420C4⋊Dic3C22×D311yescharacteristic
421Dic3⋊C4—31no—
422Dic3⋊C4—31no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3—61no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8—61no—
438D24—22no—
439D24—22no—
440D24—22no—
441#204—22no—
442ΓL(1,𝔽25)—62no—
443ΓL(1,𝔽25)—62no—
444ΓL(1,𝔽25)—122no—
445D3×C8—62no—
446D3×C8—62no—
447D3×C8—122no—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3#12112yes—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467D32—84no—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3#12112yes—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—91no—
480C22×D4—91no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—91no—
493C22×C8—91no—
494#127—31no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—31no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—91no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8D3211yescharacteristic, complemented
516#103—31no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—31no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—61no—
537C22×D3—64no—
538C22×D3—64no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—32no—
552C3×D4—32no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—241no—
562C3×D4—241no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—241no—
570C2×C3×C4—241no—
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—64no—
578#67—64no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—241no—
583#67—241no—
584#67—241no—
585#67—241no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—122no—
599C2×Dic3—241no—
600C2×Dic3—241no—
601D12—21no—
602D12—21no—
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—81no—
610D12—81no—
611D12—122no—
612D12D3×D412yes—
613D12D3×D412yes—
614C4×D3—32no—
615C4×D3—32no—
616C4×D3—32no—
617C4×D3—32no—
618C4×D3—62no—
619C4×D3—62no—
620C4×D3—81no—
621C4×D3—81no—
622C4×D3—122no—
623C4×D3—241no—
624C4×D3—241no—
625Dic6—21no—
626Dic6—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—41no—
632C3×C8—41no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—121no—
638C3⋊C8—121no—
639C2×C32C2×#12111yescharacteristic
640C2×C32#57611yescharacteristic
641C2×C32#57611yescharacteristic
642C3⋊D3—22no—
643C3×D3—42no—
644C3×D3—42no—
645C3×D3—81no—
646C3×D3—81no—
647C3×D3—81no—
648C24—181no—
649C24—181no—
650#41—182no—
651#41—182no—
652C2×Q8—31no—
653C2×D4—31no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—94no—
661C2×D4—181no—
662C2×D4—182no—
663C2×D4—182no—
664C2×D4—182no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—91no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675SD16—62no—
676SD16—182no—
677D8—62no—
678D8—62no—
679D8—62no—
680D8—182no—
681D8—182no—
682D8—182no—
683M16—182no—
684C2×C8—91no—
685C2×C8—91no—
686C2×C8—182no—
687C2×C8C2×D3211yescharacteristic
688C2×C8C2×D3211yescharacteristic
689C4⋊C4—31no—
690C4⋊C4—31no—
691C4⋊C4—91no—
692C4⋊C4—91no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—91no—
705C42—181no—
706C42C2×D3211yescharacteristic
707C22×C3—21no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—32no—
728C2×D3—32no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—62no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—244no—
750C2×D3—244no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—32no—
769Dic3—32no—
770Dic3—41no—
771Dic3—41no—
772Dic3—41no—
773Dic3—62no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—121no—
779Dic3—121no—
780C32#304111yescharacteristic, complemented, Sylow
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—61no—
786C23—91no—
787C23—184no—
788C23—362no—
789C23—721no—
790C23—721no—
791C23—721no—
792C23—721no—
793Q8—61no—
794Q8—61no—
795D4—32no—
796D4—32no—
797D4—61no—
798D4—61no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—184no—
806D4—241no—
807D4—241no—
808D4—362no—
809D4—362no—
810D4—721no—
811D4—721no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—92no—
817C2×C4—92no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—241no—
821C2×C4—241no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4—721no—
825C2×C4#380211yescharacteristic
826C2×C4#380211yescharacteristic
827C2×C4C22×D3211yescharacteristic
828C8—21no—
829C8—21no—
830C8—181no—
831C8—181no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—122no—
836C2×C3—122no—
837C2×C3—241no—
838C2×C3—241no—
839C2×C3—241no—
840C2×C3D3×#12111yescharacteristic
841C2×C3D3×#12111yescharacteristic
842C2×C3#575711yescharacteristic
843C2×C3#576911yescharacteristic
844C2×C3#577411yescharacteristic
845C2×C3#577411yescharacteristic
846D3—42no—
847D3—42no—
848D3—62no—
849D3—62no—
850D3—81no—
851D3—81no—
852D3—81no—
853D3—122no—
854C22—62no—
855C22—62no—
856C22—92no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—181no—
871C22—181no—
872C22—724no—
873C22—724no—
874C22C2×#380211yescharacteristic
875C4—21no—
876C4—21no—
877C4—92no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—181no—
882C4—181no—
883C4D32×D411yescharacteristic
884C4#6431911yescharacteristic
885C3—21no—
886C3#8033411yescharacteristic, complemented
887C3#8053611yescharacteristic, complemented
888C2—122no—
889C2—122no—
890C2—182no—
891C2—241no—
892C2—241no—
893C2—241no—
894C2#1059461211yescharacteristic
895C2#1059468711yescharacteristic
896C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3041
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×#63798C2semidirect
2. C2×#63797C2semidirect
3. #10594010C2semidirect
4. #10593996C2semidirect
5. #10592538C2semidirect
6. C3×#4844C2semidirect
7. C3×#4843C2semidirect
8. #10590956C2semidirect
9. #10590941C2semidirect
10. #10590751C2semidirect
11. #10590750C2semidirect
12. #10590749C2semidirect
13. #10590749C2semidirect
14. #10590348C2semidirect
15. #10590347C2semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
28. C3×#875C22semidirect
29. C3×#874C22semidirect
30. C3×C4×D12C22semidirect
31. C3×C4×D12C22semidirect
36. #63914C22semidirect
37. #63898C22semidirect
38. #63898C22semidirect
43. #63863C22semidirect
45. C2×#3715C22semidirect
48. C2×#3713C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63641C22semidirect
53. #63641C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
81. #4844D3semidirect
82. #4843D3semidirect
118. #3802D4semidirect
196. C2×D24C2×D3semidirect
197. C2×#204C2×D3semidirect
216. #875C2×D3semidirect
217. #874C2×D3semidirect
218. C4×D12C2×D3semidirect
219. C4×D12C2×D3semidirect
224. C3×C4⋊C8C2×D3semidirect
225. C3×C4⋊C8C2×D3semidirect
234. #821C2×D3semidirect
235. #821C2×D3semidirect
236. #821C2×D3semidirect
237. #816C2×D3semidirect
515. C4⋊C8D32semidirect
780. C32#3041semidirect
886. C3#80334semidirect
887. C3#80536semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C2×#637972
#105940102
#105939962
#105925382
C3×#48442
C3×#48432
#105909562
#105909412
#105907512
#105907502
#105907492
#105903482
#105903472
#805363
#803343