Finite Group Databasebeta

← #11866190

Subgroups — #11866190

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595233C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×#63932C211yesmaximal, characteristic, complemented
5#10592852C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7#10591486C211yesmaximal, characteristic, complemented
8#10591468C211yesmaximal, characteristic, complemented
9#10591434C211yesmaximal, characteristic, complemented
10#10591428C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590954C211yesmaximal, characteristic, complemented
13#10590755C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590694C211yesmaximal, characteristic, complemented
16#83826—31nomaximal
17#80334—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22#64145C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C3×D3×D8—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#63976—21no—
34#63976—21no—
35#67⋊Dic3—21no—
36Dic3×#67—21no—
37#63970—21no—
38#63970—21no—
39D3×#217—21no—
40C2×(C2×D3)⋊Dic3—21no—
41#63932—24no—
42#63914C2211yescharacteristic, complemented
43#63898C2211yescharacteristic, complemented
44Dic3×D12C2211yescharacteristic, complemented
45#63860C2211yescharacteristic, complemented
46#63855C2211yescharacteristic
47#63841C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64#5805—31no—
65#5798—31no—
66C2×#932—31no—
67C2×#911—31no—
68C2×D3×D8D311yescharacteristic, complemented
69#5715—31no—
70#5545—31no—
71C3×#459—31no—
72#5215—31no—
73#5153—31no—
74#5153—31no—
75#5153—31no—
76#5153—31no—
77#5153—31no—
78#5153—61no—
79#5150—31no—
80#5150—31no—
81#5150—31no—
82#5150—31no—
83#5150D311yescharacteristic, complemented
84#5113—31no—
85#5102—31no—
86#5072—31no—
87#5016—31no—
88#4844—31no—
89#4839—31no—
90#4787—31no—
91#4786—31no—
92#4772—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C3×D3×D4—22no—
108C3×D3×D4D414yescomplemented
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3795—22no—
120#3795—22no—
121C32×D8—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3757—21no—
125#3757—21no—
126#3754—22no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#213—22no—
132C3×#213—22no—
133C3×#213—22no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×D3×C8—22no—
140Dic3⋊Dic3D411yescharacteristic
141Dic3⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3D411yescharacteristic
148(C2×D3)⋊Dic3D411yescharacteristic
149Dic32—21no—
150#3716—22no—
151#3713—22no—
152#3711—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C2×#237—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—31no—
160C2×C3×D8—21no—
161C2×C3×D8—31no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8—64no—
166C2×C3×D8C2×D311yescharacteristic
167C2×C3×D8C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×#127—31no—
170C3×C4×D4—31no—
171#953—61no—
172#953—61no—
173C2×#217—61no—
174C2×#217—61no—
175#940—31no—
176#940—31no—
177#940C2×D311yescharacteristic, complemented
178#939—61no—
179#939—61no—
180#938—61no—
181#938—61no—
182#937—61no—
183#937—61no—
184#936—31no—
185#936—31no—
186#936—31no—
187#936—61no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190D4×Dic3—31no—
191D4×Dic3—31no—
192D4×Dic3—61no—
193D4×Dic3—61no—
194D4×Dic3—61no—
195D4×Dic3C2×D311yescharacteristic, complemented
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213C2×D311yescharacteristic
204C2×#213C2×D311yescharacteristic
205C2×#213C2×D311yescharacteristic, complemented
206C4×#67—61no—
207C2×(C2×D3)⋊C4—61no—
208#926—31no—
209#926—31no—
210C2×#208—31no—
211#911—64no—
212D3×D8—24no—
213C2×D24C2×D311yescharacteristic
214C2×#204—31no—
215C2×ΓL(1,𝔽25)—31no—
216C2×D3×C8C2×D311yescharacteristic
217#893—31no—
218#892—31no—
219#67⋊C4—61no—
220D3×C22⋊C4—61no—
221#875—31no—
222C4×D12—31no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#832—31no—
228#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#821—31no—
236#821C2×D311yescharacteristic, complemented
237#816—31no—
238#816—31no—
239#816—31no—
240#816—61no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C23×C32—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3—81no—
260C22×C3×D3—81no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—81no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273#634—21no—
274#634—21no—
275C3×#67—24no—
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—81no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12C2×D412yes—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292#625—42no—
293#625—81no—
294#625—81no—
295D3×Dic3—42no—
296D3×Dic3—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—31no—
304#535—91no—
305#518—91no—
306#463—91no—
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—
317C24×C3—61no—
318C24×C3—61no—
319C23×D3—21no—
320C23×D3—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—34no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—62no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C22×Dic3—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—121no—
357#237—62no—
358#237—62no—
359D3×D4—22no—
360D3×D4—22no—
361D3×D4—22no—
362D3×D4#6714yescomplemented
363#235—62no—
364#235—62no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C3×D8—22no—
376C3×D8—22no—
377C3×D8—42no—
378C3×D8—62no—
379C3×D8—62no—
380C3×D8—62no—
381C3×D8—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C22⋊C4—61no—
390C3×C42—31no—
391#217—21no—
392#217—31no—
393#217—31no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#217—121no—
407#217—121no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—122no—
412#213—22no—
413#213—22no—
414#213—22no—
415#213—62no—
416#213—62no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3C22×D311yescharacteristic
438#208—62no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—22no—
445#204—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—22no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
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—84no—
467C2×C3×D3—84no—
468C2×C3×D3#12112yes—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
481C22×D4—31no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—64no—
490C2×D8—91no—
491C2×D8D3211yescharacteristic
492C2×M16—91no—
493C22×C8—31no—
494#127—31no—
495#127—91no—
496#124—91no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
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—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—91no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—64no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—241no—
537C23×C3—241no—
538C23×C3—241no—
539C23×C3—241no—
540C22×D3—21no—
541C22×D3—24no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—81no—
546C22×D3—81no—
547C22×D3—81no—
548C22×D3—81no—
549C22×D3D3×D411yescharacteristic
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—22no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—64no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—241no—
569C3×D4—241no—
570C3×D4D3×D412yes—
571C3×D4C2×#6712yes—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—61no—
579C2×C3×C4—241no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—24no—
583#67—42no—
584#67—81no—
585#67—81no—
586#67—122no—
587#67—122no—
588#67—241no—
589#67—241no—
590#67—241no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—81no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—241no—
608C2×Dic3—241no—
609C2×Dic3—241no—
610C2×Dic3—241no—
611C2×Dic3—242no—
612C2×Dic3D3×D411yescharacteristic
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12C2×#6712yes—
621C4×D3—122no—
622C4×D3—241no—
623C4×D3—241no—
624C4×D3#23712yes—
625C4×D3C2×#6712yes—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—42no—
643C2×C32—81no—
644C2×C32C2×#12111yescharacteristic
645C2×C32#57611yescharacteristic
646C2×C32#57611yescharacteristic
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—61no—
653#41—182no—
654#41—182no—
655C2×Q8—91no—
656C2×D4—34no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—62no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4C2×D3211yescharacteristic
671C2×D4C2×D3211yescharacteristic
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678SD16—182no—
679SD16—182no—
680D8—22no—
681D8—62no—
682D8—62no—
683D8—62no—
684D8—62no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4—91no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—91no—
709C42—181no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—244no—
742C22×C3—244no—
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C2×D3×D411yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—84no—
757C2×D3—84no—
758C2×D3#93912yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—32no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—121no—
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×#23711yescharacteristic
767C3×C4D3×#4111yescharacteristic
768C3×C4C22×#6711yescharacteristic
769Dic3—21no—
770Dic3—21no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—241no—
783Dic3—241no—
784Dic3#93912yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—21no—
788C23—31no—
789C23—64no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—122no—
794C23—241no—
795C23—241no—
796C23—241no—
797C23—241no—
798Q8—181no—
799Q8—181no—
800D4—21no—
801D4—21no—
802D4—21no—
803D4—32no—
804D4—64no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—122no—
811D4—241no—
812D4—241no—
813D4—362no—
814D4—721no—
815D4—721no—
816D4D3×#6712yes—
817C2×C4—31no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—91no—
824C2×C4—91no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—241no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4—721no—
831C2×C4—721no—
832C2×C4C22×D3211yescharacteristic
833C8—21no—
834C8—61no—
835C8—61no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—62no—
843C2×C3—82no—
844C2×C3—81no—
845C2×C3—81no—
846C2×C3—122no—
847C2×C3—161no—
848C2×C3—241no—
849C2×C3—241no—
850C2×C3D3×#12111yescharacteristic
851C2×C3#575711yescharacteristic
852C2×C3#575711yescharacteristic
853C2×C3#575711yescharacteristic
854C2×C3#577411yescharacteristic
855C2×C3C2×#93911yescharacteristic
856D3—22no—
857D3—42no—
858D3—81no—
859D3—81no—
860C22—22no—
861C22—32no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—61no—
868C22—61no—
869C22—62no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—244no—
879C22—244no—
880C22D32×D411yescharacteristic
881C4—32no—
882C4—61no—
883C4—61no—
884C4—121no—
885C4—181no—
886C4—181no—
887C4—361no—
888C4—361no—
889C4D3×#23711yescharacteristic
890C4C2×D3×#6711yescharacteristic
891C3—21no—
892C3#8033411yescharacteristic, complemented
893C3#8382611yescharacteristic, complemented
894C2—42no—
895C2—62no—
896C2—81no—
897C2—122no—
898C2—241no—
899C2—241no—
900C2#1059473111yescharacteristic
901C2#1059473211yescharacteristic
902C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. #10595233C2semidirect
3. #10595215C2semidirect
4. C2×#63932C2semidirect
5. #10592852C2semidirect
6. C3×#5150C2semidirect
7. #10591486C2semidirect
8. #10591468C2semidirect
9. #10591434C2semidirect
10. #10591428C2semidirect
11. #10591421C2semidirect
12. #10590954C2semidirect
13. #10590755C2semidirect
14. #10590749C2semidirect
15. #10590694C2semidirect
22. #64145C22semidirect
23. D4×C3⋊Dic3C22semidirect
24. C2×#3754C22semidirect
25. C3×#940C22semidirect
26. C3×D4×Dic3C22semidirect
29. C2×C3×#213C22semidirect
42. #63914C22semidirect
43. #63898C22semidirect
44. Dic3×D12C22semidirect
45. #63860C22semidirect
48. C2×#3716C22semidirect
49. C2×#3713C22semidirect
51. #63659C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. C2×D3×D8D3semidirect
83. #5150D3semidirect
108. C3×D3×D4D4semidirect
177. #940C2×D3semidirect
195. D4×Dic3C2×D3semidirect
205. C2×#213C2×D3semidirect
233. #832C2×D3semidirect
236. #821C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
362. D3×D4#67semidirect
785. C32#3041semidirect
892. C3#80334semidirect
893. C3#83826semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
#105952332
#105952152
C2×#639322
#105928522
C3×#51502
#105914862
#105914682
#105914342
#105914282
#105914212
#105909542
#105907552
#105907492
#105906942
#838263
#803343