Finite Group Databasebeta

← #11884503

Subgroups — #11884503

Order 1152.

1090 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic, complemented
2C2×#63794C211yesmaximal, characteristic, complemented
3#10594007C211yesmaximal, characteristic, complemented
4#10593902C211yesmaximal, characteristic, complemented
5#10592542C211yesmaximal, characteristic, complemented
6C3×#4845C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590967C211yesmaximal, characteristic, complemented
9#10590966C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590850C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590823C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590351C211yesmaximal, characteristic, complemented
16#80628—31nomaximal
17#79497—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3745C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24#64083C2211yescharacteristic, complemented
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#875C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63922—21no—
34#63921—21no—
35#63912—21no—
36#63911—21no—
37#63910—21no—
38#63910—21no—
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic
42#63894—21no—
43#63856C2211yescharacteristic
44#63854—21no—
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63808—24no—
51#63794—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63C2×#919—31no—
64C2×#914—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5676—31no—
68#5577—31no—
69#5553—31no—
70#5550—31no—
71C3×#464—31no—
72C3×#435—31no—
73#5187—31no—
74#5172—31no—
75#5134—31no—
76#5115—31no—
77#5058—31no—
78#5026—31no—
79#4845D311yescharacteristic, complemented
80#4843—31no—
81#4843—31no—
82#4843—61no—
83#4836D311yescharacteristic, complemented
84#4812—31no—
85#4810—31no—
86#4775—31no—
87#4773—31no—
88#4734—31no—
89#4734—31no—
90#4733—31no—
91#4732—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—22no—
121#3799—22no—
122#3799—41no—
123#3799—41no—
124#3799—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C42C2311yescharacteristic
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—22no—
131#3745—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×Dic12—22no—
143C3×#204—22no—
144C3×ΓL(1,𝔽25)—22no—
145C3×D3×C8—22no—
146#3724—21no—
147#3722—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3717—22no—
152#3717—41no—
153#3717D414yescomplemented
154#3714—22no—
155#3714—41no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172#946—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—31no—
176#940—61no—
177#938—31no—
178#937—61no—
179C2×#213—31no—
180C2×#213—31no—
181#930—31no—
182#930—31no—
183#930—31no—
184#924—31no—
185#919—64no—
186#914—64no—
187#908—64no—
188C2×Dic12C2×D311yescharacteristic, complemented
189#904—64no—
190C2×D24—31no—
191C2×D24—31no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—61no—
197C2×D24—61no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic
203C2×D3×C8C2×D311yescharacteristic, complemented
204#895—31no—
205#895—31no—
206#895—61no—
207#895—61no—
208#894—61no—
209#893—61no—
210#884—61no—
211#884—61no—
212#884—61no—
213#884—61no—
214#883—61no—
215#882—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218#875C2×D311yescharacteristic
219#874—31no—
220#874—31no—
221#874—61no—
222#874—61no—
223C4×D12—31no—
224C4×D12—31no—
225C4×D12—61no—
226C4×D12—61no—
227C4×D12C2×D311yescharacteristic
228C4×Dic6C2×D311yescharacteristic, complemented
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#102—31no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244#821—61no—
245#821C2×D311yescharacteristic
246(C2×D3)⋊C8C2×D311yescharacteristic
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#818—31no—
249#816—31no—
250#816C2×D311yescharacteristic, complemented
251#809—31no—
252#807—31no—
253#803C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)—81no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—41no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#626—42no—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—81no—
297#626—81no—
298#625—81no—
299#624—42no—
300#624—42no—
301#624—42no—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337#239—62no—
338#239—62no—
339#239—62no—
340#239—121no—
341#239—121no—
342#239—121no—
343D3×D4—62no—
344D3×D4—121no—
345#235—62no—
346#235—62no—
347#235—62no—
348#235—121no—
349#235—121no—
350#235—121no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12—121no—
373C2×D12—121no—
374C2×D12D1211yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—121no—
385C2×C4×D3C22×D311yescharacteristic
386C2×C4×D3C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×SD16—62no—
391C3×M16—62no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—21no—
409C3×C42—61no—
410C3×C42C22×D311yescharacteristic
411C3×C42C22×D311yescharacteristic
412#217—61no—
413#217—61no—
414#215—34no—
415#215—62no—
416#215—121no—
417#213—62no—
418#213—121no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4D1211yescharacteristic
431(C2×D3)⋊C4D1211yescharacteristic
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3D1211yescharacteristic
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440C4×Dic3—21no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—22no—
444D24—62no—
445D24—62no—
446D24—62no—
447D24—62no—
448D24—62no—
449D24—122no—
450D24—122no—
451D24—121no—
452#204—22no—
453#204—34no—
454#204—62no—
455#204—121no—
456ΓL(1,𝔽25)—22no—
457D3×C8—22no—
458C22×C32C22×D411yescharacteristic
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—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—41no—
483C3×Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—31no—
504C22×C8—31no—
505#127—91no—
506#127—181no—
507#124—31no—
508#123—181no—
509C22⋊Q8—91no—
510#121—91no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8D3211yescharacteristic, complemented
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—61no—
536C22×D3—21no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3C2×D1211yescharacteristic
553C22×D3C2×D1211yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—121no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4C2×D1211yescharacteristic
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—241no—
584#67—241no—
585#67—241no—
586#67—241no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3C2×D1211yescharacteristic
594C2×Dic3C2×D1211yescharacteristic
595D12—21no—
596D12—21no—
597D12—32no—
598D12—32no—
599D12—41no—
600D12—62no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—121no—
614D12—121no—
615D12—121no—
616D12—122no—
617D12—122no—
618D12—122no—
619D12—122no—
620D12—122no—
621D12—122no—
622D12—242no—
623D12—241no—
624D12—241no—
625D12—242no—
626D12—241no—
627D12—241no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—241no—
639C4×D3—241no—
640C4×D3—242no—
641Dic6—21no—
642Dic6—21no—
643Dic6—21no—
644Dic6D3×D412yes—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—21no—
648C3×C8—21no—
649C3×C8—32no—
650C3×C8—41no—
651C3×C8—41no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8D3×D412yes—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3⋊D3—42no—
659C3⋊D3—81no—
660C3⋊D3—81no—
661C3×D3—41no—
662C3×D3—41no—
663C3×D3—81no—
664C24—181no—
665#41—182no—
666#41—182no—
667#41—182no—
668#41—361no—
669#41—361no—
670#41—361no—
671C2×Q8—31no—
672C2×Q8—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—361no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4—181no—
694C22×C4—181no—
695Q16—62no—
696SD16—62no—
697SD16—94no—
698SD16—182no—
699SD16—361no—
700D8—182no—
701D8—182no—
702D8—182no—
703D8—361no—
704M16—62no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C2×C8C2×D3211yescharacteristic
709C2×C8C2×D3211yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—61no—
713C4⋊C4—91no—
714C4⋊C4—181no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C42—61no—
725C42C2×D3211yescharacteristic
726C22×C3—21no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3C22×D1211yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C3×C4—22no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—41no—
784C3×C4—62no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100911yescharacteristic
792C3×C4#100911yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—22no—
796Dic3—41no—
797Dic3—41no—
798Dic3—121no—
799Dic3—121no—
800Dic3—241no—
801C32#326811yescharacteristic, complemented, Sylow
802C23—31no—
803C23—31no—
804C23—61no—
805C23—181no—
806C23—181no—
807C23—181no—
808C23—362no—
809C23—362no—
810C23—721no—
811Q8—32no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815D4—61no—
816D4—61no—
817D4—92no—
818D4—121no—
819D4—181no—
820D4—181no—
821D4—181no—
822D4—181no—
823D4—181no—
824D4—362no—
825D4—362no—
826D4—362no—
827D4—362no—
828D4—362no—
829D4—721no—
830D4—721no—
831D4—721no—
832D4—721no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—181no—
843C2×C4—362no—
844C2×C4—362no—
845C2×C4—362no—
846C2×C4—721no—
847C2×C4D3×D1211yescharacteristic
848C2×C4D3×D1211yescharacteristic
849C2×C4C22×D3211yescharacteristic
850C8—21no—
851C8—21no—
852C8—32no—
853C8—61no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—121no—
858C2×C3—121no—
859C2×C3—241no—
860C2×C3D4×D1211yescharacteristic
861C2×C3#560911yescharacteristic
862C2×C3#574811yescharacteristic
863C2×C3#575211yescharacteristic
864C2×C3#576911yescharacteristic
865C2×C3#577711yescharacteristic
866D3—41no—
867D3—41no—
868D3—81no—
869D3—122no—
870D3—122no—
871D3—242no—
872D3—241no—
873D3—241no—
874D3—241no—
875D3—241no—
876D3—481no—
877D3—481no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—182no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—361no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—724no—
897C22C2×D3×D1211yescharacteristic
898C4—21no—
899C4—21no—
900C4—61no—
901C4—61no—
902C4—62no—
903C4—121no—
904C4—121no—
905C4—361no—
906C4D32×D411yescharacteristic
907C4#6432011yescharacteristic
908C3—21no—
909C3#7949711yescharacteristic, complemented
910C3#8062811yescharacteristic, complemented
911C2—121no—
912C2—121no—
913C2—241no—
914C2—362no—
915C2—721no—
916C2—721no—
917C2#1059462111yescharacteristic
918C2#1059468011yescharacteristic
919C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3268
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×#63808C2semidirect
2. C2×#63794C2semidirect
3. #10594007C2semidirect
4. #10593902C2semidirect
5. #10592542C2semidirect
6. C3×#4845C2semidirect
7. C3×#4836C2semidirect
8. #10590967C2semidirect
9. #10590966C2semidirect
10. #10590947C2semidirect
11. #10590850C2semidirect
12. #10590826C2semidirect
13. #10590823C2semidirect
14. #10590362C2semidirect
15. #10590351C2semidirect
21. C2×#3799C22semidirect
24. #64083C22semidirect
26. C2×C3×Dic12C22semidirect
29. C2×C3×D3×C8C22semidirect
32. C3×C4×Dic6C22semidirect
40. #63909C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
52. C32×C4⋊C8C22semidirect
53. #63648C22semidirect
54. #63648C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#803C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
79. #4845D3semidirect
83. #4836D3semidirect
153. #3717D4semidirect
188. C2×Dic12C2×D3semidirect
203. C2×D3×C8C2×D3semidirect
228. C4×Dic6C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
250. #816C2×D3semidirect
253. #803C2×D3semidirect
523. C4⋊C8D32semidirect
801. C32#3268semidirect
909. C3#79497semidirect
910. C3#80628semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C2×#637942
#105940072
#105939022
#105925422
C3×#48452
C3×#48362
#105909672
#105909662
#105909472
#105908502
#105908262
#105908232
#105903622
#105903512
#806283
#794973