Finite Group Databasebeta

← #11885826

Subgroups — #11885826

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic, complemented
5C4×#3753C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590518C211yesmaximal, characteristic, complemented
12#10590499C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590353C211yesmaximal, characteristic, complemented
15#10590329C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17#80557—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×#875C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic
36#63935—24no—
37D3×#213—24no—
38#63922—21no—
39#63921—21no—
40#63912—21no—
41#63908C2211yescharacteristic, complemented
42#63856C2211yescharacteristic
43#63854—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C22×#213—31no—
66C2×#916—31no—
67C2×D3×D8—31no—
68#5676—31no—
69#5554D311yescharacteristic, complemented
70#5550—31no—
71C3×#463—31no—
72#5238—31no—
73#5218—31no—
74#5169—31no—
75#5158—31no—
76#5059—31no—
77#5059—31no—
78#5057—31no—
79#5051—31no—
80#5046—31no—
81#5038—31no—
82#5037—31no—
83#5016D311yescharacteristic, complemented
84C4×#213—31no—
85C4×#213—31no—
86C4×#213—61no—
87D4×C3⋊C8—31no—
88#4844—31no—
89#4834—31no—
90#4813—31no—
91#4810—31no—
92#4776—31no—
93#4775—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#624—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3799—22no—
122#3799—41no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126#3753D414yescomplemented
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#214—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3D411yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3718—22no—
149#3717—22no—
150#3715—41no—
151#3715—41no—
152#3714—22no—
153#3713—22no—
154D3×C3⋊C8—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#237C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—31no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#120—61no—
174C3×C4×D4—21no—
175C3×C4×D4—31no—
176C3×C4×D4C2×D311yescharacteristic, complemented
177C3×C4×D4C2×D311yescharacteristic, complemented
178C2×C3×C22⋊C4—61no—
179#950—64no—
180#946—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186#938—31no—
187#937—61no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214C2×D311yescharacteristic, complemented
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213—64no—
198C2×#213C2×D311yescharacteristic
199#930—21no—
200#930—31no—
201C2×(C2×D3)⋊C4—21no—
202#924—31no—
203C22×C3⋊C8—31no—
204C22×C3⋊C8—31no—
205#916—64no—
206D3×D8—64no—
207C2×D24—31no—
208C2×#204—31no—
209C2×D3×C8—31no—
210C2×D3×C8—31no—
211#897C2×D311yescharacteristic
212#895C2×D311yescharacteristic, complemented
213#894—61no—
214#886—21no—
215#884—61no—
216#884—61no—
217#883—61no—
218#882—21no—
219#882—61no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#875C2×D311yescharacteristic, complemented
223#875C2×D311yescharacteristic, complemented
224C4×D12—31no—
225C4×D12—31no—
226C4×D12—61no—
227C4×D12C2×D311yescharacteristic
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#102—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#830—31no—
237#830—31no—
238#821—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#810C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—61no—
246#809C2×D311yescharacteristic, complemented
247#807—31no—
248#807—31no—
249#807—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C4×C3⋊C8—31no—
252C4×C3⋊C8—31no—
253C4×C3⋊C8—61no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—81no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—81no—
277C3×#67—42no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—22no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—81no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—42no—
300#625—81no—
301#624—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×#135—91no—
307C22×D8—91no—
308#546—31no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—31no—
314#463—91no—
315#450—91no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—91no—
320C8×D4—91no—
321C24×C3—61no—
322C23×D3—21no—
323C23×D3—61no—
324C23×D3—61no—
325C3×#41—62no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—121no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—41no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C22×Dic3—21no—
353#239—62no—
354#239—121no—
355#237—22no—
356#237—41no—
357D3×D4—22no—
358D3×D4—41no—
359D3×D4—62no—
360D3×D4—121no—
361#235—62no—
362#235—121no—
363C2×D12—21no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—62no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—121no—
371C2×D12#6711yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—121no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—62no—
384C3×D8—62no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—21no—
404C3×C42C22×D311yescharacteristic
405C3×C42C22×D311yescharacteristic
406#217—61no—
407#217—61no—
408#216—62no—
409#216—62no—
410#215—62no—
411#215—121no—
412#215—121no—
413#214—22no—
414#214—121no—
415#214—121no—
416#213—22no—
417#213—34no—
418#213—34no—
419#213—64no—
420#213—62no—
421#213—62no—
422#213—62no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4#6711yescharacteristic
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—21no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3#6711yescharacteristic
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—62no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—62no—
454#204—62no—
455D3×C8—62no—
456D3×C8—62no—
457C22×C32—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—84no—
476C2×C3×D3#13512yescomplemented
477D32—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C22×D4—31no—
491C22×D4—91no—
492#135—184no—
493C2×Q16—91no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—184no—
503C22×C8—91no—
504C22×C8—91no—
505#124—31no—
506#124—31no—
507#123—61no—
508#123—181no—
509C22⋊Q8—31no—
510C22⋊Q8—91no—
511#121—31no—
512#121—61no—
513#121—91no—
514#121—181no—
515#120—61no—
516#120—181no—
517C4×D4—31no—
518C4×D4—91no—
519C4×D4D3211yescharacteristic, complemented
520C2×C22⋊C4—61no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—31no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532C4×C8—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—81no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3C2×#6711yescharacteristic
558C22×D3C2×#6711yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—22no—
566C3×D4—41no—
567C3×D4—62no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—241no—
575C3×D4D3×D412yes—
576C3×D4D3×D412yes—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—81no—
592C2×C3×C4—81no—
593C2×C3×C4—82no—
594C2×C3×C4—122no—
595C2×C3×C4D3×D411yescharacteristic
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C2×#6711yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—42no—
602#67—42no—
603#67—122no—
604#67—122no—
605#67—241no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—42no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—121no—
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615D12—22no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—32no—
621D12—32no—
622D12—62no—
623D12—61no—
624D12—61no—
625D12—81no—
626D12—121no—
627D12—122no—
628D12—122no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—241no—
636C4×D3—241no—
637C4×D3—242no—
638Dic6—21no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642C3×C8—61no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—21no—
646C3⋊C8—32no—
647C3⋊C8—32no—
648C3⋊C8—62no—
649C3⋊C8—61no—
650C3⋊C8—61no—
651C3⋊C8—121no—
652C2×C32—42no—
653C2×C32D4211yescharacteristic
654C2×C32C2×#13511yescharacteristic
655C2×C32#57611yescharacteristic
656C3⋊D3—42no—
657C3×D3—22no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—61no—
662C24—181no—
663#41—62no—
664#41—121no—
665#41—182no—
666#41—361no—
667C2×Q8—31no—
668C2×Q8—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—62no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—121no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—361no—
683C2×D4C2×D3211yescharacteristic
684C22×C4—21no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—61no—
688C22×C4—181no—
689C22×C4—181no—
690Q16—182no—
691SD16—62no—
692SD16—182no—
693SD16—361no—
694SD16—361no—
695D8—62no—
696D8—94no—
697D8—182no—
698D8—182no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—91no—
702C2×C8—91no—
703C2×C8—182no—
704C2×C8—182no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4C2×D3211yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—31no—
712C22⋊C4—31no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42C2×D3211yescharacteristic
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—32no—
727C22×C3—42no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—244no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C22×#6711yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—84no—
762C2×D3—122no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C2×D3#95012yescomplemented
772C3×C4—22no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—41no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—81no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4C2×D3×D411yescharacteristic
788C3×C4C2×D3×D411yescharacteristic
789C3×C4#100411yescharacteristic
790C3×C4#100911yescharacteristic
791Dic3—21no—
792Dic3—21no—
793Dic3—41no—
794Dic3—41no—
795Dic3—121no—
796Dic3—121no—
797Dic3—241no—
798C32#328011yescharacteristic, complemented, Sylow
799C23—21no—
800C23—31no—
801C23—31no—
802C23—61no—
803C23—61no—
804C23—122no—
805C23—122no—
806C23—181no—
807C23—241no—
808C23—362no—
809C23—362no—
810C23—721no—
811Q8—61no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815D4—21no—
816D4—62no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—92no—
822D4—122no—
823D4—122no—
824D4—181no—
825D4—241no—
826D4—362no—
827D4—362no—
828D4—721no—
829D4#380212yes—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—81no—
840C2×C4—122no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4—721no—
844C2×C4D3×#6711yescharacteristic
845C2×C4D3×#6711yescharacteristic
846C2×C4C22×D3211yescharacteristic
847C8—61no—
848C8—61no—
849C8—92no—
850C8—181no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—42no—
855C2×C3—42no—
856C2×C3—62no—
857C2×C3—82no—
858C2×C3—121no—
859C2×C3—241no—
860C2×C3—241no—
861C2×C3#560911yescharacteristic
862C2×C3D3×#13511yescharacteristic
863C2×C3#577411yescharacteristic
864C2×C3D4×#6711yescharacteristic
865C2×C3C2×#95011yescharacteristic
866C2×C3#583511yescharacteristic
867D3—22no—
868D3—41no—
869D3—81no—
870D3—81no—
871D3—122no—
872D3—122no—
873D3—242no—
874C22—22no—
875C22—32no—
876C22—41no—
877C22—41no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—182no—
890C22—244no—
891C22—361no—
892C22—361no—
893C22—724no—
894C22C2×D3×#6711yescharacteristic
895C4—21no—
896C4—21no—
897C4—41no—
898C4—61no—
899C4—61no—
900C4—121no—
901C4—121no—
902C4—361no—
903C4C2×#380211yescharacteristic
904C4#6430711yescharacteristic
905C3—21no—
906C3#8055711yescharacteristic, complemented
907C3#8350511yescharacteristic, complemented
908C2—42no—
909C2—62no—
910C2—121no—
911C2—241no—
912C2—241no—
913C2—362no—
914C2#1059506911yescharacteristic
915C2#1059509711yescharacteristic
916C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5554C2semidirect
2. C2×#63935C2semidirect
3. C2×D3×#213C2semidirect
4. #10594007C2semidirect
5. C4×#3753C2semidirect
6. C3×#5016C2semidirect
7. #10591458C2semidirect
8. #10591450C2semidirect
9. #10590615C2semidirect
10. #10590596C2semidirect
11. #10590518C2semidirect
12. #10590499C2semidirect
13. #10590356C2semidirect
14. #10590353C2semidirect
15. #10590329C2semidirect
18. C2×C3×#237C22semidirect
21. C2×#3799C22semidirect
22. C32×C4×D4C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×#214C22semidirect
30. C3×#895C22semidirect
33. C3×#875C22semidirect
34. C3×#875C22semidirect
41. #63908C22semidirect
44. C2×#3718C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63636C22semidirect
54. #63634C22semidirect
55. C4×C3⋊(C3⋊C8)C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5554D3semidirect
83. #5016D3semidirect
126. #3753D4semidirect
160. C2×#237C2×D3semidirect
176. C3×C4×D4C2×D3semidirect
177. C3×C4×D4C2×D3semidirect
190. C2×#214C2×D3semidirect
212. #895C2×D3semidirect
222. #875C2×D3semidirect
223. #875C2×D3semidirect
242. #810C2×D3semidirect
246. #809C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
476. C2×C3×D3#135semidirect
519. C4×D4D32semidirect
771. C2×D3#950semidirect
798. C32#3280semidirect
906. C3#80557semidirect
907. C3#83505semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
C2×#639352
C2×D3×#2132
#105940072
C4×#37532
C3×#50162
#105914582
#105914502
#105906152
#105905962
#105905182
#105904992
#105903562
#105903532
#105903292
#835053
#805573