Finite Group Databasebeta

← #11885828

Subgroups — #11885828

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3#10595018C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5#10592745C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7#10591609C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11C3⋊C8×#67C211yesmaximal, characteristic, complemented
12#10590615C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590534C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17#80773—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#895—21no—
31C3×#895C2211yescharacteristic, complemented
32C3×#894—21no—
33C3×#893C2211yescharacteristic, complemented
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36#63981—21no—
37#63974—21no—
38#63949—24no—
39#63910—21no—
40#63909C2211yescharacteristic, complemented
41#63897—21no—
42#63894C2211yescharacteristic, complemented
43#63864C2211yescharacteristic, complemented
44C2×#3715C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3714—24no—
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic
53#63636C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C22×#213—31no—
66C2×#919—31no—
67C22×D24—31no—
68#5630—31no—
69#5630D311yescharacteristic, complemented
70#5550—31no—
71C3×#467—31no—
72#5238—31no—
73#5218—31no—
74#5191—31no—
75C8×#67—31no—
76#5059—31no—
77#5057—31no—
78#5051D311yescharacteristic, complemented
79#5046—31no—
80#5046—31no—
81#5046—31no—
82#5046—61no—
83#5038—31no—
84#5037—31no—
85#5016—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4883—31no—
89#4872—31no—
90#4819—31no—
91#4819—31no—
92#4810—31no—
93#4810—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67D411yescharacteristic
104C3×#239—22no—
105C3×#239—41no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#624—21no—
120C2×#624—21no—
121#3799—22no—
122#3799—41no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126#3755—22no—
127#3755—41no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×#216—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3715—22no—
150#3715—41no—
151#3714—22no—
152#3714—22no—
153#3714—22no—
154#3714D414yescomplemented
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×#235—31no—
162C22×D12—31no—
163C22×D12—31no—
164C22×D12—61no—
165C22×D12C2×D311yescharacteristic
166C2×C3×Q16—31no—
167C22×C3×C8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×#121—31no—
175C3×#121—61no—
176C3×#120—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C22⋊C4—61no—
180#950—64no—
181#947—31no—
182#947C2×D311yescharacteristic, complemented
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215—61no—
192#937—61no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—64no—
200#930—31no—
201C4×#67C2×D311yescharacteristic
202#924C2×D311yescharacteristic
203C22×C3⋊C8—31no—
204C22×C3⋊C8C2×D311yescharacteristic
205#919—64no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—64no—
211C2×D3×C8—31no—
212#895—21no—
213#895—31no—
214#895—61no—
215#895C2×D311yescharacteristic, complemented
216#894—21no—
217#894—61no—
218#894—61no—
219#893—31no—
220#893C2×D311yescharacteristic, complemented
221#884—61no—
222#882—21no—
223#882—61no—
224D3×C22⋊C4—21no—
225D3×C22⋊C4—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#103—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240Dic3⋊C8—31no—
241C8×Dic3—31no—
242#810C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809—61no—
251#807C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253C4×C3⋊C8—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C32×Q8—21no—
267C32×Q8—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4⋊(C3⋊D3)C2×D412yes—
279C3×#67—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×D12—81no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3—81no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—81no—
300#624—42no—
301#624—81no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—91no—
307C22×D8—91no—
308#546—31no—
309#546—91no—
310#495—91no—
311#467—31no—
312#466—91no—
313#463—91no—
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—
325C23×D3—121no—
326C3×#41—62no—
327C3×#41—121no—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—61no—
347C2×#67—61no—
348C2×#67#6711yescharacteristic
349#239—22no—
350#239—41no—
351#239—62no—
352#239—121no—
353#235—62no—
354#235—121no—
355C2×D12—22no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—41no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—122no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—122no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C3×Q16—62no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—62no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—41no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—41no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—21no—
412#217#6711yescharacteristic
413#216—22no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—122no—
418#215—121no—
419#215—121no—
420#215—121no—
421#215—122no—
422#214—62no—
423#214—121no—
424#213—34no—
425#213—62no—
426#213—62no—
427#213—62no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4#6711yescharacteristic
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3C22×D311yescharacteristic
445C2×C3⋊C8—22no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—34no—
456D24—62no—
457D24—62no—
458D24—62no—
459D3×C8—62no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32#13512yescomplemented
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—84no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—84no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4—41no—
484C32×C4C22×D411yescharacteristic
485C32×C4H(5,𝔽2)11yescharacteristic
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4—31no—
494C22×D4—91no—
495#135—184no—
496C2×Q16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×D8—184no—
506C22×C8—31no—
507C22×C8—91no—
508#124—31no—
509#124—91no—
510#123—61no—
511#123—181no—
512C22⋊Q8—31no—
513C22⋊Q8D3211yescharacteristic
514#121—31no—
515#121—61no—
516#121—91no—
517#121—181no—
518#120—61no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C22⋊C4—61no—
524C2×C22⋊C4—181no—
525#107—31no—
526C4⋊C8—91no—
527#103—31no—
528#103—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535C4×C8—91no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C23×C3D3×D411yescharacteristic
544C23×C3C2×#6711yescharacteristic
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—81no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—242no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—242no—
565C22×D3C2×#6711yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×D4—32no—
575C3×D4—62no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—241no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—122no—
604C2×C3×C4—241no—
605C2×C3×C4D3×D411yescharacteristic
606C2×C3×C4C2×#6711yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609#67—22no—
610#67—122no—
611#67—241no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3C2×#6711yescharacteristic
615C2×Dic3C2×#6711yescharacteristic
616C2×Dic3C2×#6711yescharacteristic
617D12—21no—
618D12—21no—
619D12—21no—
620D12—32no—
621D12—32no—
622D12—42no—
623D12—42no—
624D12—62no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—81no—
633D12—121no—
634D12—121no—
635D12—122no—
636D12—122no—
637D12—124no—
638D12—122no—
639D12—241no—
640D12D3×D412yes—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—42no—
644C4×D3—81no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—241no—
648C4×D3—241no—
649Dic6—21no—
650Dic6—21no—
651C3×C8—32no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—61no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C3⋊C8—121no—
659C3⋊C8—121no—
660C3⋊C8D3×D412yes—
661C2×C32—22no—
662C2×C32D4211yescharacteristic
663C2×C32C2×#13511yescharacteristic
664C2×C32#57611yescharacteristic
665C3⋊D3—42no—
666C3⋊D3—81no—
667C3×D3—41no—
668C3×D3—42no—
669C3×D3—81no—
670C24—61no—
671C24—181no—
672#41—62no—
673#41—121no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8C2×D3211yescharacteristic
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—62no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—91no—
687C2×D4—121no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—361no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—62no—
700SD16—182no—
701SD16—182no—
702SD16—361no—
703SD16—361no—
704D8—94no—
705D8—182no—
706D8—182no—
707D8—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—91no—
712C2×C8—91no—
713C2×C8—182no—
714C4⋊C4—21no—
715C4⋊C4—31no—
716C4⋊C4—31no—
717C4⋊C4—61no—
718C4⋊C4C2×D3211yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C42—31no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—62no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—244no—
750C22×C3#91912yescomplemented
751C22×C3#95012yescomplemented
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C22×#6711yescharacteristic
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—84no—
766C2×D3—122no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3—248no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—81no—
798C3×C4—81no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4C2×D3×D411yescharacteristic
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100411yescharacteristic
804C3×C4#100911yescharacteristic
805Dic3—21no—
806Dic3—21no—
807Dic3—21no—
808Dic3—41no—
809Dic3—41no—
810C32#328011yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—61no—
814C23—122no—
815C23—122no—
816C23—181no—
817C23—181no—
818C23—241no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23D3×#6711yescharacteristic
823Q8—21no—
824Q8—21no—
825Q8—61no—
826Q8—61no—
827D4—32no—
828D4—62no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—92no—
833D4—122no—
834D4—122no—
835D4—181no—
836D4—181no—
837D4—181no—
838D4—241no—
839D4—362no—
840D4—362no—
841D4—721no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—122no—
854C2×C4—241no—
855C2×C4—362no—
856C2×C4—721no—
857C2×C4D3×#6711yescharacteristic
858C2×C4C22×D3211yescharacteristic
859C8—32no—
860C8—61no—
861C8—181no—
862C8—181no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—42no—
869C2×C3—121no—
870C2×C3—122no—
871C2×C3—241no—
872C2×C3#560911yescharacteristic
873C2×C3C2×#91911yescharacteristic
874C2×C3#576911yescharacteristic
875C2×C3D4×#6711yescharacteristic
876C2×C3C2×#95011yescharacteristic
877C2×C3#583511yescharacteristic
878D3—41no—
879D3—42no—
880D3—81no—
881D3—122no—
882D3—122no—
883D3—242no—
884D3—242no—
885D3—241no—
886D3—241no—
887C22—21no—
888C22—21no—
889C22—61no—
890C22—61no—
891C22—61no—
892C22—62no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—182no—
899C22—244no—
900C22—361no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—724no—
906C22#6394912yescomplemented
907C22C2×D3×#6711yescharacteristic
908C4—21no—
909C4—41no—
910C4—41no—
911C4—61no—
912C4—61no—
913C4—61no—
914C4—121no—
915C4—121no—
916C4D32×D411yescharacteristic
917C4#6431411yescharacteristic
918C3—21no—
919C3#8077311yescharacteristic, complemented
920C3#8350511yescharacteristic, complemented
921C2—22no—
922C2—121no—
923C2—122no—
924C2—241no—
925C2—362no—
926C2—721no—
927C2#1059529111yescharacteristic
928C2C2×#6394911yescharacteristic
929C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5630C2semidirect
2. C2×#63949C2semidirect
3. #10595018C2semidirect
4. C22×#3714C2semidirect
5. #10592745C2semidirect
6. C3×#5051C2semidirect
7. #10591609C2semidirect
8. #10591588C2semidirect
9. #10591568C2semidirect
10. #10591169C2semidirect
11. C3⋊C8×#67C2semidirect
12. #10590615C2semidirect
13. #10590576C2semidirect
14. #10590534C2semidirect
15. #10590456C2semidirect
19. C2×C3×#239C22semidirect
21. C2×#3799C22semidirect
23. C2×#3755C22semidirect
24. C2×#3755C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#216C22semidirect
31. C3×#895C22semidirect
33. C3×#893C22semidirect
40. #63909C22semidirect
42. #63894C22semidirect
43. #63864C22semidirect
44. C2×#3715C22semidirect
45. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63636C22semidirect
54. #63636C22semidirect
55. C3×#835C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
69. #5630D3semidirect
78. #5051D3semidirect
154. #3714D4semidirect
160. C2×#239C2×D3semidirect
182. #947C2×D3semidirect
183. C2×#216C2×D3semidirect
215. #895C2×D3semidirect
220. #893C2×D3semidirect
232. #835C2×D3semidirect
242. #810C2×D3semidirect
251. #807C2×D3semidirect
462. C22×C32#135semidirect
750. C22×C3#919semidirect
751. C22×C3#950semidirect
810. C32#3280semidirect
906. C22#63949semidirect
919. C3#80773semidirect
920. C3#83505semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C2×#639492
#105950182
C22×#37142
#105927452
C3×#50512
#105916092
#105915882
#105915682
#105911692
C3⋊C8×#672
#105906152
#105905762
#105905342
#105904562
#835053
#807733