Finite Group Databasebeta

← #11885818

Subgroups — #11885818

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595427C211yesmaximal, characteristic, complemented
3#10595244C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591610C211yesmaximal, characteristic, complemented
9#10591586C211yesmaximal, characteristic, complemented
10#10591452C211yesmaximal, characteristic, complemented
11#10591435C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15#10590717C211yesmaximal, characteristic, complemented
16#83918—31nomaximal
17#80168—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63980—21no—
34#63976—21no—
35#63961—21no—
36C2×(C2×D3)⋊Dic3—21no—
37D3×#213—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic, complemented
42C4×#625C2211yescharacteristic
43#63898C2211yescharacteristic, complemented
44#63886—21no—
45#63863C2211yescharacteristic, complemented
46#63856C2211yescharacteristic
47#63850—21no—
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58#63575C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5829—31no—
66#5806—31no—
67C22×#213—31no—
68C2×#916D311yescharacteristic, complemented
69C2×D3×D8—31no—
70#5630—31no—
71C3×#450—31no—
72#5238—31no—
73#5238—31no—
74#5191—31no—
75#5188—31no—
76#5172—31no—
77#5169—31no—
78#5169D311yescharacteristic, complemented
79#5168—31no—
80#5165—31no—
81#5165—31no—
82#5165—31no—
83#5165—61no—
84Dic3×D8—31no—
85#5115—31no—
86C8×#67—31no—
87#5051—31no—
88#4787—31no—
89#4781—31no—
90#4775—31no—
91#4756—31no—
92#4731—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#239—22no—
104C3×#239—41no—
105C3×#237—22no—
106C3×#237—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#625D411yescharacteristic
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3753—22no—
127#3752—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C4×C3⋊Dic3C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#216—22no—
133C3×#215—41no—
134C3×#213D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×D3×C8—22no—
142#3724—21no—
143#3724D411yescharacteristic
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3717—41no—
153#3714—22no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×#237C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×D3×D4C2×D311yescharacteristic
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175#953—61no—
176C2×#217—61no—
177#947—31no—
178#947—31no—
179#947—31no—
180#947—61no—
181#946—31no—
182#946C2×D311yescharacteristic
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215C2×D311yescharacteristic, complemented
186#939—61no—
187#939—61no—
188#939—61no—
189#938—31no—
190#937—61no—
191#937—61no—
192#936—31no—
193#935—61no—
194D4×Dic3—31no—
195D4×Dic3—31no—
196D4×Dic3—31no—
197D4×Dic3—61no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—61no—
204C2×#213—64no—
205C2×#213C2×D311yescharacteristic
206#930—31no—
207#930—31no—
208#929—61no—
209#929—61no—
210C4×#67—31no—
211C4×#67—31no—
212C2×(C2×D3)⋊C4—61no—
213C2×(C2×D3)⋊C4—61no—
214#924—31no—
215C22×C3⋊C8—31no—
216#916—24no—
217D3×D8—64no—
218C2×D24—31no—
219C2×#204—31no—
220C2×#204C2×D311yescharacteristic, complemented
221C2×D3×C8—31no—
222C2×D3×C8C2×D311yescharacteristic, complemented
223#895—31no—
224#895—61no—
225#894—61no—
226#893—31no—
227#882—61no—
228D3×C22⋊C4—61no—
229C3×#102—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#832C2×D311yescharacteristic, complemented
238#830—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8C2×D311yescharacteristic
246#818—31no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—61no—
250C8×Dic3—31no—
251C8×Dic3—31no—
252#810—31no—
253#807—31no—
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×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4C2×D412yes—
270C2×C32×C4—21no—
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—81no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#626—81no—
299#625—22no—
300#625—81no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—31no—
307C22×D8—91no—
308#546—91no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—91no—
314#463—91no—
315#450—31no—
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—62no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—31no—
350C2×#67—31no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—21no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—121no—
360#239—22no—
361#239—41no—
362#237—22no—
363#237—41no—
364D3×D4—22no—
365D3×D4—41no—
366D3×D4—62no—
367D3×D4—121no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—121no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—61no—
380C2×C4×D3C22×D311yescharacteristic
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×Q16—62no—
384C3×SD16—22no—
385C3×SD16—22no—
386C3×SD16—42no—
387C3×SD16—62no—
388C3×SD16—121no—
389C3×D8—34no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—62no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—61no—
399#217—31no—
400#217—31no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—121no—
409#216—22no—
410#215—41no—
411#215—121no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—62no—
416#213—62no—
417#213—122no—
418#213#6714yescomplemented
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
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—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—121no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444C4×Dic3—31no—
445C4×Dic3—31no—
446C4×Dic3—61no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—62no—
454#204—22no—
455#204—121no—
456D3×C8—22no—
457D3×C8—62no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—84no—
477C2×C3×D3#13512yescomplemented
478D32—84no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492C22×D4—91no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16D3211yescharacteristic, complemented
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—184no—
504C22×C8—31no—
505C22×C8—91no—
506#124—91no—
507#124—91no—
508#123—181no—
509#123—181no—
510C22⋊Q8—31no—
511C22⋊Q8—91no—
512#121—91no—
513#121—91no—
514#121—181no—
515#121—181no—
516#120—181no—
517#120—181no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—91no—
521C2×C22⋊C4—181no—
522C2×C22⋊C4—181no—
523#107—91no—
524C4⋊C8—91no—
525#103—91no—
526#103—91no—
527#102—31no—
528#102—31no—
529#102—91no—
530#102—91no—
531C22⋊C8—31no—
532C22⋊C8—91no—
533C4×C8—91no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—31no—
538C23×C3—41no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—81no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—241no—
557C22×D3—241no—
558C22×D3D3×D411yescharacteristic
559C22×D3D3×D411yescharacteristic
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—41no—
565C3×Q8—41no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4D3×D412yes—
580C3×D4C2×#6712yes—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—42no—
599#67—62no—
600#67—62no—
601#67—122no—
602#67—241no—
603#67—241no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—42no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3—241no—
618C2×Dic3—241no—
619C2×Dic3—241no—
620C2×Dic3—242no—
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—42no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—121no—
632D12—121no—
633D12—122no—
634D12—241no—
635D12C2×#6712yes—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—241no—
642Dic6—21no—
643Dic6—21no—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—32no—
647C3×C8—41no—
648C3×C8—61no—
649C3⋊C8—21no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C3⋊C8—121no—
653C3⋊C8C2×#6712yes—
654C2×C32—42no—
655C2×C32D4211yescharacteristic
656C2×C32C2×#13511yescharacteristic
657C2×C32#57611yescharacteristic
658C3⋊D3—81no—
659C3×D3—22no—
660C3×D3—42no—
661C3×D3—41no—
662C3×D3—81no—
663C24—61no—
664C24—181no—
665#41—62no—
666#41—62no—
667#41—121no—
668#41—121no—
669C2×Q8—31no—
670C2×Q8C2×D3211yescharacteristic
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—62no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—121no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—361no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—181no—
691C22×C4—181no—
692Q16—62no—
693SD16—22no—
694SD16—62no—
695SD16—121no—
696SD16—361no—
697D8—34no—
698D8—182no—
699D8—182no—
700D8—182no—
701C2×C8—31no—
702C2×C8—31no—
703C2×C8—62no—
704C2×C8—91no—
705C2×C8—182no—
706C2×C8C2×D3211yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—61no—
709C4⋊C4—91no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C22⋊C4—61no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C42—91no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—32no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—62no—
739C22×C3—61no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—244no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—84no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—244no—
772C2×D3—244no—
773C2×D3#91612yescomplemented
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—61no—
779C3×C4—61no—
780C3×C4—81no—
781C3×C4—121no—
782C3×C4—121no—
783C3×C4C2×D3×D411yescharacteristic
784C3×C4#100411yescharacteristic
785C3×C4#100411yescharacteristic
786C3×C4C22×#6711yescharacteristic
787Dic3—21no—
788Dic3—21no—
789Dic3—41no—
790Dic3—41no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—121no—
796Dic3—121no—
797Dic3—121no—
798Dic3—121no—
799Dic3—241no—
800C32#328011yescharacteristic, complemented, Sylow
801C23—21no—
802C23—31no—
803C23—31no—
804C23—61no—
805C23—61no—
806C23—122no—
807C23—122no—
808C23—181no—
809C23—241no—
810C23—362no—
811C23—362no—
812C23—721no—
813Q8—21no—
814Q8—21no—
815Q8—61no—
816Q8—61no—
817D4—21no—
818D4—32no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—122no—
823D4—122no—
824D4—122no—
825D4—182no—
826D4—181no—
827D4—181no—
828D4—362no—
829D4—721no—
830D4—721no—
831D4D3×#6712yes—
832C2×C4—21no—
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—91no—
842C2×C4—91no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—181no—
846C2×C4—721no—
847C2×C4—721no—
848C2×C4C22×D3211yescharacteristic
849C8—21no—
850C8—32no—
851C8—61no—
852C8—181no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—62no—
859C2×C3—82no—
860C2×C3—122no—
861C2×C3—121no—
862C2×C3—241no—
863C2×C3#559011yescharacteristic
864C2×C3C2×#91611yescharacteristic
865C2×C3D3×#13511yescharacteristic
866C2×C3#576911yescharacteristic
867C2×C3#577411yescharacteristic
868C2×C3D4×#6711yescharacteristic
869D3—22no—
870D3—41no—
871D3—42no—
872D3—81no—
873D3—241no—
874D3—241no—
875D3—481no—
876C22—22no—
877C22—32no—
878C22—41no—
879C22—41no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—62no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—244no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—724no—
896C22D32×D411yescharacteristic
897C4—41no—
898C4—61no—
899C4—61no—
900C4—121no—
901C4—121no—
902C4—181no—
903C4—181no—
904C4—361no—
905C4#6431311yescharacteristic
906C4C2×D3×#6711yescharacteristic
907C3—21no—
908C3#8016811yescharacteristic, complemented
909C3#8391811yescharacteristic, complemented
910C2—42no—
911C2—62no—
912C2—121no—
913C2—122no—
914C2—241no—
915C2—721no—
916C2D3×#91611yescharacteristic
917C2#1059475511yescharacteristic
918C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. #10595427C2semidirect
3. #10595244C2semidirect
4. C2×D3×#213C2semidirect
5. #10592864C2semidirect
6. C3×#5169C2semidirect
7. #10591635C2semidirect
8. #10591610C2semidirect
9. #10591586C2semidirect
10. #10591452C2semidirect
11. #10591435C2semidirect
12. #10590942C2semidirect
13. #10590826C2semidirect
14. #10590750C2semidirect
15. #10590717C2semidirect
18. C2×C3×#239C22semidirect
19. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
23. #64156C22semidirect
24. D4×C3⋊Dic3C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
31. C2×C3×#204C22semidirect
32. C2×C3×D3×C8C22semidirect
40. #63909C22semidirect
41. #63908C22semidirect
43. #63898C22semidirect
45. #63863C22semidirect
48. C2×#3717C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63641C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
58. #63575C22semidirect
59. #63565C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63553C22semidirect
68. C2×#916D3semidirect
78. #5169D3semidirect
134. C3×#213D4semidirect
160. C2×#239C2×D3semidirect
161. C2×#237C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
183. C2×#216C2×D3semidirect
185. C2×#215C2×D3semidirect
220. C2×#204C2×D3semidirect
222. C2×D3×C8C2×D3semidirect
237. #832C2×D3semidirect
243. #821C2×D3semidirect
418. #213#67semidirect
477. C2×C3×D3#135semidirect
498. C2×SD16D32semidirect
773. C2×D3#916semidirect
800. C32#3280semidirect
908. C3#80168semidirect
909. C3#83918semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954272
#105952442
C2×D3×#2132
#105928642
C3×#51692
#105916352
#105916102
#105915862
#105914522
#105914352
#105909422
#105908262
#105907502
#105907172
#839183
#801683