Finite Group Databasebeta

← #11863902

Subgroups — #11863902

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10594892C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10591420C211yesmaximal, characteristic, complemented
13#10591173C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15D3×#830C211yesmaximal, characteristic, complemented
16#84080—31nomaximal
17#80082—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×C4×D3—21no—
30C22×C3×C4×D3C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C3×#930C2211yescharacteristic, complemented
38#63976—21no—
39Dic3×#67—21no—
40#63947—24no—
41#63933—24no—
42#63908C2211yescharacteristic
43#63905—21no—
44#63879—21no—
45#63857C2211yescharacteristic
46#63841C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C22×C3×#41—31no—
66C2×D3×#41D311yescharacteristic, complemented
67C2×#950—31no—
68C2×#950—31no—
69#5791—31no—
70C2×#916—31no—
71C2×#912—31no—
72#5606—31no—
73C3×#449—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—61no—
78#5238—31no—
79#5238D311yescharacteristic, complemented
80#5233—31no—
81#5233—31no—
82#5228—31no—
83#5227—31no—
84#5218—31no—
85#5217—31no—
86C2×#830—31no—
87#5170—31no—
88#5156—31no—
89#5037—31no—
90#4809—31no—
91#4804—31no—
92#4776—31no—
93#4772—31no—
94#4733—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C23×C3×D3D411yescharacteristic
98C32×#41—22no—
99C32×#41—22no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3D411yescharacteristic
112C3×#239—22no—
113C3×#239D414yescomplemented
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×#237—28no—
117C3×#237—22no—
118C3×#237D414yescomplemented
119C3×D3×D4—28no—
120C3×D3×D4—22no—
121C3×D3×D4—22no—
122C3×#235—28no—
123C3×#235—22no—
124C3×#235—22no—
125C2×C3×D12—21no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3—28no—
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3—22no—
134C2×C3×C4×D3D411yescharacteristic
135C2×C3×C4×D3D411yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6—21no—
139C2×C3×Dic6C2311yescharacteristic
140C2×#625—21no—
141C2×#625—21no—
142C2×D3×Dic3—21no—
143#3795—22no—
144#3795—22no—
145#3757—21no—
146#3756—22no—
147#3754—22no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#215—22no—
153C3×#213—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158Dic3⋊Dic3—21no—
159(C2×D3)⋊Dic3—21no—
160(C2×D3)⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162Dic32—21no—
163#3719—22no—
164#3716—22no—
165#3715—22no—
166#3713—22no—
167D3×C3⋊C8—22no—
168D3×C3⋊C8—22no—
169#3002—91noSylow
170C2×C3×#41—21no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—61no—
175C2×C3×#41—61no—
176C2×C3×#41—64no—
177C2×C3×#41—64no—
178C2×C3×#41C2×D311yescharacteristic
179C2×C3×#41C2×D311yescharacteristic
180C22×C3×Q8—31no—
181C22×C3×D4—31no—
182C22×C3×D4—61no—
183C23×C3×C4—31no—
184C23×C3×C4—61no—
185D3×#41—24no—
186D3×#41—24no—
187C2×#239C2×D311yescharacteristic
188C2×D3×Q8C2×D311yescharacteristic
189C2×#237—21no—
190C2×#237—31no—
191C2×#237C2×D311yescharacteristic
192C2×D3×D4—21no—
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235—31no—
196C2×#235C2×D311yescharacteristic
197C22×C4×D3—21no—
198C22×C4×D3C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C3×#121—31no—
202#953—61no—
203#950—64no—
204#950—64no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—61no—
209C2×#215—31no—
210C2×#215C2×D311yescharacteristic, complemented
211#938—31no—
212#937—61no—
213D4×Dic3—61no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—61no—
219C2×#213—31no—
220C2×#213—31no—
221C2×#213C2×D311yescharacteristic, complemented
222#930—31no—
223#930C2×D311yescharacteristic, complemented
224#929—61no—
225C4×#67—61no—
226C4×#67—61no—
227#926—31no—
228#924—31no—
229#924—31no—
230#924—31no—
231#924—61no—
232C22×C3⋊C8—31no—
233C22×C3⋊C8—31no—
234#916—64no—
235#912—64no—
236C2×Dic12—31no—
237C2×#204—31no—
238C2×D3×C8—31no—
239C2×D3×C8—31no—
240#897—31no—
241#892—31no—
242#883—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—61no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#832—31no—
255#832—31no—
256#832—31no—
257#832—61no—
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—21no—
278C22×C3×D3—41no—
279C22×C3×D3—42no—
280C22×C3×D3—42no—
281C22×C3×D3C2×D411yescharacteristic
282C22×C3×D3C2×D411yescharacteristic
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C32×D4—24no—
286C32×D4—21no—
287C32×D4C2×D412yes—
288C2×C32×C4—24no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2×D411yescharacteristic
293C2×C32×C4C2411yescharacteristic
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296#634—21no—
297#634—21no—
298C3×#67—24no—
299C3×#67—24no—
300C3×#67—24no—
301C3×#67—42no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—24no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12C2×D412yes—
313C3×C4×D3—24no—
314C3×C4×D3—24no—
315C3×C4×D3—22no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—22no—
319C3×C4×D3—24no—
320C3×C4×D3C2×D412yes—
321C3×C4×D3C2×D412yes—
322C3×Dic6—24no—
323C3×Dic6—21no—
324C3×Dic6C2×D412yes—
325#625—42no—
326#625—42no—
327D3×Dic3—42no—
328C3⋊(C3⋊C8)—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—31no—
333C2×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—91no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—31no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—91no—
347C24×C3—31no—
348C24×C3—61no—
349C23×D3—21no—
350C23×D3#6711yescharacteristic
351C3×#41—22no—
352C3×#41—22no—
353C3×#41—22no—
354C3×#41—22no—
355C3×#41—34no—
356C3×#41—34no—
357C3×#41—42no—
358C3×#41—42no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—68no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—68no—
365C2×C3×Q8—21no—
366C2×C3×Q8—31no—
367C2×C3×Q8—61no—
368C2×C3×Q8—62no—
369C2×C3×Q8—62no—
370C2×C3×Q8C22×D311yescharacteristic
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—31no—
376C2×C3×D4—31no—
377C2×C3×D4—41no—
378C2×C3×D4—61no—
379C2×C3×D4—61no—
380C2×C3×D4—62no—
381C2×C3×D4—68no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C2×C3×D4—62no—
385C2×C3×D4—61no—
386C2×C3×D4C22×D311yescharacteristic
387C2×C3×D4C22×D311yescharacteristic
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—41no—
397C22×C3×C4—62no—
398C22×C3×C4—62no—
399C22×C3×C4—61no—
400C22×C3×C4—61no—
401C22×C3×C4—68no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C2×#67—21no—
407C2×#67—21no—
408C2×#67—21no—
409C2×#67—21no—
410C2×#67—61no—
411C2×#67—61no—
412C2×#67—61no—
413C2×#67—61no—
414C22×Dic3—21no—
415C22×Dic3—61no—
416C22×Dic3#6711yescharacteristic
417#239—22no—
418#239#6714yescomplemented
419D3×Q8—22no—
420D3×Q8—22no—
421#237—28no—
422#237—22no—
423#237—62no—
424#237—62no—
425#237#6714yescomplemented
426D3×D4—28no—
427D3×D4—22no—
428D3×D4—22no—
429#235—28no—
430#235—22no—
431#235—22no—
432#235—62no—
433#235—62no—
434C2×D12—21no—
435C2×D12C22×D311yescharacteristic
436C2×D12C22×D311yescharacteristic
437C2×C4×D3—28no—
438C2×C4×D3—21no—
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3—22no—
442C2×C4×D3—22no—
443C2×C4×D3—61no—
444C2×C4×D3#6711yescharacteristic
445C2×C4×D3#6711yescharacteristic
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D311yescharacteristic
448C2×Dic6—21no—
449C2×Dic6—31no—
450C2×Dic6—31no—
451C2×Dic6—61no—
452C2×Dic6C22×D311yescharacteristic
453C3×SD16—62no—
454C3×D8—62no—
455C2×C3×C8—31no—
456C2×C3×C8—31no—
457C3×C4⋊C4—31no—
458C3×C22⋊C4—61no—
459#217—61no—
460#217—61no—
461#217—61no—
462#217—61no—
463#217—61no—
464#217—121no—
465#216—62no—
466#216—62no—
467#216—62no—
468#216—122no—
469#215—22no—
470#215—62no—
471#214—62no—
472#214—62no—
473#214—62no—
474#214—62no—
475#214—122no—
476#213—22no—
477#213—62no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3C22×D311yescharacteristic
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—121no—
492C4×Dic3—61no—
493C4×Dic3—61no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—62no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—62no—
505#204—62no—
506D3×C8—62no—
507D3×C8—62no—
508C22×C32—21no—
509C22×C32—22no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—22no—
520C2×C3×D3—44no—
521C2×C3×D3—48no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3#12012yes—
528C2×C3×D3#13512yescomplemented
529C32×C4—22no—
530C32×C4—21no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—41no—
534C3⋊Dic3—41no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—61no—
543C2×#41—61no—
544C2×#41—64no—
545C2×#41—64no—
546C2×#41—91no—
547C2×#41D3211yescharacteristic
548C22×Q8—31no—
549C22×D4—31no—
550C22×D4—61no—
551C23×C4—31no—
552C23×C4—61no—
553#135—184no—
554#135—184no—
555C2×Q16—91no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—31no—
562C2×D8—91no—
563C22×C8—91no—
564C22×C8—91no—
565#123—181no—
566C22⋊Q8—91no—
567C22⋊Q8—91no—
568#121—31no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—31no—
590C23×C3—31no—
591C23×C3—41no—
592C23×C3—62no—
593C23×C3—62no—
594C23×C3—64no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—121no—
598C23×C3—122no—
599C23×C3—122no—
600C23×C3D3×D411yescharacteristic
601C23×C3C2×#6711yescharacteristic
602C22×D3—24no—
603C22×D3—21no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—21no—
607C22×D3—41no—
608C22×D3—42no—
609C22×D3—42no—
610C22×D3C2×#6711yescharacteristic
611C22×D3C2×#6711yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—22no—
615C3×Q8—32no—
616C3×Q8—41no—
617C3×Q8—64no—
618C3×Q8—61no—
619C3×Q8D3×D412yes—
620C3×Q8C2×#6712yes—
621C3×D4—24no—
622C3×D4—24no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—22no—
626C3×D4—32no—
627C3×D4—41no—
628C3×D4—44no—
629C3×D4—64no—
630C3×D4—64no—
631C3×D4—64no—
632C3×D4—64no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—122no—
637C3×D4D3×D412yes—
638C3×D4C2×#6712yes—
639C2×C3×C4—24no—
640C2×C3×C4—24no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—31no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—31no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—44no—
657C2×C3×C4—62no—
658C2×C3×C4—64no—
659C2×C3×C4—62no—
660C2×C3×C4—64no—
661C2×C3×C4—64no—
662C2×C3×C4—62no—
663C2×C3×C4—64no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4D3×D411yescharacteristic
669C2×C3×C4C2×#6711yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672#67—24no—
673#67—24no—
674#67—24no—
675#67—42no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—122no—
680C2×Dic3—21no—
681C2×Dic3—22no—
682C2×Dic3—24no—
683C2×Dic3—21no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—122no—
691C2×Dic3C2×#6711yescharacteristic
692C2×Dic3C2×#6711yescharacteristic
693D12—24no—
694D12—21no—
695D12—21no—
696D12—21no—
697D12C2×#6712yes—
698C4×D3—24no—
699C4×D3—24no—
700C4×D3—22no—
701C4×D3—21no—
702C4×D3—21no—
703C4×D3—22no—
704C4×D3—24no—
705C4×D3—122no—
706C4×D3C2×#6712yes—
707C4×D3C2×#6712yes—
708Dic6—24no—
709Dic6—21no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—121no—
715Dic6—121no—
716Dic6C2×#6712yes—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—121no—
726C3⋊C8—121no—
727C2×C32—41no—
728C2×C32—42no—
729C2×C32C2×#12011yescharacteristic
730C2×C32C2×#13511yescharacteristic
731C2×C32#57511yescharacteristic
732C3×D3—22no—
733C3×D3—22no—
734C3×D3—42no—
735C3×D3—81no—
736C24—31no—
737C24—61no—
738#41—22no—
739#41—22no—
740#41—34no—
741#41—34no—
742#41—62no—
743#41—62no—
744#41—68no—
745#41—62no—
746#41—62no—
747#41—68no—
748#41—182no—
749#41—182no—
750C2×Q8—31no—
751C2×Q8—61no—
752C2×Q8—62no—
753C2×Q8—62no—
754C2×Q8—91no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—21no—
757C2×D4—31no—
758C2×D4—31no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—62no—
762C2×D4—68no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—62no—
766C2×D4—61no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4C2×D3211yescharacteristic
770C22×C4—21no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—62no—
777C22×C4—62no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—68no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—181no—
784C22×C4C2×D3211yescharacteristic
785Q16—182no—
786Q16—182no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791D8—62no—
792D8—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—91no—
796C2×C8—91no—
797C2×C8—182no—
798C2×C8—182no—
799C4⋊C4—31no—
800C4⋊C4—91no—
801C4⋊C4—181no—
802C4⋊C4—181no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—22no—
815C22×C3—21no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—32no—
819C22×C3—32no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—61no—
831C22×C3—61no—
832C22×C3—62no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—124no—
836C22×C3—128no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3C2×D3×D411yescharacteristic
843C22×C3C22×#6711yescharacteristic
844C2×D3—21no—
845C2×D3—21no—
846C2×D3—21no—
847C2×D3—21no—
848C2×D3—22no—
849C2×D3—44no—
850C2×D3—48no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3#95012yescomplemented
857C2×D3#95312yes—
858C3×C4—22no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—22no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—32no—
865C3×C4—41no—
866C3×C4—42no—
867C3×C4—61no—
868C3×C4—62no—
869C3×C4—121no—
870C3×C4C2×D3×D411yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C22×#6711yescharacteristic
873C3×C4C22×#6711yescharacteristic
874Dic3—21no—
875Dic3—22no—
876Dic3—41no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—241no—
882Dic3—241no—
883Dic3#95312yes—
884C32#300211yescharacteristic, complemented, Sylow
885C23—21no—
886C23—31no—
887C23—31no—
888C23—62no—
889C23—62no—
890C23—64no—
891C23—61no—
892C23—61no—
893C23—121no—
894C23—122no—
895C23—122no—
896C23D3×#6711yescharacteristic
897Q8—21no—
898Q8—32no—
899Q8—64no—
900Q8—61no—
901Q8—181no—
902Q8—181no—
903Q8D3×#6712yes—
904D4—24no—
905D4—21no—
906D4—32no—
907D4—64no—
908D4—64no—
909D4—64no—
910D4—64no—
911D4—61no—
912D4—61no—
913D4—61no—
914D4—122no—
915D4—362no—
916D4—362no—
917D4D3×#6712yes—
918C2×C4—24no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—31no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—31no—
926C2×C4—62no—
927C2×C4—64no—
928C2×C4—62no—
929C2×C4—64no—
930C2×C4—64no—
931C2×C4—62no—
932C2×C4—64no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4—362no—
940C2×C4D3×#6711yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C8—61no—
943C8—61no—
944C8—181no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—42no—
953C2×C3—62no—
954C2×C3—62no—
955C2×C3—81no—
956C2×C3—82no—
957C2×C3—122no—
958C2×C3—241no—
959C2×C3D3×#12011yescharacteristic
960C2×C3D3×#13511yescharacteristic
961C2×C3#577311yescharacteristic
962C2×C3C2×#95011yescharacteristic
963C2×C3#582211yescharacteristic
964C2×C3C2×#95311yescharacteristic
965D3—22no—
966D3—22no—
967D3—42no—
968D3—81no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—32no—
974C22—32no—
975C22—41no—
976C22—41no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—62no—
982C22—124no—
983C22—128no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22C2×D3×#6711yescharacteristic
990C4—21no—
991C4—22no—
992C4—32no—
993C4—61no—
994C4—62no—
995C4—121no—
996C4—361no—
997C4—361no—
998C4C2×D3×#6711yescharacteristic
999C4C2×D3×#6711yescharacteristic
1000C3—21no—
1001C3#8008211yescharacteristic, complemented
1002C3#8408011yescharacteristic, complemented
1003C2—41no—
1004C2—42no—
1005C2—62no—
1006C2—62no—
1007C2—122no—
1008C2—241no—
1009C2D3×#95011yescharacteristic
1010C2#1059546911yescharacteristic
1011C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×#63947C2semidirect
3. C2×#63933C2semidirect
4. #10594892C2semidirect
5. #10592938C2semidirect
6. C3×#5238C2semidirect
7. #10591595C2semidirect
8. #10591583C2semidirect
9. #10591556C2semidirect
10. #10591459C2semidirect
11. #10591447C2semidirect
12. #10591420C2semidirect
13. #10591173C2semidirect
14. #10591161C2semidirect
15. D3×#830C2semidirect
31. C2×#3795C22semidirect
32. C2×#3756C22semidirect
33. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×#213C22semidirect
37. C3×#930C22semidirect
46. #63841C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
66. C2×D3×#41D3semidirect
79. #5238D3semidirect
113. C3×#239D4semidirect
118. C3×#237D4semidirect
210. C2×#215C2×D3semidirect
221. C2×#213C2×D3semidirect
223. #930C2×D3semidirect
252. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
418. #239#67semidirect
425. #237#67semidirect
528. C2×C3×D3#135semidirect
856. C2×D3#950semidirect
884. C32#3002semidirect
1001. C3#80082semidirect
1002. C3#84080semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#639472
C2×#639332
#105948922
#105929382
C3×#52382
#105915952
#105915832
#105915562
#105914592
#105914472
#105914202
#105911732
#105911612
D3×#8302
#840803
#800823