Finite Group Databasebeta

← #11864639

Subgroups — #11864639

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×C3×#916C211yesmaximal, characteristic, complemented
3#10595232C211yesmaximal, characteristic, complemented
4C2×#63925C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591516C211yesmaximal, characteristic, complemented
11#10591515C211yesmaximal, characteristic, complemented
12#10590953C211yesmaximal, characteristic, complemented
13#10590943C211yesmaximal, characteristic, complemented
14#10590942C211yesmaximal, characteristic, complemented
15D3×#821C211yesmaximal, characteristic, complemented
16#83912—31nomaximal
17#80087—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic, complemented
22#64320—24no—
23#64320—24no—
24C2×#3802—21no—
25C2×#3802C2211yescharacteristic
26C2×D3×D12—21no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×#3798—21no—
31C2×#3798C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64147C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C3×#938C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#916—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic, complemented
42#63978—21no—
43#63971—21no—
44#63970—21no—
45#63964—21no—
46#63925—24no—
47D3×C4⋊Dic3C2211yescharacteristic, complemented
48#63871C2211yescharacteristic, complemented
49#63856C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C2×C3×#135—31no—
68#5833—31no—
69C2×#949—31no—
70C2×#916D311yescharacteristic, complemented
71C2×#911—31no—
72#5608—31no—
73C3×#449—31no—
74#5239—31no—
75#5232—31no—
76#5187—31no—
77#5187—31no—
78#5172—31no—
79#5172—31no—
80#5172—61no—
81#5172D311yescharacteristic, complemented
82#5169—31no—
83#5169—31no—
84#5156—31no—
85#5156—31no—
86#5156—31no—
87C2×#821—31no—
88#5110—31no—
89#5036—31no—
90#4808—31no—
91#4803—31no—
92#4776—31no—
93D3×#102—31no—
94#4731—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102#3832—22no—
103#3832—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×#239—22no—
112C3×#239—22no—
113C3×#239—22no—
114C3×#239D414yescomplemented
115C3×#237—22no—
116C3×#237—22no—
117C2×C3×D12—21no—
118C2×C3×D12—21no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×Dic6C2311yescharacteristic
126C2×#627D411yescharacteristic
127C2×#626—21no—
128C2×#626—21no—
129C2×#626D411yescharacteristic
130C2×#626D411yescharacteristic
131C2×#625—21no—
132C2×#625D411yescharacteristic
133C2×D3×Dic3—21no—
134#3802—28no—
135#3802—22no—
136#3802—22no—
137D3×D12—28no—
138D3×D12—28no—
139D3×D12—22no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12D414yescomplemented
143#3798—28no—
144#3798—22no—
145#3798—22no—
146C32×SD16—22no—
147C2×C32×C8C2311yescharacteristic
148#3757—21no—
149#3753—22no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#217—21no—
153C3×#216—22no—
154C3×#213—22no—
155C3×#213—22no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×D3×C8—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3717—22no—
167#3715—22no—
168#3711—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176#1009—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic
182C2×#237C2×D311yescharacteristic, complemented
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C3×#135—64no—
200C2×C3×Q16—31no—
201C2×C3×SD16—21no—
202C2×C3×SD16—31no—
203C2×C3×SD16C2×D311yescharacteristic, complemented
204C2×C3×SD16C2×D311yescharacteristic, complemented
205C2×C3×D8—31no—
206C2×C3×D8—31no—
207C22×C3×C8—31no—
208C3×#121—31no—
209#949—64no—
210#946—31no—
211#946—31no—
212C2×#216C2×D311yescharacteristic, complemented
213C2×#215—31no—
214C2×#215—31no—
215#939—61no—
216#939—61no—
217#939—61no—
218#938—31no—
219#938—31no—
220#938—61no—
221#938—61no—
222#938C2×D311yescharacteristic, complemented
223C2×#214—31no—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—61no—
227C2×#213C2×D311yescharacteristic, complemented
228C2×#213C2×D311yescharacteristic, complemented
229#930—61no—
230C2×C4⋊Dic3—31no—
231#924—31no—
232#924—61no—
233C2×#208—31no—
234#916—24no—
235#911—64no—
236C2×#204—31no—
237C2×#204C2×D311yescharacteristic, complemented
238C2×ΓL(1,𝔽25)—31no—
239C2×D3×C8C2×D311yescharacteristic, complemented
240#897—31no—
241D3×C4⋊C4—31no—
242#884—61no—
243#878—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—61no—
268(C2×D3)⋊C8C2×D311yescharacteristic, complemented
269#809—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—24no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8C2×D412yes—
289C32×D4—21no—
290C32×D4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2411yescharacteristic
293#638—81no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3C2×D411yescharacteristic
296C4⋊(C3⋊D3)—24no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4×C3⋊D3—24no—
300C4×C3⋊D3—21no—
301C4×C3⋊D3—21no—
302C3×#67—42no—
303C3×#67—81no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—42no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—24no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yes—
314C3×D12C2×D412yes—
315C3×C4×D3—24no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—24no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321C3×Dic6—21no—
322C3×Dic6—21no—
323#627—22no—
324#626—24no—
325#626—22no—
326#626—22no—
327#626—24no—
328#625—24no—
329#625—22no—
330D3×Dic3—81no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—31no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—34no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—62no—
362C2×C3×Q8—21no—
363C2×C3×Q8—31no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D311yescharacteristic
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—61no—
378C22×C3×C4—61no—
379C22×C3×C4—61no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—31no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—121no—
393C22×Dic3—21no—
394C22×Dic3—61no—
395#239—22no—
396#239—22no—
397#239—22no—
398#239—62no—
399#239—62no—
400#239—62no—
401#239—62no—
402#239—122no—
403#239—122no—
404#239#6714yescomplemented
405#237—22no—
406#237—22no—
407D3×D4—34no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—68no—
411D3×D4—68no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—68no—
415D3×D4—68no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419#235—62no—
420#235—62no—
421#235—68no—
422#235—68no—
423#235—62no—
424#235—62no—
425C2×D12—21no—
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—62no—
435C2×D12—68no—
436C2×D12—68no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—62no—
442C2×D12—121no—
443C2×D12C22×D311yescharacteristic
444C2×D12C22×D311yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—121no—
454C2×C4×D3C22×D311yescharacteristic
455C2×C4×D3C22×D311yescharacteristic
456C2×Dic6—31no—
457C2×Dic6—31no—
458C2×Dic6C22×D311yescharacteristic
459C3×Q16—62no—
460C3×SD16—22no—
461C3×SD16—22no—
462C3×SD16—42no—
463C3×SD16—62no—
464C3×D8—62no—
465C3×D8—62no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8—62no—
470C2×C3×C8C22×D311yescharacteristic
471C2×C3×C8C22×D311yescharacteristic
472C3×C4⋊C4—31no—
473C3×C22⋊C4—61no—
474#217—21no—
475#217—61no—
476#217—61no—
477#217—61no—
478#217—121no—
479#216—22no—
480#215—62no—
481#215—62no—
482#214—62no—
483#213—22no—
484#213—22no—
485#213—62no—
486#213—62no—
487#213—122no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—61no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—61no—
494C4⋊Dic3—61no—
495C4⋊Dic3—61no—
496C4⋊Dic3C22×D311yescharacteristic
497Dic3⋊C4—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—61no—
500Dic3⋊C4—61no—
501#208—62no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—31no—
504C2×C3⋊C8—61no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507#204—22no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—22no—
511C22×C32—41no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3#12012yes—
533D32—84no—
534D32—84no—
535D32—84no—
536C32×C4—22no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—21no—
540C3⋊Dic3—41no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—64no—
561C2×Q16—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16D3211yescharacteristic, complemented
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—31no—
581#103—91no—
582#102—31no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—41no—
597C23×C3—61no—
598C23×C3—61no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—61no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—64no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—64no—
612C22×D3—121no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3D3×D411yescharacteristic
626C22×D3D3×D411yescharacteristic
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—22no—
630C3×Q8—41no—
631C3×Q8—61no—
632C3×Q8—61no—
633C3×Q8D3×D412yes—
634C3×Q8C2×#6712yes—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—32no—
640C3×D4—32no—
641C3×D4—41no—
642C3×D4—41no—
643C3×D4—64no—
644C3×D4—64no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—122no—
648C3×D4—241no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—31no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—31no—
656C2×C3×C4—41no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—122no—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666#67—42no—
667#67—62no—
668#67—64no—
669#67—62no—
670#67—64no—
671#67—64no—
672#67—62no—
673#67—64no—
674#67—62no—
675#67—81no—
676#67—241no—
677#67—241no—
678#67—242no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—42no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—121no—
688C2×Dic3—241no—
689C2×Dic3D3×D411yescharacteristic
690C2×Dic3D3×D411yescharacteristic
691D12—24no—
692D12—24no—
693D12—21no—
694D12—21no—
695D12—32no—
696D12—32no—
697D12—62no—
698D12—64no—
699D12—64no—
700D12—62no—
701D12—64no—
702D12—64no—
703D12—62no—
704D12—61no—
705D12—61no—
706D12—121no—
707D12—124no—
708D12D3×D412yes—
709D12C2×#6712yes—
710C4×D3—24no—
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—24no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—61no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—121no—
721C4×D3—121no—
722C4×D3—124no—
723C4×D3—241no—
724C4×D3D3×D412yes—
725C4×D3C2×#6712yes—
726Dic6—21no—
727Dic6—21no—
728Dic6—62no—
729Dic6—62no—
730C3×C8—21no—
731C3×C8—21no—
732C3×C8—41no—
733C3×C8—61no—
734C3×C8—61no—
735C3⋊C8—21no—
736C3⋊C8—21no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—121no—
740C2×C32—81no—
741C2×C32C2×#12011yescharacteristic
742C2×C32#57611yescharacteristic
743C2×C32#57711yescharacteristic
744C3⋊D3—41no—
745C3⋊D3—42no—
746C3×D3—22no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—42no—
750C24—181no—
751C24—181no—
752C24—181no—
753#41—34no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—182no—
760#41—182no—
761#41—188no—
762#41—182no—
763#41—182no—
764C2×Q8—31no—
765C2×Q8—91no—
766C2×Q8C2×D3211yescharacteristic
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—61no—
772C2×D4—61no—
773C2×D4—94no—
774C2×D4—91no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—181no—
779C2×D4—182no—
780C2×D4—181no—
781C2×D4—181no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—188no—
785C2×D4—188no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—188no—
790C2×D4—181no—
791C2×D4C2×D3211yescharacteristic
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—91no—
798C22×C4—181no—
799C22×C4—181no—
800Q16—62no—
801SD16—22no—
802SD16—62no—
803SD16—182no—
804SD16—182no—
805D8—62no—
806D8—62no—
807D8—182no—
808M16—182no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—62no—
812C2×C8—91no—
813C2×C8C2×D3211yescharacteristic
814C4⋊C4—31no—
815C4⋊C4—91no—
816C4⋊C4—181no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C22⋊C4—61no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22×C3—21no—
824C22×C3—32no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—61no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—62no—
836C22×C3—61no—
837C22×C3—62no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×D3×D411yescharacteristic
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—22no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—62no—
863C2×D3—61no—
864C2×D3—62no—
865C2×D3—61no—
866C2×D3—122no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—244no—
877C2×D3—244no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3#93712yes—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—42no—
889C3×C4—61no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C22×#6711yescharacteristic
896Dic3—21no—
897Dic3—41no—
898Dic3—41no—
899Dic3—61no—
900Dic3—61no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—241no—
905Dic3#93712yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—21no—
908C23—31no—
909C23—31no—
910C23—61no—
911C23—61no—
912C23—91no—
913C23—184no—
914C23—184no—
915C23—184no—
916C23—181no—
917C23—721no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923Q8—21no—
924Q8—61no—
925Q8—61no—
926Q8—182no—
927Q8D3×#6712yes—
928D4—21no—
929D4—21no—
930D4—32no—
931D4—32no—
932D4—64no—
933D4—64no—
934D4—61no—
935D4—61no—
936D4—92no—
937D4—122no—
938D4—184no—
939D4—184no—
940D4—182no—
941D4—182no—
942D4—184no—
943D4—182no—
944D4—184no—
945D4—181no—
946D4—241no—
947D4—721no—
948C2×C4—21no—
949C2×C4—31no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—31no—
953C2×C4—64no—
954C2×C4—64no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—91no—
960C2×C4—122no—
961C2×C4—184no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—721no—
966C2×C4C22×D3211yescharacteristic
967C8—21no—
968C8—61no—
969C8—61no—
970C8—181no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—62no—
975C2×C3—81no—
976C2×C3—81no—
977C2×C3—121no—
978C2×C3—122no—
979C2×C3—122no—
980C2×C3—161no—
981C2×C3D3×#12011yescharacteristic
982C2×C3#576911yescharacteristic
983C2×C3#577011yescharacteristic
984C2×C3#577011yescharacteristic
985C2×C3#577411yescharacteristic
986C2×C3C2×#93711yescharacteristic
987D3—22no—
988D3—42no—
989D3—41no—
990D3—42no—
991D3—121no—
992D3—122no—
993D3—121no—
994D3—122no—
995D3—241no—
996D3—242no—
997C22—32no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—61no—
1005C22—62no—
1006C22—62no—
1007C22—61no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—181no—
1013C22—181no—
1014C22—182no—
1015C22—181no—
1016C22—361no—
1017C22—361no—
1018C22—724no—
1019C22—724no—
1020C22—724no—
1021C22D32×D411yescharacteristic
1022C4—22no—
1023C4—32no—
1024C4—61no—
1025C4—121no—
1026C4—121no—
1027C4—181no—
1028C4—361no—
1029C4D32×D411yescharacteristic
1030C4C2×D3×#6711yescharacteristic
1031C3—21no—
1032C3#8008711yescharacteristic, complemented
1033C3#8391211yescharacteristic, complemented
1034C2—62no—
1035C2—81no—
1036C2—121no—
1037C2—122no—
1038C2—122no—
1039C2—361no—
1040C2—362no—
1041C2#1059475511yescharacteristic
1042C2#1059475711yescharacteristic
1043C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3012
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×#64320C2semidirect
2. C2×C3×#916C2semidirect
3. #10595232C2semidirect
4. C2×#63925C2semidirect
5. #10592871C2semidirect
6. C3×#5172C2semidirect
7. #10591602C2semidirect
8. #10591597C2semidirect
9. #10591550C2semidirect
10. #10591516C2semidirect
11. #10591515C2semidirect
12. #10590953C2semidirect
13. #10590943C2semidirect
14. #10590942C2semidirect
15. D3×#821C2semidirect
21. C2×C3×#237C22semidirect
32. C2×C32×SD16C22semidirect
33. #64147C22semidirect
34. C2×#3753C22semidirect
35. C2×C3×#216C22semidirect
36. C3×#938C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×D3×C8C22semidirect
47. D3×C4⋊Dic3C22semidirect
48. #63871C22semidirect
49. #63856C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
52. C2×#3711C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#916D3semidirect
81. #5172D3semidirect
114. C3×#239D4semidirect
142. D3×D12D4semidirect
182. C2×#237C2×D3semidirect
203. C2×C3×SD16C2×D3semidirect
204. C2×C3×SD16C2×D3semidirect
212. C2×#216C2×D3semidirect
222. #938C2×D3semidirect
227. C2×#213C2×D3semidirect
228. C2×#213C2×D3semidirect
237. C2×#204C2×D3semidirect
239. C2×D3×C8C2×D3semidirect
250. #835C2×D3semidirect
261. #821C2×D3semidirect
268. (C2×D3)⋊C8C2×D3semidirect
404. #239#67semidirect
565. C2×SD16D32semidirect
906. C32#3012semidirect
1032. C3#80087semidirect
1033. C3#83912semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×C3×#9162
#105952322
C2×#639252
#105928712
C3×#51722
#105916022
#105915972
#105915502
#105915162
#105915152
#105909532
#105909432
#105909422
D3×#8212
#839123
#800873