Finite Group Databasebeta

← #11864644

Subgroups — #11864644

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×C3×#919C211yesmaximal, characteristic, complemented
3#10595398C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591550C211yesmaximal, characteristic, complemented
12#10590953C211yesmaximal, characteristic, complemented
13#10590945C211yesmaximal, characteristic, complemented
14#10590944C211yesmaximal, characteristic, complemented
15D3×#821C211yesmaximal, characteristic, complemented
16#83912—31nomaximal
17#80231—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic, 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×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C3×#919—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic, complemented
42#63939—24no—
43#63916C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic, complemented
47#63886—21no—
48#63885—21no—
49#63851—21no—
50C2×#3714C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, 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×#919D311yescharacteristic, complemented
71C2×#914—31no—
72#5629—31no—
73C3×#452—31no—
74#5238—31no—
75#5232—31no—
76#5187—31no—
77#5187—31no—
78#5187—61no—
79#5187D311yescharacteristic, complemented
80#5172—31no—
81#5172—31no—
82#5169—31no—
83#5169—31no—
84#5169—31no—
85#5156—31no—
86#5156—31no—
87C2×#821—31no—
88#5110—31no—
89#5046—31no—
90#4810—31no—
91#4803—31no—
92#4773—31no—
93D3×#102—31no—
94#4732—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101#3832—22no—
102#3832—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239—22no—
112C3×#239D414yescomplemented
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×#627D411yescharacteristic
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626D411yescharacteristic
129C2×#626D411yescharacteristic
130C2×#625—21no—
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×Q16—22no—
147C2×C32×C8C2311yescharacteristic
148#3755—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151#3750—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#215—22no—
154C3×#215—22no—
155C3×#215—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×D3×C8—22no—
163Dic3⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3714—22no—
167#3713—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×#239C2×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—21no—
201C2×C3×Q16C2×D311yescharacteristic, complemented
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×D8—31no—
207C22×C3×C8—31no—
208C3×C22⋊Q8—31no—
209#949—64no—
210#946—31no—
211#946—31no—
212#946—61no—
213#946C2×D311yescharacteristic, complemented
214C2×#215—31no—
215C2×#215—31no—
216C2×#215—61no—
217C2×#215C2×D311yescharacteristic, complemented
218C2×#215C2×D311yescharacteristic, complemented
219C2×#215C2×D311yescharacteristic, complemented
220#939—61no—
221#939—61no—
222#938—31no—
223#938—31no—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—31no—
227#930—31no—
228#930—61no—
229C2×C4⋊Dic3—31no—
230#924—61no—
231C2×#208—31no—
232#919—24no—
233#914—64no—
234C2×D24—31no—
235C2×D24C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8C2×D311yescharacteristic, complemented
238#896—61no—
239#895—31no—
240#895—61no—
241D3×C4⋊C4—31no—
242#884—61no—
243#884—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—
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
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×Q8—21no—
289C32×Q8—21no—
290C32×Q8C2×D412yes—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2411yescharacteristic
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—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—24no—
306C3×D12—24no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—42no—
312C3×D12C2×D412yes—
313C3×D12C2×D412yes—
314C3×C4×D3—24no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—24no—
318C3×C4×D3—42no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321#627—22no—
322#626—24no—
323#626—22no—
324#626—22no—
325#626—24no—
326#626—81no—
327#625—24no—
328#625—22no—
329#625—81no—
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—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
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—21no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—61no—
377C22×C3×C4—61no—
378C22×C3×C4—61no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C22×Dic3—61no—
391#239—22no—
392#239—22no—
393#239—22no—
394#239—22no—
395#239—22no—
396#239—62no—
397#239—62no—
398#239—62no—
399#239—62no—
400#239—122no—
401#239—122no—
402#239#6714yescomplemented
403D3×D4—34no—
404D3×D4—62no—
405D3×D4—62no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—68no—
411D3×D4—68no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—62no—
415#235—62no—
416#235—62no—
417#235—68no—
418#235—68no—
419#235—62no—
420#235—62no—
421C2×D12—21no—
422C2×D12—21no—
423C2×D12—21no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—34no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—68no—
433C2×D12—68no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—121no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—21no—
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—
458C3×Q16—22no—
459C3×Q16—22no—
460C3×Q16—42no—
461C3×SD16—62no—
462C3×SD16—62no—
463C3×SD16—62no—
464C3×D8—62no—
465C2×C3×C8—21no—
466C2×C3×C8—31no—
467C2×C3×C8—31no—
468C2×C3×C8—62no—
469C2×C3×C8C22×D311yescharacteristic
470C2×C3×C8C22×D311yescharacteristic
471C3×C4⋊C4—31no—
472C3×C4⋊C4—61no—
473C3×C22⋊C4—61no—
474#217—61no—
475#217—61no—
476#215—22no—
477#215—22no—
478#215—22no—
479#215—62no—
480#215—62no—
481#215—122no—
482#213—62no—
483#213—62no—
484#213—62no—
485(C2×D3)⋊C4—21no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—121no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—61no—
494C4⋊Dic3—61no—
495C4⋊Dic3C22×D311yescharacteristic
496Dic3⋊C4—21no—
497Dic3⋊C4—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—61no—
500Dic3⋊C4—121no—
501#208—62no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—31no—
504C2×C3⋊C8—61no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—22no—
508D24—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—22no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
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×C4—41no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—21no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
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×Q16D3211yescharacteristic, complemented
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—31no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—31no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
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—31no—
593C23×C3—31no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—61no—
603C22×D3—64no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—64no—
611C22×D3—121no—
612C22×D3—241no—
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×D3D3×D411yescharacteristic
625C22×D3D3×D411yescharacteristic
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—21no—
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—22no—
633C3×Q8—41no—
634C3×Q8—41no—
635C3×Q8—41no—
636C3×Q8D3×D412yes—
637C3×Q8C2×#6712yes—
638C3×D4—32no—
639C3×D4—32no—
640C3×D4—64no—
641C3×D4—64no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—122no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
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—41no—
658C2×C3×C4—64no—
659C2×C3×C4—64no—
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—62no—
667#67—64no—
668#67—62no—
669#67—64no—
670#67—64no—
671#67—62no—
672#67—64no—
673#67—62no—
674#67—241no—
675#67—241no—
676#67—241no—
677C2×Dic3—21no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—121no—
684C2×Dic3—241no—
685C2×Dic3D3×D411yescharacteristic
686C2×Dic3D3×D411yescharacteristic
687D12—24no—
688D12—24no—
689D12—21no—
690D12—21no—
691D12—21no—
692D12—21no—
693D12—32no—
694D12—32no—
695D12—42no—
696D12—62no—
697D12—64no—
698D12—64no—
699D12—62no—
700D12—64no—
701D12—64no—
702D12—62no—
703D12—61no—
704D12—61no—
705D12—121no—
706D12—124no—
707D12—241no—
708D12D3×D412yes—
709D12C2×#6712yes—
710C4×D3—24no—
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—24no—
714C4×D3—42no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—121no—
722C4×D3—121no—
723C4×D3—124no—
724C4×D3—241no—
725C4×D3D3×D412yes—
726C4×D3C2×#6712yes—
727Dic6—62no—
728Dic6—62no—
729C3×C8—21no—
730C3×C8—21no—
731C3×C8—41no—
732C3×C8—61no—
733C3×C8—61no—
734C3⋊C8—21no—
735C3⋊C8—21no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—121no—
739C2×C32C2×#12011yescharacteristic
740C2×C32#57611yescharacteristic
741C2×C32#57711yescharacteristic
742C3⋊D3—41no—
743C3⋊D3—42no—
744C3×D3—22no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—42no—
748C3×D3—81no—
749C24—181no—
750C24—181no—
751C24—181no—
752#41—34no—
753#41—62no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—182no—
759#41—182no—
760#41—188no—
761#41—182no—
762#41—182no—
763C2×Q8—91no—
764C2×Q8C2×D3211yescharacteristic
765C2×Q8C2×D3211yescharacteristic
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—61no—
772C2×D4—94no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—181no—
778C2×D4—182no—
779C2×D4—181no—
780C2×D4—181no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—188no—
784C2×D4—188no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—188no—
790C2×D4—181no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—91no—
797C22×C4—181no—
798C22×C4—181no—
799Q16—22no—
800SD16—62no—
801SD16—62no—
802SD16—62no—
803SD16—182no—
804D8—62no—
805D8—182no—
806D8—182no—
807M16—182no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—62no—
811C2×C8—91no—
812C2×C8C2×D3211yescharacteristic
813C4⋊C4—31no—
814C4⋊C4—61no—
815C4⋊C4—91no—
816C4⋊C4—181no—
817C4⋊C4—181no—
818C22⋊C4—61no—
819C22⋊C4—181no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22×C3—21no—
823C22×C3—32no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—61no—
828C22×C3—62no—
829C22×C3—61no—
830C22×C3—62no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3C2×D3×D411yescharacteristic
839C22×C3C2×D3×D411yescharacteristic
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—21no—
844C2×D3—22no—
845C2×D3—21no—
846C2×D3—22no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—122no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—241no—
871C2×D3—241no—
872C2×D3—244no—
873C2×D3—244no—
874C2×D3—244no—
875C2×D3—244no—
876C2×D3—244no—
877C2×D3—244no—
878C2×D3#93712yes—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—21no—
882C3×C4—21no—
883C3×C4—32no—
884C3×C4—42no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—61no—
888C3×C4—81no—
889C3×C4—121no—
890C3×C4C2×D3×D411yescharacteristic
891C3×C4C2×D3×D411yescharacteristic
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C22×#6711yescharacteristic
894Dic3—21no—
895Dic3—41no—
896Dic3—61no—
897Dic3—61no—
898Dic3—121no—
899Dic3—121no—
900Dic3—121no—
901Dic3—241no—
902Dic3#93712yes—
903C32#301211yescharacteristic, complemented, Sylow
904C23—31no—
905C23—31no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—91no—
910C23—184no—
911C23—184no—
912C23—184no—
913C23—181no—
914C23—721no—
915C23—721no—
916C23—721no—
917C23—721no—
918C23—721no—
919C23—721no—
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—182no—
924Q8D3×#6712yes—
925D4—32no—
926D4—32no—
927D4—64no—
928D4—64no—
929D4—61no—
930D4—61no—
931D4—61no—
932D4—61no—
933D4—92no—
934D4—122no—
935D4—184no—
936D4—184no—
937D4—182no—
938D4—182no—
939D4—184no—
940D4—182no—
941D4—184no—
942D4—181no—
943D4—721no—
944D4—721no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—31no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—31no—
951C2×C4—64no—
952C2×C4—64no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—91no—
957C2×C4—122no—
958C2×C4—184no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—721no—
963C2×C4C22×D3211yescharacteristic
964C8—21no—
965C8—61no—
966C8—61no—
967C8—181no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—62no—
972C2×C3—122no—
973C2×C3—121no—
974C2×C3—122no—
975C2×C3—241no—
976C2×C3D3×#12011yescharacteristic
977C2×C3#576911yescharacteristic
978C2×C3#576911yescharacteristic
979C2×C3#577011yescharacteristic
980C2×C3#577811yescharacteristic
981C2×C3C2×#93711yescharacteristic
982D3—22no—
983D3—41no—
984D3—42no—
985D3—42no—
986D3—81no—
987D3—121no—
988D3—122no—
989D3—121no—
990D3—122no—
991D3—241no—
992D3—242no—
993C22—32no—
994C22—61no—
995C22—61no—
996C22—62no—
997C22—62no—
998C22—61no—
999C22—61no—
1000C22—61no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—182no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—361no—
1013C22—361no—
1014C22—724no—
1015C22—724no—
1016C22—724no—
1017C22D32×D411yescharacteristic
1018C4—22no—
1019C4—32no—
1020C4—41no—
1021C4—61no—
1022C4—121no—
1023C4—181no—
1024C4—361no—
1025C4D32×D411yescharacteristic
1026C4C2×D3×#6711yescharacteristic
1027C3—21no—
1028C3#8023111yescharacteristic, complemented
1029C3#8391211yescharacteristic, complemented
1030C2—62no—
1031C2—121no—
1032C2—122no—
1033C2—122no—
1034C2—241no—
1035C2—361no—
1036C2—362no—
1037C2#1059477011yescharacteristic
1038C2#1059477111yescharacteristic
1039C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×C3×#919C2semidirect
3. #10595398C2semidirect
4. C2×#63939C2semidirect
5. #10592886C2semidirect
6. C3×#5187C2semidirect
7. #10591652C2semidirect
8. #10591651C2semidirect
9. #10591593C2semidirect
10. #10591586C2semidirect
11. #10591550C2semidirect
12. #10590953C2semidirect
13. #10590945C2semidirect
14. #10590944C2semidirect
15. D3×#821C2semidirect
21. C2×C3×#239C22semidirect
32. C2×C32×Q16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×D24C22semidirect
41. C2×C3×D3×C8C22semidirect
43. #63916C22semidirect
44. #63908C22semidirect
46. D3×C4⋊Dic3C22semidirect
50. C2×#3714C22semidirect
51. C2×#3713C22semidirect
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×#919D3semidirect
79. #5187D3semidirect
112. C3×#239D4semidirect
142. D3×D12D4semidirect
182. C2×#239C2×D3semidirect
201. C2×C3×Q16C2×D3semidirect
202. C2×C3×Q16C2×D3semidirect
213. #946C2×D3semidirect
217. C2×#215C2×D3semidirect
218. C2×#215C2×D3semidirect
219. C2×#215C2×D3semidirect
235. C2×D24C2×D3semidirect
237. C2×D3×C8C2×D3semidirect
250. #835C2×D3semidirect
261. #821C2×D3semidirect
268. (C2×D3)⋊C8C2×D3semidirect
402. #239#67semidirect
561. C2×Q16D32semidirect
903. C32#3012semidirect
1028. C3#80231semidirect
1029. 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×#9192
#105953982
C2×#639392
#105928862
C3×#51872
#105916522
#105916512
#105915932
#105915862
#105915502
#105909532
#105909452
#105909442
D3×#8212
#839123
#802313