Finite Group Databasebeta

← #11864308

Subgroups — #11864308

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595231C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591593C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591516C211yesmaximal, characteristic, complemented
11#10591515C211yesmaximal, characteristic, complemented
12#10590955C211yesmaximal, characteristic, complemented
13#10590945C211yesmaximal, characteristic, complemented
14#10590944C211yesmaximal, characteristic, complemented
15#10590939C211yesmaximal, characteristic, complemented
16#83947—31nomaximal
17#80085—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22#64320—24no—
23#64320—24no—
24C2×#3802—21no—
25C2×#3802C2211yescharacteristic, complemented
26C2×D3×D12—21no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic, complemented
30C2×#3798—21no—
31C2×#3798C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64147C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C3×#938C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#914—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63979—21no—
43#63977—21no—
44#63976—21no—
45#63959—21no—
46D3×#213—24no—
47#63916C2211yescharacteristic, complemented
48#63908C2211yescharacteristic, complemented
49#63841C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, 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×AGL(1,ℤ/8)—31no—
68#5805—31no—
69C22×#213—31no—
70C2×#914D311yescharacteristic, complemented
71C2×D3×D8—31no—
72#5607—31no—
73C3×#449—31no—
74#5238—31no—
75#5233—31no—
76#5172—31no—
77#5172—31no—
78#5172—31no—
79#5172—31no—
80#5172—61no—
81#5172D311yescharacteristic, complemented
82#5156—31no—
83#5156—31no—
84#5156—31no—
85#5156—31no—
86#5156—31no—
87#5131—31no—
88#5129—31no—
89#5036—31no—
90#4810—31no—
91#4804—31no—
92#4773—31no—
93#4770—31no—
94#4732—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×D32—21no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×#638—21no—
103#3832—22no—
104#3832—22no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C3×#239—22no—
112C3×#239—22no—
113C3×#239—22no—
114C3×#239D414yescomplemented
115C3×D3×D4—22no—
116C3×D3×D4—22no—
117C2×C3×D12—21no—
118C2×C3×D12—21no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×#627D411yescharacteristic
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626D411yescharacteristic
131C2×#626D411yescharacteristic
132C2×#625—21no—
133C2×#625—21no—
134C2×#625D411yescharacteristic
135#3802—28no—
136#3802—22no—
137#3802—22no—
138D3×D12—28no—
139D3×D12—28no—
140D3×D12—22no—
141D3×D12—22no—
142D3×D12—22no—
143D3×D12D414yescomplemented
144#3798—28no—
145#3798—22no—
146#3798—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic
149#3757—21no—
150#3753—22no—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#217—21no—
154C3×#215—22no—
155C3×#213—22no—
156C3×#213—22no—
157C3×C4⋊Dic3C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×ΓL(1,𝔽25)—22no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3714—22no—
167#3713—22no—
168D3×C3⋊C8—22no—
169#3008—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×D4—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, complemented
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4C2×D311yescharacteristic, complemented
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×AGL(1,ℤ/8)—64no—
200C2×C3×SD16—21no—
201C2×C3×SD16—31no—
202C2×C3×SD16C2×D311yescharacteristic, complemented
203C2×C3×SD16C2×D311yescharacteristic, complemented
204C2×C3×D8—31no—
205C2×C3×D8—31no—
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C3×#121—31no—
209#953—61no—
210#953—61no—
211C2×#215C2×D311yescharacteristic, complemented
212#940—61no—
213#940—61no—
214#938—31no—
215#938—31no—
216#938—31no—
217#938—31no—
218#938—61no—
219#938C2×D311yescharacteristic, complemented
220#937—61no—
221#936—61no—
222C2×#213—31no—
223C2×#213—31no—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—61no—
228C2×#213—64no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#213C2×D311yescharacteristic, complemented
231#930—31no—
232#926—31no—
233C22×C3⋊C8—31no—
234#914—24no—
235D3×D8—64no—
236C2×D24—31no—
237C2×D24C2×D311yescharacteristic, complemented
238C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
239C2×D3×C8—31no—
240#895—31no—
241#892—31no—
242#885—61no—
243#882—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×D3—21no—
277C22×C3×D3—42no—
278C22×C3×D3—81no—
279C22×C3×D3—81no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—24no—
283C2×D32—24no—
284C2×D32—24no—
285C2×D32—81no—
286C2×D32—81no—
287C2×D32—81no—
288C2×D32—81no—
289C2×D32—81no—
290C2×D32—81no—
291C32×Q8—21no—
292C32×Q8C2×D412yes—
293C32×D4—21no—
294C32×D4—21no—
295C2×C32×C4—21no—
296C2×C32×C4C2411yescharacteristic
297#638—81no—
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3C2×D411yescharacteristic
300C4⋊(C3⋊D3)—24no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)C2×D412yes—
303C4×C3⋊D3—24no—
304C4×C3⋊D3—21no—
305C4×C3⋊D3—21no—
306C3×#67—42no—
307C3×#67—81no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3C2×D411yescharacteristic
310C2×C3×Dic3C2×D411yescharacteristic
311C3×D12—24no—
312C3×D12—24no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12C2×D412yes—
318C3×D12C2×D412yes—
319C3×C4×D3—24no—
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—24no—
323C3×C4×D3C2×D412yes—
324C3×C4×D3C2×D412yes—
325#627—22no—
326#626—24no—
327#626—22no—
328#626—22no—
329#626—24no—
330#626—81no—
331#625—24no—
332#625—22no—
333#625—81no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C2×H(5,𝔽2)—91no—
339C2×AGL(1,ℤ/8)—31no—
340C22×D8—91no—
341#535—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#447—91no—
347#447—91no—
348#447—91no—
349#447—91no—
350#418—91no—
351#416—91no—
352#408—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—61no—
361C3×#41—34no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—62no—
365C2×C3×Q8—21no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—62no—
375C2×C3×D4—62no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4C22×D311yescharacteristic
379C2×C3×D4C22×D311yescharacteristic
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—61no—
383C22×C3×C4—61no—
384C2×#67—21no—
385C2×#67—21no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—31no—
389C2×#67—31no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—121no—
400#239—22no—
401#239—22no—
402#239—22no—
403#239—62no—
404#239—62no—
405#239—62no—
406#239—62no—
407#239—122no—
408#239—122no—
409#239#6714yescomplemented
410D3×D4—22no—
411D3×D4—22no—
412D3×D4—34no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—68no—
416D3×D4—68no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—68no—
420D3×D4—68no—
421D3×D4—62no—
422D3×D4—62no—
423D3×D4—62no—
424#235—62no—
425#235—62no—
426#235—68no—
427#235—68no—
428#235—62no—
429#235—62no—
430C2×D12—21no—
431C2×D12—21no—
432C2×D12—31no—
433C2×D12—31no—
434C2×D12—34no—
435C2×D12—31no—
436C2×D12—31no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—62no—
440C2×D12—68no—
441C2×D12—68no—
442C2×D12—61no—
443C2×D12—61no—
444C2×D12—61no—
445C2×D12—61no—
446C2×D12—62no—
447C2×D12—61no—
448C2×D12—121no—
449C2×D12C22×D311yescharacteristic
450C2×D12C22×D311yescharacteristic
451C2×D12C22×D311yescharacteristic
452C2×C4×D3—21no—
453C2×C4×D3—21no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—121no—
460C2×C4×D3C22×D311yescharacteristic
461C2×C4×D3C22×D311yescharacteristic
462C2×Dic6—31no—
463C2×Dic6—31no—
464C3×SD16—22no—
465C3×SD16—22no—
466C3×SD16—42no—
467C3×SD16—62no—
468C3×D8—62no—
469C3×D8—62no—
470C3×D8—62no—
471C3×M16—62no—
472C2×C3×C8—21no—
473C2×C3×C8—31no—
474C2×C3×C8—31no—
475C2×C3×C8C22×D311yescharacteristic
476C2×C3×C8C22×D311yescharacteristic
477C3×C4⋊C4—31no—
478C3×C22⋊C4—61no—
479#217—21no—
480#217—61no—
481#217—61no—
482#217—61no—
483#217—61no—
484#217—61no—
485#217—121no—
486#215—22no—
487#213—22no—
488#213—22no—
489#213—62no—
490#213—62no—
491#213—62no—
492#213—62no—
493#213—62no—
494#213—122no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498C4⋊Dic3—31no—
499C4⋊Dic3—31no—
500C4⋊Dic3—61no—
501C4⋊Dic3C22×D311yescharacteristic
502C4×Dic3—61no—
503C4×Dic3—61no—
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—61no—
507C2×C3⋊C8—62no—
508C2×C3⋊C8C22×D311yescharacteristic
509C2×C3⋊C8C22×D311yescharacteristic
510D24—22no—
511D24—62no—
512ΓL(1,𝔽25)—22no—
513D3×C8—62no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3⋊D3—21no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—84no—
539C2×C3×D3#12012yes—
540D32—84no—
541D32—84no—
542D32—84no—
543C32×C4—22no—
544C32×C4C22×D411yescharacteristic
545C32×C4C22×D411yescharacteristic
546C3⋊Dic3—21no—
547C3⋊Dic3—41no—
548C3×Dic3—21no—
549C3×Dic3—41no—
550C3×Dic3#12012yes—
551H(5,𝔽2)—184no—
552H(5,𝔽2)—184no—
553C2×#41—31no—
554C2×#41—31no—
555C2×#41—91no—
556C2×#41—91no—
557C2×#41—181no—
558C22×D4—31no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—181no—
563C22×D4—181no—
564C22×D4—181no—
565AGL(1,ℤ/8)—64no—
566C2×SD16—31no—
567C2×SD16D3211yescharacteristic, complemented
568C2×D8—31no—
569C2×D8—31no—
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C2×M16—31no—
576C22×C8—91no—
577#127—181no—
578#124—181no—
579#121—31no—
580#121—91no—
581#121—91no—
582#121—91no—
583#120—181no—
584#120—181no—
585#117—91no—
586#103—31no—
587#103—91no—
588#102—31no—
589#102—91no—
590#102—91no—
591#102—91no—
592#102—91no—
593#102—91no—
594C22⋊C8—31no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C22⋊C8—91no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—41no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—122no—
607C23×C3—241no—
608C23×C3—241no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—31no—
613C22×D3—31no—
614C22×D3—42no—
615C22×D3—61no—
616C22×D3—64no—
617C22×D3—64no—
618C22×D3—64no—
619C22×D3—64no—
620C22×D3—64no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—64no—
624C22×D3—81no—
625C22×D3—81no—
626C22×D3—121no—
627C22×D3—241no—
628C22×D3—241no—
629C22×D3—241no—
630C22×D3—241no—
631C22×D3—241no—
632C22×D3—241no—
633C22×D3—241no—
634C22×D3—241no—
635C22×D3—241no—
636C22×D3—241no—
637C22×D3—241no—
638C22×D3—241no—
639C22×D3D3×D411yescharacteristic
640C22×D3D3×D411yescharacteristic
641C3×Q8—21no—
642C3×Q8—21no—
643C3×Q8—22no—
644C3×Q8—41no—
645C3×Q8D3×D412yes—
646C3×Q8C2×#6712yes—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—32no—
652C3×D4—32no—
653C3×D4—41no—
654C3×D4—41no—
655C3×D4—64no—
656C3×D4—64no—
657C3×D4—61no—
658C3×D4—61no—
659C3×D4—61no—
660C3×D4—61no—
661C3×D4—122no—
662C3×D4—241no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—31no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—31no—
670C2×C3×C4—41no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678#67—42no—
679#67—62no—
680#67—64no—
681#67—62no—
682#67—64no—
683#67—64no—
684#67—62no—
685#67—64no—
686#67—62no—
687#67—81no—
688#67—241no—
689#67—241no—
690#67—241no—
691#67—241no—
692#67—241no—
693#67—242no—
694C2×Dic3—21no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—121no—
701C2×Dic3D3×D411yescharacteristic
702C2×Dic3D3×D411yescharacteristic
703D12—24no—
704D12—24no—
705D12—21no—
706D12—21no—
707D12—21no—
708D12—21no—
709D12—32no—
710D12—32no—
711D12—62no—
712D12—64no—
713D12—64no—
714D12—62no—
715D12—64no—
716D12—64no—
717D12—62no—
718D12—61no—
719D12—61no—
720D12—121no—
721D12—124no—
722D12—241no—
723D12D3×D412yes—
724D12C2×#6712yes—
725C4×D3—24no—
726C4×D3—21no—
727C4×D3—21no—
728C4×D3—24no—
729C4×D3—64no—
730C4×D3—64no—
731C4×D3—61no—
732C4×D3—61no—
733C4×D3—61no—
734C4×D3—61no—
735C4×D3—121no—
736C4×D3—121no—
737C4×D3—124no—
738C4×D3D3×D412yes—
739C4×D3C2×#6712yes—
740Dic6—62no—
741Dic6—62no—
742C3×C8—21no—
743C3×C8—21no—
744C3×C8—41no—
745C3×C8—61no—
746C3×C8—61no—
747C3⋊C8—21no—
748C3⋊C8—21no—
749C3⋊C8—61no—
750C3⋊C8—61no—
751C3⋊C8—121no—
752C2×C32—81no—
753C2×C32C2×#12011yescharacteristic
754C2×C32#57611yescharacteristic
755C2×C32#57611yescharacteristic
756C3⋊D3—41no—
757C3⋊D3—42no—
758C3×D3—22no—
759C3×D3—41no—
760C3×D3—42no—
761C3×D3—42no—
762C3×D3—81no—
763C24—61no—
764C24—181no—
765C24—181no—
766C24—181no—
767#41—34no—
768#41—62no—
769#41—62no—
770#41—62no—
771#41—182no—
772#41—182no—
773#41—188no—
774#41—182no—
775#41—182no—
776C2×Q8—91no—
777C2×Q8C2×D3211yescharacteristic
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—31no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—62no—
785C2×D4—61no—
786C2×D4—61no—
787C2×D4—94no—
788C2×D4—91no—
789C2×D4—91no—
790C2×D4—91no—
791C2×D4—91no—
792C2×D4—181no—
793C2×D4—182no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—182no—
797C2×D4—182no—
798C2×D4—188no—
799C2×D4—188no—
800C2×D4—181no—
801C2×D4—181no—
802C2×D4—182no—
803C2×D4—182no—
804C2×D4—188no—
805C2×D4—181no—
806C2×D4—181no—
807C2×D4C2×D3211yescharacteristic
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—91no—
813C22×C4—181no—
814SD16—22no—
815SD16—62no—
816D8—62no—
817D8—62no—
818D8—62no—
819D8—182no—
820D8—182no—
821D8—182no—
822M16—62no—
823C2×C8—31no—
824C2×C8—31no—
825C2×C8—91no—
826C2×C8—182no—
827C2×C8C2×D3211yescharacteristic
828C4⋊C4—31no—
829C4⋊C4—91no—
830C22⋊C4—61no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22⋊C4—181no—
834C22⋊C4—181no—
835C42—181no—
836C22×C3—21no—
837C22×C3—32no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—61no—
848C22×C3—62no—
849C22×C3—61no—
850C22×C3—62no—
851C22×C3—81no—
852C22×C3—81no—
853C22×C3—81no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—244no—
862C22×C3C2×D3×D411yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—22no—
869C2×D3—21no—
870C2×D3—22no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—62no—
883C2×D3—61no—
884C2×D3—62no—
885C2×D3—61no—
886C2×D3—84no—
887C2×D3—122no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3—241no—
896C2×D3—241no—
897C2×D3—244no—
898C2×D3—244no—
899C2×D3—244no—
900C2×D3—244no—
901C2×D3—244no—
902C2×D3—244no—
903C2×D3#93712yes—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—21no—
907C3×C4—21no—
908C3×C4—32no—
909C3×C4—42no—
910C3×C4—61no—
911C3×C4—121no—
912C3×C4C2×D3×D411yescharacteristic
913C3×C4C2×D3×D411yescharacteristic
914C3×C4C2×D3×D411yescharacteristic
915C3×C4C22×#6711yescharacteristic
916Dic3—21no—
917Dic3—41no—
918Dic3—61no—
919Dic3—61no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—241no—
924Dic3#93712yes—
925C32#300811yescharacteristic, complemented, Sylow
926C23—21no—
927C23—31no—
928C23—31no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—91no—
933C23—122no—
934C23—184no—
935C23—184no—
936C23—184no—
937C23—181no—
938C23—241no—
939C23—241no—
940C23—721no—
941C23—721no—
942C23—721no—
943C23—721no—
944C23—721no—
945C23—721no—
946Q8—21no—
947Q8—182no—
948Q8D3×#6712yes—
949D4—21no—
950D4—21no—
951D4—32no—
952D4—32no—
953D4—64no—
954D4—64no—
955D4—61no—
956D4—61no—
957D4—61no—
958D4—61no—
959D4—92no—
960D4—122no—
961D4—184no—
962D4—184no—
963D4—182no—
964D4—182no—
965D4—184no—
966D4—182no—
967D4—184no—
968D4—181no—
969D4—241no—
970D4—721no—
971D4—721no—
972D4—721no—
973C2×C4—21no—
974C2×C4—31no—
975C2×C4—32no—
976C2×C4—32no—
977C2×C4—31no—
978C2×C4—64no—
979C2×C4—64no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—91no—
984C2×C4—184no—
985C2×C4—181no—
986C2×C4—181no—
987C2×C4—181no—
988C2×C4C22×D3211yescharacteristic
989C8—21no—
990C8—61no—
991C8—61no—
992C8—181no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—62no—
997C2×C3—81no—
998C2×C3—81no—
999C2×C3—122no—
1000C2×C3—121no—
1001C2×C3—122no—
1002C2×C3—161no—
1003C2×C3—241no—
1004C2×C3D3×#12011yescharacteristic
1005C2×C3#576911yescharacteristic
1006C2×C3#577411yescharacteristic
1007C2×C3#577411yescharacteristic
1008C2×C3#577411yescharacteristic
1009C2×C3C2×#93711yescharacteristic
1010D3—22no—
1011D3—41no—
1012D3—42no—
1013D3—42no—
1014D3—81no—
1015D3—121no—
1016D3—122no—
1017D3—121no—
1018D3—122no—
1019D3—241no—
1020D3—242no—
1021C22—32no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—61no—
1026C22—61no—
1027C22—61no—
1028C22—61no—
1029C22—62no—
1030C22—62no—
1031C22—61no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—181no—
1040C22—181no—
1041C22—182no—
1042C22—181no—
1043C22—244no—
1044C22—361no—
1045C22—361no—
1046C22—724no—
1047C22—724no—
1048C22—724no—
1049C22D32×D411yescharacteristic
1050C4—22no—
1051C4—32no—
1052C4—61no—
1053C4—121no—
1054C4—181no—
1055C4—361no—
1056C4D32×D411yescharacteristic
1057C4C2×D3×#6711yescharacteristic
1058C3—21no—
1059C3#8008511yescharacteristic, complemented
1060C3#8394711yescharacteristic, complemented
1061C2—62no—
1062C2—81no—
1063C2—121no—
1064C2—122no—
1065C2—122no—
1066C2—241no—
1067C2—361no—
1068C2—362no—
1069C2#1059475011yescharacteristic
1070C2#1059475511yescharacteristic
1071C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3008
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×#914C2semidirect
3. #10595231C2semidirect
4. C2×D3×#213C2semidirect
5. #10592871C2semidirect
6. C3×#5172C2semidirect
7. #10591593C2semidirect
8. #10591586C2semidirect
9. #10591556C2semidirect
10. #10591516C2semidirect
11. #10591515C2semidirect
12. #10590955C2semidirect
13. #10590945C2semidirect
14. #10590944C2semidirect
15. #10590939C2semidirect
18. C2×#3832C22semidirect
20. C2×C3×#239C22semidirect
21. C2×C3×D3×D4C22semidirect
25. C2×#3802C22semidirect
29. C2×D3×D12C22semidirect
32. C2×C32×SD16C22semidirect
33. #64147C22semidirect
34. C2×#3753C22semidirect
35. C2×C3×#215C22semidirect
36. C3×#938C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×D24C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
47. #63916C22semidirect
48. #63908C22semidirect
49. #63841C22semidirect
50. C2×#3714C22semidirect
51. C2×#3713C22semidirect
52. C2×D3×C3⋊C8C22semidirect
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×#914D3semidirect
81. #5172D3semidirect
114. C3×#239D4semidirect
143. D3×D12D4semidirect
181. C2×#239C2×D3semidirect
190. C2×D3×D4C2×D3semidirect
202. C2×C3×SD16C2×D3semidirect
203. C2×C3×SD16C2×D3semidirect
211. C2×#215C2×D3semidirect
219. #938C2×D3semidirect
229. C2×#213C2×D3semidirect
230. C2×#213C2×D3semidirect
237. C2×D24C2×D3semidirect
238. C2×ΓL(1,𝔽25)C2×D3semidirect
250. #835C2×D3semidirect
261. #821C2×D3semidirect
268. (C2×D3)⋊C8C2×D3semidirect
409. #239#67semidirect
567. C2×SD16D32semidirect
925. C32#3008semidirect
1059. C3#80085semidirect
1060. C3#83947semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×C3×#9142
#105952312
C2×D3×#2132
#105928712
C3×#51722
#105915932
#105915862
#105915562
#105915162
#105915152
#105909552
#105909452
#105909442
#105909392
#839473
#800853