Finite Group Databasebeta

← #11864163

Subgroups — #11864163

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4726C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12#10590944C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590671C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#78639—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23C2×#3804—21no—
24D3×#235—24no—
25D3×#235—24no—
26C2×D3×D12C2211yescharacteristic, complemented
27C2×D3×D12C2211yescharacteristic, complemented
28C2×C4×D32—21no—
29C2×#3799C2211yescharacteristic
30C2×#3798—21no—
31C2×#3795C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic, complemented
33#64139C2211yescharacteristic, complemented
34C2×#3745C2211yescharacteristic, complemented
35C2×#3744C2211yescharacteristic, complemented
36C3×#930C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
41#63978—21no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic
44#63908C2211yescharacteristic
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63795—24no—
52#63794—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#235—31no—
67C2×#930—31no—
68C2×#914—31no—
69C2×#911—31no—
70C2×#908—31no—
71C2×#908—31no—
72D3×#121—31no—
73C3×#449—31no—
74C3×#407—31no—
75#5238—31no—
76#5170—31no—
77#5156—31no—
78#5133—31no—
79#5133—31no—
80#5037—31no—
81#4806—31no—
82#4803—31no—
83#4773—31no—
84#4771—31no—
85#4738—31no—
86#4738—31no—
87#4734—31no—
88#4734—31no—
89#4734—31no—
90#4734—31no—
91#4734—61no—
92#4734D311yescharacteristic, complemented
93#4732—31no—
94#4732—31no—
95#4726D311yescharacteristic, complemented
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3D411yescharacteristic
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3D411yescharacteristic
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—28no—
124D3×#67—44no—
125C2×#627—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#625—21no—
132C2×#624—21no—
133#3804—28no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—22no—
141C4×D32—28no—
142#3799—22no—
143#3799D414yescomplemented
144#3798—28no—
145#3795—22no—
146#3795D414yescomplemented
147D3×Dic6—22no—
148D3×Dic6—22no—
149C2×C32×C8C2311yescharacteristic
150C2×C32×C8C2311yescharacteristic
151#3752—21no—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153#3745—22no—
154#3744—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×#204—22no—
161C3×ΓL(1,𝔽25)—22no—
162C3×ΓL(1,𝔽25)—22no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3717—22no—
167#3716—22no—
168#3714—22no—
169#3714—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C23×C3×C4—31no—
173C22×#67—61no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—61no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—61no—
184C2×D3×D4—61no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—31no—
188C2×#235—31no—
189C2×#235—61no—
190C2×#235—61no—
191C2×#235—64no—
192C2×#235—64no—
193C2×#235—61no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic, complemented
196C22×D12—31no—
197C22×D12—31no—
198C22×C4×D3—61no—
199C22×C4×D3—61no—
200C22×C4×D3C2×D311yescharacteristic
201C22×Dic6—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C2×C3×M16—31no—
205C2×C3×M16—31no—
206C3×#121—31no—
207C2×#215—31no—
208#939—61no—
209#938—31no—
210C2×#214—31no—
211C2×#213—31no—
212C2×#213—31no—
213#930—31no—
214#930—31no—
215#930—31no—
216#930—31no—
217#930—61no—
218#930—61no—
219#930—61no—
220#930C2×D311yescharacteristic, complemented
221C2×(C2×D3)⋊C4—61no—
222C2×C4⋊Dic3—31no—
223#914—64no—
224#911—64no—
225#908—64no—
226#908—64no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—31no—
230C2×D24—31no—
231C2×D24—61no—
232C2×D24C2×D311yescharacteristic, complemented
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—31no—
236C2×#204—31no—
237C2×#204—61no—
238C2×#204C2×D311yescharacteristic, complemented
239C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
240C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—21no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8—31no—
251C3×C22⋊C8C2×D311yescharacteristic, complemented
252C3×C22⋊C8C2×D311yescharacteristic, complemented
253#835—31no—
254#832—31no—
255#830C2×D311yescharacteristic, complemented
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#816—31no—
265#816—31no—
266#816—31no—
267#816—31no—
268#816—61no—
269#816C2×D311yescharacteristic, complemented
270#810—31no—
271#809—31no—
272C23×C32C2×D411yescharacteristic
273C22×C3⋊D3—21no—
274C22×C3⋊D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—21no—
279C22×C3×D3—41no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—24no—
283C2×D32—42no—
284C2×D32—42no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2×D411yescharacteristic
291C2×C32×C4C2411yescharacteristic
292#638—24no—
293#638—42no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—42no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yescomplemented
314C3×C4×D3—24no—
315C3×C4×D3—22no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—22no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#627—24no—
324#626—24no—
325#626—24no—
326#626—42no—
327#626—42no—
328#625—24no—
329#625—42no—
330#624—24no—
331D3×Dic3—24no—
332D3×Dic3—24no—
333D3×Dic3—42no—
334C32×C8—21no—
335C32×C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—91no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
347#448—91no—
348#447—91no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—31no—
353C24×C3—31no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3D1211yescharacteristic
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—121no—
393C2×#67—121no—
394C2×#67—124no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3D1211yescharacteristic
399#239—34no—
400#239—62no—
401D3×Q8—62no—
402D3×Q8—62no—
403#237—34no—
404#237—68no—
405#237—62no—
406D3×D4—62no—
407D3×D4—62no—
408D3×D4—68no—
409D3×D4—62no—
410D3×D4—62no—
411D3×D4—124no—
412#235—22no—
413#235—22no—
414#235—34no—
415#235—34no—
416#235—62no—
417#235—62no—
418#235—62no—
419#235—68no—
420#235—68no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—68no—
425#235—122no—
426#235—122no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×C4×D3—21no—
444C2×C4×D3—22no—
445C2×C4×D3—22no—
446C2×C4×D3—68no—
447C2×C4×D3—68no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—121no—
456C2×C4×D3D1211yescharacteristic
457C2×C4×D3D1211yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—61no—
463C2×Dic6—62no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6—62no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C3×M16—62no—
471C3×M16—62no—
472C2×C3×C8—21no—
473C2×C3×C8—21no—
474C2×C3×C8—31no—
475C2×C3×C8—31no—
476C2×C3×C8C22×D311yescharacteristic
477C2×C3×C8C22×D311yescharacteristic
478C2×C3×C8C22×D311yescharacteristic
479C2×C3×C8C22×D311yescharacteristic
480C3×C4⋊C4—31no—
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#214—62no—
485#213—62no—
486#213—62no—
487(C2×D3)⋊C4—21no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—121no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—61no—
497C4⋊Dic3—61no—
498C4⋊Dic3C22×D311yescharacteristic
499Dic3⋊C4—61no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502D24—22no—
503D24—62no—
504D24—62no—
505D24—62no—
506D24—62no—
507D24—122no—
508#204—22no—
509#204—62no—
510#204—62no—
511#204—62no—
512#204—62no—
513#204—122no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—22no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—22no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—44no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3#12012yes—
538C2×C3×D3AGL(1,ℤ/8)12yescomplemented
539D32—48no—
540D32—84no—
541C32×C4—21no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—22no—
545C3⋊Dic3—41no—
546C3×Dic3—22no—
547C3×Dic3—21no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—31no—
564C23×C4—181no—
565AGL(1,ℤ/8)—184no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—31no—
576C2×M16—31no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—31no—
595C22⋊C8—31no—
596C22⋊C8D3211yescharacteristic, complemented
597C23×C3—21no—
598C23×C3—31no—
599C23×C3—31no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—121no—
605C23×C3C2×D1211yescharacteristic
606C23×C3D3×D411yescharacteristic
607C22×D3—21no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—21no—
611C22×D3—41no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3C2×D1211yescharacteristic
631C22×D3C2×D1211yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—32no—
635C3×D4—64no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—122no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—64no—
655C2×C3×C4—62no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4C2×D1211yescharacteristic
661C2×C3×C4D3×D411yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—24no—
665#67—42no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—64no—
671#67—64no—
672#67—124no—
673#67—122no—
674#67—122no—
675#67—122no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—242no—
680C2×Dic3—21no—
681C2×Dic3—22no—
682C2×Dic3—21no—
683C2×Dic3—64no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—64no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—122no—
692C2×Dic3C2×D1211yescharacteristic
693C2×Dic3C2×D1211yescharacteristic
694D12—21no—
695D12—21no—
696D12—21no—
697D12—32no—
698D12—32no—
699D12—62no—
700D12—64no—
701D12—64no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—61no—
707D12—61no—
708D12—121no—
709D12—121no—
710D12—121no—
711D12—122no—
712D12—122no—
713D12D3×D412yescomplemented
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—21no—
717C4×D3—21no—
718C4×D3—22no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—124no—
726C4×D3—122no—
727C4×D3D3×D412yes—
728C4×D3D3×D412yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6D3×D412yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—41no—
744C3×C8—41no—
745C3×C8—61no—
746C3×C8—61no—
747C3⋊C8—21no—
748C3⋊C8—21no—
749C2×C32—41no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
752C2×C32#57511yescharacteristic
753C3⋊D3—42no—
754C3⋊D3—81no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—31no—
760C24—181no—
761C24—181no—
762#41—62no—
763#41—62no—
764#41—94no—
765#41—94no—
766#41—182no—
767#41—182no—
768#41—182no—
769#41—182no—
770#41—188no—
771#41—188no—
772C2×Q8—31no—
773C2×Q8—91no—
774C2×Q8—181no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—91no—
782C2×D4—91no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—188no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—364no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—61no—
805C22×C4—181no—
806C22×C4—181no—
807C22×C4—188no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4C2×D3211yescharacteristic
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820M16—62no—
821M16—62no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8C2×D3211yescharacteristic
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—91no—
828C4⋊C4—181no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—32no—
841C22×C3—32no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—62no—
850C22×C3—124no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C22×D1211yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—22no—
863C2×D3—44no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—122no—
872C2×D3—128no—
873C2×D3—128no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—241no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—241no—
889C2×D3—244no—
890C2×D3—244no—
891C2×D3#88212yes—
892C2×D3#90812yescomplemented
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—61no—
901C3×C4—121no—
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C2×D3×D411yescharacteristic
906Dic3—21no—
907Dic3—22no—
908Dic3—41no—
909Dic3—62no—
910Dic3—62no—
911Dic3—122no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#88212yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—31no—
918C23—31no—
919C23—62no—
920C23—62no—
921C23—61no—
922C23—61no—
923C23—121no—
924C23—184no—
925C23—181no—
926C23—181no—
927C23—362no—
928C23—362no—
929C23—362no—
930C23—362no—
931C23—362no—
932C23D3×D1211yescharacteristic
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—32no—
939D4—64no—
940D4—61no—
941D4—61no—
942D4—61no—
943D4—92no—
944D4—122no—
945D4—184no—
946D4—184no—
947D4—184no—
948D4—184no—
949D4—181no—
950D4—181no—
951D4—181no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4—362no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—31no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—31no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—64no—
965C2×C4—62no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—184no—
971C2×C4—184no—
972C2×C4—184no—
973C2×C4—184no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—362no—
977C2×C4D3×D1211yescharacteristic
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—21no—
981C8—61no—
982C8—61no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—41no—
988C2×C3—62no—
989C2×C3—62no—
990C2×C3—81no—
991C2×C3—122no—
992C2×C3—241no—
993C2×C3C2×#88211yescharacteristic
994C2×C3D3×#12011yescharacteristic
995C2×C3C2×#90811yescharacteristic
996C2×C3#574811yescharacteristic
997C2×C3#576811yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999D3—22no—
1000D3—22no—
1001D3—42no—
1002D3—81no—
1003D3—122no—
1004D3—122no—
1005D3—242no—
1006D3—241no—
1007D3—241no—
1008D3—481no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—32no—
1013C22—32no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—62no—
1019C22—124no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—182no—
1026C22—368no—
1027C22—361no—
1028C22—361no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22C2×D3×D1211yescharacteristic
1034C4—21no—
1035C4—32no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—182no—
1040C4—361no—
1041C4D32×D411yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3#7863911yescharacteristic, complemented
1045C3#8008411yescharacteristic, complemented
1046C2—41no—
1047C2—62no—
1048C2—62no—
1049C2—122no—
1050C2—241no—
1051C2—362no—
1052C2—721no—
1053C2D3×#88211yescharacteristic
1054C2#1059467611yescharacteristic
1055C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. D3×#930C2semidirect
3. C2×#63795C2semidirect
4. C2×#63794C2semidirect
5. #10592433C2semidirect
6. C3×#4734C2semidirect
7. C3×#4726C2semidirect
8. #10591182C2semidirect
9. #10591163C2semidirect
10. #10590951C2semidirect
11. #10590947C2semidirect
12. #10590944C2semidirect
13. #10590822C2semidirect
14. #10590671C2semidirect
15. #10590670C2semidirect
18. C2×#3828C22semidirect
19. C2×C3×#235C22semidirect
26. C2×D3×D12C22semidirect
27. C2×D3×D12C22semidirect
32. C2×D3×Dic6C22semidirect
33. #64139C22semidirect
34. C2×#3745C22semidirect
35. C2×#3744C22semidirect
36. C3×#930C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C2×C3×ΓL(1,𝔽25)C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63643C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×#816C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
63. #63564C22semidirect
64. #63563C22semidirect
92. #4734D3semidirect
95. #4726D3semidirect
143. #3799D4semidirect
146. #3795D4semidirect
195. C2×#235C2×D3semidirect
220. #930C2×D3semidirect
232. C2×D24C2×D3semidirect
238. C2×#204C2×D3semidirect
239. C2×ΓL(1,𝔽25)C2×D3semidirect
240. C2×ΓL(1,𝔽25)C2×D3semidirect
251. C3×C22⋊C8C2×D3semidirect
252. C3×C22⋊C8C2×D3semidirect
255. #830C2×D3semidirect
261. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
269. #816C2×D3semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
302. #634C2×D4semidirect
313. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
538. C2×C3×D3AGL(1,ℤ/8)semidirect
596. C22⋊C8D32semidirect
713. D12D3×D4semidirect
738. Dic6D3×D4semidirect
892. C2×D3#908semidirect
916. C32#3006semidirect
1044. C3#78639semidirect
1045. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
D3×#9302
C2×#637952
C2×#637942
#105924332
C3×#47342
C3×#47262
#105911822
#105911632
#105909512
#105909472
#105909442
#105908222
#105906712
#105906702
#800843
#786393