Finite Group Databasebeta

← #11864603

Subgroups — #11864603

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic, complemented
3C2×#63806C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5#10592430C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4727C211yesmaximal, characteristic, complemented
8#10591173C211yesmaximal, characteristic, complemented
9#10591168C211yesmaximal, characteristic, complemented
10#10590970C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590944C211yesmaximal, characteristic, complemented
13D3×#821C211yesmaximal, characteristic, complemented
14#10590823C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#80087—31nomaximal
17#78672—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3811—21no—
22C2×#3811—21no—
23#64308—24no—
24#64308—24no—
25C2×D3×D12—21no—
26C2×D3×D12C2211yescharacteristic
27C2×D3×D12C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3799C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32#64133C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic, complemented
40#63970—21no—
41#63970—21no—
42#63908C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63887—21no—
45#63885—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63806—24no—
52#63795—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67#5833—31no—
68C2×#916—31no—
69C2×#911—31no—
70C2×#908—31no—
71C2×#904—31no—
72#5608—31no—
73C3×#449—31no—
74C3×#408—31no—
75#5239—31no—
76#5172—31no—
77#5156—31no—
78#5133—31no—
79C2×#821—31no—
80#5036—31no—
81#4808—31no—
82#4803—31no—
83#4776—31no—
84D3×#102—31no—
85#4734—31no—
86#4734D311yescharacteristic, complemented
87#4733—31no—
88#4733—31no—
89#4732—31no—
90#4732—31no—
91#4731—31no—
92#4731—31no—
93#4731—31no—
94#4731—61no—
95#4727D311yescharacteristic, complemented
96C23×C3⋊D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C3×#235—22no—
111C3×#235—22no—
112C3×#235—22no—
113C3×#235—22no—
114C2×C3×D12D411yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122#3811—28no—
123#3811—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#625—21no—
129C2×#625—21no—
130C2×#624—21no—
131C2×#624—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134D3×D12—28no—
135D3×D12—22no—
136D3×D12—22no—
137D3×D12—22no—
138D3×D12D414yescomplemented
139#3799—28no—
140#3799—22no—
141#3799—22no—
142#3799—22no—
143#3799D414yescomplemented
144#3795—22no—
145#3795—22no—
146C2×C32×C8C2311yescharacteristic
147C2×C32×C8C2311yescharacteristic
148#3757—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151#3744—22no—
152#3744—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×D24—22no—
158C3×#204—22no—
159C3×ΓL(1,𝔽25)—22no—
160C3×D3×C8—22no—
161Dic3⋊Dic3—21no—
162Dic3⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165#3719—22no—
166#3716—22no—
167#3714—22no—
168#3714—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172#1009—64no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#237—31no—
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—61no—
183C2×D3×D4—61no—
184C2×D3×D4—61no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×#235—31no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—61no—
191C2×#235C2×D311yescharacteristic
192C2×#235C2×D311yescharacteristic
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C2×C3×M16—31no—
202C22×C3×C8—31no—
203C3×#121—31no—
204#946—61no—
205C2×#216—31no—
206#939—61no—
207#939—61no—
208#939—61no—
209#938—31no—
210#938—61no—
211#938—61no—
212C2×#214—31no—
213C2×#213—31no—
214C2×#213—31no—
215#930—31no—
216#930C2×D311yescharacteristic, complemented
217C2×C4⋊Dic3—31no—
218#924—31no—
219#924—31no—
220#924—31no—
221#924—61no—
222#916—64no—
223#911—64no—
224#908—64no—
225C2×Dic12—31no—
226#904—64no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24C2×D311yescharacteristic, complemented
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—61no—
236C2×#204—61no—
237C2×#204C2×D311yescharacteristic, complemented
238C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
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—21no—
247C3×C22⋊C8—31no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8C2×D311yescharacteristic, complemented
251C3×C22⋊C8C2×D311yescharacteristic, complemented
252#835—31no—
253#832—31no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—31no—
262#821—61no—
263#821—61no—
264#821C2×D311yescharacteristic, complemented
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267#816—31no—
268#816C2×D311yescharacteristic, complemented
269#809—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3—81no—
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3C2×D411yescharacteristic
280C22×C3×D3C2×D411yescharacteristic
281C2×D32—24no—
282C2×D32—24no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3—21no—
293C4⋊(C3⋊D3)—24no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)C2×D412yes—
297C4⋊(C3⋊D3)C2×D412yes—
298#634—21no—
299#634—21no—
300C3×#67—24no—
301C3×#67—22no—
302C3×#67—22no—
303C3×#67—81no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—22no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12C2×D412yes—
313C3×C4×D3—24no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—21no—
319C3×Dic6—22no—
320C3×Dic6C2×D412yes—
321#626—24no—
322#626—24no—
323#626—24no—
324#626—24no—
325#625—42no—
326#625—81no—
327#624—24no—
328#624—24no—
329D3×Dic3—42no—
330D3×Dic3—81no—
331C32×C8—21no—
332C32×C8—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
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—31no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—121no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×Q8—31no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C22×C3×C4—21no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67D1211yescharacteristic
387C2×#67D1211yescharacteristic
388C22×Dic3—61no—
389C22×Dic3—61no—
390#239—34no—
391#239—62no—
392#239—62no—
393#239—68no—
394#239—62no—
395#237—62no—
396#237—62no—
397D3×D4—34no—
398D3×D4—62no—
399D3×D4—62no—
400D3×D4—68no—
401D3×D4—68no—
402D3×D4—68no—
403D3×D4—68no—
404D3×D4—68no—
405D3×D4—62no—
406#235—22no—
407#235—22no—
408#235—22no—
409#235—22no—
410#235—34no—
411#235—62no—
412#235—62no—
413#235—68no—
414#235—62no—
415#235—62no—
416#235—62no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—34no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—62no—
425C2×D12—62no—
426C2×D12—68no—
427C2×D12—62no—
428C2×D12—62no—
429C2×D12—62no—
430C2×D12—62no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—62no—
438C2×D12—122no—
439C2×D12—122no—
440C2×D12—121no—
441C2×D12D1211yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3C22×D311yescharacteristic
452C2×C4×D3C22×D311yescharacteristic
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—61no—
456C2×Dic6D1211yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×SD16—62no—
459C3×D8—62no—
460C3×M16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—21no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
465C2×C3×C8—62no—
466C2×C3×C8C22×D311yescharacteristic
467C2×C3×C8C22×D311yescharacteristic
468C2×C3×C8C22×D311yescharacteristic
469C2×C3×C8C22×D311yescharacteristic
470C3×C4⋊C4—31no—
471C3×C22⋊C4—61no—
472#217—61no—
473#217—61no—
474#217—61no—
475#217—61no—
476#217—121no—
477#216—62no—
478#214—62no—
479#213—62no—
480#213—62no—
481(C2×D3)⋊C4—21no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3C22×D311yescharacteristic
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—121no—
495C2×C3⋊C8C22×D311yescharacteristic
496C2×C3⋊C8C22×D311yescharacteristic
497Dic12—62no—
498D24—22no—
499D24—62no—
500D24—62no—
501#204—22no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—62no—
506#204—62no—
507#204—122no—
508#204—122no—
509ΓL(1,𝔽25)—22no—
510D3×C8—22no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—84no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
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—41no—
533C2×C3×D3#12012yes—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—41no—
540C3⋊Dic3—41no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—91no—
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—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—31no—
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—31no—
590C22⋊C8—31no—
591C22⋊C8D3211yescharacteristic, complemented
592C23×C3—21no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3C2×D1211yescharacteristic
598C23×C3D3×D411yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—124no—
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×D3—241no—
626C22×D3—242no—
627C22×D3—242no—
628C22×D3C2×D1211yescharacteristic
629C22×D3C2×D1211yescharacteristic
630C3×Q8—32no—
631C3×Q8—62no—
632C3×Q8—61no—
633C3×D4—32no—
634C3×D4—62no—
635C3×D4—62no—
636C3×D4—62no—
637C3×D4—64no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—241no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—31no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—64no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4C2×D1211yescharacteristic
660C2×C3×C4D3×D411yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—24no—
664#67—22no—
665#67—22no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—81no—
671#67—122no—
672#67—122no—
673#67—241no—
674#67—241no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—122no—
684C2×Dic3—241no—
685C2×Dic3C2×D1211yescharacteristic
686C2×Dic3C2×D1211yescharacteristic
687D12—22no—
688D12—21no—
689D12—21no—
690D12—21no—
691D12—32no—
692D12—32no—
693D12—32no—
694D12—32no—
695D12—62no—
696D12—62no—
697D12—64no—
698D12—64no—
699D12—64no—
700D12—64no—
701D12—64no—
702D12—64no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—61no—
707D12—121no—
708D12—121no—
709D12—124no—
710D12D3×D412yes—
711C4×D3—24no—
712C4×D3—21no—
713C4×D3—21no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—122no—
719C4×D3—241no—
720C4×D3D3×D412yes—
721C4×D3D3×D412yes—
722Dic6—21no—
723Dic6—22no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—61no—
728Dic6—121no—
729Dic6—121no—
730Dic6D3×D412yes—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—21no—
735C3×C8—41no—
736C3×C8—41no—
737C3×C8—61no—
738C3×C8—61no—
739C3⋊C8—21no—
740C3⋊C8—21no—
741C2×C32—41no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—42no—
746C3⋊D3—42no—
747C3×D3—22no—
748C3×D3—41no—
749C3×D3—42no—
750C3×D3—81no—
751C24—181no—
752C24—181no—
753C24—181no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—94no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—182no—
763#41—182no—
764#41—188no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8—91no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—61no—
774C2×D4—61no—
775C2×D4—94no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—182no—
779C2×D4—182no—
780C2×D4—182no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—188no—
786C2×D4—181no—
787C2×D4—181no—
788C2×D4—188no—
789C2×D4—188no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4C2×D3211yescharacteristic
801Q16—182no—
802SD16—62no—
803SD16—182no—
804SD16—182no—
805SD16—182no—
806D8—62no—
807D8—182no—
808D8—182no—
809M16—62no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—62no—
813C2×C8C2×D3211yescharacteristic
814C2×C8C2×D3211yescharacteristic
815C4⋊C4—31no—
816C4⋊C4—91no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C4⋊C4—181no—
820C22⋊C4—61no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—32no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—62no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3C22×D1211yescharacteristic
847C22×C3C2×D3×D411yescharacteristic
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—241no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—241no—
877C2×D3—244no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—248no—
884C2×D3#88212yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—41no—
891C3×C4—62no—
892C3×C4—61no—
893C3×C4—121no—
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898Dic3—21no—
899Dic3—22no—
900Dic3—41no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—241no—
906Dic3—241no—
907Dic3#88212yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—31no—
910C23—31no—
911C23—61no—
912C23—61no—
913C23—184no—
914C23—184no—
915C23—184no—
916C23—181no—
917C23—181no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923C23—721no—
924C23D3×D1211yescharacteristic
925Q8—32no—
926Q8—62no—
927Q8—61no—
928Q8—181no—
929Q8—181no—
930D4—32no—
931D4—62no—
932D4—62no—
933D4—62no—
934D4—64no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—92no—
939D4—92no—
940D4—184no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—181no—
946D4—181no—
947D4—241no—
948D4—362no—
949D4—721no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—31no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—31no—
956C2×C4—64no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—362no—
966C2×C4—721no—
967C2×C4D3×D1211yescharacteristic
968C2×C4C22×D3211yescharacteristic
969C8—21no—
970C8—21no—
971C8—61no—
972C8—61no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—41no—
978C2×C3—41no—
979C2×C3—62no—
980C2×C3—122no—
981C2×C3—121no—
982C2×C3—241no—
983C2×C3C2×#88211yescharacteristic
984C2×C3D3×#12011yescharacteristic
985C2×C3#575111yescharacteristic
986C2×C3#575211yescharacteristic
987C2×C3#577011yescharacteristic
988C2×C3#577411yescharacteristic
989D3—22no—
990D3—41no—
991D3—42no—
992D3—81no—
993D3—122no—
994D3—122no—
995D3—122no—
996D3—122no—
997D3—242no—
998D3—242no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—32no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—62no—
1008C22—61no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—182no—
1015C22—182no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22—361no—
1020C22—724no—
1021C22—724no—
1022C22—724no—
1023C22C2×D3×D1211yescharacteristic
1024C4—21no—
1025C4—32no—
1026C4—61no—
1027C4—62no—
1028C4—121no—
1029C4—361no—
1030C4—361no—
1031C4D32×D411yescharacteristic
1032C4D32×D411yescharacteristic
1033C3—21no—
1034C3#7867211yescharacteristic, complemented
1035C3#8008711yescharacteristic, complemented
1036C2—41no—
1037C2—62no—
1038C2—121no—
1039C2—122no—
1040C2—241no—
1041C2—362no—
1042C2—362no—
1043C2D3×#88211yescharacteristic
1044C2#1059467911yescharacteristic
1045C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3012
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×#64308C2semidirect
2. #10595004C2semidirect
3. C2×#63806C2semidirect
4. C2×#63795C2semidirect
5. #10592430C2semidirect
6. C3×#4734C2semidirect
7. C3×#4727C2semidirect
8. #10591173C2semidirect
9. #10591168C2semidirect
10. #10590970C2semidirect
11. #10590946C2semidirect
12. #10590944C2semidirect
13. D3×#821C2semidirect
14. #10590823C2semidirect
15. #10590671C2semidirect
31. C2×#3795C22semidirect
32. #64133C22semidirect
33. C2×#3744C22semidirect
34. C2×#3744C22semidirect
35. C3×#930C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×C3×D3×C8C22semidirect
42. #63908C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63648C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×#816C22semidirect
61. #63566C22semidirect
62. #63564C22semidirect
63. #63564C22semidirect
64. #63563C22semidirect
86. #4734D3semidirect
95. #4727D3semidirect
138. D3×D12D4semidirect
143. #3799D4semidirect
216. #930C2×D3semidirect
229. C2×D24C2×D3semidirect
237. C2×#204C2×D3semidirect
238. C2×ΓL(1,𝔽25)C2×D3semidirect
239. C2×D3×C8C2×D3semidirect
250. C3×C22⋊C8C2×D3semidirect
251. C3×C22⋊C8C2×D3semidirect
254. #830C2×D3semidirect
264. #821C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
591. C22⋊C8D32semidirect
908. C32#3012semidirect
1034. C3#78672semidirect
1035. C3#80087semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
#105950042
C2×#638062
C2×#637952
#105924302
C3×#47342
C3×#47272
#105911732
#105911682
#105909702
#105909462
#105909442
D3×#8212
#105908232
#105906712
#800873
#786723