Finite Group Databasebeta

← #11864594

Subgroups — #11864594

Order 1152.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592431C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4727C211yesmaximal, characteristic, complemented
8#10591183C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590966C211yesmaximal, characteristic, complemented
12#10590947C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14D3×#821C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#80231—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×#3799C2211yescharacteristic, complemented
32#64139C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34C2×#3745C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic, complemented
40#63971—21no—
41#63958—21no—
42#63909C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63888—21no—
45#63886—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63808—24no—
52#63794—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×#919—31no—
69C2×#914—31no—
70C2×#908—31no—
71C2×#904—31no—
72#5629—31no—
73C3×#452—31no—
74C3×#408—31no—
75#5238—31no—
76#5187—31no—
77#5169—31no—
78#5133—31no—
79C2×#821—31no—
80#5046—31no—
81#4810—31no—
82#4803—31no—
83#4773—31no—
84D3×#102—31no—
85#4734—31no—
86#4734—31no—
87#4733—31no—
88#4733D311yescharacteristic, complemented
89#4732—31no—
90#4732—31no—
91#4732—31no—
92#4732—61no—
93#4731—31no—
94#4731—31no—
95#4727D311yescharacteristic, complemented
96C23×C3⋊D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
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×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6D411yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122#3811—28no—
123#3811—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#624—21no—
131C2×#624—21no—
132C2×#624—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#3799—22no—
144#3799—22no—
145#3799D414yescomplemented
146C2×C32×C8C2311yescharacteristic
147C2×C32×C8C2311yescharacteristic
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3745—22no—
151#3745—22no—
152C3×#217—21no—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×Dic3⋊C4—21no—
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—22no—
158C3×#204—22no—
159C3×ΓL(1,𝔽25)—22no—
160C3×D3×C8—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3717—22no—
167#3717—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—31no—
179C2×#239—61no—
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×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C22×C3×C8—31no—
203C3×C22⋊Q8—31no—
204#946—31no—
205#946—61no—
206C2×#215—31no—
207C2×#215—31no—
208C2×#215—31no—
209#939—61no—
210#939—61no—
211#938—61no—
212C2×#213—31no—
213#930—31no—
214#930—31no—
215#930—31no—
216#930—61no—
217C2×C4⋊Dic3—31no—
218#924—31no—
219#924C2×D311yescharacteristic, complemented
220#919—64no—
221#914—64no—
222#908—64no—
223C2×Dic12C2×D311yescharacteristic, complemented
224#904—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—31no—
230C2×D24—61no—
231C2×D24—61no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
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—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—21no—
276C22×C3⋊D3—81no—
277C22×C3⋊D3—81no—
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
291#638—81no—
292C2×C3⋊Dic3—21no—
293C4⋊(C3⋊D3)—24no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4⋊(C3⋊D3)C2×D412yes—
300C3×#67—24no—
301C3×#67—22no—
302C3×#67—22no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—22no—
309C3×D12—21no—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3C2×D412yes—
315C3×C4×D3C2×D412yes—
316C3×Dic6—21no—
317C3×Dic6—22no—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6C2×D412yes—
321#626—24no—
322#626—24no—
323#626—24no—
324#626—24no—
325#626—42no—
326#626—81no—
327#624—24no—
328#624—24no—
329#624—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—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—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×Q8—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—21no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—121no—
385C2×#67D1211yescharacteristic
386C2×#67D1211yescharacteristic
387C22×Dic3—61no—
388#239—34no—
389#239—62no—
390#239—62no—
391#239—68no—
392#239—62no—
393#239—62no—
394#239—62no—
395D3×D4—34no—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399D3×D4—68no—
400D3×D4—68no—
401D3×D4—68no—
402D3×D4—68no—
403D3×D4—62no—
404#235—22no—
405#235—22no—
406#235—22no—
407#235—22no—
408#235—34no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—62no—
413#235—62no—
414#235—62no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—62no—
426C2×D12—62no—
427C2×D12—68no—
428C2×D12—62no—
429C2×D12—62no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12—122no—
442C2×D12—122no—
443C2×D12—121no—
444C2×D12D1211yescharacteristic
445C2×D12C22×D311yescharacteristic
446C2×C4×D3—21no—
447C2×C4×D3—61no—
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×D3C22×D311yescharacteristic
455C2×C4×D3C22×D311yescharacteristic
456C2×Dic6D1211yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×Q16—62no—
460C3×SD16—62no—
461C3×M16—62no—
462C2×C3×C8—21no—
463C2×C3×C8—21no—
464C2×C3×C8—31no—
465C2×C3×C8—31no—
466C2×C3×C8—62no—
467C2×C3×C8C22×D311yescharacteristic
468C2×C3×C8C22×D311yescharacteristic
469C2×C3×C8C22×D311yescharacteristic
470C2×C3×C8C22×D311yescharacteristic
471C3×C4⋊C4—31no—
472C3×C4⋊C4—61no—
473C3×C22⋊C4—61no—
474#217—21no—
475#217—61no—
476#215—62no—
477#215—62no—
478#215—62no—
479#213—62no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—121no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—21no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495C2×C3⋊C8C22×D311yescharacteristic
496C2×C3⋊C8C22×D311yescharacteristic
497Dic12—22no—
498D24—62no—
499D24—62no—
500D24—62no—
501D24—62no—
502D24—62no—
503D24—122no—
504D24—122no—
505#204—22no—
506#204—62no—
507#204—62no—
508#204—62no—
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—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—84no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—22no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
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—21no—
541C3×Dic3—22no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—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—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—31no—
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—31no—
590C22⋊C8—31no—
591C22⋊C8D3211yescharacteristic, complemented
592C23×C3—21no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—61no—
596C23×C3C2×D1211yescharacteristic
597C23×C3D3×D411yescharacteristic
598C22×D3—21no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—64no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—64no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—124no—
614C22×D3—121no—
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—241no—
627C22×D3—242no—
628C22×D3—242no—
629C22×D3C2×D1211yescharacteristic
630C22×D3C2×D1211yescharacteristic
631C3×Q8—32no—
632C3×Q8—62no—
633C3×Q8—61no—
634C3×Q8—61no—
635C3×Q8—61no—
636C3×D4—32no—
637C3×D4—62no—
638C3×D4—62no—
639C3×D4—62no—
640C3×D4—64no—
641C3×D4—61no—
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×C4—61no—
660C2×C3×C4C2×D1211yescharacteristic
661C2×C3×C4D3×D411yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—24no—
665#67—22no—
666#67—22no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—64no—
671#67—122no—
672#67—241no—
673#67—241no—
674#67—241no—
675#67—242no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—121no—
682C2×Dic3—241no—
683C2×Dic3C2×D1211yescharacteristic
684C2×Dic3C2×D1211yescharacteristic
685D12—22no—
686D12—21no—
687D12—32no—
688D12—32no—
689D12—32no—
690D12—32no—
691D12—62no—
692D12—62no—
693D12—64no—
694D12—64no—
695D12—64no—
696D12—64no—
697D12—64no—
698D12—64no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—61no—
707D12—121no—
708D12—121no—
709D12—121no—
710D12—121no—
711D12—124no—
712D12—122no—
713D12—241no—
714D12D3×D412yes—
715C4×D3—24no—
716C4×D3—21no—
717C4×D3—21no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3—241no—
725C4×D3D3×D412yes—
726C4×D3D3×D412yes—
727Dic6—21no—
728Dic6—22no—
729Dic6—21no—
730Dic6—21no—
731Dic6D3×D412yes—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—21no—
735C3×C8—21no—
736C3×C8—41no—
737C3×C8—41no—
738C3×C8—61no—
739C3×C8—61no—
740C3⋊C8—21no—
741C3⋊C8—21no—
742C2×C32—41no—
743C2×C32C2×#12011yescharacteristic
744C2×C32#57611yescharacteristic
745C2×C32#57711yescharacteristic
746C3⋊D3—42no—
747C3⋊D3—42no—
748C3⋊D3—81no—
749C3×D3—22no—
750C3×D3—41no—
751C3×D3—42no—
752C24—181no—
753C24—181no—
754C24—181no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—94no—
760#41—182no—
761#41—182no—
762#41—182no—
763#41—182no—
764#41—182no—
765#41—188no—
766C2×Q8—31no—
767C2×Q8—31no—
768C2×Q8—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—61no—
774C2×D4—94no—
775C2×D4—91no—
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—181no—
789C2×D4—181no—
790C2×D4—188no—
791C2×D4—188no—
792C2×D4—181no—
793C2×D4—181no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—61no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4—181no—
801C22×C4C2×D3211yescharacteristic
802Q16—62no—
803SD16—62no—
804SD16—182no—
805SD16—182no—
806SD16—182no—
807D8—182no—
808D8—182no—
809D8—182no—
810M16—62no—
811C2×C8—31no—
812C2×C8—31no—
813C2×C8—62no—
814C2×C8C2×D3211yescharacteristic
815C2×C8C2×D3211yescharacteristic
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—91no—
819C4⋊C4—181no—
820C4⋊C4—181no—
821C22⋊C4—61no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22⋊C4—181no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—32no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—62no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3C22×D1211yescharacteristic
845C22×C3C2×D3×D411yescharacteristic
846C2×D3—21no—
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—22no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—121no—
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—121no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—241no—
877C2×D3—241no—
878C2×D3—241no—
879C2×D3—241no—
880C2×D3—241no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—244no—
884C2×D3—244no—
885C2×D3—244no—
886C2×D3—244no—
887C2×D3—248no—
888C2×D3#88212yes—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—32no—
894C3×C4—41no—
895C3×C4—62no—
896C3×C4—61no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4C2×D3×D411yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902C3×C4C2×D3×D411yescharacteristic
903Dic3—21no—
904Dic3—22no—
905Dic3—41no—
906Dic3—41no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910Dic3#88212yes—
911C32#301211yescharacteristic, complemented, Sylow
912C23—31no—
913C23—31no—
914C23—61no—
915C23—184no—
916C23—184no—
917C23—184no—
918C23—181no—
919C23—181no—
920C23—181no—
921C23—721no—
922C23—721no—
923C23—721no—
924C23—721no—
925C23—721no—
926C23—721no—
927C23D3×D1211yescharacteristic
928Q8—32no—
929Q8—62no—
930Q8—61no—
931Q8—61no—
932Q8—61no—
933D4—32no—
934D4—62no—
935D4—62no—
936D4—62no—
937D4—64no—
938D4—61no—
939D4—92no—
940D4—92no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—184no—
946D4—181no—
947D4—181no—
948D4—181no—
949D4—181no—
950D4—362no—
951D4—721no—
952D4—721no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—31no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—31no—
959C2×C4—64no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—184no—
966C2×C4—184no—
967C2×C4—181no—
968C2×C4—362no—
969C2×C4—721no—
970C2×C4D3×D1211yescharacteristic
971C2×C4C22×D3211yescharacteristic
972C8—21no—
973C8—21no—
974C8—61no—
975C8—61no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—42no—
980C2×C3—41no—
981C2×C3—41no—
982C2×C3—62no—
983C2×C3—122no—
984C2×C3—121no—
985C2×C3C2×#88211yescharacteristic
986C2×C3D3×#12011yescharacteristic
987C2×C3#575111yescharacteristic
988C2×C3#575211yescharacteristic
989C2×C3#576911yescharacteristic
990C2×C3#577811yescharacteristic
991D3—22no—
992D3—41no—
993D3—42no—
994D3—122no—
995D3—122no—
996D3—122no—
997D3—122no—
998D3—242no—
999D3—242no—
1000D3—241no—
1001D3—241no—
1002D3—481no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—32no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—62no—
1012C22—61no—
1013C22—121no—
1014C22—121no—
1015C22—182no—
1016C22—182no—
1017C22—361no—
1018C22—361no—
1019C22—361no—
1020C22—361no—
1021C22—361no—
1022C22—361no—
1023C22—361no—
1024C22—724no—
1025C22—724no—
1026C22—724no—
1027C22C2×D3×D1211yescharacteristic
1028C4—21no—
1029C4—32no—
1030C4—61no—
1031C4—62no—
1032C4—121no—
1033C4—121no—
1034C4—361no—
1035C4D32×D411yescharacteristic
1036C4D32×D411yescharacteristic
1037C3—21no—
1038C3#7867211yescharacteristic, complemented
1039C3#8023111yescharacteristic, complemented
1040C2—41no—
1041C2—62no—
1042C2—121no—
1043C2—122no—
1044C2—362no—
1045C2—362no—
1046C2—721no—
1047C2D3×#88211yescharacteristic
1048C2#1059468011yescharacteristic
1049C2#1059471511yescharacteristic
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. #10594894C2semidirect
3. C2×#63808C2semidirect
4. C2×#63794C2semidirect
5. #10592431C2semidirect
6. C3×#4733C2semidirect
7. C3×#4727C2semidirect
8. #10591183C2semidirect
9. #10591163C2semidirect
10. #10590967C2semidirect
11. #10590966C2semidirect
12. #10590947C2semidirect
13. #10590942C2semidirect
14. D3×#821C2semidirect
15. #10590671C2semidirect
31. C2×#3799C22semidirect
32. #64139C22semidirect
33. C2×#3745C22semidirect
34. C2×#3745C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×C3×D3×C8C22semidirect
42. #63909C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63856C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
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
88. #4733D3semidirect
95. #4727D3semidirect
138. D3×D12D4semidirect
145. #3799D4semidirect
219. #924C2×D3semidirect
223. C2×Dic12C2×D3semidirect
235. C2×#204C2×D3semidirect
236. C2×ΓL(1,𝔽25)C2×D3semidirect
237. 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
911. C32#3012semidirect
1038. C3#78672semidirect
1039. C3#80231semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
#105948942
C2×#638082
C2×#637942
#105924312
C3×#47332
C3×#47272
#105911832
#105911632
#105909672
#105909662
#105909472
#105909422
D3×#8212
#105906712
#802313
#786723