Finite Group Databasebeta

← #11864605

Subgroups — #11864605

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3C2×#63806C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4731C211yesmaximal, characteristic, complemented
7C3×#4727C211yesmaximal, characteristic, complemented
8#10591184C211yesmaximal, characteristic, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590960C211yesmaximal, characteristic, complemented
12#10590947C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14D3×#821C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80149—31nomaximal
17#78672—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23#64307—24no—
24#64307—24no—
25C2×#3802—21no—
26C2×D3×D12C2211yescharacteristic
27C2×D3×D12C2211yescharacteristic
28C2×#3799C2211yescharacteristic, complemented
29C2×#3796—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32#64139C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, 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×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63806—24no—
52#63794—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63563C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67#5833—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#908—31no—
71C2×#904—31no—
72#5629—31no—
73C3×#450—31no—
74C3×#408—31no—
75#5217—31no—
76#5173—31no—
77#5169—31no—
78#5133—31no—
79C2×#821—31no—
80#5047—31no—
81#4781—31no—
82#4773—31no—
83#4771—31no—
84D3×#102—31no—
85#4734—31no—
86#4734—31no—
87#4734—31no—
88#4734—61no—
89#4733—31no—
90#4733—31no—
91#4732—31no—
92#4732—31no—
93#4731—31no—
94#4731D311yescharacteristic, complemented
95#4727D311yescharacteristic, complemented
96C23×C3×D3—21no—
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×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C3×#235—22no—
111C3×#235—22no—
112C2×C3×D12—21no—
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12D411yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123D3×#67—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#625—21no—
129C2×#625—21no—
130C2×#624—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134#3802—28no—
135D3×D12—22no—
136D3×D12—22no—
137D3×D12—22no—
138D3×D12D414yescomplemented
139#3799—22no—
140#3799—22no—
141#3796—28no—
142#3795—22no—
143#3795—22no—
144#3795—22no—
145#3795D414yescomplemented
146C2×C32×C8C2311yescharacteristic
147C2×C32×C8C2311yescharacteristic
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3745—22no—
151#3744—22no—
152C3×#217—21no—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×Dic3⋊C4—21no—
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×#204—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#3719—22no—
166#3717—22no—
167#3714—22no—
168#3714—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—61no—
178#1004—64no—
179#1004—64no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—61no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×D12C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C22×C3×C8—31no—
203C3×C22⋊Q8—31no—
204#946—31no—
205#946—61no—
206C2×#216—31no—
207C2×#215—31no—
208#939—61no—
209#939—61no—
210#938—61no—
211C2×#213—31no—
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#916—64no—
221#914—64no—
222#908—64no—
223C2×Dic12—31no—
224#904—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—61no—
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—31no—
233C2×#204—61no—
234C2×#204C2×D311yescharacteristic, complemented
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×#102—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#832—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—61no—
261#821C2×D311yescharacteristic, complemented
262#821C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#816—31no—
267#816—31no—
268#816—61no—
269#810—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—24no—
277C22×C3×D3—81no—
278C22×C3×D3—81no—
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—24no—
292#638—81no—
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4×C3⋊D3—24no—
300#634—21no—
301#634C2×D412yes—
302C3×#67—22no—
303C3×#67—22no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—24no—
309C3×D12—22no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12C2×D412yes—
313C3×D12C2×D412yes—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—22no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321#626—24no—
322#626—24no—
323#626—42no—
324#626—81no—
325#625—24no—
326#625—24no—
327#624—42no—
328D3×Dic3—24no—
329D3×Dic3—24no—
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—31no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—31no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—62no—
357C3×#41—62no—
358C2×C3×Q8—31no—
359C2×C3×Q8—31no—
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—61no—
368C22×C3×C4—21no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—68no—
376C2×#67—68no—
377C2×#67—61no—
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×#67—61no—
387C2×#67—121no—
388C2×#67—121no—
389C2×#67D1211yescharacteristic
390C2×#67D1211yescharacteristic
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394#239—68no—
395#239—62no—
396#239—62no—
397#237—34no—
398#237—68no—
399#237—62no—
400#237—62no—
401#237—62no—
402D3×D4—34no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—68no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—68no—
409D3×D4—62no—
410#235—22no—
411#235—22no—
412#235—34no—
413#235—62no—
414#235—62no—
415#235—62no—
416#235—62no—
417#235—62no—
418#235—62no—
419#235—62no—
420#235—62no—
421#235—62no—
422#235—122no—
423#235—122no—
424C2×D12—21no—
425C2×D12—22no—
426C2×D12—22no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12D1211yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×D12C22×D311yescharacteristic
444C2×C4×D3—61no—
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×D3—121no—
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6D1211yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×SD16—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#216—62no—
477#215—62no—
478#213—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—62no—
498D24—62no—
499D24—62no—
500D24—62no—
501D24—62no—
502D24—122no—
503#204—22no—
504#204—22no—
505#204—62no—
506#204—62no—
507#204—62no—
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—41no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
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—84no—
533C2×C3×D3#12012yes—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—22no—
540C3⋊Dic3—41no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
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—31no—
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—91no—
581#103—91no—
582#102—31no—
583#102—31no—
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—64no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—241no—
599C23×C3—241no—
600C23×C3C2×D1211yescharacteristic
601C23×C3D3×D411yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—24no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—64no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—81no—
614C22×D3—81no—
615C22×D3—121no—
616C22×D3—121no—
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×D3C2×D1211yescharacteristic
626C22×D3C2×D1211yescharacteristic
627C3×Q8—62no—
628C3×Q8—61no—
629C3×Q8—61no—
630C3×D4—32no—
631C3×D4—32no—
632C3×D4—62no—
633C3×D4—64no—
634C3×D4—62no—
635C3×D4—62no—
636C3×D4—61no—
637C3×D4—61no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4C2×D1211yescharacteristic
655C2×C3×C4D3×D411yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658#67—22no—
659#67—22no—
660#67—64no—
661#67—64no—
662#67—64no—
663#67—64no—
664#67—64no—
665#67—64no—
666#67—64no—
667#67—64no—
668#67—124no—
669#67—122no—
670#67—241no—
671#67—241no—
672#67—241no—
673#67—242no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—64no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—64no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—241no—
685C2×Dic3C2×D1211yescharacteristic
686C2×Dic3C2×D1211yescharacteristic
687D12—24no—
688D12—22no—
689D12—21no—
690D12—21no—
691D12—32no—
692D12—32no—
693D12—62no—
694D12—64no—
695D12—64no—
696D12—61no—
697D12—61no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—121no—
704D12—121no—
705D12—122no—
706D12—241no—
707D12D3×D412yes—
708D12D3×D412yes—
709C4×D3—21no—
710C4×D3—21no—
711C4×D3—64no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—124no—
716C4×D3—122no—
717C4×D3—122no—
718C4×D3—241no—
719C4×D3D3×D412yes—
720C4×D3D3×D412yes—
721Dic6—22no—
722Dic6—21no—
723Dic6—21no—
724Dic6—32no—
725Dic6—32no—
726Dic6—62no—
727Dic6—61no—
728Dic6—61no—
729Dic6—121no—
730C3×C8—21no—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—41no—
735C3×C8—41no—
736C3×C8—61no—
737C3×C8—61no—
738C3⋊C8—21no—
739C3⋊C8—21no—
740C2×C32—41no—
741C2×C32C2×#12011yescharacteristic
742C2×C32#57611yescharacteristic
743C2×C32#57711yescharacteristic
744C3⋊D3—42no—
745C3⋊D3—81no—
746C3×D3—22no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—42no—
750C24—61no—
751C24—181no—
752C24—181no—
753#41—62no—
754#41—62no—
755#41—94no—
756#41—182no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—182no—
763#41—188no—
764C2×Q8—31no—
765C2×Q8—31no—
766C2×Q8—91no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—61no—
775C2×D4—94no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—182no—
779C2×D4—181no—
780C2×D4—181no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—181no—
784C2×D4—181no—
785C2×D4—188no—
786C2×D4—188no—
787C2×D4—188no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—181no—
795C22×C4—181no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4C2×D3211yescharacteristic
800Q16—182no—
801SD16—62no—
802SD16—62no—
803SD16—182no—
804SD16—182no—
805D8—182no—
806D8—182no—
807D8—182no—
808M16—62no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—62no—
812C2×C8C2×D3211yescharacteristic
813C2×C8C2×D3211yescharacteristic
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—91no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C22⋊C4—61no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—32no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—62no—
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—244no—
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—22no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—84no—
862C2×D3—122no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—241no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—241no—
877C2×D3—241no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3#88212yes—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—41no—
889C3×C4—61no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896Dic3—21no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—62no—
901Dic3—122no—
902Dic3—121no—
903Dic3—121no—
904Dic3—241no—
905Dic3#88212yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—31no—
908C23—31no—
909C23—64no—
910C23—61no—
911C23—61no—
912C23—184no—
913C23—184no—
914C23—181no—
915C23—181no—
916C23—241no—
917C23—241no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23D3×D1211yescharacteristic
923Q8—62no—
924Q8—61no—
925Q8—61no—
926Q8—92no—
927Q8—181no—
928D4—32no—
929D4—32no—
930D4—62no—
931D4—64no—
932D4—62no—
933D4—62no—
934D4—61no—
935D4—61no—
936D4—92no—
937D4—184no—
938D4—184no—
939D4—184no—
940D4—184no—
941D4—184no—
942D4—181no—
943D4—181no—
944D4—181no—
945D4—362no—
946D4—721no—
947D4—721no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—31no—
951C2×C4—32no—
952C2×C4—32no—
953C2×C4—31no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—184no—
959C2×C4—184no—
960C2×C4—184no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—362no—
964C2×C4—721no—
965C2×C4D3×D1211yescharacteristic
966C2×C4C22×D3211yescharacteristic
967C8—21no—
968C8—21no—
969C8—61no—
970C8—61no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—41no—
975C2×C3—41no—
976C2×C3—62no—
977C2×C3—81no—
978C2×C3—121no—
979C2×C3—122no—
980C2×C3—122no—
981C2×C3C2×#88211yescharacteristic
982C2×C3D3×#12011yescharacteristic
983C2×C3#575111yescharacteristic
984C2×C3#575211yescharacteristic
985C2×C3#576211yescharacteristic
986C2×C3#577411yescharacteristic
987D3—22no—
988D3—42no—
989D3—42no—
990D3—41no—
991D3—122no—
992D3—122no—
993D3—242no—
994D3—241no—
995D3—241no—
996D3—481no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—32no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—62no—
1007C22—62no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—182no—
1013C22—244no—
1014C22—361no—
1015C22—361no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22—724no—
1020C22—724no—
1021C22C2×D3×D1211yescharacteristic
1022C4—21no—
1023C4—32no—
1024C4—61no—
1025C4—121no—
1026C4—121no—
1027C4—182no—
1028C4—361no—
1029C4D32×D411yescharacteristic
1030C4D32×D411yescharacteristic
1031C3—21no—
1032C3#7867211yescharacteristic, complemented
1033C3#8014911yescharacteristic, complemented
1034C2—41no—
1035C2—62no—
1036C2—121no—
1037C2—122no—
1038C2—122no—
1039C2—362no—
1040C2—721no—
1041C2D3×#88211yescharacteristic
1042C2#1059467711yescharacteristic
1043C2#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×#64307C2semidirect
2. #10594894C2semidirect
3. C2×#63806C2semidirect
4. C2×#63794C2semidirect
5. #10592433C2semidirect
6. C3×#4731C2semidirect
7. C3×#4727C2semidirect
8. #10591184C2semidirect
9. #10591162C2semidirect
10. #10590968C2semidirect
11. #10590960C2semidirect
12. #10590947C2semidirect
13. #10590942C2semidirect
14. D3×#821C2semidirect
15. #10590670C2semidirect
28. C2×#3799C22semidirect
32. #64139C22semidirect
33. C2×#3745C22semidirect
34. C2×#3744C22semidirect
35. C3×#924C22semidirect
36. C2×C3×#204C22semidirect
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×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63643C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×(C2×D3)⋊C8C22semidirect
61. #63567C22semidirect
62. #63564C22semidirect
63. #63563C22semidirect
64. #63563C22semidirect
94. #4731D3semidirect
95. #4727D3semidirect
138. D3×D12D4semidirect
145. #3795D4semidirect
219. #924C2×D3semidirect
234. C2×#204C2×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
261. #821C2×D3semidirect
262. #821C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
591. C22⋊C8D32semidirect
906. C32#3012semidirect
1032. C3#78672semidirect
1033. C3#80149semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105948942
C2×#638062
C2×#637942
#105924332
C3×#47312
C3×#47272
#105911842
#105911622
#105909682
#105909602
#105909472
#105909422
D3×#8212
#105906702
#801493
#786723