Finite Group Databasebeta

← #11864355

Subgroups — #11864355

Order 1152.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic, complemented
3C2×#63801C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592430C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4727C211yesmaximal, characteristic, complemented
8#10591183C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10590970C211yesmaximal, characteristic, complemented
11#10590966C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14#10590939C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80229—31nomaximal
17#78671—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×D3×Dic6C2211yescharacteristic, complemented
32#64133C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, 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#63969—21no—
41#63959—21no—
42#63884—21no—
43#63857C2211yescharacteristic, complemented
44#63856C2211yescharacteristic, complemented
45#63841C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51#63801—24no—
52D3×#204—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#5825—31no—
68C2×#918—31no—
69C2×D3×SD16—31no—
70C2×#909—31no—
71C22×#204—31no—
72#5628—31no—
73C3×#452—31no—
74C3×#408—31no—
75#5239—31no—
76#5187—31no—
77#5169—31no—
78#5131—31no—
79#5113—31no—
80#5046—31no—
81#4808—31no—
82#4804—31no—
83#4776—31no—
84#4770—31no—
85#4733—31no—
86#4733—31no—
87#4733—31no—
88#4733D311yescharacteristic, complemented
89#4731—31no—
90#4731—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×#67D411yescharacteristic
108C2×C3×#67D411yescharacteristic
109C3×#235—22no—
110C3×#235—22no—
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12D411yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6D411yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121#3811—28no—
122#3811—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129C2×#624—21no—
130C2×D3×Dic3—21no—
131D3×D12—28no—
132D3×D12—22no—
133D3×D12—22no—
134D3×D12—22no—
135D3×D12D414yes—
136#3799—28no—
137#3799—22no—
138#3799—22no—
139#3799—22no—
140#3799D414yes—
141D3×Dic6—22no—
142D3×Dic6—22no—
143C2×C32×C8C2311yescharacteristic
144C2×C32×C8C2311yescharacteristic
145#3757—21no—
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147#3750—21no—
148#3744—22no—
149#3744—22no—
150C3×#217—21no—
151C3×C4⋊Dic3C2311yescharacteristic
152C3×Dic3⋊C4—21no—
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C3×Dic12—22no—
156C3×#204—22no—
157C3×ΓL(1,𝔽25)—22no—
158C3×D3×C8—22no—
159#3724—21no—
160Dic3⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164Dic32—21no—
165#3719—22no—
166#3717—22no—
167#3717—22no—
168#3716—22no—
169#3009—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×D3×Q8—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—61no—
190C2×#235C2×D311yescharacteristic
191C2×#235C2×D311yescharacteristic
192C22×D12—31no—
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—61no—
197C22×D12—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C22×C3×C8—31no—
203C3×C22⋊Q8—31no—
204#946—31no—
205#944—61no—
206C2×#216—31no—
207C2×#215—31no—
208C2×#215—31no—
209#936—61no—
210#935—61no—
211#935—61no—
212C2×#214—31no—
213#926—31no—
214#924—31no—
215#924—31no—
216#924—31no—
217#924—31no—
218#924—61no—
219#924C2×D311yescharacteristic, complemented
220#918—64no—
221D3×SD16—64no—
222#909—64no—
223C2×Dic12—31no—
224C2×Dic12C2×D311yescharacteristic, complemented
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—61no—
233C2×#204—61no—
234C2×#204—64no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
237C2×D3×C8C2×D311yescharacteristic, complemented
238#897—31no—
239#894—61no—
240#892—31no—
241#888—61no—
242#885—61no—
243#883—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×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2×D411yescharacteristic
289C2×C32×C4C2411yescharacteristic
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
292C4⋊(C3⋊D3)—24no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)C2×D412yes—
296C4⋊(C3⋊D3)C2×D412yes—
297#634—21no—
298#634—21no—
299C3×#67—24no—
300C3×#67—22no—
301C3×#67—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—22no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—22no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6C2×D412yes—
320#627—42no—
321#626—24no—
322#626—24no—
323#626—24no—
324#626—24no—
325#624—24no—
326#624—24no—
327D3×Dic3—42no—
328C32×C8—21no—
329C32×C8—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×H(5,𝔽2)—91no—
333C2×#137—91no—
334C22×SD16—91no—
335#536—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—91no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—91no—
346#408—31no—
347C23×D3—61no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—121no—
354C3×#41—62no—
355C3×#41—62no—
356C3×#41—62no—
357C3×#41—62no—
358C2×C3×Q8—31no—
359C2×C3×Q8—31no—
360C2×C3×Q8—31no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—21no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67D1211yescharacteristic
378C2×#67D1211yescharacteristic
379C22×Dic3—61no—
380#239—34no—
381#239—62no—
382#239—62no—
383#239—68no—
384#239—62no—
385D3×Q8—62no—
386D3×Q8—62no—
387D3×D4—34no—
388D3×D4—62no—
389D3×D4—62no—
390D3×D4—68no—
391D3×D4—68no—
392D3×D4—68no—
393D3×D4—68no—
394D3×D4—68no—
395D3×D4—62no—
396#235—22no—
397#235—22no—
398#235—22no—
399#235—22no—
400#235—34no—
401#235—62no—
402#235—62no—
403#235—68no—
404#235—62no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—34no—
410C2×D12—61no—
411C2×D12—61no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—68no—
415C2×D12—62no—
416C2×D12—62no—
417C2×D12—62no—
418C2×D12—62no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—62no—
426C2×D12—122no—
427C2×D12—122no—
428C2×D12—121no—
429C2×D12D1211yescharacteristic
430C2×D12C22×D311yescharacteristic
431C2×C4×D3—21no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×Dic6—31no—
440C2×Dic6—31no—
441C2×Dic6—61no—
442C2×Dic6—62no—
443C2×Dic6—62no—
444C2×Dic6—61no—
445C2×Dic6—61no—
446C2×Dic6D1211yescharacteristic
447C2×Dic6C22×D311yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C3×Q16—62no—
450C3×SD16—62no—
451C3×M16—62no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—31no—
455C2×C3×C8—31no—
456C2×C3×C8—62no—
457C2×C3×C8C22×D311yescharacteristic
458C2×C3×C8C22×D311yescharacteristic
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C3×C4⋊C4—31no—
462C3×C4⋊C4—61no—
463C3×C22⋊C4—61no—
464#217—21no—
465#217—61no—
466#217—61no—
467#217—61no—
468#217—61no—
469#217—61no—
470#217—121no—
471#216—62no—
472#215—62no—
473#215—62no—
474#214—62no—
475(C2×D3)⋊C4—61no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—61no—
481C4⋊Dic3—61no—
482C4⋊Dic3C22×D311yescharacteristic
483Dic3⋊C4—21no—
484Dic3⋊C4—61no—
485Dic3⋊C4—61no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—121no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C2×C3⋊C8C22×D311yescharacteristic
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—22no—
495Dic12—62no—
496#204—22no—
497#204—62no—
498#204—62no—
499#204—62no—
500#204—62no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—122no—
505#204—122no—
506ΓL(1,𝔽25)—22no—
507D3×C8—22no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—22no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—84no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3#12012yes—
528D32—84no—
529D32—84no—
530C32×C4—21no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—41no—
534C3⋊Dic3—41no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3#12012yes—
540H(5,𝔽2)—184no—
541H(5,𝔽2)—184no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C22×Q8—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—181no—
552C22×D4—181no—
553C22×D4—181no—
554#137—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—31no—
565C22×C8—31no—
566C4⋊Q8—181no—
567#124—181no—
568#123—181no—
569#123—181no—
570C22⋊Q8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—91no—
574#117—91no—
575#103—31no—
576#103—91no—
577#102—31no—
578#102—91no—
579#102—91no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—31no—
584C22⋊C8—31no—
585C22⋊C8—31no—
586C22⋊C8D3211yescharacteristic, complemented
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—61no—
591C23×C3C2×D1211yescharacteristic
592C23×C3D3×D411yescharacteristic
593C22×D3—21no—
594C22×D3—64no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—124no—
607C22×D3—241no—
608C22×D3—241no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—242no—
620C22×D3—242no—
621C22×D3C2×D1211yescharacteristic
622C22×D3C2×D1211yescharacteristic
623C3×Q8—32no—
624C3×Q8—62no—
625C3×Q8—61no—
626C3×Q8—61no—
627C3×Q8—61no—
628C3×D4—32no—
629C3×D4—62no—
630C3×D4—62no—
631C3×D4—62no—
632C3×D4—64no—
633C3×D4—61no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—31no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—31no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—64no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4C2×D1211yescharacteristic
653C2×C3×C4D3×D411yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—24no—
657#67—22no—
658#67—22no—
659#67—64no—
660#67—64no—
661#67—64no—
662#67—64no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—122no—
673C2×Dic3C2×D1211yescharacteristic
674C2×Dic3C2×D1211yescharacteristic
675D12—22no—
676D12—21no—
677D12—32no—
678D12—32no—
679D12—32no—
680D12—32no—
681D12—62no—
682D12—62no—
683D12—64no—
684D12—64no—
685D12—64no—
686D12—64no—
687D12—64no—
688D12—64no—
689D12—61no—
690D12—61no—
691D12—61no—
692D12—61no—
693D12—121no—
694D12—121no—
695D12—124no—
696D12D3×D412yes—
697C4×D3—24no—
698C4×D3—21no—
699C4×D3—21no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—122no—
705C4×D3D3×D412yes—
706C4×D3D3×D412yes—
707Dic6—21no—
708Dic6—22no—
709Dic6—21no—
710Dic6—21no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—61no—
715Dic6—121no—
716Dic6—121no—
717Dic6—122no—
718Dic6—122no—
719Dic6D3×D412yes—
720C3×C8—21no—
721C3×C8—21no—
722C3×C8—21no—
723C3×C8—21no—
724C3×C8—41no—
725C3×C8—41no—
726C3×C8—61no—
727C3×C8—61no—
728C3⋊C8—21no—
729C3⋊C8—21no—
730C2×C32—41no—
731C2×C32C2×#12011yescharacteristic
732C2×C32#57711yescharacteristic
733C2×C32#57711yescharacteristic
734C3⋊D3—42no—
735C3⋊D3—42no—
736C3×D3—22no—
737C3×D3—41no—
738C3×D3—42no—
739C24—181no—
740C24—181no—
741C24—181no—
742#41—62no—
743#41—62no—
744#41—62no—
745#41—62no—
746#41—94no—
747#41—182no—
748#41—182no—
749#41—182no—
750#41—188no—
751C2×Q8—31no—
752C2×Q8—31no—
753C2×Q8—31no—
754C2×Q8—91no—
755C2×Q8—181no—
756C2×Q8—182no—
757C2×Q8—182no—
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—31no—
761C2×D4—31no—
762C2×D4—61no—
763C2×D4—94no—
764C2×D4—91no—
765C2×D4—91no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—181no—
770C2×D4—181no—
771C2×D4—182no—
772C2×D4—182no—
773C2×D4—188no—
774C2×D4—181no—
775C2×D4—181no—
776C2×D4—188no—
777C2×D4—188no—
778C2×D4—181no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—61no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—181no—
785C22×C4C2×D3211yescharacteristic
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792SD16—182no—
793SD16—182no—
794M16—62no—
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—62no—
798C2×C8C2×D3211yescharacteristic
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4—91no—
803C4⋊C4—181no—
804C4⋊C4—181no—
805C4⋊C4—181no—
806C22⋊C4—61no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C22⋊C4—181no—
810C22⋊C4—181no—
811C42—181no—
812C22×C3—22no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—32no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—61no—
827C22×C3—61no—
828C22×C3—61no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3C22×D1211yescharacteristic
832C22×C3C2×D3×D411yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—244no—
860C2×D3—244no—
861C2×D3—244no—
862C2×D3—244no—
863C2×D3—244no—
864C2×D3—244no—
865C2×D3—248no—
866C2×D3#88212yes—
867C3×C4—21no—
868C3×C4—21no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—32no—
872C3×C4—41no—
873C3×C4—62no—
874C3×C4—61no—
875C3×C4—121no—
876C3×C4—121no—
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879C3×C4C2×D3×D411yescharacteristic
880C3×C4C2×D3×D411yescharacteristic
881Dic3—21no—
882Dic3—22no—
883Dic3—41no—
884Dic3—41no—
885Dic3—121no—
886Dic3—121no—
887Dic3—121no—
888Dic3—121no—
889Dic3—241no—
890Dic3—241no—
891Dic3#88212yes—
892C32#300911yescharacteristic, complemented, Sylow
893C23—31no—
894C23—31no—
895C23—61no—
896C23—184no—
897C23—184no—
898C23—184no—
899C23—181no—
900C23—181no—
901C23—721no—
902C23—721no—
903C23—721no—
904C23—721no—
905C23—721no—
906C23—721no—
907C23D3×D1211yescharacteristic
908Q8—32no—
909Q8—62no—
910Q8—61no—
911Q8—61no—
912Q8—61no—
913Q8—181no—
914Q8—181no—
915Q8—362no—
916D4—32no—
917D4—62no—
918D4—62no—
919D4—62no—
920D4—64no—
921D4—61no—
922D4—92no—
923D4—92no—
924D4—184no—
925D4—184no—
926D4—184no—
927D4—184no—
928D4—184no—
929D4—181no—
930D4—181no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—31no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—31no—
937C2×C4—64no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—184no—
944C2×C4—184no—
945C2×C4—181no—
946C2×C4—181no—
947C2×C4—362no—
948C2×C4D3×D1211yescharacteristic
949C2×C4C22×D3211yescharacteristic
950C8—21no—
951C8—21no—
952C8—61no—
953C8—61no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—42no—
958C2×C3—41no—
959C2×C3—41no—
960C2×C3—62no—
961C2×C3—122no—
962C2×C3—121no—
963C2×C3C2×#88211yescharacteristic
964C2×C3D3×#12011yescharacteristic
965C2×C3#575111yescharacteristic
966C2×C3#575111yescharacteristic
967C2×C3#577011yescharacteristic
968C2×C3#577811yescharacteristic
969D3—22no—
970D3—41no—
971D3—42no—
972D3—122no—
973D3—122no—
974D3—122no—
975D3—122no—
976D3—242no—
977D3—242no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—32no—
982C22—61no—
983C22—61no—
984C22—61no—
985C22—61no—
986C22—62no—
987C22—61no—
988C22—121no—
989C22—121no—
990C22—182no—
991C22—182no—
992C22—361no—
993C22—361no—
994C22—361no—
995C22—361no—
996C22—724no—
997C22—724no—
998C22—724no—
999C22C2×D3×D1211yescharacteristic
1000C4—21no—
1001C4—32no—
1002C4—61no—
1003C4—62no—
1004C4—121no—
1005C4—121no—
1006C4—361no—
1007C4—361no—
1008C4D32×D411yescharacteristic
1009C4D32×D411yescharacteristic
1010C3—21no—
1011C3#7867111yescharacteristic, complemented
1012C3#8022911yescharacteristic, complemented
1013C2—41no—
1014C2—62no—
1015C2—121no—
1016C2—122no—
1017C2—362no—
1018C2—362no—
1019C2D3×#88211yescharacteristic
1020C2#1059467911yescharacteristic
1021C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#64308C2
hypercenterC22⋊C8D32
hypocenterC32#3009
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
2. #10594884C2semidirect
3. C2×#63801C2semidirect
4. C2×D3×#204C2semidirect
5. #10592430C2semidirect
6. C3×#4733C2semidirect
7. C3×#4727C2semidirect
8. #10591183C2semidirect
9. #10591173C2semidirect
10. #10590970C2semidirect
11. #10590966C2semidirect
12. #10590946C2semidirect
13. #10590942C2semidirect
14. #10590939C2semidirect
15. #10590690C2semidirect
31. C2×D3×Dic6C22semidirect
32. #64133C22semidirect
33. C2×#3744C22semidirect
34. C2×#3744C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×C3×D3×C8C22semidirect
43. #63857C22semidirect
44. #63856C22semidirect
45. #63841C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3716C22semidirect
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
219. #924C2×D3semidirect
224. 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
586. C22⋊C8D32semidirect
892. C32#3009semidirect
1011. C3#78671semidirect
1012. C3#80229semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
#105948842
C2×#638012
C2×D3×#2042
#105924302
C3×#47332
C3×#47272
#105911832
#105911732
#105909702
#105909662
#105909462
#105909422
#105909392
#105906902
#802293
#786713