Finite Group Databasebeta

← #11903614

Subgroups — #11903614

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3830C211yesmaximal, characteristic, complemented
2C3×#5563C211yesmaximal, characteristic, complemented
3C3×#5551C211yesmaximal, characteristic, complemented
4#10595306C212yesmaximal, complemented
5#10595245C212yesmaximal, complemented
6#10595070C212yesmaximal, complemented
7#10594970C212yesmaximal, complemented
8#10594965C212yesmaximal, complemented
9#10594958C212yesmaximal, complemented
10D3×#892C212yesmaximal, complemented
11#10594550C212yesmaximal, complemented
12#10594305C214yesmaximal, complemented
13#10594111C214yesmaximal, complemented
14C4×#3802C211yesmaximal, characteristic, complemented
15#10593956C211yesmaximal, characteristic, complemented
16#10593866C211yesmaximal, characteristic, complemented
17#10593863C211yesmaximal, characteristic, complemented
18#86958—31nomaximal
19#86675—31nomaximal
20C2×#3830C2211yescharacteristic
21C2×C3×#235C2212yes—
22C2×#3802C2211yescharacteristic
23C2×C4×D32C2212yes—
24C32×C4×D4C2211yescharacteristic, complemented
25D4×C3⋊Dic3C2211yescharacteristic, complemented
26C4×#638C2212yes—
27C2×C4×C3⋊Dic3C2212yescomplemented
28#64101C2211yescharacteristic
29#64096C2211yescharacteristic, complemented
30#64090C2212yes—
31#64086C2212yescomplemented
32C42×C3⋊D3C2211yescharacteristic
33C4×#634C2211yescharacteristic, complemented
34C3×#938C2212yescomplemented
35C3×#938C2212yescomplemented
36C3×#930C2212yes—
37C3×#926C2212yescomplemented
38C3×#924C2212yescomplemented
39C3×#892C2212yescomplemented
40C3×D3×C4⋊C4C2212yescomplemented
41C3×#885C2214yescomplemented
42C3×#883C2214yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×#869C2211yescharacteristic, complemented
47#63983C2214yes—
48#63975C2214yes—
49#67⋊Dic3C2214yescomplemented
50#67⋊Dic3C2214yescomplemented
51#67⋊Dic3C2214yescomplemented
52#63970C2214yes—
53#63962C2214yescomplemented
54#63956C2214yescomplemented
55#63921C2212yes—
56D3×(C2×D3)⋊C4C2214yes—
57#63905C2214yes—
58#63902C2212yes—
59C4×#625C2212yes—
60#63900C2211yescharacteristic
61#63898C2211yescharacteristic
62#63898C2212yes—
63#63898C2211yescharacteristic
64D3×C4⋊Dic3C2212yescomplemented
65#63887C2214yescomplemented
66#63878C2214yescomplemented
67C4×D3×Dic3C2214yescomplemented
68#63872C2212yescomplemented
69#63872C2212yescomplemented
70#63871C2212yes—
71#63871C2212yes—
72#63867C2214yescomplemented
73#63863C2212yes—
74#63862C2214yescomplemented
75#63858C2214yescomplemented
76#63857C2212yescomplemented
77#63857C2212yescomplemented
78#63855C2214yescomplemented
79#63849C2212yes—
80#63843C2212yescomplemented
81#63843C2212yescomplemented
82#63843C2212yescomplemented
83#63841C2212yescomplemented
84#63836C2214yes—
85C3×#555—31no—
86C3×#547—31no—
87#5829—32no—
88Dic3×#41—32no—
89#5732—31no—
90#5730—31no—
91#5728—31no—
92#5728—31no—
93#5680—34no—
94#5679—34no—
95#5658—34no—
96#5649—34no—
97#5639—32no—
98#5624—32no—
99#5618—32no—
100#5614—32no—
101#5612—32no—
102#5606—32no—
103#5606—32no—
104#5600—32no—
105#5563D311yescharacteristic, complemented
106#5551D311yescharacteristic, complemented
107C4×D3×D4—31no—
108C4×D3×D4—31no—
109#5543—31no—
110#5542—31no—
111C4×#237—31no—
112C4×#237—31no—
113C4×#237—61no—
114#5529—32no—
115#5529—32no—
116#5522—32no—
117D3×#117—32no—
118#5513—32no—
119C2×#892—32no—
120C22×D32C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2312yes—
124C22×C3⋊Dic3C2312yes—
125C22×C3⋊Dic3C2312yes—
126#3830—24no—
127C2×C4×C3⋊D3C2311yescharacteristic
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×C4×C3⋊D3C2311yescharacteristic
130C2×#634C2311yescharacteristic
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C3×#235—28no—
134C2×C3×D12C2311yescharacteristic
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×Dic6C2312yes—
140C2×C3×Dic6C2312yes—
141C2×#625C2312yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2314yes—
146#3802—24no—
147C4×D32—28no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3757C2312yes—
152#3752C2312yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155#3750C2312yes—
156C4×C3⋊Dic3C2312yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2312yes—
162C3×#217C2314yes—
163C3×#217C2314yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2311yescharacteristic
171C3×C4⋊Dic3C2311yescharacteristic
172C3×C4⋊Dic3C2312yes—
173C3×Dic3⋊C4C2314yes—
174C3×C4×Dic3C2314yes—
175#3724C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3475—91noSylow
190C2×C3×#41—32no—
191C2×#237—31no—
192C2×#237—31no—
193C2×#237—61no—
194C2×D3×D4—31no—
195C2×D3×D4—31no—
196C2×#235C2×D312yes—
197C22×C4×D3—32no—
198C22×C4×D3—32no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—31no—
201C3×#124—34no—
202C3×#123—34no—
203C3×C22⋊Q8—32no—
204C3×#121—32no—
205C3×#121—32no—
206C3×#121—32no—
207C3×C4×D4—21no—
208C3×C4×D4—31no—
209C3×C4×D4—31no—
210C3×C4×D4C2×D311yescharacteristic, complemented
211C3×C4×D4C2×D311yescharacteristic, complemented
212C3×#117—32no—
213C3×#117—32no—
214C2×C3×C4⋊C4—32no—
215#947—32no—
216#946—34no—
217#946—32no—
218#946—32no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222#939—34no—
223#938—34no—
224#938C2×D312yescomplemented
225#938C2×D312yescomplemented
226#937—34no—
227#937—34no—
228#936—32no—
229#935—34no—
230D4×Dic3—31no—
231D4×Dic3—31no—
232D4×Dic3—34no—
233D4×Dic3—34no—
234D4×Dic3—34no—
235D4×Dic3—32no—
236D4×Dic3—31no—
237D4×Dic3—31no—
238D4×Dic3—61no—
239#930C2×D312yes—
240#929—34no—
241C4×#67—32no—
242C4×#67—32no—
243C4×#67—32no—
244C4×#67—32no—
245C4×#67—62no—
246C2×(C2×D3)⋊C4—34no—
247#926—32no—
248#926—34no—
249#926C2×D312yescomplemented
250C2×C4⋊Dic3—32no—
251#924—32no—
252#924—32no—
253#924C2×D312yescomplemented
254C2×C4×Dic3—32no—
255C2×C4×Dic3—32no—
256C2×C4×Dic3—34no—
257C2×C4×Dic3—62no—
258#898—34no—
259#898—34no—
260#897—32no—
261#897—32no—
262#897—32no—
263#897—32no—
264#893—32no—
265#893—31no—
266#893—31no—
267#892—32no—
268#892—31no—
269#892—31no—
270#892—34no—
271#892—32no—
272#892—32no—
273#892—34no—
274#892—61no—
275#892C2×D312yescomplemented
276D3×C4⋊C4—32no—
277D3×C4⋊C4—31no—
278D3×C4⋊C4—31no—
279D3×C4⋊C4C2×D312yescomplemented
280#890—32no—
281#890—32no—
282#890—32no—
283#890—32no—
284#889—34no—
285#887—32no—
286#887—32no—
287#887—32no—
288#887—31no—
289#887—31no—
290#887—61no—
291#886—34no—
292#885C2×D314yescomplemented
293#883—34no—
294#883—34no—
295#883—34no—
296#883C2×D314yescomplemented
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—32no—
301#67⋊C4—32no—
302#67⋊C4—32no—
303#67⋊C4—32no—
304#67⋊C4—62no—
305D3×C22⋊C4—34no—
306D3×C22⋊C4—32no—
307D3×C22⋊C4—32no—
308#879—34no—
309#879—34no—
310#879—34no—
311#879—34no—
312#878—34no—
313#877—32no—
314#877—32no—
315#877—34no—
316#877—62no—
317C4×D12C2×D311yescharacteristic
318C4×D12C2×D311yescharacteristic
319#872—34no—
320#872—34no—
321C42×D3—34no—
322C42×D3—31no—
323C42×D3—31no—
324C42×D3—61no—
325#870—34no—
326#869C2×D311yescharacteristic, complemented
327#869C2×D311yescharacteristic, complemented
328C4×Dic6—31no—
329C4×Dic6—31no—
330C4×Dic6—61no—
331C23×C32C2412yes—
332C22×C3⋊D3C2411yescharacteristic
333C22×C3×D3C2412yes—
334C22×C3×D3C2412yes—
335C2×D32—24no—
336C2×D32—24no—
337C2×D32—42no—
338C32×D4—22no—
339C2×C32×C4—24no—
340C2×C32×C4C2412yes—
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344#638—24no—
345C2×C3⋊Dic3—24no—
346C2×C3⋊Dic3—42no—
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2411yescharacteristic
349C2×C3⋊Dic3C2412yes—
350C2×C3⋊Dic3C2411yescharacteristic
351C2×C3⋊Dic3C2411yescharacteristic
352C4×C3⋊D3—22no—
353C4×C3⋊D3—41no—
354C4×C3⋊D3#4114yescomplemented
355#634—22no—
356C3×#67—28no—
357C3×#67—44no—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2412yes—
362C3×D12—22no—
363C3×D12#4114yescomplemented
364C3×C4×D3—28no—
365C3×C4×D3—24no—
366C3×C4×D3—24no—
367C3×Dic6—24no—
368C3×Dic6—42no—
369#625—24no—
370#624—24no—
371D3×Dic3—24no—
372D3×Dic3—24no—
373D3×Dic3—44no—
374#556—91no—
375#555—31no—
376#554—91no—
377#553—92no—
378#552—92no—
379#552—92no—
380#551—94no—
381#547—31no—
382#546—92no—
383#533—91no—
384#529—92no—
385#529—94no—
386#525—92no—
387C4×#41—92no—
388C4×#41—91no—
389C2×C4×D4—91no—
390C2×#117—92no—
391C23×D3—32no—
392C23×D3—32no—
393C3×#41—68no—
394C2×C3×Q8—32no—
395C2×C3×Q8—32no—
396C2×C3×D4—21no—
397C2×C3×D4—34no—
398C2×C3×D4—34no—
399C2×C3×D4—31no—
400C2×C3×D4—31no—
401C2×C3×D4C22×D311yescharacteristic
402C2×C3×D4C22×D311yescharacteristic
403C22×C3×C4—22no—
404C22×C3×C4—34no—
405C22×C3×C4—32no—
406C22×C3×C4—32no—
407C22×C3×C4C22×D312yes—
408C22×C3×C4C22×D312yes—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—62no—
414C2×#67C22×D314yes—
415C2×#67C22×D314yes—
416C22×Dic3—32no—
417C22×Dic3—32no—
418C22×Dic3—32no—
419C22×Dic3—32no—
420C22×Dic3—32no—
421C22×Dic3—32no—
422C22×Dic3—34no—
423C22×Dic3—62no—
424C22×Dic3—62no—
425#237—64no—
426#237—64no—
427#237—68no—
428D3×D4—64no—
429D3×D4—64no—
430#235—28no—
431C2×D12C22×D311yescharacteristic
432C2×D12C22×D311yescharacteristic
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—34no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—68no—
448C2×C4×D3—68no—
449C2×C4×D3C22×D314yes—
450C2×C4×D3C22×D312yes—
451C2×C4×D3C22×D312yes—
452C2×Dic6—31no—
453C2×Dic6—31no—
454C2×Dic6—61no—
455C2×Dic6C22×D312yes—
456C2×Dic6C22×D312yes—
457C3×C4⋊C4—21no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—22no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—32no—
472C3×C22⋊C4—32no—
473C3×C22⋊C4C22×D312yes—
474C3×C22⋊C4C22×D312yes—
475C3×C42—21no—
476C3×C42—34no—
477C3×C42C22×D311yescharacteristic
478C3×C42C22×D311yescharacteristic
479#217—32no—
480#217—32no—
481#217—34no—
482#217—34no—
483#217—32no—
484#217—34no—
485#217—32no—
486#217—62no—
487#217C22×D314yes—
488#217C22×D314yes—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—62no—
499(C2×D3)⋊C4C22×D312yes—
500(C2×D3)⋊C4C22×D312yes—
501(C2×D3)⋊C4C22×D314yes—
502C4⋊Dic3—31no—
503C4⋊Dic3—31no—
504C4⋊Dic3—34no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—61no—
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D312yes—
513C4⋊Dic3C22×D312yes—
514C4⋊Dic3C22×D311yescharacteristic
515C4⋊Dic3C22×D311yescharacteristic
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—32no—
526Dic3⋊C4—34no—
527Dic3⋊C4—62no—
528Dic3⋊C4—62no—
529Dic3⋊C4C22×D314yes—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—32no—
540C4×Dic3—32no—
541C4×Dic3—32no—
542C4×Dic3—34no—
543C4×Dic3—34no—
544C4×Dic3—34no—
545C4×Dic3—34no—
546C4×Dic3—62no—
547C4×Dic3—61no—
548C4×Dic3—61no—
549C4×Dic3—61no—
550C4×Dic3—62no—
551C4×Dic3—62no—
552C4×Dic3C22×D314yes—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32—22no—
556C22×C32C2511yescharacteristic
557C2×C3⋊D3—21no—
558C2×C3⋊D3—21no—
559C2×C3⋊D3C2×#4112yes—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3C2×#4114yes—
566D32—48no—
567C32×C4—22no—
568C32×C4—21no—
569C32×C4C2×#4112yes—
570C32×C4C2×#4112yes—
571C3⋊Dic3—22no—
572C3⋊Dic3—21no—
573C3⋊Dic3—21no—
574C3⋊Dic3—22no—
575C3⋊Dic3C2×#4112yes—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—24no—
579C3×Dic3—24no—
580C2×#41—32no—
581C2×#41—91no—
582C22×D4—91no—
583C23×C4—92no—
584C4⋊Q8—31no—
585C4⋊Q8—31no—
586#126—94no—
587#126—94no—
588#126—94no—
589#125—94no—
590#125—92no—
591#125—92no—
592#124—34no—
593#124—92no—
594#123—34no—
595#123—94no—
596#123—94no—
597#123—94no—
598C22⋊Q8—32no—
599C22⋊Q8—94no—
600C22⋊Q8—92no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604#121—32no—
605#121—32no—
606#121—32no—
607#121—94no—
608#120—94no—
609C4×Q8—92no—
610C4×Q8—92no—
611C4×Q8—92no—
612C4×Q8—91no—
613C4×Q8—91no—
614C4×D4—31no—
615C4×D4—31no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—91no—
621C4×D4—91no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—91no—
625C4×D4—92no—
626C4×D4—92no—
627C4×D4D3211yescharacteristic, complemented
628#117—32no—
629#117—32no—
630#117—94no—
631#117—94no—
632#117—94no—
633#117—92no—
634#117—92no—
635#117—91no—
636#117—92no—
637C2×C4⋊C4—32no—
638C2×C4⋊C4—91no—
639C2×C4⋊C4—92no—
640C2×C22⋊C4—92no—
641C2×C22⋊C4—94no—
642C2×C42—94no—
643C2×C42—92no—
644C2×C42—91no—
645C23×C3—22no—
646C23×C3—32no—
647C23×C3—32no—
648C23×C3C23×D312yes—
649C23×C3C23×D312yes—
650C22×D3—31no—
651C22×D3—31no—
652C22×D3—61no—
653C22×D3—64no—
654C22×D3—64no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3C23×D312yes—
660C22×D3C23×D312yes—
661C3×Q8—64no—
662C3×Q8—122no—
663C3×D4—24no—
664C3×D4—22no—
665C3×D4—22no—
666C3×D4—34no—
667C3×D4—68no—
668C3×D4—62no—
669C3×D4—124no—
670C2×C3×C4—24no—
671C2×C3×C4—24no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—22no—
675C2×C3×C4—21no—
676C2×C3×C4—32no—
677C2×C3×C4—34no—
678C2×C3×C4—34no—
679C2×C3×C4—32no—
680C2×C3×C4—44no—
681C2×C3×C4—68no—
682C2×C3×C4—64no—
683C2×C3×C4—64no—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D311yescharacteristic
692#67—28no—
693#67—44no—
694#67—64no—
695#67—64no—
696#67—64no—
697#67—68no—
698#67—64no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—62no—
712C2×Dic3—61no—
713C2×Dic3—62no—
714C2×Dic3—64no—
715C2×Dic3—64no—
716C2×Dic3—64no—
717C2×Dic3—64no—
718C2×Dic3—68no—
719C2×Dic3—124no—
720C2×Dic3—122no—
721C2×Dic3—122no—
722C2×Dic3—124no—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D314yes—
725C2×Dic3C23×D314yes—
726C2×Dic3C23×D312yes—
727D12—22no—
728D12#23714yescomplemented
729C4×D3—28no—
730C4×D3—24no—
731C4×D3—24no—
732C4×D3—34no—
733C4×D3—34no—
734C4×D3—64no—
735C4×D3—64no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—62no—
740C4×D3—62no—
741C4×D3—122no—
742C4×D3—121no—
743C4×D3—121no—
744C4×D3—122no—
745C4×D3—124no—
746Dic6—24no—
747Dic6—42no—
748Dic6—64no—
749Dic6—62no—
750Dic6—62no—
751C2×C32—42no—
752C2×C32C22×#4111yescharacteristic
753C2×C32C22×#4111yescharacteristic
754C2×C32#58511yescharacteristic
755C3⋊D3—22no—
756C3×D3—24no—
757C3×D3—42no—
758C24—92no—
759#41—68no—
760#41—184no—
761C2×Q8—32no—
762C2×Q8—32no—
763C2×Q8—91no—
764C2×D4—34no—
765C2×D4—34no—
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—92no—
769C2×D4—92no—
770C2×D4—184no—
771C2×D4C2×D3211yescharacteristic
772C22×C4—34no—
773C22×C4—32no—
774C22×C4—32no—
775C22×C4—92no—
776C22×C4—92no—
777C22×C4—92no—
778C22×C4—94no—
779C22×C4—91no—
780C22×C4—92no—
781C22×C4—92no—
782C22×C4—91no—
783C22×C4—91no—
784C22×C4—188no—
785C22×C4C2×D3212yes—
786C4⋊C4—32no—
787C4⋊C4—34no—
788C4⋊C4—31no—
789C4⋊C4—32no—
790C4⋊C4—31no—
791C4⋊C4—32no—
792C4⋊C4—32no—
793C4⋊C4—94no—
794C4⋊C4—92no—
795C4⋊C4—94no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—91no—
800C4⋊C4—92no—
801C4⋊C4—92no—
802C4⋊C4C2×D3211yescharacteristic
803C22⋊C4—34no—
804C22⋊C4—34no—
805C22⋊C4—34no—
806C22⋊C4—32no—
807C22⋊C4—32no—
808C22⋊C4—94no—
809C22⋊C4—92no—
810C22⋊C4—94no—
811C22⋊C4—92no—
812C22⋊C4—94no—
813C22⋊C4—94no—
814C22⋊C4—92no—
815C22⋊C4—92no—
816C22⋊C4C2×D3212yes—
817C42—34no—
818C42—94no—
819C42—94no—
820C42—92no—
821C42—91no—
822C42—91no—
823C42—92no—
824C42—91no—
825C42—92no—
826C42C2×D3211yescharacteristic
827C22×C3—24no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—21no—
835C22×C3—34no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3C24×D311yescharacteristic
844C22×C3C24×D311yescharacteristic
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—32no—
851C2×D3—32no—
852C2×D3—62no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—128no—
860C2×D3—128no—
861C2×D3C2×#23714yes—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—41no—
869C3×C4—42no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—64no—
873C3×C4—64no—
874C3×C4C2×#23712yes—
875C3×C4D3×#4112yes—
876C3×C4D3×#4112yes—
877C3×C4D3×#4112yes—
878Dic3—24no—
879Dic3—22no—
880Dic3—22no—
881Dic3—24no—
882Dic3—32no—
883Dic3—32no—
884Dic3—62no—
885Dic3—64no—
886Dic3—62no—
887Dic3—61no—
888Dic3—62no—
889Dic3—62no—
890Dic3—61no—
891Dic3—61no—
892Dic3—62no—
893Dic3—62no—
894Dic3—61no—
895Dic3—121no—
896Dic3—122no—
897C32#347511yescharacteristic, complemented, Sylow
898C23—32no—
899C23—32no—
900C23—91no—
901C23—184no—
902C23—184no—
903C23—362no—
904C23C22×D3212yes—
905Q8—64no—
906Q8—122no—
907Q8—182no—
908D4—22no—
909D4—34no—
910D4—68no—
911D4—62no—
912D4—124no—
913D4—184no—
914D4—184no—
915C2×C4—24no—
916C2×C4—32no—
917C2×C4—34no—
918C2×C4—34no—
919C2×C4—32no—
920C2×C4—68no—
921C2×C4—64no—
922C2×C4—64no—
923C2×C4—91no—
924C2×C4—94no—
925C2×C4—91no—
926C2×C4—92no—
927C2×C4—92no—
928C2×C4—91no—
929C2×C4—184no—
930C2×C4—184no—
931C2×C4—184no—
932C2×C4—184no—
933C2×C4—182no—
934C2×C4—361no—
935C2×C4—364no—
936C2×C4—362no—
937C2×C4C22×D3212yes—
938C2×C4C22×D3211yescharacteristic
939C2×C4C22×D3211yescharacteristic
940C2×C4C22×D3211yescharacteristic
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—44no—
945C2×C3—42no—
946C2×C3—42no—
947C2×C3—64no—
948C2×C3—122no—
949C2×C3C22×#23711yescharacteristic
950C2×C3C2×D3×#4111yescharacteristic
951C2×C3C2×D3×#4111yescharacteristic
952C2×C3C2×D3×#4111yescharacteristic
953C2×C3#596611yescharacteristic
954C2×C3#596811yescharacteristic
955D3—24no—
956D3—42no—
957D3—62no—
958D3—62no—
959D3—122no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—34no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—92no—
970C22—181no—
971C22—181no—
972C22—368no—
973C22C23×D3211yescharacteristic
974C4—22no—
975C4—21no—
976C4—62no—
977C4—62no—
978C4—64no—
979C4—64no—
980C4—92no—
981C4—182no—
982C4—181no—
983C4—181no—
984C4—182no—
985C4#6430612yes—
986C4D3×#23712yes—
987C3—21no—
988C3#8667511yescharacteristic, complemented
989C3#8695811yescharacteristic, complemented
990C2—42no—
991C2—64no—
992C2—122no—
993C2—182no—
994C2C2×#6430611yescharacteristic
995C2C2×D3×#23711yescharacteristic
996C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#3830C2semidirect
2. C3×#5563C2semidirect
3. C3×#5551C2semidirect
4. #10595306C2semidirect
5. #10595245C2semidirect
6. #10595070C2semidirect
7. #10594970C2semidirect
8. #10594965C2semidirect
9. #10594958C2semidirect
10. D3×#892C2semidirect
11. #10594550C2semidirect
12. #10594305C2semidirect
13. #10594111C2semidirect
14. C4×#3802C2semidirect
15. #10593956C2semidirect
16. #10593866C2semidirect
17. #10593863C2semidirect
24. C32×C4×D4C22semidirect
25. D4×C3⋊Dic3C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
29. #64096C22semidirect
31. #64086C22semidirect
33. C4×#634C22semidirect
34. C3×#938C22semidirect
35. C3×#938C22semidirect
37. C3×#926C22semidirect
38. C3×#924C22semidirect
39. C3×#892C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C3×#885C22semidirect
42. C3×#883C22semidirect
45. C3×#869C22semidirect
46. C3×#869C22semidirect
49. #67⋊Dic3C22semidirect
50. #67⋊Dic3C22semidirect
51. #67⋊Dic3C22semidirect
53. #63962C22semidirect
54. #63956C22semidirect
64. D3×C4⋊Dic3C22semidirect
65. #63887C22semidirect
66. #63878C22semidirect
67. C4×D3×Dic3C22semidirect
68. #63872C22semidirect
69. #63872C22semidirect
72. #63867C22semidirect
74. #63862C22semidirect
75. #63858C22semidirect
76. #63857C22semidirect
77. #63857C22semidirect
78. #63855C22semidirect
80. #63843C22semidirect
81. #63843C22semidirect
82. #63843C22semidirect
83. #63841C22semidirect
105. #5563D3semidirect
106. #5551D3semidirect
210. C3×C4×D4C2×D3semidirect
211. C3×C4×D4C2×D3semidirect
224. #938C2×D3semidirect
225. #938C2×D3semidirect
249. #926C2×D3semidirect
253. #924C2×D3semidirect
275. #892C2×D3semidirect
279. D3×C4⋊C4C2×D3semidirect
292. #885C2×D3semidirect
296. #883C2×D3semidirect
326. #869C2×D3semidirect
327. #869C2×D3semidirect
354. C4×C3⋊D3#41semidirect
363. C3×D12#41semidirect
627. C4×D4D32semidirect
728. D12#237semidirect
897. C32#3475semidirect
988. C3#86675semidirect
989. C3#86958semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
C3×#55632
C3×#55512
#105953062
#105952452
#105950702
#105949702
#105949652
#105949582
D3×#8922
#105945502
#105943052
#105941112
C4×#38022
#105939562
#105938662
#105938632
#869583
#866753