Finite Group Databasebeta

← #11904347

Subgroups — #11904347

Order 1152.

3969 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3#10595992C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595040C211yesmaximal, characteristic, complemented
7#10595022C211yesmaximal, characteristic, complemented
8#10594633C214yesmaximal, complemented
9#10594618C214yesmaximal, complemented
10#10594296C214yesmaximal, complemented
11#10594258C214yesmaximal, complemented
12#10594007C214yesmaximal, complemented
13#10594004C214yesmaximal, complemented
14#86330—31nomaximal
15#86039—31nomaximal
16C23×D32C2212yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic, complemented
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C2×#3811C2214yescomplemented
23C22×#626C2212yescomplemented
24#64308—28no—
25C2×#3802C2218yescomplemented
26C2×D3×D12—28no—
27C2×D3×D12C2214yescomplemented
28C2×D3×D12C2214yescomplemented
29C2×D3×D12C2212yescomplemented
30C2×D3×D12C2212yescomplemented
31C2×#3799C2212yescomplemented
32C2×#3799C2212yescomplemented
33C32×#117C2211yescharacteristic, complemented
34#64135C2211yescharacteristic, complemented
35#64102C2214yescomplemented
36C22⋊C4×C3⋊D3C2214yescomplemented
37C4×C4⋊(C3⋊D3)C2214yescomplemented
38C3×#897C2212yescomplemented
39C3×#895C2212yescomplemented
40C3×#895C2214yescomplemented
41C3×#886C2212yescomplemented
42C3×#882C2212yescomplemented
43C3×#882C2214yescomplemented
44C3×#875C2212yescomplemented
45C3×#874C2212yescomplemented
46C3×C4×D12C2214yescomplemented
47#63976C2212yescomplemented
48#63976C2214yescomplemented
49#63961C2212yescomplemented
50#63922C2218yescomplemented
51#63922C2218yescomplemented
52#63922C2218yescomplemented
53#63921C2218yescomplemented
54#63916C2218yescomplemented
55#63914C2212yescomplemented
56#63912C2218yescomplemented
57#63908C2212yescomplemented
58#63908C2214yescomplemented
59C4×#625C2214yescomplemented
60#63863C2212yescomplemented
61#63856C2212yescomplemented
62#63854C2218yescomplemented
63C2×#1009—31no—
64C2×#1009—31no—
65C22×D3×D4—31no—
66C23×D12—31no—
67C3×#535—31no—
68C3×#525—31no—
69#5830—31no—
70#5828—31no—
71#5805—31no—
72#5791—31no—
73#5717—34no—
74#5676—34no—
75#5653—34no—
76#5630—34no—
77#5612—34no—
78#5609—34no—
79#5609—34no—
80#5589—34no—
81D3×#120—34no—
82D3×#120—34no—
83#5550—34no—
84D4×D12—34no—
85#5525D311yescharacteristic, complemented
86#5524D311yescharacteristic, complemented
87#5521—31no—
88#5521—31no—
89#5521—61no—
90C23×C3⋊D3C2312yes—
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2312yes—
93C22×D32—28no—
94C22×D32—48no—
95C22×D32C2318yes—
96C22×D32C2314yescomplemented
97C22×C32×C4C2311yescharacteristic
98C2×C4⋊(C3⋊D3)D418yescomplemented
99C2×C4⋊(C3⋊D3)C2312yes—
100C2×C4⋊(C3⋊D3)C2312yes—
101C2×C4×C3⋊D3C2318yescomplemented
102C2×C3×#67C2312yes—
103C2×C3×#67C2312yes—
104C22×C3×Dic3C2311yescharacteristic
105C3×#235—24no—
106C3×#235—24no—
107C2×C3×D12—24no—
108C2×C3×D12C2314yes—
109C2×C3×D12C2312yes—
110C2×C3×D12C2312yes—
111C2×C3×D12C2311yescharacteristic, complemented
112C2×C3×D12C2311yescharacteristic, complemented
113C2×C3×D12C2318yescomplemented
114C2×C3×C4×D3—24no—
115C2×C3×C4×D3C2312yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2312yescomplemented
118C2×C3×C4×D3C2312yescomplemented
119C2×C3×Dic6C2311yescharacteristic, complemented
120C2×C3×Dic6C2311yescharacteristic, complemented
121#3811—216no—
122C2×#626—28no—
123C2×#626C2318yes—
124C2×#626C2314yescomplemented
125C2×#626C2314yescomplemented
126C2×#625C2314yes—
127C2×#625C2318yescomplemented
128C2×#624C2314yescomplemented
129#3802—416no—
130D3×D12—216no—
131D3×D12—216no—
132D3×D12—28no—
133D3×D12—28no—
134#3799—28no—
135#3799—28no—
136C32×C4⋊C4C2312yescomplemented
137C32×C22⋊C4C2312yes—
138C32×C42C2312yescomplemented
139#3757C2312yes—
140#3752C2318yescomplemented
141C4⋊(C3⋊Dic3)C2312yescomplemented
142C4×C3⋊Dic3C2312yescomplemented
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2318yescomplemented
145C3×(C2×D3)⋊C4C2314yescomplemented
146C3×C4⋊Dic3C2314yescomplemented
147#3724C2314yescomplemented
148(C2×D3)⋊Dic3C2314yes—
149(C2×D3)⋊Dic3C2318yescomplemented
150(C2×D3)⋊Dic3C2314yescomplemented
151#3484—91noSylow
152C24×D3—32no—
153C24×D3—32no—
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C22×C3×D4—31no—
157C23×C3×C4—31no—
158C22×#67—32no—
159#1009—68no—
160#1009—68no—
161C2×#239—32no—
162C2×#239—32no—
163C2×D3×D4—34no—
164C2×D3×D4—34no—
165C2×D3×D4—38no—
166C2×D3×D4—38no—
167C2×D3×D4—34no—
168C2×D3×D4—34no—
169C2×D3×D4—32no—
170C2×D3×D4—32no—
171C2×D3×D4—68no—
172C2×#235—32no—
173C2×#235—32no—
174C2×#235C2×D311yescharacteristic, complemented
175C2×#235C2×D311yescharacteristic, complemented
176C22×D12—31no—
177C22×D12—31no—
178C22×D12—32no—
179C22×D12—34no—
180C22×D12—34no—
181C22×D12—32no—
182C22×D12—32no—
183C22×D12—61no—
184C22×D12—68no—
185C22×D12C2×D311yescharacteristic, complemented
186C22×C4×D3C2×D311yescharacteristic, complemented
187C3×#127—32no—
188C3×#124—32no—
189C3×#123—32no—
190C3×C22⋊Q8—32no—
191C3×#121—32no—
192C3×#121—34no—
193C3×#120—32no—
194C3×#120—34no—
195C3×C4×D4—34no—
196C3×#117—21no—
197C3×#117C2×D311yescharacteristic, complemented
198C3×#117C2×D311yescharacteristic, complemented
199#953—32no—
200#953—34no—
201#947—32no—
202#946—32no—
203#940—32no—
204#940—32no—
205#938—32no—
206#938—34no—
207#938—38no—
208#937—34no—
209#937—32no—
210#937—38no—
211#937—38no—
212#937—38no—
213#936—32no—
214#935—32no—
215#930—34no—
216#930—32no—
217#929—32no—
218C4×#67—34no—
219C4×#67—34no—
220#926—31no—
221#926—31no—
222#926—61no—
223#924—32no—
224#897C2×D312yescomplemented
225#895—38no—
226#895C2×D312yescomplemented
227#895C2×D314yescomplemented
228#894—38no—
229#893—34no—
230#893—34no—
231#893—64no—
232#886C2×D312yescomplemented
233#884—38no—
234#884—38no—
235#883—38no—
236#882—38no—
237#882—38no—
238#882—38no—
239#882C2×D312yescomplemented
240#882C2×D314yescomplemented
241D3×C22⋊C4—34no—
242D3×C22⋊C4—34no—
243D3×C22⋊C4—38no—
244D3×C22⋊C4—38no—
245D3×C22⋊C4—64no—
246#875C2×D312yescomplemented
247#874C2×D312yescomplemented
248C4×D12—34no—
249C4×D12—34no—
250C4×D12—64no—
251C4×D12C2×D314yescomplemented
252C23×C32C2411yescharacteristic
253C22×C3⋊D3—44no—
254C22×C3⋊D3C2×D418yescomplemented
255C22×C3⋊D3C2414yes—
256C22×C3×D3—22no—
257C22×C3×D3—24no—
258C22×C3×D3—24no—
259C22×C3×D3—44no—
260C22×C3×D3C2414yes—
261C22×C3×D3C2412yes—
262C22×C3×D3C2412yes—
263C22×C3×D3C2412yes—
264C2×D32—216no—
265C2×D32—216no—
266C2×D32—28no—
267C2×D32—48no—
268C2×D32—432no—
269C2×D32—48no—
270C2×C32×C4C2×D414yescomplemented
271C2×C32×C4C2414yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3C2414yes—
275C4⋊(C3⋊D3)C2×D418yescomplemented
276C4⋊(C3⋊D3)C2×D418yescomplemented
277C4×C3⋊D3—48no—
278C3×#67—24no—
279C3×#67—24no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3C2412yes—
282C2×C3×Dic3C2412yes—
283C2×C3×Dic3C2412yes—
284C3×D12—28no—
285C3×D12—24no—
286C3×D12—24no—
287C3×D12—22no—
288C3×D12—22no—
289C3×D12—48no—
290C3×C4×D3—24no—
291C3×C4×D3—24no—
292C3×C4×D3—24no—
293C3×C4×D3—24no—
294C3×Dic6—22no—
295C3×Dic6—22no—
296#626—28no—
297#626—28no—
298#626—216no—
299#625—28no—
300#625—48no—
301#624—28no—
302C2×H(5,𝔽2)—91no—
303C23×D4—91no—
304#546—94no—
305#546—94no—
306D42—94no—
307D42—94no—
308#535—31no—
309#535—91no—
310#534—94no—
311#525—31no—
312#525—91no—
313C2×#120—94no—
314#518—91no—
315C24×C3—31no—
316C24×C3—32no—
317C23×D3—32no—
318C23×D3—32no—
319C23×D3—38no—
320C23×D3—38no—
321C23×D3—34no—
322C23×D3—34no—
323C23×D3—62no—
324C23×D3—68no—
325C23×D3—68no—
326C23×D3—128no—
327C23×D3—128no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D312yes—
330C3×#41—64no—
331C3×#41—64no—
332C2×C3×Q8—31no—
333C2×C3×Q8—31no—
334C2×C3×D4—32no—
335C2×C3×D4—32no—
336C2×C3×D4—32no—
337C2×C3×D4—34no—
338C2×C3×D4—32no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—38no—
342C2×C3×D4—64no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—32no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4—64no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—38no—
355C2×#67—38no—
356C2×#67—38no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—68no—
360C2×#67C22×D312yes—
361C2×#67C22×D312yes—
362C22×Dic3C22×D311yescharacteristic
363#239—68no—
364#239—68no—
365D3×D4—616no—
366D3×D4—616no—
367D3×D4—68no—
368D3×D4—68no—
369D3×D4—616no—
370D3×D4—616no—
371D3×D4—1216no—
372D3×D4—1216no—
373#235—24no—
374#235—24no—
375#235—68no—
376#235—68no—
377C2×D12—24no—
378C2×D12—38no—
379C2×D12—38no—
380C2×D12—32no—
381C2×D12—32no—
382C2×D12—32no—
383C2×D12—32no—
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—38no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—68no—
390C2×D12—616no—
391C2×D12—616no—
392C2×D12—68no—
393C2×D12—68no—
394C2×D12—68no—
395C2×D12C22×D314yes—
396C2×D12C22×D312yes—
397C2×D12C22×D312yes—
398C2×D12C22×D311yescharacteristic, complemented
399C2×D12C22×D311yescharacteristic, complemented
400C2×D12C22×D318yescomplemented
401C2×C4×D3—24no—
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—38no—
405C2×C4×D3—38no—
406C2×C4×D3—68no—
407C2×C4×D3C22×D312yes—
408C2×C4×D3C22×D312yes—
409C2×C4×D3C22×D312yescomplemented
410C2×C4×D3C22×D312yescomplemented
411C2×Dic6C22×D311yescharacteristic, complemented
412C2×Dic6C22×D311yescharacteristic, complemented
413C3×C4⋊C4—22no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4C22×D312yescomplemented
416C3×C4⋊C4C22×D312yescomplemented
417C3×C22⋊C4—22no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—38no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4C22×D312yes—
422C3×C22⋊C4C22×D312yes—
423C3×C42—22no—
424C3×C42C22×D312yescomplemented
425C3×C42C22×D312yescomplemented
426#217—32no—
427#217—32no—
428#217—34no—
429#217—38no—
430#217—34no—
431#217—62no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—38no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—38no—
436(C2×D3)⋊C4—38no—
437(C2×D3)⋊C4—68no—
438(C2×D3)⋊C4C22×D314yes—
439(C2×D3)⋊C4C22×D314yescomplemented
440(C2×D3)⋊C4C22×D318yescomplemented
441C4⋊Dic3—32no—
442C4⋊Dic3—32no—
443C4⋊Dic3—62no—
444C4⋊Dic3C22×D314yescomplemented
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447C4×Dic3—32no—
448C4×Dic3—32no—
449C4×Dic3—62no—
450C22×C32—22no—
451C22×C32C22×D412yes—
452C22×C32C2511yescharacteristic
453C2×C3⋊D3—28no—
454C2×C3⋊D3—48no—
455C2×C3⋊D3C22×D418yes—
456C2×C3×D3—28no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—28no—
465C2×C3×D3—48no—
466C2×C3×D3H(5,𝔽2)14yescomplemented
467D32—432no—
468D32—88no—
469C32×C4—24no—
470C32×C4C22×D412yes—
471C32×C4C22×D412yes—
472C3⋊Dic3—24no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C25—92no—
477H(5,𝔽2)—188no—
478C2×#41—31no—
479C2×#41—31no—
480C2×#41—92no—
481C2×#41—92no—
482C22×D4—31no—
483C22×D4—92no—
484C22×D4—92no—
485C22×D4—94no—
486C22×D4—94no—
487C22×D4—92no—
488C22×D4—94no—
489C22×D4—98no—
490C22×D4—91no—
491C22×D4—188no—
492C23×C4—31no—
493#127—32no—
494#127—92no—
495#124—32no—
496#124—92no—
497#123—32no—
498#123—98no—
499#123—92no—
500C22⋊Q8—32no—
501C22⋊Q8—92no—
502#121—32no—
503#121—34no—
504#121—98no—
505#121—98no—
506#121—92no—
507#121—94no—
508#120—32no—
509#120—34no—
510#120—98no—
511#120—98no—
512#120—98no—
513#120—92no—
514#120—94no—
515C4×D4—34no—
516C4×D4—94no—
517C4×D4—94no—
518C4×D4—94no—
519#117—91no—
520#117D3211yescharacteristic, complemented
521C2×C22⋊C4—98no—
522C2×C22⋊C4—94no—
523C23×C3—21no—
524C23×C3—32no—
525C23×C3—34no—
526C23×C3—32no—
527C23×C3—32no—
528C23×C3—64no—
529C23×C3—62no—
530C23×C3—64no—
531C23×C3—124no—
532C23×C3C23×D311yescharacteristic
533C23×C3C23×D311yescharacteristic
534C22×D3—22no—
535C22×D3—24no—
536C22×D3—24no—
537C22×D3—34no—
538C22×D3—34no—
539C22×D3—38no—
540C22×D3—38no—
541C22×D3—44no—
542C22×D3—64no—
543C22×D3—68no—
544C22×D3—616no—
545C22×D3—616no—
546C22×D3—68no—
547C22×D3—68no—
548C22×D3—616no—
549C22×D3—616no—
550C22×D3—128no—
551C22×D3—128no—
552C22×D3—128no—
553C22×D3—128no—
554C22×D3—1232no—
555C22×D3—1232no—
556C22×D3—124no—
557C22×D3—124no—
558C22×D3—244no—
559C22×D3C23×D314yes—
560C22×D3C23×D312yes—
561C22×D3C23×D312yes—
562C22×D3C23×D312yes—
563C3×Q8—62no—
564C3×Q8—62no—
565C3×D4—68no—
566C3×D4—64no—
567C3×D4—64no—
568C3×D4—64no—
569C3×D4—64no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—128no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—24no—
576C2×C3×C4—24no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—62no—
581C2×C3×C4—64no—
582C2×C3×C4—64no—
583C2×C3×C4—64no—
584C2×C3×C4—64no—
585C2×C3×C4D3×D414yescomplemented
586C2×C3×C4D3×D414yescomplemented
587C2×C3×C4C23×D314yes—
588C2×C3×C4C23×D314yes—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—24no—
594#67—24no—
595#67—68no—
596#67—68no—
597#67—616no—
598#67—68no—
599#67—68no—
600#67—128no—
601#67—128no—
602C2×Dic3—22no—
603C2×Dic3—34no—
604C2×Dic3—34no—
605C2×Dic3—64no—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609D12—28no—
610D12—24no—
611D12—24no—
612D12—22no—
613D12—22no—
614D12—38no—
615D12—38no—
616D12—38no—
617D12—38no—
618D12—48no—
619D12—68no—
620D12—68no—
621D12—616no—
622D12—68no—
623D12—68no—
624C4×D3—24no—
625C4×D3—24no—
626C4×D3—24no—
627C4×D3—24no—
628C4×D3—68no—
629C4×D3—68no—
630C4×D3—128no—
631C4×D3—128no—
632C4×D3—248no—
633Dic6—22no—
634Dic6—22no—
635C2×C32—22no—
636C2×C32C23×D411yescharacteristic
637C2×C32C2×H(5,𝔽2)12yes—
638C3⋊D3—28no—
639C3×D3—24no—
640C3×D3—44no—
641C3×D3—42no—
642C3×D3—42no—
643C24—31no—
644C24—32no—
645C24—98no—
646C24—94no—
647C24—92no—
648C24—188no—
649C24—368no—
650#41—64no—
651#41—64no—
652#41—188no—
653#41—188no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×D4—32no—
657C2×D4—32no—
658C2×D4—34no—
659C2×D4—32no—
660C2×D4—31no—
661C2×D4—32no—
662C2×D4—31no—
663C2×D4—38no—
664C2×D4—64no—
665C2×D4—94no—
666C2×D4—94no—
667C2×D4—98no—
668C2×D4—94no—
669C2×D4—98no—
670C2×D4—92no—
671C2×D4—92no—
672C2×D4—98no—
673C2×D4—1816no—
674C2×D4—1816no—
675C2×D4—188no—
676C2×D4—188no—
677C2×D4—188no—
678C2×D4—1816no—
679C2×D4—3616no—
680C22×C4—31no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—64no—
686C22×C4—94no—
687C22×C4—98no—
688C22×C4C2×D3211yescharacteristic
689C4⋊C4—34no—
690C4⋊C4—94no—
691C4⋊C4—92no—
692C4⋊C4C2×D3212yescomplemented
693C22⋊C4—34no—
694C22⋊C4—38no—
695C22⋊C4—34no—
696C22⋊C4—94no—
697C22⋊C4—98no—
698C22⋊C4—94no—
699C22⋊C4—92no—
700C22⋊C4—98no—
701C22⋊C4C2×D3212yes—
702C42—92no—
703C42C2×D3212yescomplemented
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—34no—
709C22×C3—42no—
710C22×C3—68no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—64no—
716C22×C3—64no—
717C22×C3—68no—
718C22×C3—64no—
719C22×C3—128no—
720C22×C3C2×D3×D412yes—
721C22×C3C2×D3×D412yes—
722C22×C3C24×D311yescharacteristic
723C22×C3C24×D311yescharacteristic
724C2×D3—28no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—24no—
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—28no—
733C2×D3—38no—
734C2×D3—38no—
735C2×D3—48no—
736C2×D3—68no—
737C2×D3—68no—
738C2×D3—68no—
739C2×D3—128no—
740C2×D3—1232no—
741C2×D3—1232no—
742C2×D3—128no—
743C2×D3—128no—
744C2×D3—248no—
745C2×D3—248no—
746C2×D3—248no—
747C2×D3#100914yescomplemented
748C3×C4—24no—
749C3×C4—24no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—44no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4C2×D3×D412yes—
757C3×C4C2×D3×D412yes—
758C3×C4C2×D3×D412yes—
759C3×C4C2×D3×D412yes—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—64no—
764Dic3—64no—
765Dic3—124no—
766C32#348411yescharacteristic, complemented, Sylow
767C23—32no—
768C23—34no—
769C23—32no—
770C23—32no—
771C23—64no—
772C23—62no—
773C23—64no—
774C23—94no—
775C23—98no—
776C23—124no—
777C23—1816no—
778C23—1816no—
779C23—188no—
780C23—364no—
781C23—368no—
782C23—368no—
783C23—3632no—
784C23C22×D3211yescharacteristic
785Q8—62no—
786Q8—62no—
787D4—68no—
788D4—64no—
789D4—64no—
790D4—64no—
791D4—64no—
792D4—62no—
793D4—62no—
794D4—98no—
795D4—98no—
796D4—128no—
797D4—1816no—
798D4—188no—
799D4—188no—
800D4—188no—
801D4—368no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—62no—
806C2×C4—64no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—64no—
810C2×C4—94no—
811C2×C4—188no—
812C2×C4—368no—
813C2×C4#380214yescomplemented
814C2×C4C22×D3214yes—
815C2×C4C22×D3211yescharacteristic
816C2×C4C22×D3211yescharacteristic
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—22no—
821C2×C3—42no—
822C2×C3—64no—
823C2×C3—124no—
824C2×C3—122no—
825C2×C3—122no—
826C2×C3C22×D3×D411yescharacteristic
827C2×C3C22×D3×D411yescharacteristic
828C2×C3C2×#100912yes—
829C2×C3D3×H(5,𝔽2)12yes—
830D3—24no—
831D3—42no—
832D3—44no—
833D3—42no—
834D3—68no—
835D3—68no—
836D3—128no—
837C22—22no—
838C22—34no—
839C22—68no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—64no—
845C22—64no—
846C22—64no—
847C22—68no—
848C22—98no—
849C22—128no—
850C22—188no—
851C22—368no—
852C22—3632no—
853C22—728no—
854C22C2×#380212yes—
855C22C23×D3211yescharacteristic
856C4—24no—
857C4—62no—
858C4—62no—
859C4—62no—
860C4—184no—
861C4C2×#380212yes—
862C4C2×#380212yes—
863C3—21no—
864C3#8603911yescharacteristic, complemented
865C3#8633011yescharacteristic, complemented
866C2—22no—
867C2—64no—
868C2—124no—
869C2—122no—
870C2—122no—
871C2—188no—
872C2C22×#380211yescharacteristic
873C2D3×#100912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C22×D3×D12C2semidirect
3. #10595992C2semidirect
4. C3×#5525C2semidirect
5. C3×#5524C2semidirect
6. #10595040C2semidirect
7. #10595022C2semidirect
8. #10594633C2semidirect
9. #10594618C2semidirect
10. #10594296C2semidirect
11. #10594258C2semidirect
12. #10594007C2semidirect
13. #10594004C2semidirect
16. C23×D32C22semidirect
18. C2×C3×#235C22semidirect
19. C2×C3×#235C22semidirect
20. C22×C3×D12C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C2×#3811C22semidirect
23. C22×#626C22semidirect
25. C2×#3802C22semidirect
27. C2×D3×D12C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×D3×D12C22semidirect
31. C2×#3799C22semidirect
32. C2×#3799C22semidirect
33. C32×#117C22semidirect
34. #64135C22semidirect
35. #64102C22semidirect
36. C22⋊C4×C3⋊D3C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
40. C3×#895C22semidirect
41. C3×#886C22semidirect
42. C3×#882C22semidirect
43. C3×#882C22semidirect
44. C3×#875C22semidirect
45. C3×#874C22semidirect
46. C3×C4×D12C22semidirect
47. #63976C22semidirect
48. #63976C22semidirect
49. #63961C22semidirect
50. #63922C22semidirect
51. #63922C22semidirect
52. #63922C22semidirect
53. #63921C22semidirect
54. #63916C22semidirect
55. #63914C22semidirect
56. #63912C22semidirect
57. #63908C22semidirect
58. #63908C22semidirect
59. C4×#625C22semidirect
60. #63863C22semidirect
61. #63856C22semidirect
62. #63854C22semidirect
85. #5525D3semidirect
86. #5524D3semidirect
96. C22×D32C23semidirect
98. C2×C4⋊(C3⋊D3)D4semidirect
101. C2×C4×C3⋊D3C23semidirect
111. C2×C3×D12C23semidirect
112. C2×C3×D12C23semidirect
113. C2×C3×D12C23semidirect
117. C2×C3×C4×D3C23semidirect
118. C2×C3×C4×D3C23semidirect
119. C2×C3×Dic6C23semidirect
120. C2×C3×Dic6C23semidirect
124. C2×#626C23semidirect
125. C2×#626C23semidirect
127. C2×#625C23semidirect
128. C2×#624C23semidirect
136. C32×C4⋊C4C23semidirect
138. C32×C42C23semidirect
140. #3752C23semidirect
141. C4⋊(C3⋊Dic3)C23semidirect
142. C4×C3⋊Dic3C23semidirect
144. C3×(C2×D3)⋊C4C23semidirect
145. C3×(C2×D3)⋊C4C23semidirect
146. C3×C4⋊Dic3C23semidirect
147. #3724C23semidirect
149. (C2×D3)⋊Dic3C23semidirect
150. (C2×D3)⋊Dic3C23semidirect
174. C2×#235C2×D3semidirect
175. C2×#235C2×D3semidirect
185. C22×D12C2×D3semidirect
186. C22×C4×D3C2×D3semidirect
197. C3×#117C2×D3semidirect
198. C3×#117C2×D3semidirect
224. #897C2×D3semidirect
226. #895C2×D3semidirect
227. #895C2×D3semidirect
232. #886C2×D3semidirect
239. #882C2×D3semidirect
240. #882C2×D3semidirect
246. #875C2×D3semidirect
247. #874C2×D3semidirect
251. C4×D12C2×D3semidirect
254. C22×C3⋊D3C2×D4semidirect
270. C2×C32×C4C2×D4semidirect
275. C4⋊(C3⋊D3)C2×D4semidirect
276. C4⋊(C3⋊D3)C2×D4semidirect
398. C2×D12C22×D3semidirect
399. C2×D12C22×D3semidirect
400. C2×D12C22×D3semidirect
409. C2×C4×D3C22×D3semidirect
410. C2×C4×D3C22×D3semidirect
411. C2×Dic6C22×D3semidirect
412. C2×Dic6C22×D3semidirect
415. C3×C4⋊C4C22×D3semidirect
416. C3×C4⋊C4C22×D3semidirect
424. C3×C42C22×D3semidirect
425. C3×C42C22×D3semidirect
439. (C2×D3)⋊C4C22×D3semidirect
440. (C2×D3)⋊C4C22×D3semidirect
444. C4⋊Dic3C22×D3semidirect
466. C2×C3×D3H(5,𝔽2)semidirect
520. #117D32semidirect
585. C2×C3×C4D3×D4semidirect
586. C2×C3×C4D3×D4semidirect
692. C4⋊C4C2×D32semidirect
703. C42C2×D32semidirect
747. C2×D3#1009semidirect
766. C32#3484semidirect
813. C2×C4#3802semidirect
864. C3#86039semidirect
865. C3#86330semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C22×D3×D122
#105959922
C3×#55252
C3×#55242
#105950402
#105950222
#105946332
#105946182
#105942962
#105942582
#105940072
#105940042
#863303
#860393