Finite Group Databasebeta

← #11902006

Subgroups — #11902006

Order 1152.

2533 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C3×#5493C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4#10595519C212yesmaximal, complemented
5C2×#67⋊Dic3C212yesmaximal, complemented
6#10594979C212yesmaximal, complemented
7#10594974C212yesmaximal, complemented
8#10594965C212yesmaximal, complemented
9#10594922C212yesmaximal, complemented
10#10594179C214yesmaximal, complemented
11#10594173C214yesmaximal, complemented
12#10594144C214yesmaximal, complemented
13#10594055C214yesmaximal, complemented
14#86572—31nomaximal
15#86295—31nomaximal
16C22×#638C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C22×C3×#67C2212yes—
20C22×D3×Dic3C2212yescomplemented
21C2×#3796C2212yescomplemented
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic, complemented
24C2×#3750C2211yescharacteristic, complemented
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26#64090C2214yescomplemented
27#64090C2214yescomplemented
28C2×C3×#217C2212yes—
29C3×#930C2212yes—
30C3×#930C2212yes—
31C3×#924C2212yescomplemented
32C3×#924C2212yescomplemented
33C3×#886C2214yescomplemented
34C3×#882C2214yescomplemented
35C3×#878C2214yescomplemented
36C3×#878C2214yescomplemented
37#63981C2214yescomplemented
38#63978C2214yes—
39#63978C2214yes—
40#63977C2214yescomplemented
41#67⋊Dic3C2214yescomplemented
42#67⋊Dic3C2214yescomplemented
43#67⋊Dic3C2214yescomplemented
44#67⋊Dic3C2214yescomplemented
45#63966C2214yescomplemented
46C2×Dic3⋊Dic3C2212yescomplemented
47#63962C2214yescomplemented
48C2×(C2×D3)⋊Dic3C2212yescomplemented
49C2×Dic32C2212yescomplemented
50#63916C2212yescomplemented
51#63907C2214yescomplemented
52#63898C2212yescomplemented
53#63890C2214yescomplemented
54#63887C2214yescomplemented
55#63886C2214yescomplemented
56#63884C2214yescomplemented
57#63881C2214yescomplemented
58#63878C2214yescomplemented
59#63872C2212yescomplemented
60#63871C2212yescomplemented
61#63863C2212yescomplemented
62#63862C2214yescomplemented
63#63858C2214yescomplemented
64#63853C2214yescomplemented
65#63849C2212yescomplemented
66#63848C2214yescomplemented
67#63846C2214yescomplemented
68#63843C2212yescomplemented
69C3×#543—31no—
70C3×#534—31no—
71#5804—32no—
72C2×D4×Dic3—32no—
73#5665—34no—
74#5649—34no—
75#5645—32no—
76#5645—34no—
77#5644—32no—
78#5644—34no—
79#5627—32no—
80#5627—34no—
81#5624—32no—
82#5624—34no—
83#5617—32no—
84#5606—32no—
85#5602—32no—
86#5600—32no—
87#5593—34no—
88#5586—34no—
89#5493—32no—
90#5493D311yescharacteristic, complemented
91C2×#67⋊C4—32no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—61no—
95#5483D311yescharacteristic, complemented
96C24×C32C2311yescharacteristic
97C23×C3⋊D3C2311yescharacteristic
98C23×C3×D3C2312yes—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—24no—
102C2×#638C2314yes—
103C22×C3⋊Dic3—42no—
104C22×C3⋊Dic3C2312yes—
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2312yes—
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4×C3⋊D3—42no—
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2312yes—
112C2×C3×#67—28no—
113C2×C3×#67C2314yes—
114C2×C3×#67C2314yes—
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2312yes—
118C2×C3×D12C2312yes—
119C2×C3×D12C2312yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×#626C2314yes—
123C2×#626C2314yes—
124C2×D3×Dic3—44no—
125C2×D3×Dic3C2314yes—
126C2×D3×Dic3C2314yes—
127#3796—44no—
128C32×C22⋊C4C2314yes—
129#3752C2314yes—
130#3750C2314yes—
131C4×C3⋊Dic3C2312yes—
132C4×C3⋊Dic3C2312yes—
133C3×#217C2314yes—
134C3×#217C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2312yes—
138C3×C4⋊Dic3C2312yes—
139C3×C4⋊Dic3C2312yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147#3722C2314yes—
148#3722C2314yes—
149(C2×D3)⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155#3459—91noSylow
156C22×C3×D4—32no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—61no—
160C22×#67C2×D312yes—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3—32no—
164C23×Dic3—61no—
165C2×#239—32no—
166C2×#237—32no—
167C22×C4×D3—32no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—61no—
171C3×#123—34no—
172C3×C22⋊Q8—32no—
173C3×C22⋊Q8—32no—
174C3×C22⋊Q8—34no—
175C3×C22⋊Q8—34no—
176C3×#121—32no—
177C3×#121—32no—
178C3×#120—34no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C22⋊C4C2×D311yescharacteristic
182C2×C3×C22⋊C4C2×D311yescharacteristic
183#953—34no—
184C2×#217—32no—
185C2×#217C2×D312yes—
186#947—32no—
187#947—34no—
188#946—34no—
189#946—32no—
190Q8×Dic3—32no—
191#939—34no—
192#939—34no—
193#939—34no—
194#938—32no—
195#937—34no—
196#936—32no—
197#935—34no—
198#935—34no—
199D4×Dic3—34no—
200D4×Dic3—34no—
201D4×Dic3—34no—
202D4×Dic3—34no—
203D4×Dic3—32no—
204#930—34no—
205#930—34no—
206#930C2×D312yes—
207#930C2×D312yes—
208#929—34no—
209C2×(C2×D3)⋊C4—32no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—61no—
213C2×C4⋊Dic3—32no—
214#924C2×D312yescomplemented
215#924C2×D312yescomplemented
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—32no—
219C2×Dic3⋊C4—61no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—32no—
223C2×C4×Dic3—32no—
224C2×C4×Dic3—61no—
225#898—34no—
226#898—34no—
227#898—34no—
228#898—34no—
229#897—32no—
230#895—34no—
231#895—32no—
232#894—34no—
233#894—34no—
234#894—34no—
235#893—32no—
236#893—34no—
237#892—34no—
238#892—32no—
239#892—32no—
240#890—34no—
241#890—32no—
242#890—32no—
243#889—34no—
244#887—32no—
245#886—34no—
246#886—34no—
247#886—34no—
248#886C2×D314yescomplemented
249#885—34no—
250#883—34no—
251#882—34no—
252#882—34no—
253#882C2×D314yescomplemented
254#67⋊C4—34no—
255#67⋊C4—34no—
256#67⋊C4—34no—
257#67⋊C4—34no—
258#67⋊C4—34no—
259#67⋊C4—34no—
260#67⋊C4—34no—
261#67⋊C4—34no—
262#67⋊C4—34no—
263#67⋊C4—64no—
264#67⋊C4—64no—
265#879—34no—
266#879—34no—
267#878—34no—
268#878C2×D314yescomplemented
269#878C2×D314yescomplemented
270#877—34no—
271C23×C32—41no—
272C23×C32—41no—
273C23×C32#4114yescomplemented
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C22×C3⋊D3—22no—
277C22×C3⋊D3—41no—
278C22×C3⋊D3—41no—
279C22×C3⋊D3C2412yes—
280C22×C3×D3—24no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2414yes—
284C2×C32×C4—41no—
285C2×C32×C4—41no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288#638—28no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—24no—
292C2×C3⋊Dic3—42no—
293C2×C3⋊Dic3—41no—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2411yescharacteristic
297C2×C3⋊Dic3C2411yescharacteristic
298C4×C3⋊D3—24no—
299C4×C3⋊D3—42no—
300C3×#67—28no—
301C3×#67—28no—
302C2×C3×Dic3—24no—
303C2×C3×Dic3—42no—
304C2×C3×Dic3—42no—
305C2×C3×Dic3C2414yes—
306C2×C3×Dic3C2414yes—
307C2×C3×Dic3C2414yes—
308C3×D12—42no—
309C3×D12—42no—
310C3×Dic6—42no—
311C3×Dic6—42no—
312#626—44no—
313#626—44no—
314D3×Dic3—28no—
315D3×Dic3—44no—
316#543—31no—
317#539—92no—
318#539—94no—
319#538—94no—
320#538—92no—
321#534—31no—
322#534—92no—
323#529—92no—
324#529—94no—
325#525—94no—
326#525—92no—
327C2×C4×D4—92no—
328C2×C4×D4—91no—
329C24×C3—21no—
330C24×C3—32no—
331C24×C3C22×D311yescharacteristic
332C24×C3C22×D311yescharacteristic
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3C22×D312yes—
337C2×C3×Q8—32no—
338C2×C3×Q8—32no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—68no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—28no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—64no—
359C2×#67—68no—
360C2×#67—64no—
361C2×#67—64no—
362C2×#67C22×D314yes—
363C2×#67C22×D314yes—
364C22×Dic3—31no—
365C22×Dic3—32no—
366C22×Dic3—32no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—32no—
372C22×Dic3—32no—
373C22×Dic3—31no—
374C22×Dic3—34no—
375C22×Dic3—34no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—62no—
379C22×Dic3—62no—
380C22×Dic3—61no—
381C22×Dic3—124no—
382C22×Dic3—122no—
383C22×Dic3—122no—
384C22×Dic3—124no—
385C22×Dic3C22×D312yes—
386C22×Dic3C22×D312yes—
387C22×Dic3C22×D312yes—
388#239—124no—
389#237—124no—
390C2×D12—34no—
391C2×D12—34no—
392C2×D12C22×D312yes—
393C2×D12C22×D312yes—
394C2×C4×D3—34no—
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—34no—
398C2×C4×D3—32no—
399C2×C4×D3—32no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—122no—
403C2×C4×D3—122no—
404C2×C4×D3—124no—
405C2×C4×D3—124no—
406C2×Dic6C22×D312yes—
407C2×Dic6C22×D312yes—
408C3×C4⋊C4—32no—
409C3×C4⋊C4—32no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—32no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—32no—
414C3×C22⋊C4—24no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4C22×D314yes—
420C3×C22⋊C4C22×D314yes—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217C22×D314yes—
426#217C22×D314yes—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—64no—
438(C2×D3)⋊C4C22×D314yes—
439(C2×D3)⋊C4C22×D314yes—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3C22×D312yes—
445C4⋊Dic3C22×D312yes—
446C4⋊Dic3C22×D312yes—
447C4⋊Dic3C22×D312yes—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—64no—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D314yes—
457C4×Dic3—32no—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—32no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—62no—
466C4×Dic3—62no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—44no—
472C22×C32C2×#4114yes—
473C22×C32C2×#4112yes—
474C22×C32C2511yescharacteristic
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—44no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482C2×C3×D3—48no—
483C32×C4—22no—
484C32×C4—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3—21no—
487C3⋊Dic3—22no—
488C3⋊Dic3H(5,𝔽2)12yes—
489C3×Dic3—24no—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C2×#41—92no—
493C22×D4—32no—
494C22×D4—91no—
495C23×C4—92no—
496C23×C4—91no—
497C23×C4—91no—
498#126—94no—
499#126—94no—
500#126—94no—
501#125—94no—
502#125—92no—
503#124—94no—
504#124—92no—
505#123—34no—
506#123—94no—
507#123—94no—
508#123—94no—
509#123—94no—
510#123—94no—
511C22⋊Q8—32no—
512C22⋊Q8—32no—
513C22⋊Q8—34no—
514C22⋊Q8—34no—
515C22⋊Q8—94no—
516C22⋊Q8—92no—
517#121—32no—
518#121—32no—
519#121—92no—
520#121—94no—
521#121—94no—
522#121—94no—
523#120—34no—
524#120—94no—
525#120—94no—
526C4×Q8—92no—
527C4×D4—94no—
528C4×D4—94no—
529C4×D4—94no—
530C4×D4—94no—
531C4×D4—94no—
532C4×D4—92no—
533C4×D4—94no—
534C4×D4—94no—
535#117—94no—
536#117—92no—
537C2×C4⋊C4—92no—
538C2×C4⋊C4—91no—
539C2×C22⋊C4—32no—
540C2×C22⋊C4—92no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4D3211yescharacteristic
543C2×C42—92no—
544C2×C42—91no—
545C23×C3—21no—
546C23×C3—22no—
547C23×C3—24no—
548C23×C3—34no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—64no—
556C23×C3—122no—
557C23×C3—122no—
558C23×C3#23714yescomplemented
559C23×C3#23914yescomplemented
560C23×C3C23×D311yescharacteristic
561C23×C3C23×D312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D312yes—
564C22×D3—24no—
565C22×D3—32no—
566C22×D3—32no—
567C22×D3—42no—
568C22×D3—42no—
569C22×D3—62no—
570C22×D3—64no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3C23×D314yes—
580C3×Q8—122no—
581C3×Q8—122no—
582C3×D4—68no—
583C3×D4—68no—
584C3×D4—122no—
585C3×D4—122no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—34no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—64no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D312yes—
603C2×C3×C4C23×D312yes—
604#67—28no—
605#67—28no—
606#67—616no—
607#67—68no—
608#67—68no—
609#67—124no—
610#67—124no—
611C2×Dic3—24no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—31no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—31no—
620C2×Dic3—42no—
621C2×Dic3—42no—
622C2×Dic3—62no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—62no—
626C2×Dic3—68no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—64no—
630C2×Dic3—64no—
631C2×Dic3—64no—
632C2×Dic3—64no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—124no—
636C2×Dic3—124no—
637C2×Dic3—121no—
638C2×Dic3—122no—
639C2×Dic3—122no—
640C2×Dic3—121no—
641C2×Dic3—124no—
642C2×Dic3—122no—
643C2×Dic3C23×D314yes—
644C2×Dic3C23×D314yes—
645C2×Dic3C23×D314yes—
646D12—42no—
647D12—42no—
648D12—124no—
649D12—124no—
650C4×D3—64no—
651C4×D3—64no—
652C4×D3—68no—
653C4×D3—124no—
654C4×D3—122no—
655C4×D3—122no—
656C4×D3—124no—
657C4×D3—124no—
658Dic6—42no—
659Dic6—42no—
660C2×C32—22no—
661C2×C32—24no—
662C2×C32C22×#4111yescharacteristic
663C2×C32C2×H(5,𝔽2)11yescharacteristic
664C2×C32#58511yescharacteristic
665C3⋊D3—42no—
666C3×D3—44no—
667C24—32no—
668C24—91no—
669C24C2×D3211yescharacteristic
670#41—364no—
671C2×Q8—32no—
672C2×Q8—32no—
673C2×D4—34no—
674C2×D4—34no—
675C2×D4—32no—
676C2×D4—32no—
677C2×D4—68no—
678C2×D4—94no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—184no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—94no—
686C22×C4—94no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—92no—
690C22×C4—91no—
691C22×C4—92no—
692C22×C4—92no—
693C22×C4—92no—
694C22×C4—362no—
695C22×C4—364no—
696C22×C4—362no—
697C22×C4C2×D3211yescharacteristic
698C22×C4C2×D3211yescharacteristic
699C4⋊C4—32no—
700C4⋊C4—34no—
701C4⋊C4—32no—
702C4⋊C4—34no—
703C4⋊C4—32no—
704C4⋊C4—32no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C22⋊C4C2×D3214yes—
722C42—94no—
723C42—94no—
724C42—92no—
725C42—92no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—24no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—44no—
742C22×C3—44no—
743C22×C3—48no—
744C22×C3—64no—
745C22×C3—64no—
746C22×C3—64no—
747C22×C3—128no—
748C22×C3C2×#23714yes—
749C22×C3C2×#23712yes—
750C22×C3C2×#23912yes—
751C22×C3C2×#23914yes—
752C22×C3C24×D311yescharacteristic
753C22×C3C24×D311yescharacteristic
754C2×D3—24no—
755C2×D3—24no—
756C2×D3—24no—
757C2×D3—48no—
758C2×D3—64no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—122no—
766C2×D3—122no—
767C2×D3—128no—
768C2×D3—124no—
769C2×D3—124no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—22no—
773C3×C4—22no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—64no—
777C3×C4—64no—
778C3×C4—64no—
779Dic3—24no—
780Dic3—24no—
781Dic3—24no—
782Dic3—32no—
783Dic3—32no—
784Dic3—62no—
785Dic3—62no—
786Dic3—64no—
787Dic3—62no—
788Dic3—62no—
789Dic3—61no—
790Dic3—61no—
791Dic3—62no—
792Dic3—62no—
793Dic3—122no—
794C32#345911yescharacteristic, complemented, Sylow
795C23—34no—
796C23—41no—
797C23—41no—
798C23—64no—
799C23—92no—
800C23—122no—
801C23—122no—
802C23—182no—
803C23—361no—
804C23—361no—
805C23#379614yescomplemented
806C23C22×D3211yescharacteristic
807C23C22×D3212yes—
808Q8—122no—
809Q8—122no—
810D4—68no—
811D4—68no—
812D4—122no—
813D4—122no—
814D4—188no—
815D4—364no—
816D4—364no—
817C2×C4—34no—
818C2×C4—34no—
819C2×C4—34no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—64no—
823C2×C4—91no—
824C2×C4—92no—
825C2×C4—91no—
826C2×C4—92no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—184no—
830C2×C4—188no—
831C2×C4—182no—
832C2×C4—184no—
833C2×C4—182no—
834C2×C4—362no—
835C2×C4—364no—
836C2×C4—362no—
837C2×C4—361no—
838C2×C4C22×D3212yes—
839C2×C4C22×D3212yes—
840C2×C3—24no—
841C2×C3—24no—
842C2×C3—22no—
843C2×C3—22no—
844C2×C3—24no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—44no—
849C2×C3—124no—
850C2×C3C22×#23711yescharacteristic
851C2×C3C22×#23911yescharacteristic
852C2×C3D3×H(5,𝔽2)11yescharacteristic
853C2×C3D3×H(5,𝔽2)11yescharacteristic
854C2×C3#596611yescharacteristic
855C2×C3#596611yescharacteristic
856D3—44no—
857D3—124no—
858D3—122no—
859D3—122no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—22no—
864C22—44no—
865C22—64no—
866C22—64no—
867C22—64no—
868C22—128no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22—364no—
873C22C2×#379614yes—
874C22C2×#379612yes—
875C22C23×D3211yescharacteristic
876C4—22no—
877C4—22no—
878C4—64no—
879C4—64no—
880C4—64no—
881C4—92no—
882C4—182no—
883C4—181no—
884C4—182no—
885C3—21no—
886C3#8629511yescharacteristic, complemented
887C3#8657211yescharacteristic, complemented
888C2—24no—
889C2—22no—
890C2—124no—
891C2—362no—
892C2C22×#379611yescharacteristic
893C2#1059667511yescharacteristic
894C2#1059667911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64090C2semidirect
2. C3×#5493C2semidirect
3. C3×#5483C2semidirect
4. #10595519C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. #10594979C2semidirect
7. #10594974C2semidirect
8. #10594965C2semidirect
9. #10594922C2semidirect
10. #10594179C2semidirect
11. #10594173C2semidirect
12. #10594144C2semidirect
13. #10594055C2semidirect
18. C22×C4×C3⋊D3C22semidirect
20. C22×D3×Dic3C22semidirect
21. C2×#3796C22semidirect
23. C2×#3752C22semidirect
24. C2×#3750C22semidirect
25. C2×C4×C3⋊Dic3C22semidirect
26. #64090C22semidirect
27. #64090C22semidirect
31. C3×#924C22semidirect
32. C3×#924C22semidirect
33. C3×#886C22semidirect
34. C3×#882C22semidirect
35. C3×#878C22semidirect
36. C3×#878C22semidirect
37. #63981C22semidirect
40. #63977C22semidirect
41. #67⋊Dic3C22semidirect
42. #67⋊Dic3C22semidirect
43. #67⋊Dic3C22semidirect
44. #67⋊Dic3C22semidirect
45. #63966C22semidirect
46. C2×Dic3⋊Dic3C22semidirect
47. #63962C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
50. #63916C22semidirect
51. #63907C22semidirect
52. #63898C22semidirect
53. #63890C22semidirect
54. #63887C22semidirect
55. #63886C22semidirect
56. #63884C22semidirect
57. #63881C22semidirect
58. #63878C22semidirect
59. #63872C22semidirect
60. #63871C22semidirect
61. #63863C22semidirect
62. #63862C22semidirect
63. #63858C22semidirect
64. #63853C22semidirect
65. #63849C22semidirect
66. #63848C22semidirect
67. #63846C22semidirect
68. #63843C22semidirect
90. #5493D3semidirect
95. #5483D3semidirect
214. #924C2×D3semidirect
215. #924C2×D3semidirect
248. #886C2×D3semidirect
253. #882C2×D3semidirect
268. #878C2×D3semidirect
269. #878C2×D3semidirect
273. C23×C32#41semidirect
558. C23×C3#237semidirect
559. C23×C3#239semidirect
794. C32#3459semidirect
805. C23#3796semidirect
886. C3#86295semidirect
887. C3#86572semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C3×#54932
C3×#54832
#105955192
C2×#67⋊Dic32
#105949792
#105949742
#105949652
#105949222
#105941792
#105941732
#105941442
#105940552
#865723
#862953