Finite Group Databasebeta

← #11904909

Subgroups — #11904909

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C3×#5486C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4#10595519C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6#10595510C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8#10595035C214yesmaximal, complemented
9#10595018C214yesmaximal, complemented
10#10594243C214yesmaximal, complemented
11#10594187C214yesmaximal, complemented
12#10594166C214yesmaximal, complemented
13#10594066C214yesmaximal, complemented
14#86579—31nomaximal
15#85868—31nomaximal
16C24×C3⋊D3C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C22×C4⋊(C3⋊D3)C2212yescomplemented
19C22×C3×#67C2211yescharacteristic
20C22×#626C2212yescomplemented
21C22×#624C2212yescomplemented
22C2×#3799C2214yescomplemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3752C2212yescomplemented
25#64091C2214yes—
26#64091C2212yescomplemented
27#64091C2212yescomplemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C3×C4×#67C2214yescomplemented
32C3×#924C2214yescomplemented
33C3×#67⋊C4C2214yescomplemented
34C3×D3×C22⋊C4C2212yescomplemented
35C3×#878C2214yescomplemented
36C3×#878C2214yescomplemented
37C3×#877C2212yescomplemented
38#63981C2214yes—
39#63981C2212yescomplemented
40#63981C2212yescomplemented
41#63981C2212yescomplemented
42#63978C2214yescomplemented
43#63977C2212yescomplemented
44#63974C2214yescomplemented
45#63974C2214yescomplemented
46#63974C2212yescomplemented
47#63966C2212yescomplemented
48C2×#3722C2212yescomplemented
49C2×#3722C2212yescomplemented
50#63962C2212yescomplemented
51#63957C2212yescomplemented
52#63952C2214yescomplemented
53#63952C2214yescomplemented
54#63910C2214yescomplemented
55#63910C2214yescomplemented
56#63909C2214yescomplemented
57#63907C2214yescomplemented
58#63904C2214yescomplemented
59#63897C2214yescomplemented
60#63897C2214yescomplemented
61#63894C2214yescomplemented
62#63888C2214yescomplemented
63#63868C2214yescomplemented
64#63864C2214yescomplemented
65#63854C2214yescomplemented
66#63850C2214yescomplemented
67#63848C2214yescomplemented
68#63836C2214yescomplemented
69C3×#543—31no—
70C3×#518—31no—
71#5804—31no—
72C2×#937—31no—
73#5644—34no—
74#5637—34no—
75#5637—34no—
76#5630—34no—
77#5630—34no—
78#5627—34no—
79#5560—34no—
80#5556—34no—
81#5550—34no—
82#5547—34no—
83#5527—34no—
84#5493—31no—
85#5490—34no—
86C2×#882—31no—
87C2×#882—31no—
88C2×#882—31no—
89C2×#882—61no—
90#5486—31no—
91#5486—31no—
92#5486D311yescharacteristic, complemented
93C2×D3×C22⋊C4—31no—
94C2×D3×C22⋊C4—31no—
95#5483D311yescharacteristic, complemented
96C24×C32C2311yescharacteristic
97C23×C3⋊D3—24no—
98C23×C3⋊D3—44no—
99C23×C3⋊D3C2311yescharacteristic
100C23×C3⋊D3C2312yes—
101C23×C3⋊D3C2312yes—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2312yes—
106C2×#638—24no—
107C2×#638C2312yes—
108C2×#638C2312yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4⋊(C3⋊D3)—44no—
111C2×C4⋊(C3⋊D3)C2314yes—
112C2×C4⋊(C3⋊D3)C2314yes—
113C2×C3×#67—24no—
114C2×C3×#67C2312yes—
115C2×C3×#67C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2312yes—
118C22×C3×Dic3C2312yes—
119C22×C3×Dic3C2312yes—
120C2×C3×C4×D3C2314yescomplemented
121C2×C3×Dic6C2314yescomplemented
122C2×#626—44no—
123C2×#626C2314yes—
124C2×#626C2314yes—
125C2×#626C2314yescomplemented
126C2×#624—44no—
127C2×#624C2314yes—
128C2×#624C2314yes—
129C2×#624C2314yescomplemented
130#3799—48no—
131C32×C22⋊C4C2312yes—
132C32×C22⋊C4C2312yes—
133#3752C2314yes—
134#3752C2314yes—
135C3×#217C2312yes—
136C3×#217C2312yes—
137C3×#217C2312yes—
138C3×#217C2312yes—
139C3×#217C2312yes—
140C3×#217C2312yes—
141C3×(C2×D3)⋊C4C2314yescomplemented
142C3×C4⋊Dic3C2314yescomplemented
143C3×Dic3⋊C4C2314yescomplemented
144C3×Dic3⋊C4C2314yescomplemented
145C3×Dic3⋊C4C2314yescomplemented
146C3×C4×Dic3C2314yescomplemented
147#3724C2314yescomplemented
148Dic3⋊Dic3C2314yescomplemented
149#3722C2314yes—
150#3722C2314yes—
151#3722C2314yes—
152#3722C2314yes—
153#3722C2314yescomplemented
154#3722C2314yescomplemented
155(C2×D3)⋊Dic3C2314yescomplemented
156Dic32C2314yescomplemented
157#3490—91noSylow
158C24×D3—31no—
159C24×D3—31no—
160C24×D3—61no—
161C22×C3×D4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—32no—
165C22×#67—61no—
166C22×#67C2×D311yescharacteristic
167C2×#239—34no—
168C2×#235—34no—
169C22×D12—32no—
170C22×D12—32no—
171C22×D12—32no—
172C22×D12—62no—
173C22×C4×D3—32no—
174C22×C4×D3—32no—
175C3×C22⋊Q8—34no—
176C3×C22⋊Q8—34no—
177C3×C22⋊Q8—34no—
178C3×C4×D4—34no—
179C3×C4×D4—34no—
180C3×#117—32no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—32no—
186C2×C3×C22⋊C4C2×D311yescharacteristic
187C2×C3×C22⋊C4C2×D311yescharacteristic
188#953—32no—
189C2×#217C2×D311yescharacteristic
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192#947—34no—
193#947—34no—
194#946—34no—
195#939—34no—
196#937—32no—
197#937—34no—
198#937—32no—
199#937—32no—
200#935—32no—
201#930—34no—
202#930—34no—
203#929—32no—
204#929—34no—
205C4×#67—34no—
206C4×#67—34no—
207C4×#67—34no—
208C4×#67C2×D314yescomplemented
209C2×(C2×D3)⋊C4—32no—
210C2×(C2×D3)⋊C4—32no—
211C2×(C2×D3)⋊C4—32no—
212C2×(C2×D3)⋊C4—32no—
213C2×(C2×D3)⋊C4—32no—
214C2×(C2×D3)⋊C4—32no—
215C2×(C2×D3)⋊C4—62no—
216#924C2×D314yescomplemented
217#898—34no—
218#898—34no—
219#898—34no—
220#896—34no—
221#895—34no—
222#895—34no—
223#895—34no—
224#894—34no—
225#894—34no—
226#894—34no—
227#894—34no—
228#894—34no—
229#894—34no—
230#893—34no—
231#893—34no—
232#892—34no—
233#886—32no—
234#886—32no—
235#885—34no—
236#884—34no—
237#884—34no—
238#883—34no—
239#882—32no—
240#882—34no—
241#882—32no—
242#882—32no—
243#882—32no—
244#882—34no—
245#882—32no—
246#882—34no—
247#882—32no—
248#882—32no—
249#882—32no—
250#882—64no—
251#882—62no—
252#882—62no—
253#67⋊C4—34no—
254#67⋊C4—34no—
255#67⋊C4C2×D314yescomplemented
256D3×C22⋊C4—34no—
257D3×C22⋊C4—34no—
258D3×C22⋊C4—34no—
259D3×C22⋊C4—34no—
260D3×C22⋊C4—32no—
261D3×C22⋊C4—32no—
262D3×C22⋊C4C2×D312yescomplemented
263#878C2×D314yescomplemented
264#878C2×D314yescomplemented
265#877—32no—
266#877—32no—
267#877C2×D312yescomplemented
268#876—34no—
269#875—34no—
270C4×D12—34no—
271#872—34no—
272C23×C32—42no—
273C23×C32#4114yescomplemented
274C23×C32C2411yescharacteristic
275C23×C32C2411yescharacteristic
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—24no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3—24no—
280C22×C3⋊D3—24no—
281C22×C3⋊D3—24no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—24no—
285C22×C3⋊D3—42no—
286C22×C3⋊D3—42no—
287C22×C3⋊D3—42no—
288C22×C3⋊D3—42no—
289C22×C3⋊D3—416no—
290C22×C3⋊D3C2412yes—
291C22×C3⋊D3C2412yes—
292C22×C3⋊D3C2412yes—
293C22×C3×D3—22no—
294C22×C3×D3—42no—
295C22×C3×D3C2412yes—
296C2×C32×C4—42no—
297C2×C32×C4C2414yes—
298#638—24no—
299#638—24no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3C2412yes—
302C4⋊(C3⋊D3)—28no—
303C4⋊(C3⋊D3)—44no—
304C3×#67—24no—
305C3×#67—24no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—42no—
308C2×C3×Dic3—42no—
309C2×C3×Dic3—42no—
310C2×C3×Dic3C2414yes—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2414yes—
313C2×C3×Dic3C2412yes—
314C3×C4×D3—44no—
315C3×Dic6—44no—
316#626—28no—
317#626—44no—
318#626—44no—
319#624—28no—
320#624—44no—
321#624—44no—
322#551—94no—
323#551—94no—
324#546—94no—
325#546—94no—
326#543—31no—
327#538—94no—
328#534—91no—
329#525—94no—
330C2×#120—91no—
331C2×#120—91no—
332#518—31no—
333#518—91no—
334C22×C22⋊C4—91no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—31no—
340C23×D3—31no—
341C23×D3—32no—
342C23×D3—32no—
343C23×D3—32no—
344C23×D3—32no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—62no—
350C23×D3—61no—
351C23×D3—62no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—64no—
355C23×D3—64no—
356C23×D3—124no—
357C23×D3—124no—
358C23×D3—124no—
359C23×D3—128no—
360C23×D3C22×D311yescharacteristic
361C2×C3×Q8—34no—
362C2×C3×D4—32no—
363C2×C3×D4—32no—
364C2×C3×D4—64no—
365C22×C3×C4—22no—
366C22×C3×C4—31no—
367C22×C3×C4—32no—
368C22×C3×C4—32no—
369C22×C3×C4—32no—
370C22×C3×C4—34no—
371C22×C3×C4C22×D312yes—
372C22×C3×C4C22×D312yes—
373C2×#67—24no—
374C2×#67—32no—
375C2×#67—32no—
376C2×#67—32no—
377C2×#67—32no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—124no—
386C2×#67—124no—
387C2×#67C22×D312yes—
388C2×#67C22×D312yes—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—61no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D312yes—
394C22×Dic3C22×D312yes—
395C22×Dic3C22×D312yes—
396#239—128no—
397#235—128no—
398C2×D12—34no—
399C2×D12—34no—
400C2×D12—34no—
401C2×D12—34no—
402C2×D12—34no—
403C2×D12—34no—
404C2×D12—34no—
405C2×D12—64no—
406C2×D12—64no—
407C2×D12—124no—
408C2×D12—124no—
409C2×D12—124no—
410C2×D12—128no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—124no—
418C2×C4×D3—124no—
419C2×C4×D3C22×D314yescomplemented
420C2×Dic6C22×D314yescomplemented
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—34no—
424C3×C4⋊C4—34no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—32no—
428C3×C22⋊C4—32no—
429C3×C22⋊C4—32no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4C22×D312yes—
435C3×C22⋊C4C22×D312yes—
436C3×C22⋊C4C22×D312yes—
437C3×C22⋊C4C22×D312yes—
438C3×C42—34no—
439#217—34no—
440#217C22×D312yes—
441#217C22×D312yes—
442#217C22×D312yes—
443#217C22×D312yes—
444#217C22×D312yes—
445#217C22×D312yes—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—64no—
464(C2×D3)⋊C4—64no—
465(C2×D3)⋊C4C22×D314yescomplemented
466C4⋊Dic3—34no—
467C4⋊Dic3C22×D314yescomplemented
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4C22×D314yescomplemented
472Dic3⋊C4C22×D314yescomplemented
473Dic3⋊C4C22×D314yescomplemented
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3C22×D314yescomplemented
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—44no—
481C22×C32C2×#4112yes—
482C22×C32C2×#4112yes—
483C22×C32C2×#4112yes—
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—22no—
486C2×C3⋊D3—28no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—24no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—48no—
494C2×C3⋊D3—48no—
495C2×C3⋊D3—44no—
496C2×C3⋊D3—82no—
497C2×C3⋊D3H(5,𝔽2)14yes—
498C2×C3×D3—22no—
499C2×C3×D3—24no—
500C2×C3×D3—82no—
501C32×C4—24no—
502C3⋊Dic3—22no—
503C3×Dic3—22no—
504C3×Dic3—24no—
505C3×Dic3—24no—
506C3×Dic3—24no—
507C25—91no—
508C2×#41—94no—
509C22×D4—31no—
510C22×D4—92no—
511C22×D4—91no—
512C22×D4—92no—
513C23×C4—92no—
514#126—94no—
515#126—94no—
516#124—94no—
517#124—94no—
518#123—94no—
519#123—92no—
520#123—92no—
521#123—94no—
522#123—94no—
523#123—94no—
524C22⋊Q8—34no—
525C22⋊Q8—34no—
526C22⋊Q8—34no—
527C22⋊Q8—94no—
528#121—94no—
529#121—94no—
530#121—94no—
531#121—94no—
532#120—92no—
533#120—92no—
534#120—94no—
535#120—92no—
536#120—92no—
537#120—92no—
538#120—92no—
539#120—94no—
540C4×D4—34no—
541C4×D4—34no—
542C4×D4—94no—
543C4×D4—94no—
544C4×D4—94no—
545C4×D4—94no—
546#117—32no—
547#117—94no—
548#117—92no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—94no—
554C2×C22⋊C4—94no—
555C2×C22⋊C4—92no—
556C2×C22⋊C4—92no—
557C2×C22⋊C4—92no—
558C2×C22⋊C4—92no—
559C2×C22⋊C4D3211yescharacteristic
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—24no—
564C23×C3—32no—
565C23×C3—42no—
566C23×C3—42no—
567C23×C3—44no—
568C23×C3—62no—
569C23×C3—122no—
570C23×C3#23514yescomplemented
571C23×C3#23914yescomplemented
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C23×C3C23×D311yescharacteristic
575C23×C3C23×D311yescharacteristic
576C23×C3C23×D311yescharacteristic
577C23×C3C23×D311yescharacteristic
578C22×D3—22no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—32no—
582C22×D3—32no—
583C22×D3—32no—
584C22×D3—32no—
585C22×D3—42no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—64no—
590C22×D3—64no—
591C22×D3—64no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—64no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—68no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—62no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—124no—
607C22×D3—124no—
608C22×D3—122no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3—122no—
612C22×D3—122no—
613C22×D3—122no—
614C22×D3—122no—
615C22×D3—122no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—122no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—1216no—
624C22×D3—1216no—
625C22×D3—124no—
626C22×D3—1232no—
627C22×D3—124no—
628C22×D3C23×D312yes—
629C3×Q8—124no—
630C3×D4—64no—
631C3×D4—64no—
632C2×C3×C4—24no—
633C2×C3×C4—34no—
634C2×C3×C4—34no—
635C2×C3×C4—32no—
636C2×C3×C4—34no—
637C2×C3×C4—42no—
638C2×C3×C4—42no—
639C2×C3×C4—44no—
640C2×C3×C4—62no—
641C2×C3×C4—124no—
642C2×C3×C4—122no—
643C2×C3×C4—122no—
644C2×C3×C4—122no—
645C2×C3×C4C23×D314yes—
646C2×C3×C4C23×D314yes—
647#67—24no—
648#67—24no—
649#67—68no—
650#67—64no—
651#67—64no—
652#67—64no—
653#67—64no—
654#67—124no—
655#67—124no—
656#67—124no—
657#67—124no—
658C2×Dic3—22no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—42no—
662C2×Dic3—42no—
663C2×Dic3—42no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—122no—
668C2×Dic3C23×D314yes—
669C2×Dic3C23×D314yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D314yes—
672D12—68no—
673D12—68no—
674D12—68no—
675D12—128no—
676D12—124no—
677D12—124no—
678D12—128no—
679D12—124no—
680D12—124no—
681C4×D3—44no—
682C4×D3—68no—
683C4×D3—68no—
684C4×D3—124no—
685C4×D3—124no—
686C4×D3—124no—
687C4×D3—124no—
688Dic6—44no—
689C2×C32—22no—
690C2×C32—22no—
691C2×C32—22no—
692C2×C32C22×#4111yescharacteristic
693C2×C32C2×H(5,𝔽2)12yes—
694C3⋊D3—24no—
695C3⋊D3—42no—
696C3⋊D3—42no—
697C3×D3—42no—
698C24—31no—
699C24—91no—
700C24—92no—
701C24—92no—
702C24—91no—
703C24—91no—
704C24—184no—
705C24—364no—
706C24C2×D3211yescharacteristic
707#41—368no—
708C2×Q8—34no—
709C2×D4—32no—
710C2×D4—32no—
711C2×D4—64no—
712C2×D4—94no—
713C2×D4—94no—
714C2×D4—94no—
715C2×D4—92no—
716C2×D4—92no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—184no—
720C2×D4—364no—
721C2×D4—364no—
722C22×C4—31no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—34no—
727C22×C4—94no—
728C22×C4—94no—
729C22×C4—94no—
730C22×C4—91no—
731C22×C4—364no—
732C22×C4C2×D3212yes—
733C4⋊C4—34no—
734C4⋊C4—34no—
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C22⋊C4—32no—
740C22⋊C4—32no—
741C22⋊C4—32no—
742C22⋊C4—32no—
743C22⋊C4—32no—
744C22⋊C4—32no—
745C22⋊C4—34no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4C2×D3212yes—
756C22⋊C4C2×D3212yes—
757C42—34no—
758C42—94no—
759C22×C3—24no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—21no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—44no—
773C22×C3—44no—
774C22×C3—48no—
775C22×C3—62no—
776C22×C3—64no—
777C22×C3—242no—
778C22×C3C2×#23512yes—
779C22×C3C2×#23512yes—
780C22×C3C2×#23512yes—
781C22×C3C2×#23912yes—
782C22×C3C2×#23912yes—
783C22×C3C2×#23912yes—
784C22×C3C24×D311yescharacteristic
785C22×C3C24×D311yescharacteristic
786C2×D3—22no—
787C2×D3—24no—
788C2×D3—34no—
789C2×D3—34no—
790C2×D3—64no—
791C2×D3—68no—
792C2×D3—68no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—64no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—64no—
803C2×D3—64no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—82no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—128no—
814C2×D3—124no—
815C2×D3—122no—
816C2×D3—128no—
817C2×D3—128no—
818C2×D3—128no—
819C2×D3—128no—
820C2×D3—1216no—
821C2×D3—124no—
822C2×D3—124no—
823C2×D3—1216no—
824C2×D3—128no—
825C2×D3—242no—
826C2×D3—242no—
827C2×D3—244no—
828C3×C4—24no—
829C3×C4—24no—
830C3×C4—44no—
831C3×C4—62no—
832C3×C4—64no—
833C3×C4—64no—
834C3×C4—64no—
835Dic3—22no—
836Dic3—24no—
837Dic3—24no—
838Dic3—24no—
839Dic3—62no—
840Dic3—62no—
841Dic3—122no—
842C32#349011yescharacteristic, complemented, Sylow
843C23—32no—
844C23—42no—
845C23—62no—
846C23—92no—
847C23—92no—
848C23—92no—
849C23—122no—
850C23—184no—
851C23—184no—
852C23—184no—
853C23—182no—
854C23—184no—
855C23—184no—
856C23—182no—
857C23—182no—
858C23—362no—
859C23—362no—
860C23—362no—
861C23—362no—
862C23—3616no—
863C23#379914yescomplemented
864C23C22×D3211yescharacteristic
865C23C22×D3211yescharacteristic
866C23C22×D3211yescharacteristic
867Q8—124no—
868D4—64no—
869D4—64no—
870D4—188no—
871D4—188no—
872D4—184no—
873D4—184no—
874D4—364no—
875D4—364no—
876D4—364no—
877C2×C4—32no—
878C2×C4—34no—
879C2×C4—34no—
880C2×C4—34no—
881C2×C4—42no—
882C2×C4—62no—
883C2×C4—92no—
884C2×C4—124no—
885C2×C4—122no—
886C2×C4—122no—
887C2×C4—122no—
888C2×C4—188no—
889C2×C4—182no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4C22×D3214yes—
893C2×C3—24no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—21no—
901C2×C3—22no—
902C2×C3—42no—
903C2×C3—42no—
904C2×C3—122no—
905C2×C3C22×#23511yescharacteristic
906C2×C3C22×#23911yescharacteristic
907C2×C3D3×H(5,𝔽2)12yes—
908C2×C3D3×H(5,𝔽2)12yes—
909D3—42no—
910D3—64no—
911D3—64no—
912D3—124no—
913D3—124no—
914D3—122no—
915D3—122no—
916D3—122no—
917D3—122no—
918D3—242no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—44no—
923C22—62no—
924C22—64no—
925C22—94no—
926C22—188no—
927C22—182no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—184no—
932C22—182no—
933C22—182no—
934C22—242no—
935C22—368no—
936C22—368no—
937C22—364no—
938C22—722no—
939C22C2×#379912yes—
940C22C2×#379912yes—
941C22C2×#379912yes—
942C22C23×D3211yescharacteristic
943C4—24no—
944C4—62no—
945C4—64no—
946C4—64no—
947C4—64no—
948C4—182no—
949C3—21no—
950C3#8586811yescharacteristic, complemented
951C3#8657911yescharacteristic, complemented
952C2—22no—
953C2—22no—
954C2—22no—
955C2—122no—
956C2—184no—
957C2—362no—
958C2—362no—
959C2C22×#379911yescharacteristic
960C2#1059667512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
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×#64091C2semidirect
2. C3×#5486C2semidirect
3. C3×#5483C2semidirect
4. #10595519C2semidirect
5. C2×#63981C2semidirect
6. #10595510C2semidirect
7. C2×#63974C2semidirect
8. #10595035C2semidirect
9. #10595018C2semidirect
10. #10594243C2semidirect
11. #10594187C2semidirect
12. #10594166C2semidirect
13. #10594066C2semidirect
18. C22×C4⋊(C3⋊D3)C22semidirect
20. C22×#626C22semidirect
21. C22×#624C22semidirect
22. C2×#3799C22semidirect
24. C2×#3752C22semidirect
26. #64091C22semidirect
27. #64091C22semidirect
31. C3×C4×#67C22semidirect
32. C3×#924C22semidirect
33. C3×#67⋊C4C22semidirect
34. C3×D3×C22⋊C4C22semidirect
35. C3×#878C22semidirect
36. C3×#878C22semidirect
37. C3×#877C22semidirect
39. #63981C22semidirect
40. #63981C22semidirect
41. #63981C22semidirect
42. #63978C22semidirect
43. #63977C22semidirect
44. #63974C22semidirect
45. #63974C22semidirect
46. #63974C22semidirect
47. #63966C22semidirect
48. C2×#3722C22semidirect
49. C2×#3722C22semidirect
50. #63962C22semidirect
51. #63957C22semidirect
52. #63952C22semidirect
53. #63952C22semidirect
54. #63910C22semidirect
55. #63910C22semidirect
56. #63909C22semidirect
57. #63907C22semidirect
58. #63904C22semidirect
59. #63897C22semidirect
60. #63897C22semidirect
61. #63894C22semidirect
62. #63888C22semidirect
63. #63868C22semidirect
64. #63864C22semidirect
65. #63854C22semidirect
66. #63850C22semidirect
67. #63848C22semidirect
68. #63836C22semidirect
92. #5486D3semidirect
95. #5483D3semidirect
120. C2×C3×C4×D3C23semidirect
121. C2×C3×Dic6C23semidirect
125. C2×#626C23semidirect
129. C2×#624C23semidirect
141. C3×(C2×D3)⋊C4C23semidirect
142. C3×C4⋊Dic3C23semidirect
143. C3×Dic3⋊C4C23semidirect
144. C3×Dic3⋊C4C23semidirect
145. C3×Dic3⋊C4C23semidirect
146. C3×C4×Dic3C23semidirect
147. #3724C23semidirect
148. Dic3⋊Dic3C23semidirect
153. #3722C23semidirect
154. #3722C23semidirect
155. (C2×D3)⋊Dic3C23semidirect
156. Dic32C23semidirect
208. C4×#67C2×D3semidirect
216. #924C2×D3semidirect
255. #67⋊C4C2×D3semidirect
262. D3×C22⋊C4C2×D3semidirect
263. #878C2×D3semidirect
264. #878C2×D3semidirect
267. #877C2×D3semidirect
273. C23×C32#41semidirect
419. C2×C4×D3C22×D3semidirect
420. C2×Dic6C22×D3semidirect
465. (C2×D3)⋊C4C22×D3semidirect
467. C4⋊Dic3C22×D3semidirect
471. Dic3⋊C4C22×D3semidirect
472. Dic3⋊C4C22×D3semidirect
473. Dic3⋊C4C22×D3semidirect
476. C4×Dic3C22×D3semidirect
570. C23×C3#235semidirect
571. C23×C3#239semidirect
842. C32#3490semidirect
863. C23#3799semidirect
950. C3#85868semidirect
951. C3#86579semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
C3×#54862
C3×#54832
#105955192
C2×#639812
#105955102
C2×#639742
#105950352
#105950182
#105942432
#105941872
#105941662
#105940662
#865793
#858683