Finite Group Databasebeta

← #11904908

Subgroups — #11904908

Order 1152.

2825 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595957C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4#10595519C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6#10595506C211yesmaximal, characteristic, complemented
7C2×D3×#217C211yesmaximal, characteristic, complemented
8#10594941C214yesmaximal, complemented
9#10594889C214yesmaximal, complemented
10#10594173C214yesmaximal, complemented
11#10594119C214yesmaximal, complemented
12#10594063C214yesmaximal, complemented
13#10594055C214yesmaximal, complemented
14#86579—31nomaximal
15#85913—31nomaximal
16C24×C3×D3C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×D12C2212yescomplemented
20C22×#626C2212yescomplemented
21C22×D3×Dic3C2212yescomplemented
22C2×#3796C2214yescomplemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C4×#638C2214yescomplemented
26#64090C2214yescomplemented
27C22⋊C4×C3⋊D3C2212yescomplemented
28#64086C2212yescomplemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C3×#924C2214yescomplemented
33C3×#882C2214yes—
34C3×#882C2212yescomplemented
35C3×#882C2212yescomplemented
36C3×#878C2214yescomplemented
37C3×#878C2214yescomplemented
38#63981C2212yescomplemented
39#63978C2214yescomplemented
40#63977C2214yes—
41#63977C2212yescomplemented
42#63977C2212yescomplemented
43#63977C2212yescomplemented
44#67⋊Dic3C2214yescomplemented
45Dic3×#67C2214yescomplemented
46D3×#217C2214yescomplemented
47D3×#217C2214yescomplemented
48D3×#217C2212yescomplemented
49#63966C2212yescomplemented
50#63962C2212yescomplemented
51C2×(C2×D3)⋊Dic3C2212yescomplemented
52C2×(C2×D3)⋊Dic3C2212yescomplemented
53#63955C2212yescomplemented
54#63916C2214yescomplemented
55#63907C2214yescomplemented
56#63898C2214yescomplemented
57#63890C2214yescomplemented
58#63887C2214yescomplemented
59#63886C2214yescomplemented
60#63886C2214yescomplemented
61#63884C2214yescomplemented
62#63884C2214yescomplemented
63#63881C2214yescomplemented
64#63878C2214yescomplemented
65#63863C2214yescomplemented
66#63862C2214yescomplemented
67#63858C2214yescomplemented
68#63853C2214yescomplemented
69C3×#543—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C22×#217—31no—
73#5806—34no—
74#5804—31no—
75#5798—31no—
76#5644—34no—
77#5637—34no—
78#5637—34no—
79#5630—34no—
80#5630—34no—
81#5627—34no—
82#5593—34no—
83#5591—34no—
84#5587—34no—
85#5586—34no—
86#5495—34no—
87#5493—31no—
88C2×#882—31no—
89C2×#882D311yescharacteristic, complemented
90#5486—31no—
91#5486—31no—
92#5486—31no—
93#5486—61no—
94C2×D3×C22⋊C4—31no—
95#5483D311yescharacteristic, complemented
96C24×C32C2311yescharacteristic
97C23×C3⋊D3C2311yescharacteristic
98C23×C3×D3—24no—
99C23×C3×D3—44no—
100C23×C3×D3C2311yescharacteristic
101C23×C3×D3C2312yes—
102C23×C3×D3C2312yes—
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2312yes—
106C2×#638—24no—
107C2×#638C2312yes—
108C2×#638C2312yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2312yes—
111C2×C4×C3⋊D3C2314yescomplemented
112C2×C3×#67—24no—
113C2×C3×#67C2312yes—
114C2×C3×#67C2312yes—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2312yes—
118C2×C3×D12—44no—
119C2×C3×D12C2314yes—
120C2×C3×D12C2314yes—
121C2×C3×Dic6C2314yescomplemented
122C2×#626—44no—
123C2×#626C2314yes—
124C2×#626C2314yes—
125C2×#626C2314yescomplemented
126C2×D3×Dic3—44no—
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2314yes—
129C2×D3×Dic3C2314yescomplemented
130#3796—48no—
131C32×C22⋊C4C2312yes—
132C32×C22⋊C4C2312yes—
133#3757C2312yes—
134#3757C2312yes—
135#3752C2314yescomplemented
136#3750C2314yescomplemented
137C4×C3⋊Dic3C2314yescomplemented
138C3×#217C2312yes—
139C3×#217C2312yes—
140C3×#217C2312yes—
141C3×#217C2312yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yescomplemented
145C3×Dic3⋊C4C2314yescomplemented
146C3×Dic3⋊C4C2314yescomplemented
147Dic3⋊Dic3C2314yescomplemented
148Dic3⋊Dic3C2314yescomplemented
149#3722C2314yescomplemented
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yescomplemented
155(C2×D3)⋊Dic3C2314yescomplemented
156Dic32C2314yescomplemented
157#3490—91noSylow
158C25×C3—31no—
159C24×D3C2×D311yescharacteristic
160C22×C3×D4—31no—
161C22×C3×D4—32no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—32no—
165C22×#67—61no—
166C22×#67C2×D311yescharacteristic
167C23×Dic3—32no—
168C2×#239—34no—
169C2×#237—34no—
170C22×D12—32no—
171C22×D12C2×D312yescomplemented
172C22×C4×D3—32no—
173C3×C22⋊Q8—34no—
174C3×C22⋊Q8—34no—
175C3×C22⋊Q8—34no—
176C3×#120—34no—
177C3×#120—32no—
178C3×#120—32no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—32no—
183C2×C3×C22⋊C4C2×D311yescharacteristic
184C2×C3×C22⋊C4C2×D311yescharacteristic
185#953—34no—
186#953—32no—
187#953—32no—
188#953—32no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—32no—
192C2×#217—32no—
193C2×#217—34no—
194C2×#217—32no—
195C2×#217—34no—
196C2×#217—61no—
197C2×#217C2×D311yescharacteristic
198C2×#217C2×D311yescharacteristic
199#947—34no—
200#947—34no—
201#946—34no—
202#939—34no—
203#939—34no—
204#939—34no—
205#938—34no—
206#937—32no—
207#936—34no—
208#935—32no—
209#935—34no—
210#935—34no—
211D4×Dic3—34no—
212D4×Dic3—34no—
213D4×Dic3—34no—
214#930—34no—
215#929—32no—
216C4×#67—34no—
217C4×#67—34no—
218C4×#67—34no—
219C4×#67—64no—
220C2×(C2×D3)⋊C4—32no—
221C2×(C2×D3)⋊C4—32no—
222C2×(C2×D3)⋊C4C2×D312yescomplemented
223#926—32no—
224#924C2×D314yescomplemented
225#898—34no—
226#898—34no—
227#895—34no—
228#895—34no—
229#895—34no—
230#894—34no—
231#894—34no—
232#894—34no—
233#894—34no—
234#893—34no—
235#893—34no—
236#892—34no—
237#886—32no—
238#886—32no—
239#886—34no—
240#885—34no—
241#883—34no—
242#882—34no—
243#882—32no—
244#882—32no—
245#882—32no—
246#882—32no—
247#882C2×D314yes—
248#882C2×D312yescomplemented
249#882C2×D312yescomplemented
250#67⋊C4—34no—
251#67⋊C4—34no—
252#67⋊C4—34no—
253#67⋊C4—34no—
254#67⋊C4—64no—
255D3×C22⋊C4—34no—
256D3×C22⋊C4—34no—
257D3×C22⋊C4—32no—
258D3×C22⋊C4—32no—
259D3×C22⋊C4—32no—
260D3×C22⋊C4—62no—
261#879—34no—
262#879—34no—
263#878—34no—
264#878C2×D314yescomplemented
265#878C2×D314yescomplemented
266#877—32no—
267#877—32no—
268#877—32no—
269#877—34no—
270#877—62no—
271C23×C32—42no—
272C23×C32#4114yescomplemented
273C23×C32C2411yescharacteristic
274C23×C32C2411yescharacteristic
275C23×C32C2411yescharacteristic
276C22×C3⋊D3—22no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—24no—
281C22×C3×D3—24no—
282C22×C3×D3—24no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—24no—
286C22×C3×D3—24no—
287C22×C3×D3—42no—
288C22×C3×D3—42no—
289C22×C3×D3—42no—
290C22×C3×D3—42no—
291C22×C3×D3—416no—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C22×C3×D3C2412yes—
295C2×C32×C4—42no—
296C2×C32×C4C2414yes—
297#638—24no—
298#638—24no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—42no—
301C2×C3⋊Dic3C2414yes—
302C2×C3⋊Dic3C2412yes—
303C4×C3⋊D3—44no—
304C3×#67—24no—
305C3×#67—24no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—42no—
308C2×C3×Dic3—42no—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2414yes—
311C2×C3×Dic3C2414yes—
312C3×D12—28no—
313C3×D12—44no—
314C3×Dic6—44no—
315#626—28no—
316#626—44no—
317#626—44no—
318D3×Dic3—28no—
319D3×Dic3—44no—
320D3×Dic3—44no—
321#551—94no—
322#551—94no—
323#546—94no—
324#546—94no—
325#543—31no—
326#538—94no—
327#534—91no—
328#525—94no—
329C2×#120—31no—
330C2×#120—91no—
331#518—91no—
332#518—91no—
333C22×C22⋊C4—91no—
334C24×C3—21no—
335C24×C3—31no—
336C24×C3—32no—
337C24×C3—32no—
338C24×C3—31no—
339C24×C3—31no—
340C24×C3—64no—
341C24×C3—124no—
342C24×C3C22×D311yescharacteristic
343C24×C3C22×D311yescharacteristic
344C23×D3—24no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—44no—
348C23×D3—61no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D312yes—
351C23×D3C22×D312yes—
352C23×D3C22×D311yescharacteristic
353C23×D3C22×D311yescharacteristic
354C2×C3×Q8—34no—
355C2×C3×D4—32no—
356C2×C3×D4—32no—
357C2×C3×D4—34no—
358C2×C3×D4—34no—
359C2×C3×D4—64no—
360C2×C3×D4—124no—
361C22×C3×C4—22no—
362C22×C3×C4—31no—
363C22×C3×C4—32no—
364C22×C3×C4—32no—
365C22×C3×C4C22×D312yes—
366C22×C3×C4C22×D312yes—
367C2×#67—24no—
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—32no—
371C2×#67—32no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—68no—
378C2×#67—64no—
379C2×#67—64no—
380C2×#67—124no—
381C2×#67C22×D312yes—
382C2×#67C22×D312yes—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—32no—
386C22×Dic3—32no—
387C22×Dic3—34no—
388C22×Dic3—34no—
389C22×Dic3—34no—
390C22×Dic3—61no—
391C22×Dic3—62no—
392C22×Dic3—124no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D312yes—
395C22×Dic3C22×D312yes—
396#239—128no—
397#237—128no—
398C2×D12—34no—
399C2×D12—34no—
400C2×D12—34no—
401C2×D12—44no—
402C2×D12—124no—
403C2×D12C22×D314yes—
404C2×D12C22×D314yes—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—64no—
411C2×C4×D3—124no—
412C2×Dic6C22×D314yescomplemented
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C22⋊C4—22no—
417C3×C22⋊C4—22no—
418C3×C22⋊C4—32no—
419C3×C22⋊C4—32no—
420C3×C22⋊C4—32no—
421C3×C22⋊C4—32no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4C22×D312yes—
425C3×C22⋊C4C22×D312yes—
426C3×C22⋊C4C22×D312yes—
427C3×C22⋊C4C22×D312yes—
428#217—32no—
429#217—32no—
430#217—32no—
431#217—32no—
432#217—34no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—62no—
439#217—62no—
440#217C22×D312yes—
441#217C22×D312yes—
442#217C22×D312yes—
443#217C22×D312yes—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
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—64no—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3C22×D314yescomplemented
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—64no—
465Dic3⋊C4C22×D314yescomplemented
466Dic3⋊C4C22×D314yescomplemented
467C4×Dic3—34no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—34no—
471C4×Dic3—64no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—44no—
476C22×C32C2×#4112yes—
477C22×C32C2×#4112yes—
478C22×C32C2×#4112yes—
479C22×C32C2511yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—24no—
482C2×C3⋊D3—82no—
483C2×C3×D3—28no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—24no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—48no—
492C2×C3×D3—48no—
493C2×C3×D3—44no—
494C2×C3×D3—82no—
495C2×C3×D3H(5,𝔽2)14yes—
496C32×C4—24no—
497C3⋊Dic3—22no—
498C3⋊Dic3—24no—
499C3×Dic3—22no—
500C3×Dic3—24no—
501C3×Dic3—24no—
502C25—31no—
503C2×#41—94no—
504C22×D4—31no—
505C22×D4—32no—
506C22×D4—92no—
507C22×D4—91no—
508C23×C4—92no—
509#126—94no—
510#126—94no—
511#124—94no—
512#124—94no—
513#123—94no—
514#123—94no—
515#123—92no—
516#123—92no—
517#123—94no—
518#123—94no—
519C22⋊Q8—34no—
520C22⋊Q8—34no—
521C22⋊Q8—34no—
522C22⋊Q8—94no—
523#121—94no—
524#121—94no—
525#121—94no—
526#121—94no—
527#120—32no—
528#120—32no—
529#120—34no—
530#120—92no—
531#120—92no—
532#120—92no—
533#120—94no—
534#120—92no—
535C4×D4—94no—
536C4×D4—94no—
537C4×D4—94no—
538C4×D4—94no—
539C4×D4—94no—
540C4×D4—94no—
541#117—94no—
542#117—92no—
543#117—92no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—94no—
548C2×C22⋊C4—94no—
549C2×C22⋊C4—92no—
550C2×C22⋊C4—92no—
551C2×C22⋊C4—92no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—92no—
554C2×C22⋊C4D3211yescharacteristic
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—24no—
559C23×C3—32no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—64no—
565C23×C3—64no—
566C23×C3—64no—
567C23×C3—62no—
568C23×C3—64no—
569C23×C3—64no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—82no—
573C23×C3—122no—
574C23×C3—122no—
575C23×C3—122no—
576C23×C3—122no—
577C23×C3—1216no—
578C23×C3#23714yescomplemented
579C23×C3#23914yescomplemented
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C23×C3C23×D311yescharacteristic
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—22no—
587C22×D3—24no—
588C22×D3—24no—
589C22×D3—24no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—24no—
593C22×D3—24no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—42no—
600C22×D3—416no—
601C22×D3—62no—
602C22×D3—64no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—242no—
608C22×D3C23×D312yes—
609C22×D3C23×D312yes—
610C22×D3C23×D312yes—
611C3×Q8—124no—
612C3×D4—68no—
613C3×D4—64no—
614C3×D4—64no—
615C3×D4—124no—
616C2×C3×C4—24no—
617C2×C3×C4—32no—
618C2×C3×C4—34no—
619C2×C3×C4—34no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—62no—
623C2×C3×C4—82no—
624C2×C3×C4—122no—
625C2×C3×C4—122no—
626C2×C3×C4C23×D314yes—
627C2×C3×C4C23×D314yes—
628#67—24no—
629#67—24no—
630#67—68no—
631#67—68no—
632#67—68no—
633#67—64no—
634#67—64no—
635#67—64no—
636#67—64no—
637#67—124no—
638#67—124no—
639C2×Dic3—22no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—34no—
643C2×Dic3—34no—
644C2×Dic3—42no—
645C2×Dic3—42no—
646C2×Dic3—62no—
647C2×Dic3—64no—
648C2×Dic3—68no—
649C2×Dic3—64no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—124no—
653C2×Dic3—124no—
654C2×Dic3—122no—
655C2×Dic3—122no—
656C2×Dic3—242no—
657C2×Dic3C23×D312yes—
658C2×Dic3C23×D314yes—
659C2×Dic3C23×D314yes—
660D12—28no—
661D12—44no—
662D12—68no—
663D12—124no—
664D12—124no—
665C4×D3—68no—
666C4×D3—124no—
667C4×D3—124no—
668C4×D3—124no—
669C4×D3—124no—
670C4×D3—244no—
671Dic6—44no—
672C2×C32—22no—
673C2×C32—22no—
674C2×C32—22no—
675C2×C32C22×#4111yescharacteristic
676C2×C32C2×H(5,𝔽2)12yes—
677C3⋊D3—42no—
678C3×D3—24no—
679C3×D3—42no—
680C3×D3—42no—
681C24—31no—
682C24—32no—
683C24—32no—
684C24—31no—
685C24—31no—
686C24—64no—
687C24—91no—
688C24—124no—
689C24C2×D3211yescharacteristic
690#41—368no—
691C2×Q8—34no—
692C2×D4—32no—
693C2×D4—32no—
694C2×D4—34no—
695C2×D4—34no—
696C2×D4—64no—
697C2×D4—94no—
698C2×D4—94no—
699C2×D4—94no—
700C2×D4—92no—
701C2×D4—92no—
702C2×D4—124no—
703C2×D4—184no—
704C2×D4—364no—
705C22×C4—31no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—94no—
709C22×C4—94no—
710C22×C4—94no—
711C22×C4—91no—
712C22×C4—92no—
713C22×C4—94no—
714C22×C4—364no—
715C22×C4C2×D3212yes—
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—34no—
719C4⋊C4—94no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C22⋊C4—32no—
723C22⋊C4—32no—
724C22⋊C4—32no—
725C22⋊C4—32no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—94no—
729C22⋊C4—94no—
730C22⋊C4—94no—
731C22⋊C4—94no—
732C22⋊C4—94no—
733C22⋊C4—94no—
734C22⋊C4—94no—
735C22⋊C4—92no—
736C22⋊C4—92no—
737C22⋊C4—94no—
738C22⋊C4C2×D3212yes—
739C22⋊C4C2×D3212yes—
740C42—94no—
741C42—94no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—34no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—44no—
757C22×C3—44no—
758C22×C3—68no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—64no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—84no—
767C22×C3—128no—
768C22×C3—128no—
769C22×C3—124no—
770C22×C3—242no—
771C22×C3C2×#23712yes—
772C22×C3C2×#23712yes—
773C22×C3C2×#23712yes—
774C22×C3C2×#23912yes—
775C22×C3C2×#23912yes—
776C22×C3C2×#23912yes—
777C22×C3C24×D311yescharacteristic
778C22×C3C24×D311yescharacteristic
779C2×D3—28no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—24no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—48no—
788C2×D3—48no—
789C2×D3—44no—
790C2×D3—64no—
791C2×D3—62no—
792C2×D3—64no—
793C2×D3—62no—
794C2×D3—64no—
795C2×D3—82no—
796C2×D3—124no—
797C2×D3—242no—
798C2×D3—242no—
799C2×D3—244no—
800C2×D3#100414yes—
801C3×C4—24no—
802C3×C4—24no—
803C3×C4—44no—
804C3×C4—64no—
805C3×C4—64no—
806C3×C4—62no—
807Dic3—22no—
808Dic3—24no—
809Dic3—24no—
810Dic3—64no—
811Dic3—62no—
812Dic3—64no—
813Dic3—62no—
814Dic3—64no—
815Dic3—124no—
816C32#349011yescharacteristic, complemented, Sylow
817C23—32no—
818C23—32no—
819C23—32no—
820C23—42no—
821C23—64no—
822C23—64no—
823C23—64no—
824C23—62no—
825C23—64no—
826C23—64no—
827C23—62no—
828C23—62no—
829C23—92no—
830C23—122no—
831C23—122no—
832C23—122no—
833C23—122no—
834C23—1216no—
835C23—182no—
836C23—362no—
837C23#379614yescomplemented
838C23C22×D3211yescharacteristic
839C23C22×D3211yescharacteristic
840C23C22×D3211yescharacteristic
841Q8—124no—
842D4—68no—
843D4—64no—
844D4—64no—
845D4—124no—
846D4—188no—
847D4—184no—
848D4—184no—
849D4—364no—
850D4—364no—
851C2×C4—32no—
852C2×C4—34no—
853C2×C4—34no—
854C2×C4—42no—
855C2×C4—62no—
856C2×C4—92no—
857C2×C4—94no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—188no—
861C2×C4—182no—
862C2×C4—364no—
863C2×C4—364no—
864C2×C4—364no—
865C2×C4—362no—
866C2×C4C22×D3214yes—
867C2×C3—22no—
868C2×C3—22no—
869C2×C3—22no—
870C2×C3—22no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—22no—
875C2×C3—42no—
876C2×C3—42no—
877C2×C3—42no—
878C2×C3—64no—
879C2×C3—122no—
880C2×C3—122no—
881C2×C3C22×#23711yescharacteristic
882C2×C3C2×#100412yes—
883C2×C3C22×#23911yescharacteristic
884C2×C3D3×H(5,𝔽2)12yes—
885D3—24no—
886D3—42no—
887D3—42no—
888D3—124no—
889D3—122no—
890D3—122no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—34no—
895C22—44no—
896C22—68no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—64no—
902C22—62no—
903C22—62no—
904C22—128no—
905C22—128no—
906C22—124no—
907C22—182no—
908C22—184no—
909C22—242no—
910C22—722no—
911C22C2×#379612yes—
912C22C2×#379612yes—
913C22C2×#379612yes—
914C22C23×D3211yescharacteristic
915C4—24no—
916C4—62no—
917C4—64no—
918C4—64no—
919C4—182no—
920C4—184no—
921C3—21no—
922C3#8591311yescharacteristic, complemented
923C3#8657911yescharacteristic, complemented
924C2—22no—
925C2—22no—
926C2—22no—
927C2—64no—
928C2—122no—
929C2—122no—
930C2—362no—
931C2C22×#379611yescharacteristic
932C2D3×#100412yes—
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. #10595957C2semidirect
2. C2×C3×#882C2semidirect
3. C3×#5483C2semidirect
4. #10595519C2semidirect
5. C2×#63977C2semidirect
6. #10595506C2semidirect
7. C2×D3×#217C2semidirect
8. #10594941C2semidirect
9. #10594889C2semidirect
10. #10594173C2semidirect
11. #10594119C2semidirect
12. #10594063C2semidirect
13. #10594055C2semidirect
19. C22×C3×D12C22semidirect
20. C22×#626C22semidirect
21. C22×D3×Dic3C22semidirect
22. C2×#3796C22semidirect
25. C4×#638C22semidirect
26. #64090C22semidirect
27. C22⋊C4×C3⋊D3C22semidirect
28. #64086C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C3×#924C22semidirect
34. C3×#882C22semidirect
35. C3×#882C22semidirect
36. C3×#878C22semidirect
37. C3×#878C22semidirect
38. #63981C22semidirect
39. #63978C22semidirect
41. #63977C22semidirect
42. #63977C22semidirect
43. #63977C22semidirect
44. #67⋊Dic3C22semidirect
45. Dic3×#67C22semidirect
46. D3×#217C22semidirect
47. D3×#217C22semidirect
48. D3×#217C22semidirect
49. #63966C22semidirect
50. #63962C22semidirect
51. C2×(C2×D3)⋊Dic3C22semidirect
52. C2×(C2×D3)⋊Dic3C22semidirect
53. #63955C22semidirect
54. #63916C22semidirect
55. #63907C22semidirect
56. #63898C22semidirect
57. #63890C22semidirect
58. #63887C22semidirect
59. #63886C22semidirect
60. #63886C22semidirect
61. #63884C22semidirect
62. #63884C22semidirect
63. #63881C22semidirect
64. #63878C22semidirect
65. #63863C22semidirect
66. #63862C22semidirect
67. #63858C22semidirect
68. #63853C22semidirect
89. C2×#882D3semidirect
95. #5483D3semidirect
111. C2×C4×C3⋊D3C23semidirect
121. C2×C3×Dic6C23semidirect
125. C2×#626C23semidirect
129. C2×D3×Dic3C23semidirect
135. #3752C23semidirect
136. #3750C23semidirect
137. C4×C3⋊Dic3C23semidirect
144. C3×C4⋊Dic3C23semidirect
145. C3×Dic3⋊C4C23semidirect
146. C3×Dic3⋊C4C23semidirect
147. Dic3⋊Dic3C23semidirect
148. Dic3⋊Dic3C23semidirect
149. #3722C23semidirect
154. (C2×D3)⋊Dic3C23semidirect
155. (C2×D3)⋊Dic3C23semidirect
156. Dic32C23semidirect
171. C22×D12C2×D3semidirect
222. C2×(C2×D3)⋊C4C2×D3semidirect
224. #924C2×D3semidirect
248. #882C2×D3semidirect
249. #882C2×D3semidirect
264. #878C2×D3semidirect
265. #878C2×D3semidirect
272. C23×C32#41semidirect
412. C2×Dic6C22×D3semidirect
459. C4⋊Dic3C22×D3semidirect
465. Dic3⋊C4C22×D3semidirect
466. Dic3⋊C4C22×D3semidirect
578. C23×C3#237semidirect
579. C23×C3#239semidirect
816. C32#3490semidirect
837. C23#3796semidirect
922. C3#85913semidirect
923. C3#86579semidirect

Maximal subgroups

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

subgroupindex
#105959572
C2×C3×#8822
C3×#54832
#105955192
C2×#639772
#105955062
C2×D3×#2172
#105949412
#105948892
#105941732
#105941192
#105940632
#105940552
#865793
#859133