Finite Group Databasebeta

← #11901899

Subgroups — #11901899

Order 1152.

2273 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#125C211yesmaximal, characteristic, complemented
2C3×#5689C212yesmaximal, complemented
3#10594631C212yesmaximal
4#10594624C212yesmaximal
5#10594602C211yesmaximal, characteristic
6D32×C4⋊C4C211yesmaximal, characteristic
7#10594505C212yesmaximal, complemented
8#10594482C211yesmaximal, characteristic, complemented
9#10594399C212yesmaximal, complemented
10#10594391C214yesmaximal, complemented
11#10594389C214yesmaximal, complemented
12#10594374C211yesmaximal, characteristic, complemented
13#10594374C212yesmaximal, complemented
14#10594342C212yesmaximal, complemented
15#10593992C211yesmaximal, characteristic
16#10593954C212yesmaximal, complemented
17#10593909C211yesmaximal, characteristic, complemented
18D3×#544—32nomaximal
19C2×C4×D32C2212yes—
20C2×C4×D32C2211yescharacteristic
21C2×#3797C2212yes—
22C2×#3797C2212yes—
23C32×#125C2211yescharacteristic, complemented
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C4⋊C4×C3⋊D3C2212yes—
27C4⋊C4×C3⋊D3C2212yes—
28#64099C2211yescharacteristic, complemented
29#64099C2211yescharacteristic, complemented
30#64098C2212yescomplemented
31#64098C2212yescomplemented
32C42×C3⋊D3C2211yescharacteristic
33#64079C2211yescharacteristic, complemented
34C3×#897C2214yes—
35C3×#896C2214yes—
36C3×#892C2212yes—
37C3×D3×C4⋊C4C2212yes—
38C3×#890C2212yescomplemented
39C3×#889C2214yescomplemented
40C3×#888C2212yescomplemented
41C3×#888C2214yescomplemented
42C3×#872C2212yes—
43C3×#869C2212yescomplemented
44#63921C2212yes—
45#63921C2211yescharacteristic
46#63921C2211yescharacteristic
47#63919C2212yescomplemented
48#63919C2212yescomplemented
49#63918C2214yescomplemented
50#63918C2212yescomplemented
51#63900C2211yescharacteristic
52#63900C2211yescharacteristic
53#63900C2212yes—
54#63900C2212yes—
55#63899C2214yes—
56#63899C2214yes—
57#63893C2214yes—
58D3×C4⋊Dic3C2212yes—
59#63887C2214yes—
60#63883C2212yes—
61#63883C2212yes—
62#63883C2212yes—
63#63883C2211yescharacteristic
64#63883C2211yescharacteristic
65C4×#624C2212yes—
66C4×#624C2211yescharacteristic
67#63878C2212yes—
68#63878C2212yes—
69#63877C2214yes—
70D3×Dic3⋊C4C2214yes—
71#63873C2212yescomplemented
72#63869C2212yescomplemented
73#63867C2214yescomplemented
74#63856C2214yes—
75#63855C2212yes—
76#63851C2214yes—
77#63847C2214yescomplemented
78#63846C2214yescomplemented
79#63845C2214yescomplemented
80#63841C2212yes—
81#63839C2214yescomplemented
82#63839C2214yescomplemented
83#63839C2214yescomplemented
84C3×#544—32no—
85#5729—34no—
86#5729—32no—
87#5729—32no—
88D3×C4⋊Q8—34no—
89D3×C4⋊Q8—32no—
90D3×C4⋊Q8—32no—
91#5689—34no—
92#5689—32no—
93#5689D312yescomplemented
94D3×#125—32no—
95D3×#125—32no—
96D3×#125—34no—
97D3×#125—61no—
98D3×C22⋊Q8—34no—
99D3×C22⋊Q8—34no—
100#5623—34no—
101#5623—34no—
102D3×#117—32no—
103D3×#117—32no—
104#5519—32no—
105#5519—32no—
106C2×D3×C4⋊C4—32no—
107#5500—32no—
108C22×D32C2311yescharacteristic
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×C4×D3C2314yes—
115C2×C3×C4×D3C2312yes—
116C2×C3×Dic6C2314yes—
117C2×C3×Dic6C2314yes—
118C2×#627C2314yes—
119C2×#627C2314yes—
120C2×#624C2312yes—
121C2×#624C2311yescharacteristic
122C2×#624C2312yes—
123C2×#624C2311yescharacteristic
124C2×#624C2311yescharacteristic
125C2×D3×Dic3C2314yes—
126C2×D3×Dic3C2312yes—
127C4×D32—44no—
128C4×D32Q818yescomplemented
129#3797—44no—
130#3797—44no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C4⋊C4C2312yes—
134C32×C4⋊C4C2311yescharacteristic
135C32×C42C2311yescharacteristic
136C4⋊(C3⋊Dic3)C2311yescharacteristic
137C4⋊(C3⋊Dic3)C2311yescharacteristic
138C4⋊(C3⋊Dic3)C2312yes—
139C4⋊(C3⋊Dic3)C2312yes—
140#3750C2312yes—
141#3750C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144#3750C2312yes—
145#3750C2312yes—
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2311yescharacteristic
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2312yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2314yes—
155C3×C4⋊Dic3C2312yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2312yes—
163#3724C2314yes—
164#3724C2312yes—
165#3724C2314yes—
166#3724C2312yes—
167Dic3⋊Dic3C2312yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2312yes—
171Dic3⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2314yes—
176Dic32C2312yes—
177C2×#544—91noSylow
178C2×D3×Q8—34no—
179C2×D3×Q8—34no—
180C22×C4×D3—32no—
181C22×C4×D3—34no—
182C3×C4⋊Q8—34no—
183C3×C4⋊Q8—32no—
184C3×C4⋊Q8—32no—
185C3×#125—21no—
186C3×#125—34no—
187C3×#125—32no—
188C3×#125C2×D312yescomplemented
189C3×C22⋊Q8—34no—
190C3×C22⋊Q8—34no—
191C3×#117—32no—
192C3×#117—32no—
193C2×C3×C4⋊C4—32no—
194#946—34no—
195#946—34no—
196#944—34no—
197#944—34no—
198#944—34no—
199#944—34no—
200#926—32no—
201#926—32no—
202C2×C4⋊Dic3—32no—
203#924—34no—
204#924—34no—
205C2×Dic3⋊C4—34no—
206#897—34no—
207#897C2×D314yes—
208#896—34no—
209#896—34no—
210#896—34no—
211#896C2×D314yes—
212#892—32no—
213#892—32no—
214#892—32no—
215#892C2×D312yes—
216D3×C4⋊C4—34no—
217D3×C4⋊C4—32no—
218D3×C4⋊C4—32no—
219D3×C4⋊C4—34no—
220D3×C4⋊C4—32no—
221D3×C4⋊C4—34no—
222D3×C4⋊C4—32no—
223D3×C4⋊C4—34no—
224D3×C4⋊C4—34no—
225D3×C4⋊C4—32no—
226D3×C4⋊C4—32no—
227D3×C4⋊C4—34no—
228D3×C4⋊C4—34no—
229D3×C4⋊C4—34no—
230D3×C4⋊C4—32no—
231D3×C4⋊C4—61no—
232D3×C4⋊C4—61no—
233D3×C4⋊C4—62no—
234D3×C4⋊C4—62no—
235D3×C4⋊C4C2×D312yes—
236#890—32no—
237#890—32no—
238#890—34no—
239#890—34no—
240#890—32no—
241#890—61no—
242#890—61no—
243#890C2×D312yescomplemented
244#889—34no—
245#889—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#889—34no—
250#889—34no—
251#889—62no—
252#889—62no—
253#889C2×D314yescomplemented
254#888—34no—
255#888—34no—
256#888—34no—
257#888—32no—
258#888—34no—
259#888—32no—
260#888—34no—
261#888—32no—
262#888C2×D312yescomplemented
263#888C2×D314yescomplemented
264D3×C22⋊C4—32no—
265D3×C22⋊C4—34no—
266D3×C22⋊C4—32no—
267#878—34no—
268#878—34no—
269#878—34no—
270#878—34no—
271#877—32no—
272#877—32no—
273#877—34no—
274#872—32no—
275#872—34no—
276#872C2×D312yes—
277C42×D3—32no—
278C42×D3—34no—
279C42×D3—32no—
280C42×D3—61no—
281#870—32no—
282#870—32no—
283#870—34no—
284#870—61no—
285#869—32no—
286#869—34no—
287#869C2×D312yescomplemented
288C22×C3⋊D3C2411yescharacteristic
289C22×C3×D3C2412yes—
290C2×D32—22no—
291C2×D32—22no—
292C2×D32C2×Q814yes—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C32×C4C2411yescharacteristic
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2411yescharacteristic
298C2×C3⋊Dic3C2412yes—
299C2×C3⋊Dic3C2411yescharacteristic
300C2×C3⋊Dic3C2411yescharacteristic
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2411yescharacteristic
303C4×C3⋊D3—22no—
304C4×C3⋊D3—24no—
305C4×C3⋊D3—22no—
306C4×C3⋊D3—24no—
307C4×C3⋊D3C2×Q814yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2414yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2412yes—
313C3×C4×D3—44no—
314C3×C4×D3C2×Q818yescomplemented
315C3×Dic6—44no—
316C3×Dic6—44no—
317#627—44no—
318#627—44no—
319#624—22no—
320#624—24no—
321#624—24no—
322#624—22no—
323#624C2×Q814yes—
324D3×Dic3—44no—
325D3×Dic3C2×Q818yescomplemented
326#544—32no—
327#544—92no—
328#544—92no—
329#544—92no—
330#544—94no—
331#544—94no—
332C2×C4⋊Q8—92no—
333C2×C4⋊Q8—91no—
334C2×C4⋊Q8—91no—
335C2×#125—92no—
336C2×#125—91no—
337C2×#125—91no—
338C2×C22⋊Q8—92no—
339C2×C22⋊Q8—92no—
340C2×#117—91no—
341C2×#117—91no—
342C22×C4⋊C4—91no—
343C23×D3—32no—
344C2×C3×Q8—34no—
345C2×C3×Q8—34no—
346C22×C3×C4—32no—
347C22×C3×C4—34no—
348C22×Dic3—32no—
349C22×Dic3—34no—
350D3×Q8—128no—
351D3×Q8—128no—
352C2×C4×D3—32no—
353C2×C4×D3—32no—
354C2×C4×D3—32no—
355C2×C4×D3—316no—
356C2×C4×D3—32no—
357C2×C4×D3—34no—
358C2×C4×D3—32no—
359C2×C4×D3—34no—
360C2×C4×D3—32no—
361C2×C4×D3—32no—
362C2×C4×D3—34no—
363C2×C4×D3—34no—
364C2×C4×D3—34no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—128no—
371C2×C4×D3C22×D314yes—
372C2×C4×D3C22×D312yes—
373C2×Dic6—34no—
374C2×Dic6—34no—
375C2×Dic6—34no—
376C2×Dic6—34no—
377C2×Dic6C22×D314yes—
378C2×Dic6C22×D314yes—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—32no—
384C3×C4⋊C4—32no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—32no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—32no—
392C3×C4⋊C4C22×D314yes—
393C3×C4⋊C4C22×D312yes—
394C3×C4⋊C4C22×D314yes—
395C3×C4⋊C4C22×D312yes—
396C3×C22⋊C4—32no—
397C3×C22⋊C4—32no—
398C3×C22⋊C4—34no—
399C3×C42—21no—
400C3×C42—34no—
401C3×C42—32no—
402C3×C42C22×D312yes—
403#217—32no—
404#217—34no—
405#217—32no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4C22×D314yes—
410(C2×D3)⋊C4C22×D312yes—
411(C2×D3)⋊C4C22×D312yes—
412C4⋊Dic3—32no—
413C4⋊Dic3—34no—
414C4⋊Dic3—32no—
415C4⋊Dic3—34no—
416C4⋊Dic3—32no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—32no—
420C4⋊Dic3—34no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—62no—
424C4⋊Dic3—62no—
425C4⋊Dic3C22×D312yes—
426C4⋊Dic3C22×D314yes—
427C4⋊Dic3C22×D312yes—
428C4⋊Dic3C22×D314yes—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—32no—
440Dic3⋊C4—34no—
441Dic3⋊C4—32no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D312yes—
454Dic3⋊C4C22×D312yes—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D314yes—
457C4×Dic3—32no—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—34no—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—34no—
464C4×Dic3—61no—
465C4×Dic3—61no—
466C4×Dic3—61no—
467C4×Dic3C22×D312yes—
468C4×Dic3C22×D314yes—
469C22×C32C2511yescharacteristic
470C2×C3⋊D3C22×Q812yes—
471C2×C3⋊D3H(5,𝔽2)12yes—
472C2×C3⋊D32−1+412yes—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3C22×Q814yes—
476D32—28no—
477C32×C4—21no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—21no—
481C32×C4C22×Q812yes—
482C3⋊Dic3—22no—
483C3⋊Dic3—21no—
484C3⋊Dic3—22no—
485C3⋊Dic3—21no—
486C3⋊Dic3C22×Q812yes—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3C22×Q814yes—
492C22×Q8—92no—
493C22×Q8—92no—
494C23×C4—91no—
495C23×C4—92no—
496C4⋊Q8—34no—
497C4⋊Q8—32no—
498C4⋊Q8—32no—
499C4⋊Q8—92no—
500C4⋊Q8—94no—
501C4⋊Q8—92no—
502C4⋊Q8—92no—
503C4⋊Q8—94no—
504C4⋊Q8—94no—
505C4⋊Q8—94no—
506C4⋊Q8—92no—
507#125—34no—
508#125—32no—
509#125—94no—
510#125—92no—
511#125—94no—
512#125—94no—
513#125—94no—
514#125—92no—
515#125—92no—
516#125—91no—
517#125—91no—
518#125—91no—
519#125D3211yescharacteristic, complemented
520C22⋊Q8—34no—
521C22⋊Q8—34no—
522C22⋊Q8—94no—
523C22⋊Q8—94no—
524C22⋊Q8—94no—
525C22⋊Q8—94no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528#117—32no—
529#117—32no—
530#117—94no—
531#117—92no—
532#117—92no—
533#117—92no—
534#117—92no—
535C2×C4⋊C4—32no—
536C2×C4⋊C4—92no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—92no—
542C2×C4⋊C4—92no—
543C2×C4⋊C4—92no—
544C2×C4⋊C4—92no—
545C2×C4⋊C4—94no—
546C2×C4⋊C4—92no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—92no—
550C2×C4⋊C4—92no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—92no—
553C2×C22⋊C4—91no—
554C2×C42—92no—
555C2×C42—91no—
556C2×C42—91no—
557C23×C3—32no—
558C22×D3—32no—
559C22×D3—38no—
560C22×D3—61no—
561C22×D3—64no—
562C22×D3—64no—
563C22×D3C23×D312yes—
564C3×Q8—124no—
565C3×Q8—124no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—32no—
572C2×C3×C4—38no—
573C2×C3×C4—32no—
574C2×C3×C4—34no—
575C2×C3×C4—32no—
576C2×C3×C4—34no—
577C2×C3×C4—124no—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D314yes—
581C2×C3×C4C23×D314yes—
582C2×C3×C4C23×D312yes—
583C2×Dic3—32no—
584C2×Dic3—38no—
585C2×Dic3—34no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—34no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—124no—
595C2×Dic3C23×D312yes—
596C2×Dic3C23×D314yes—
597C2×Dic3C23×D312yes—
598C2×Dic3C23×D314yes—
599C2×Dic3C23×D312yes—
600C4×D3—38no—
601C4×D3—38no—
602C4×D3—38no—
603C4×D3—44no—
604C4×D3—64no—
605C4×D3—64no—
606C4×D3—68no—
607C4×D3—64no—
608C4×D3—68no—
609C4×D3—64no—
610C4×D3—68no—
611C4×D3—68no—
612C4×D3—64no—
613C4×D3—124no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—124no—
617C4×D3—124no—
618C4×D3D3×Q818yescomplemented
619Dic6—44no—
620Dic6—44no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624Dic6—124no—
625C2×C32C23×Q811yescharacteristic
626C2×C32C2×H(5,𝔽2)11yescharacteristic
627C2×C32C2×2−1+411yescharacteristic
628C3⋊D3#54414yescomplemented
629C3×D3—24no—
630C24—91no—
631C2×Q8—34no—
632C2×Q8—34no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—364no—
636C2×Q8—364no—
637C22×C4—32no—
638C22×C4—34no—
639C22×C4—91no—
640C22×C4—98no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—92no—
644C22×C4—92no—
645C22×C4—92no—
646C22×C4—94no—
647C22×C4—91no—
648C22×C4—92no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—92no—
652C22×C4—364no—
653C4⋊C4—34no—
654C4⋊C4—32no—
655C4⋊C4—32no—
656C4⋊C4—32no—
657C4⋊C4—32no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—92no—
663C4⋊C4—94no—
664C4⋊C4—92no—
665C4⋊C4—92no—
666C4⋊C4—92no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—92no—
672C4⋊C4—91no—
673C4⋊C4—92no—
674C4⋊C4—91no—
675C4⋊C4—92no—
676C4⋊C4—92no—
677C4⋊C4—92no—
678C4⋊C4—92no—
679C4⋊C4—92no—
680C4⋊C4—92no—
681C4⋊C4C2×D3211yescharacteristic
682C4⋊C4C2×D3211yescharacteristic
683C4⋊C4C2×D3212yes—
684C4⋊C4C2×D3212yes—
685C22⋊C4—32no—
686C22⋊C4—34no—
687C22⋊C4—32no—
688C22⋊C4—92no—
689C22⋊C4—94no—
690C22⋊C4—92no—
691C42—34no—
692C42—32no—
693C42—94no—
694C42—92no—
695C42—91no—
696C42—91no—
697C42—91no—
698C42C2×D3211yescharacteristic
699C22×C3—21no—
700C22×C3—34no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3C24×D312yes—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—34no—
707C2×D3—34no—
708C2×D3—34no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—616no—
713C2×D3C2×D3×Q814yes—
714C3×C4—22no—
715C3×C4—24no—
716C3×C4—22no—
717C3×C4—24no—
718C3×C4—22no—
719C3×C4—34no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—42no—
724C3×C4—62no—
725C3×C4—64no—
726C3×C4—64no—
727C3×C4—62no—
728C3×C4C2×D3×Q814yes—
729Dic3—22no—
730Dic3—24no—
731Dic3—24no—
732Dic3—22no—
733Dic3—34no—
734Dic3—62no—
735Dic3—62no—
736Dic3—64no—
737Dic3—64no—
738Dic3—62no—
739Dic3—122no—
740Dic3—121no—
741Dic3—121no—
742Dic3—122no—
743Dic3C2×D3×Q814yes—
744C32C2×#54411yescharacteristic, complemented, Sylow
745C23—32no—
746C23—94no—
747C23—91no—
748C23—182no—
749C23—182no—
750Q8—124no—
751Q8—124no—
752Q8—364no—
753Q8—364no—
754C2×C4—32no—
755C2×C4—38no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—34no—
760C2×C4—94no—
761C2×C4—98no—
762C2×C4—91no—
763C2×C4—94no—
764C2×C4—92no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—92no—
768C2×C4—124no—
769C2×C4—184no—
770C2×C4—182no—
771C2×C4—184no—
772C2×C4—182no—
773C2×C4—184no—
774C2×C4—182no—
775C2×C4—184no—
776C2×C4—182no—
777C2×C4—364no—
778C2×C4C22×D3212yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C4C22×D3212yes—
782C2×C4C22×D3211yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—64no—
787C2×C3C22×D3×Q812yes—
788C2×C3D3×H(5,𝔽2)12yes—
789C2×C3D3×2−1+412yes—
790D3—24no—
791D3—38no—
792D3—64no—
793C22—34no—
794C22—62no—
795C22—62no—
796C22—92no—
797C22—92no—
798C22—92no—
799C22—188no—
800C22C23×D3211yescharacteristic
801C4—22no—
802C4—21no—
803C4—22no—
804C4—21no—
805C4—34no—
806C4—64no—
807C4—62no—
808C4—64no—
809C4—62no—
810C4—92no—
811C4—182no—
812C4—181no—
813C4—182no—
814C4—181no—
815C4D32×Q812yes—
816C3—21no—
817C3D3×#54412yescomplemented
818C2—64no—
819C2—94no—
820C2C2×D32×Q811yescharacteristic
821C2#1059669211yescharacteristic
822C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
prime radicalC22×D32C23
hypercenter#125D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#125C2semidirect
2. C3×#5689C2semidirect
7. #10594505C2semidirect
8. #10594482C2semidirect
9. #10594399C2semidirect
10. #10594391C2semidirect
11. #10594389C2semidirect
12. #10594374C2semidirect
13. #10594374C2semidirect
14. #10594342C2semidirect
16. #10593954C2semidirect
17. #10593909C2semidirect
23. C32×#125C22semidirect
28. #64099C22semidirect
29. #64099C22semidirect
30. #64098C22semidirect
31. #64098C22semidirect
33. #64079C22semidirect
38. C3×#890C22semidirect
39. C3×#889C22semidirect
40. C3×#888C22semidirect
41. C3×#888C22semidirect
43. C3×#869C22semidirect
47. #63919C22semidirect
48. #63919C22semidirect
49. #63918C22semidirect
50. #63918C22semidirect
71. #63873C22semidirect
72. #63869C22semidirect
73. #63867C22semidirect
77. #63847C22semidirect
78. #63846C22semidirect
79. #63845C22semidirect
81. #63839C22semidirect
82. #63839C22semidirect
83. #63839C22semidirect
93. #5689D3semidirect
128. C4×D32Q8semidirect
188. C3×#125C2×D3semidirect
243. #890C2×D3semidirect
253. #889C2×D3semidirect
262. #888C2×D3semidirect
263. #888C2×D3semidirect
287. #869C2×D3semidirect
314. C3×C4×D3C2×Q8semidirect
325. D3×Dic3C2×Q8semidirect
519. #125D32semidirect
618. C4×D3D3×Q8semidirect
628. C3⋊D3#544semidirect
744. C32C2×#544semidirect
817. C3D3×#544semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
C3×#56892
#105946312
#105946242
#105946022
D32×C4⋊C42
#105945052
#105944822
#105943992
#105943912
#105943892
#105943742
#105943422
#105939922
#105939542
#105939092
D3×#5443