Finite Group Databasebeta

← #11903377

Subgroups — #11903377

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5568C212yesmaximal, complemented
3#10595432C211yesmaximal, characteristic
4#10595384C212yesmaximal, complemented
5#10595365C211yesmaximal, characteristic, complemented
6#10594656C212yesmaximal, complemented
7#10594624C212yesmaximal, complemented
8#10594605C211yesmaximal, characteristic
9#10594554C214yesmaximal, complemented
10#10594363C211yesmaximal, characteristic, complemented
11#10594335C212yesmaximal, complemented
12#10594020C212yesmaximal, complemented
13#10594009C211yesmaximal, characteristic
14#10593992C212yesmaximal, complemented
15#10593932C212yesmaximal, complemented
16#10593931C214yesmaximal, complemented
17C4×#3797C211yesmaximal, characteristic, complemented
18D3×#556—32nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2212yes—
22C2×#3797C2211yescharacteristic
23C2×#3797C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic, complemented
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2212yes—
28#64096C2211yescharacteristic, complemented
29#64096C2212yescomplemented
30C42×C3⋊D3C2211yescharacteristic
31C42×C3⋊D3C2212yes—
32C4×#634C2212yescomplemented
33C4×#634C2211yescharacteristic, complemented
34C3×#947C2212yes—
35C3×#944C2212yescomplemented
36C3×#898C2214yescomplemented
37C3×#896C2214yescomplemented
38C3×#893C2212yes—
39C3×#887C2212yescomplemented
40C3×#876C2214yescomplemented
41C3×#875C2212yes—
42C3×#872C2214yescomplemented
43C3×C4×Dic6C2212yescomplemented
44#63921C2212yes—
45#63921C2212yes—
46#63921C2212yes—
47#63921C2212yes—
48#63921C2212yes—
49C4×#627C2212yescomplemented
50#63915C2212yes—
51#63915C2212yes—
52#63913C2214yes—
53#63900C2211yescharacteristic
54#63893C2214yescomplemented
55Dic3×D12C2212yes—
56#63887C2214yescomplemented
57#63883C2212yes—
58#63883C2212yes—
59#63883C2212yes—
60#63883C2211yescharacteristic
61#63883C2211yescharacteristic
62C4×#624C2211yescharacteristic
63C4×#624C2212yes—
64C4×#624C2211yescharacteristic
65#63879C2214yes—
66#63878C2214yescomplemented
67#63878C2214yescomplemented
68#63866C2212yescomplemented
69#63863C2212yes—
70#63862C2214yescomplemented
71#63862C2214yescomplemented
72#63862C2214yescomplemented
73#63861C2214yescomplemented
74#63860C2212yes—
75#63859C2214yescomplemented
76#63858C2214yescomplemented
77#63855C2214yescomplemented
78#63851C2214yescomplemented
79#63843C2212yescomplemented
80Dic3×Dic6C2212yescomplemented
81#63840C2214yescomplemented
82#63838C2212yescomplemented
83#63837C2214yescomplemented
84C3×#556—32no—
85#5732—32no—
86D3×C4⋊Q8—32no—
87D3×#126—34no—
88D3×#126—34no—
89#5702—34no—
90#5702—34no—
91D3×#124—32no—
92D3×#124—32no—
93#5671—32no—
94#5671—32no—
95#5641—34no—
96D3×C22⋊Q8—34no—
97#5584—32no—
98C4×D3×Q8—32no—
99C4×D3×Q8—32no—
100C4×D3×Q8—32no—
101C4×D3×Q8—61no—
102#5568—32no—
103#5568D312yescomplemented
104C4×D3×D4—32no—
105#5542—32no—
106#5533—34no—
107D3×#117—34no—
108C22×D32C2312yes—
109C2×C32×Q8C2311yescharacteristic
110Q8×C3⋊D3—24no—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2312yes—
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×#634C2312yes—
117C2×#634C2311yescharacteristic
118C2×C3×D12C2312yes—
119C2×C3×C4×D3C2314yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×#627C2312yes—
123C2×#627C2312yes—
124C2×#625C2312yes—
125C2×#624C2312yes—
126C2×#624C2311yescharacteristic
127C2×#624C2311yescharacteristic
128C2×#624C2311yescharacteristic
129C2×#624C2311yescharacteristic
130C2×D3×Dic3C2314yes—
131#3802—24no—
132C4×D32—28no—
133#3797—24no—
134#3797—24no—
135C32×C4⋊C4C2311yescharacteristic
136C32×C4⋊C4C2312yes—
137C32×C42C2311yescharacteristic
138C32×C42C2312yes—
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2312yes—
141#3750C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2312yes—
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2312yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2312yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2312yes—
163C3×C4×Dic3C2312yes—
164#3724C2312yes—
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2312yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175Dic32C2312yes—
176Dic32C2314yes—
177Dic32C2312yes—
178C2×#556—91noSylow
179C2×D3×Q8—32no—
180C2×D3×Q8—32no—
181C2×D3×Q8—32no—
182C2×D3×Q8—61no—
183C2×D3×D4—32no—
184C22×C4×D3—34no—
185C3×C4⋊Q8—32no—
186C3×#126—34no—
187C3×#126—34no—
188C3×#124—32no—
189C3×#124—32no—
190C3×C22⋊Q8—34no—
191C3×C4×Q8—21no—
192C3×C4×Q8—32no—
193C3×C4×Q8—32no—
194C3×C4×Q8C2×D312yescomplemented
195C3×C4×D4—32no—
196C3×#117—34no—
197#947—32no—
198#947C2×D312yes—
199#946—34no—
200Q8×Dic3—32no—
201Q8×Dic3—32no—
202Q8×Dic3—32no—
203Q8×Dic3—61no—
204#944—32no—
205#944C2×D312yescomplemented
206#936—32no—
207#936—32no—
208D4×Dic3—32no—
209C4×#67—34no—
210#926—34no—
211#924—34no—
212#898—34no—
213#898—34no—
214#898—34no—
215#898—34no—
216#898—34no—
217#898C2×D314yescomplemented
218#897—34no—
219#896—34no—
220#896C2×D314yescomplemented
221#893C2×D312yes—
222#892—34no—
223#892—34no—
224D3×C4⋊C4—34no—
225D3×C4⋊C4—32no—
226D3×C4⋊C4—32no—
227D3×C4⋊C4—34no—
228D3×C4⋊C4—32no—
229D3×C4⋊C4—34no—
230D3×C4⋊C4—34no—
231D3×C4⋊C4—32no—
232D3×C4⋊C4—61no—
233D3×C4⋊C4—62no—
234#888—34no—
235#888—34no—
236#887—32no—
237#887—34no—
238#887—32no—
239#887—32no—
240#887—32no—
241#887—34no—
242#887—61no—
243#887—62no—
244#887C2×D312yescomplemented
245#885—34no—
246#885—34no—
247#885—34no—
248#885—34no—
249#67⋊C4—34no—
250D3×C22⋊C4—34no—
251D3×C22⋊C4—34no—
252D3×C22⋊C4—34no—
253D3×C22⋊C4—34no—
254D3×C22⋊C4—34no—
255#879—34no—
256#879—34no—
257#879—34no—
258#879—34no—
259#879—34no—
260#879—34no—
261#878—34no—
262#878—34no—
263#877—34no—
264#877—34no—
265#876—34no—
266#876C2×D314yescomplemented
267#875—32no—
268#875C2×D312yes—
269C4×D12—32no—
270#872—34no—
271#872C2×D314yescomplemented
272C42×D3—32no—
273C42×D3—34no—
274C42×D3—32no—
275C42×D3—34no—
276C42×D3—32no—
277C42×D3—62no—
278C42×D3—61no—
279#869—32no—
280C4×Dic6—32no—
281C4×Dic6—32no—
282C4×Dic6—34no—
283C4×Dic6—34no—
284C4×Dic6—32no—
285C4×Dic6—32no—
286C4×Dic6—62no—
287C4×Dic6—61no—
288C4×Dic6C2×D312yescomplemented
289C22×C3⋊D3C2411yescharacteristic
290C22×C3×D3C2414yes—
291C2×D32—24no—
292C2×D32—24no—
293C2×D32—24no—
294C32×Q8—22no—
295C2×C32×C4C2412yes—
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2411yescharacteristic
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2411yescharacteristic
305C4×C3⋊D3—24no—
306C4×C3⋊D3—22no—
307C4×C3⋊D3—22no—
308C4×C3⋊D3—24no—
309C4×C3⋊D3#4114yes—
310#634—22no—
311#634—24no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C3×D12—24no—
318C3×C4×D3—28no—
319C3×Dic6—24no—
320C3×Dic6—24no—
321#627—24no—
322#627—24no—
323#625—24no—
324#624—24no—
325#624—22no—
326#624—22no—
327#624—22no—
328#624#4114yes—
329D3×Dic3—28no—
330#556—32no—
331#556—94no—
332#556—92no—
333#556—92no—
334#556—94no—
335#556—92no—
336C2×C4⋊Q8—91no—
337C2×#126—92no—
338C2×#126—92no—
339C2×#124—91no—
340C2×#124—91no—
341C2×C22⋊Q8—92no—
342C2×C4×Q8—91no—
343C2×C4×Q8—91no—
344C2×C4×Q8—91no—
345C2×C4×D4—91no—
346C2×#117—92no—
347C23×D3—34no—
348C2×C3×Q8—21no—
349C2×C3×Q8—32no—
350C2×C3×Q8—32no—
351C2×C3×Q8C22×D312yes—
352C2×C3×D4—32no—
353C22×C3×C4—34no—
354C2×#67—34no—
355C22×Dic3—34no—
356D3×Q8—68no—
357D3×Q8—68no—
358D3×Q8—68no—
359D3×Q8—68no—
360D3×D4—68no—
361C2×D12C22×D312yes—
362C2×C4×D3—32no—
363C2×C4×D3—32no—
364C2×C4×D3—34no—
365C2×C4×D3—32no—
366C2×C4×D3—34no—
367C2×C4×D3—32no—
368C2×C4×D3—34no—
369C2×C4×D3—32no—
370C2×C4×D3—32no—
371C2×C4×D3—32no—
372C2×C4×D3—34no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—61no—
378C2×C4×D3—616no—
379C2×C4×D3C22×D314yes—
380C2×Dic6—32no—
381C2×Dic6—34no—
382C2×Dic6—32no—
383C2×Dic6—34no—
384C2×Dic6—32no—
385C2×Dic6—62no—
386C2×Dic6—61no—
387C2×Dic6C22×D312yes—
388C2×Dic6C22×D312yes—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—32no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—32no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4C22×D312yes—
398C3×C4⋊C4C22×D314yes—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C42—22no—
405C3×C42—21no—
406C3×C42—32no—
407C3×C42—32no—
408C3×C42—34no—
409C3×C42C22×D312yes—
410C3×C42C22×D314yes—
411#217—34no—
412#217—34no—
413#217—34no—
414#217—34no—
415#217—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4C22×D314yes—
422(C2×D3)⋊C4C22×D314yes—
423(C2×D3)⋊C4C22×D314yes—
424(C2×D3)⋊C4C22×D314yes—
425(C2×D3)⋊C4C22×D314yes—
426C4⋊Dic3—32no—
427C4⋊Dic3—34no—
428C4⋊Dic3—34no—
429C4⋊Dic3—32no—
430C4⋊Dic3—32no—
431C4⋊Dic3—34no—
432C4⋊Dic3—34no—
433C4⋊Dic3—61no—
434C4⋊Dic3—62no—
435C4⋊Dic3C22×D312yes—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—32no—
440Dic3⋊C4—32no—
441Dic3⋊C4—34no—
442Dic3⋊C4—32no—
443Dic3⋊C4—32no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4C22×D314yes—
450Dic3⋊C4C22×D312yes—
451Dic3⋊C4C22×D312yes—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D314yes—
454C4×Dic3—34no—
455C4×Dic3—32no—
456C4×Dic3—32no—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—32no—
460C4×Dic3—34no—
461C4×Dic3—32no—
462C4×Dic3—34no—
463C4×Dic3—32no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—62no—
467C4×Dic3—61no—
468C4×Dic3—62no—
469C4×Dic3—61no—
470C4×Dic3—62no—
471C4×Dic3—61no—
472C4×Dic3C22×D312yes—
473C4×Dic3C22×D312yes—
474C4×Dic3C22×D314yes—
475C22×C32C2511yescharacteristic
476C2×C3⋊D3C2×#4112yes—
477C2×C3⋊D3C2×#4112yes—
478C2×C3⋊D32−1+412yes—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482D32—48no—
483C32×C4—22no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—22no—
487C32×C4C2×#4112yes—
488C3⋊Dic3—22no—
489C3⋊Dic3—21no—
490C3⋊Dic3—22no—
491C3⋊Dic3—21no—
492C3⋊Dic3C2×#4112yes—
493C3×Dic3—24no—
494C3×Dic3—22no—
495C3×Dic3—22no—
496C3×Dic3—22no—
497C3×Dic3C2×#4114yes—
498C22×Q8—91no—
499C22×Q8—91no—
500C22×Q8—91no—
501C22×D4—91no—
502C23×C4—92no—
503C4⋊Q8—32no—
504C4⋊Q8—92no—
505C4⋊Q8—94no—
506#126—34no—
507#126—34no—
508#126—94no—
509#126—94no—
510#126—94no—
511#126—94no—
512#126—94no—
513#126—94no—
514#124—32no—
515#124—32no—
516#124—92no—
517#124—94no—
518#124—92no—
519#124—92no—
520#124—92no—
521C22⋊Q8—34no—
522C22⋊Q8—94no—
523C22⋊Q8—94no—
524C22⋊Q8—94no—
525C4×Q8—32no—
526C4×Q8—32no—
527C4×Q8—92no—
528C4×Q8—94no—
529C4×Q8—92no—
530C4×Q8—92no—
531C4×Q8—92no—
532C4×Q8—91no—
533C4×Q8—92no—
534C4×Q8—91no—
535C4×Q8—91no—
536C4×Q8—92no—
537C4×Q8D3211yescharacteristic, complemented
538C4×D4—32no—
539C4×D4—92no—
540C4×D4—94no—
541#117—34no—
542#117—94no—
543#117—94no—
544#117—94no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—92no—
547C2×C4⋊C4—92no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—91no—
550C2×C4⋊C4—92no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—92no—
553C2×C22⋊C4—92no—
554C2×C22⋊C4—92no—
555C2×C22⋊C4—92no—
556C2×C22⋊C4—92no—
557C2×C22⋊C4—92no—
558C2×C42—92no—
559C2×C42—91no—
560C2×C42—91no—
561C2×C42—92no—
562C2×C42—91no—
563C23×C3—34no—
564C22×D3—32no—
565C22×D3—61no—
566C22×D3—68no—
567C22×D3—68no—
568C22×D3—68no—
569C22×D3C23×D314yes—
570C3×Q8—24no—
571C3×Q8—24no—
572C3×Q8—64no—
573C3×Q8—64no—
574C3×D4—64no—
575C2×C3×C4—21no—
576C2×C3×C4—22no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—34no—
584C2×C3×C4—32no—
585C2×C3×C4—68no—
586C2×C3×C4C23×D312yes—
587C2×C3×C4C23×D314yes—
588C2×C3×C4C23×D312yes—
589C2×C3×C4C23×D314yes—
590C2×C3×C4C23×D312yes—
591#67—68no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—34no—
595C2×Dic3—34no—
596C2×Dic3—32no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—61no—
602C2×Dic3—68no—
603C2×Dic3C23×D312yes—
604C2×Dic3C23×D312yes—
605C2×Dic3C23×D314yes—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D312yes—
608D12—24no—
609C4×D3—28no—
610C4×D3—38no—
611C4×D3—38no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—68no—
616C4×D3—64no—
617C4×D3—64no—
618C4×D3—68no—
619C4×D3—68no—
620C4×D3—64no—
621C4×D3—64no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3—124no—
625C4×D3—122no—
626Dic6—24no—
627Dic6—24no—
628Dic6—68no—
629Dic6—64no—
630Dic6—68no—
631Dic6—68no—
632Dic6—64no—
633Dic6—64no—
634Dic6—64no—
635C2×C32C22×#4111yescharacteristic
636C2×C32C22×#4111yescharacteristic
637C2×C32C2×2−1+411yescharacteristic
638C3⋊D3#55614yescomplemented
639C3×D3—44no—
640C24—92no—
641C2×Q8—32no—
642C2×Q8—32no—
643C2×Q8—92no—
644C2×Q8—92no—
645C2×Q8—92no—
646C2×Q8—91no—
647C2×Q8—184no—
648C2×Q8—184no—
649C2×Q8—184no—
650C2×Q8C2×D3211yescharacteristic
651C2×D4—32no—
652C2×D4—92no—
653C2×D4—184no—
654C22×C4—34no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—92no—
659C22×C4—91no—
660C22×C4—94no—
661C22×C4—91no—
662C22×C4—91no—
663C22×C4—92no—
664C22×C4—92no—
665C22×C4—91no—
666C22×C4—188no—
667C4⋊C4—32no—
668C4⋊C4—34no—
669C4⋊C4—34no—
670C4⋊C4—32no—
671C4⋊C4—32no—
672C4⋊C4—34no—
673C4⋊C4—92no—
674C4⋊C4—94no—
675C4⋊C4—94no—
676C4⋊C4—92no—
677C4⋊C4—92no—
678C4⋊C4—94no—
679C4⋊C4—92no—
680C4⋊C4—91no—
681C4⋊C4—92no—
682C4⋊C4—92no—
683C4⋊C4—92no—
684C4⋊C4C2×D3211yescharacteristic
685C4⋊C4C2×D3212yes—
686C22⋊C4—34no—
687C22⋊C4—34no—
688C22⋊C4—34no—
689C22⋊C4—34no—
690C22⋊C4—34no—
691C22⋊C4—94no—
692C22⋊C4—94no—
693C22⋊C4—94no—
694C22⋊C4—94no—
695C22⋊C4—94no—
696C42—34no—
697C42—32no—
698C42—32no—
699C42—94no—
700C42—92no—
701C42—92no—
702C42—92no—
703C42—92no—
704C42—92no—
705C42—91no—
706C42—91no—
707C42—91no—
708C42C2×D3212yes—
709C42C2×D3211yescharacteristic
710C22×C3—21no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—64no—
714C22×C3C24×D312yes—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—24no—
718C2×D3—34no—
719C2×D3—34no—
720C2×D3—34no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—1216no—
725C3×C4—24no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—24no—
729C3×C4—24no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—34no—
733C3×C4—42no—
734C3×C4—41no—
735C3×C4—64no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4D3×#4114yes—
740Dic3—24no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—34no—
745Dic3—62no—
746Dic3—64no—
747Dic3—62no—
748Dic3—64no—
749Dic3—62no—
750Dic3—64no—
751Dic3—62no—
752Dic3—122no—
753Dic3—121no—
754Dic3D3×#4114yes—
755C32C2×#55611yescharacteristic, complemented, Sylow
756C23—34no—
757C23—91no—
758C23—184no—
759C23—184no—
760C23—184no—
761Q8—22no—
762Q8—64no—
763Q8—64no—
764Q8—184no—
765Q8—184no—
766Q8—184no—
767Q8—182no—
768D4—64no—
769D4—184no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—68no—
776C2×C4—94no—
777C2×C4—91no—
778C2×C4—94no—
779C2×C4—91no—
780C2×C4—92no—
781C2×C4—92no—
782C2×C4—91no—
783C2×C4—184no—
784C2×C4—184no—
785C2×C4—182no—
786C2×C4—182no—
787C2×C4—188no—
788C2×C4—184no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4C22×D3212yes—
793C2×C4C22×D3211yescharacteristic
794C2×C4C22×D3212yes—
795C2×C4C22×D3211yescharacteristic
796C2×C4C22×D3211yescharacteristic
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—124no—
801C2×C3C2×D3×#4112yes—
802C2×C3C2×D3×#4112yes—
803C2×C3D3×2−1+412yes—
804D3—38no—
805D3—44no—
806D3—64no—
807C22—64no—
808C22—64no—
809C22—64no—
810C22—92no—
811C22—92no—
812C22—92no—
813C22—368no—
814C22C23×D3211yescharacteristic
815C4—22no—
816C4—21no—
817C4—22no—
818C4—21no—
819C4—34no—
820C4—64no—
821C4—62no—
822C4—62no—
823C4—62no—
824C4—92no—
825C4—182no—
826C4—181no—
827C4—182no—
828C4—181no—
829C4#6430612yes—
830C3—21no—
831C3D3×#55612yescomplemented
832C2—94no—
833C2—124no—
834C2C2×#6430611yescharacteristic
835C2#1059668711yescharacteristic
836C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3802C22
hypercenterC4×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5568C2semidirect
4. #10595384C2semidirect
5. #10595365C2semidirect
6. #10594656C2semidirect
7. #10594624C2semidirect
9. #10594554C2semidirect
10. #10594363C2semidirect
11. #10594335C2semidirect
12. #10594020C2semidirect
14. #10593992C2semidirect
15. #10593932C2semidirect
16. #10593931C2semidirect
17. C4×#3797C2semidirect
24. C32×C4×Q8C22semidirect
25. Q8×C3⋊Dic3C22semidirect
28. #64096C22semidirect
29. #64096C22semidirect
32. C4×#634C22semidirect
33. C4×#634C22semidirect
35. C3×#944C22semidirect
36. C3×#898C22semidirect
37. C3×#896C22semidirect
39. C3×#887C22semidirect
40. C3×#876C22semidirect
42. C3×#872C22semidirect
43. C3×C4×Dic6C22semidirect
49. C4×#627C22semidirect
54. #63893C22semidirect
56. #63887C22semidirect
66. #63878C22semidirect
67. #63878C22semidirect
68. #63866C22semidirect
70. #63862C22semidirect
71. #63862C22semidirect
72. #63862C22semidirect
73. #63861C22semidirect
75. #63859C22semidirect
76. #63858C22semidirect
77. #63855C22semidirect
78. #63851C22semidirect
79. #63843C22semidirect
80. Dic3×Dic6C22semidirect
81. #63840C22semidirect
82. #63838C22semidirect
83. #63837C22semidirect
103. #5568D3semidirect
194. C3×C4×Q8C2×D3semidirect
205. #944C2×D3semidirect
217. #898C2×D3semidirect
220. #896C2×D3semidirect
244. #887C2×D3semidirect
266. #876C2×D3semidirect
271. #872C2×D3semidirect
288. C4×Dic6C2×D3semidirect
537. C4×Q8D32semidirect
638. C3⋊D3#556semidirect
755. C32C2×#556semidirect
831. C3D3×#556semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55682
#105954322
#105953842
#105953652
#105946562
#105946242
#105946052
#105945542
#105943632
#105943352
#105940202
#105940092
#105939922
#105939322
#105939312
C4×#37972
D3×#5563