Finite Group Databasebeta

← #11903379

Subgroups — #11903379

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic, complemented
2C3×#5533C212yesmaximal, complemented
3C4×#3811C211yesmaximal, characteristic
4#10594925C211yesmaximal, characteristic, complemented
5#10594841C212yesmaximal, complemented
6#10594631C211yesmaximal, characteristic, complemented
7#10594602C211yesmaximal, characteristic, complemented
8#10594565C212yesmaximal, complemented
9#10594557C212yesmaximal, complemented
10#10594374C211yesmaximal, characteristic, complemented
11#10594363C211yesmaximal, characteristic, complemented
12#10594288C212yesmaximal
13#10594154C212yesmaximal, complemented
14#10594145C214yesmaximal, complemented
15#10594020C212yesmaximal, complemented
16#10593940C214yesmaximal, complemented
17C4×#3797C212yesmaximal, complemented
18D3×#556—32nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×#3811C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22C2×#3797C2211yescharacteristic
23C2×#3797C2212yes—
24C32×#117C2211yescharacteristic, complemented
25#64135C2211yescharacteristic, complemented
26#64101C2211yescharacteristic, complemented
27#64101C2211yescharacteristic, complemented
28C4⋊C4×C3⋊D3C2211yescharacteristic
29C4⋊C4×C3⋊D3C2211yescharacteristic
30C22⋊C4×C3⋊D3C2212yes—
31#64086C2212yescomplemented
32#64081C2212yescomplemented
33C42×C3⋊D3C2212yes—
34C3×C4×#67C2212yes—
35C3×#924C2212yescomplemented
36C3×#897C2212yescomplemented
37C3×#892C2212yescomplemented
38C3×#888C2212yescomplemented
39C3×#887C2212yescomplemented
40C3×#885C2214yes—
41C3×#879C2214yescomplemented
42C3×#876C2214yescomplemented
43C3×C4×Dic6C2214yescomplemented
44#63982C2212yescomplemented
45#63974C2211yescharacteristic
46#63974C2212yes—
47#67⋊Dic3C2212yes—
48#63959C2214yes—
49#63956C2214yescomplemented
50#63921C2212yes—
51#63921C2212yes—
52#63921C2211yescharacteristic
53#63918C2212yescomplemented
54C4×#627C2214yescomplemented
55#63907C2214yes—
56C4×#626C2212yes—
57#63900C2211yescharacteristic
58#63900C2212yes—
59#63899C2214yescomplemented
60#63883C2212yes—
61#63883C2212yes—
62#63883C2211yescharacteristic
63#63883C2212yes—
64C4×#624C2212yes—
65C4×#624C2211yescharacteristic
66C4×#624C2212yes—
67#63881C2212yes—
68#63877C2214yescomplemented
69#63871C2212yescomplemented
70#63868C2214yescomplemented
71#63865C2212yescomplemented
72#63862C2214yescomplemented
73#63862C2214yescomplemented
74#63862C2214yescomplemented
75#63856C2212yescomplemented
76#63852C2214yes—
77#63848C2214yescomplemented
78#63843C2214yescomplemented
79Dic3×Dic6C2212yescomplemented
80#63841C2212yescomplemented
81#63839C2214yescomplemented
82#63838C2214yescomplemented
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—34no—
92#5671—34no—
93#5641—32no—
94#5641—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97#5584—32no—
98C4×D3×Q8—32no—
99C4×D3×Q8—34no—
100#5568—34no—
101C4×D3×D4—32no—
102#5542—32no—
103#5533—32no—
104#5533D312yescomplemented
105D3×#117—32no—
106D3×#117—32no—
107D3×#117—61no—
108C23×C3⋊D3C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4×C3⋊D3—24no—
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C3×#67C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×Dic6C2314yes—
122C2×C3×Dic6C2312yes—
123#3811—24no—
124C2×#627C2312yes—
125C2×#627C2314yes—
126C2×#626C2312yes—
127C2×#624C2312yes—
128C2×#624C2312yes—
129C2×#624C2311yescharacteristic
130C2×#624C2311yescharacteristic
131C2×#624C2311yescharacteristic
132C2×D3×Dic3C2312yes—
133C4×D32—24no—
134#3797—24no—
135#3797—28no—
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2311yescharacteristic
138C32×C22⋊C4C2312yes—
139C32×C42C2312yes—
140#3757C2312yes—
141#3752C2312yes—
142#3752C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145#3750C2312yes—
146#3750C2312yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C3×#217C2312yes—
151C3×#217C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2314yes—
156C3×C4⋊Dic3C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2312yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2314yes—
163C3×C4×Dic3C2312yes—
164#3724C2314yes—
165#3724C2312yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2314yes—
170#3722C2312yes—
171#3722C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2312yes—
176Dic32C2314yes—
177Dic32C2314yes—
178C2×#556—91noSylow
179C2×D3×Q8—34no—
180C2×D3×Q8—32no—
181C2×D3×D4—32no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C22×C4×D3—61no—
185C3×C4⋊Q8—32no—
186C3×#126—34no—
187C3×#126—34no—
188C3×#124—34no—
189C3×C22⋊Q8—32no—
190C3×C22⋊Q8—32no—
191C3×C4×Q8—32no—
192C3×C4×Q8—34no—
193C3×C4×D4—32no—
194C3×#117—21no—
195C3×#117—32no—
196C3×#117C2×D312yescomplemented
197#947—34no—
198#946—32no—
199#946—32no—
200Q8×Dic3—34no—
201Q8×Dic3—32no—
202#944—34no—
203#936—34no—
204D4×Dic3—32no—
205C4×#67—32no—
206C4×#67C2×D312yes—
207#926—32no—
208#926—32no—
209#926—61no—
210#924—32no—
211#924C2×D312yescomplemented
212#898—34no—
213#898—34no—
214#898—34no—
215#898—34no—
216#898—34no—
217#898—34no—
218#897—32no—
219#897C2×D312yescomplemented
220#896—34no—
221#896—34no—
222#893—32no—
223#892—32no—
224#892—32no—
225#892—32no—
226#892—61no—
227#892—61no—
228#892C2×D312yescomplemented
229D3×C4⋊C4—32no—
230D3×C4⋊C4—32no—
231D3×C4⋊C4—34no—
232D3×C4⋊C4—32no—
233D3×C4⋊C4—34no—
234D3×C4⋊C4—34no—
235D3×C4⋊C4—34no—
236D3×C4⋊C4—32no—
237D3×C4⋊C4—61no—
238D3×C4⋊C4—61no—
239#888—34no—
240#888—32no—
241#888C2×D312yescomplemented
242#887—34no—
243#887—34no—
244#887—34no—
245#887—34no—
246#887C2×D312yescomplemented
247#885—34no—
248#885—34no—
249#885—34no—
250#885C2×D314yes—
251#67⋊C4—32no—
252#67⋊C4—32no—
253D3×C22⋊C4—34no—
254D3×C22⋊C4—34no—
255D3×C22⋊C4—32no—
256D3×C22⋊C4—34no—
257D3×C22⋊C4—34no—
258D3×C22⋊C4—32no—
259D3×C22⋊C4—62no—
260#879—34no—
261#879—34no—
262#879—34no—
263#879—34no—
264#879—34no—
265#879C2×D314yescomplemented
266#878—34no—
267#878—34no—
268#877—34no—
269#877—34no—
270#877—62no—
271#876—34no—
272#876C2×D314yescomplemented
273#875—34no—
274C4×D12—32no—
275#872—34no—
276#872—34no—
277#872—62no—
278C42×D3—34no—
279C42×D3—34no—
280C42×D3—34no—
281C42×D3—32no—
282C42×D3—62no—
283#869—32no—
284C4×Dic6—32no—
285C4×Dic6—34no—
286C4×Dic6—34no—
287C4×Dic6—34no—
288C4×Dic6C2×D314yescomplemented
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3C2411yescharacteristic
294C22×C3⋊D3C2411yescharacteristic
295C22×C3×D3C2412yes—
296C2×D32—22no—
297C2×D32—22no—
298C2×D32—22no—
299C2×C32×C4—22no—
300C2×C32×C4C2412yes—
301C2×C32×C4C2411yescharacteristic
302C2×C32×C4C2412yes—
303C2×C32×C4C2411yescharacteristic
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2411yescharacteristic
309C4×C3⋊D3—22no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—22no—
312C4×C3⋊D3—24no—
313C4×C3⋊D3—24no—
314C4×C3⋊D3#4114yes—
315C3×#67—24no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2414yes—
319C2×C3×Dic3C2414yes—
320C2×C3×Dic3C2412yes—
321C3×C4×D3—24no—
322C3×Dic6—24no—
323C3×Dic6—28no—
324#627—24no—
325#627—28no—
326#626—24no—
327#624—24no—
328#624—24no—
329#624—22no—
330#624—22no—
331#624#4114yes—
332D3×Dic3—24no—
333#556—32no—
334#556—92no—
335#556—92no—
336#556—94no—
337#556—92no—
338#556—94no—
339C2×C4⋊Q8—91no—
340C2×#126—92no—
341C2×#126—92no—
342C2×#124—92no—
343C2×C22⋊Q8—91no—
344C2×C22⋊Q8—91no—
345C2×C4×Q8—92no—
346C2×C4×Q8—91no—
347C2×C4×D4—91no—
348C2×#117—91no—
349C2×#117—91no—
350C23×D3—32no—
351C23×D3—32no—
352C23×D3—61no—
353C2×C3×Q8—34no—
354C2×C3×Q8—32no—
355C2×C3×D4—32no—
356C22×C3×C4—21no—
357C22×C3×C4—32no—
358C22×C3×C4C22×D312yes—
359C2×#67—32no—
360C2×#67C22×D312yes—
361C22×Dic3—32no—
362C22×Dic3—32no—
363C22×Dic3—61no—
364D3×Q8—68no—
365D3×Q8—616no—
366D3×D4—68no—
367C2×D12—32no—
368C2×C4×D3—32no—
369C2×C4×D3—32no—
370C2×C4×D3—32no—
371C2×C4×D3—34no—
372C2×C4×D3—32no—
373C2×C4×D3—34no—
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—34no—
379C2×C4×D3—34no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—68no—
387C2×C4×D3—68no—
388C2×C4×D3—68no—
389C2×C4×D3C22×D312yes—
390C2×Dic6—34no—
391C2×Dic6—34no—
392C2×Dic6—34no—
393C2×Dic6C22×D312yes—
394C2×Dic6C22×D314yes—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—32no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4C22×D312yes—
404C3×C4⋊C4C22×D312yes—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—32no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—32no—
411C3×C22⋊C4C22×D314yes—
412C3×C42—22no—
413C3×C42—34no—
414C3×C42—32no—
415C3×C42—34no—
416C3×C42C22×D314yes—
417#217—34no—
418#217—34no—
419#217—34no—
420#217—32no—
421#217—62no—
422#217C22×D314yes—
423#217C22×D312yes—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—32no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D312yes—
437(C2×D3)⋊C4C22×D314yes—
438C4⋊Dic3—32no—
439C4⋊Dic3—32no—
440C4⋊Dic3—32no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—61no—
445C4⋊Dic3—61no—
446C4⋊Dic3C22×D314yes—
447C4⋊Dic3C22×D312yes—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—32no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D312yes—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3—32no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—32no—
471C4×Dic3—34no—
472C4×Dic3—62no—
473C4×Dic3—62no—
474C4×Dic3—62no—
475C4×Dic3C22×D314yes—
476C4×Dic3C22×D314yes—
477C4×Dic3C22×D312yes—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32C2511yescharacteristic
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—44no—
486C2×C3⋊D3C2×#4112yes—
487C2×C3⋊D3C2×#4112yes—
488C2×C3⋊D32−1+412yes—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492D32—44no—
493C32×C4—21no—
494C32×C4—22no—
495C32×C4—22no—
496C32×C4C2×#4112yes—
497C3⋊Dic3—21no—
498C3⋊Dic3—22no—
499C3⋊Dic3—22no—
500C3⋊Dic3C2×#4112yes—
501C3×Dic3—22no—
502C3×Dic3—24no—
503C3×Dic3—24no—
504C3×Dic3—22no—
505C3×Dic3C2×#4114yes—
506C22×Q8—91no—
507C22×Q8—92no—
508C22×D4—91no—
509C23×C4—91no—
510C23×C4—91no—
511C4⋊Q8—32no—
512C4⋊Q8—92no—
513C4⋊Q8—94no—
514#126—34no—
515#126—34no—
516#126—94no—
517#126—94no—
518#126—94no—
519#126—94no—
520#126—94no—
521#126—94no—
522#124—34no—
523#124—94no—
524#124—94no—
525#124—94no—
526C22⋊Q8—32no—
527C22⋊Q8—32no—
528C22⋊Q8—92no—
529C22⋊Q8—94no—
530C22⋊Q8—92no—
531C22⋊Q8—92no—
532C22⋊Q8—92no—
533C4×Q8—32no—
534C4×Q8—34no—
535C4×Q8—94no—
536C4×Q8—94no—
537C4×Q8—92no—
538C4×Q8—94no—
539C4×Q8—94no—
540C4×D4—32no—
541C4×D4—92no—
542C4×D4—92no—
543C4×D4—92no—
544#117—32no—
545#117—94no—
546#117—92no—
547#117—91no—
548#117—91no—
549#117—91no—
550#117—92no—
551#117—92no—
552#117D3211yescharacteristic, complemented
553C2×C4⋊C4—91no—
554C2×C4⋊C4—91no—
555C2×C4⋊C4—92no—
556C2×C4⋊C4—92no—
557C2×C4⋊C4—92no—
558C2×C4⋊C4—92no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C22⋊C4—92no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—92no—
565C2×C22⋊C4—92no—
566C2×C22⋊C4—92no—
567C2×C42—92no—
568C2×C42—91no—
569C2×C42—92no—
570C2×C42—92no—
571C23×C3—21no—
572C23×C3—32no—
573C23×C3C23×D312yes—
574C22×D3—32no—
575C22×D3—32no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—64no—
579C22×D3—64no—
580C22×D3—64no—
581C22×D3—64no—
582C22×D3—64no—
583C22×D3—64no—
584C22×D3—64no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3C23×D312yes—
588C3×Q8—68no—
589C3×Q8—64no—
590C3×D4—64no—
591C2×C3×C4—24no—
592C2×C3×C4—24no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—34no—
601C2×C3×C4—34no—
602C2×C3×C4—64no—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D314yes—
605C2×C3×C4C23×D314yes—
606C2×C3×C4C23×D312yes—
607#67—24no—
608#67—64no—
609C2×Dic3—32no—
610C2×Dic3—34no—
611C2×Dic3—32no—
612C2×Dic3—34no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—64no—
618C2×Dic3—64no—
619C2×Dic3—64no—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D314yes—
623C2×Dic3C23×D314yes—
624C2×Dic3C23×D312yes—
625D12—64no—
626C4×D3—24no—
627C4×D3—38no—
628C4×D3—38no—
629C4×D3—64no—
630C4×D3—64no—
631C4×D3—64no—
632C4×D3—68no—
633C4×D3—68no—
634C4×D3—64no—
635C4×D3—64no—
636C4×D3—68no—
637C4×D3—64no—
638C4×D3—68no—
639C4×D3—64no—
640C4×D3—64no—
641C4×D3—64no—
642C4×D3—64no—
643C4×D3—124no—
644C4×D3—124no—
645Dic6—24no—
646Dic6—28no—
647Dic6—68no—
648Dic6—68no—
649Dic6—68no—
650C2×C32—41no—
651C2×C32C22×#4111yescharacteristic
652C2×C32C22×#4111yescharacteristic
653C2×C32C2×2−1+411yescharacteristic
654C3⋊D3—41no—
655C3⋊D3#55614yescomplemented
656C3×D3—42no—
657C24—91no—
658C24—91no—
659C2×Q8—32no—
660C2×Q8—34no—
661C2×Q8—92no—
662C2×Q8—94no—
663C2×Q8—188no—
664C2×Q8—184no—
665C2×D4—32no—
666C2×D4—92no—
667C2×D4—184no—
668C22×C4—32no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—92no—
673C22×C4—92no—
674C22×C4—92no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—92no—
678C22×C4—91no—
679C22×C4—92no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—184no—
683C22×C4—184no—
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—34no—
688C4⋊C4—34no—
689C4⋊C4—34no—
690C4⋊C4—34no—
691C4⋊C4—92no—
692C4⋊C4—92no—
693C4⋊C4—94no—
694C4⋊C4—94no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—92no—
698C4⋊C4—91no—
699C4⋊C4—92no—
700C4⋊C4—91no—
701C4⋊C4C2×D3211yescharacteristic
702C4⋊C4C2×D3211yescharacteristic
703C22⋊C4—32no—
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—32no—
707C22⋊C4—34no—
708C22⋊C4—92no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—92no—
712C22⋊C4—94no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C22⋊C4C2×D3212yes—
717C42—34no—
718C42—32no—
719C42—34no—
720C42—94no—
721C42—92no—
722C42—94no—
723C42—92no—
724C42—92no—
725C42—92no—
726C42C2×D3212yes—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3C24×D312yes—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—34no—
742C2×D3—34no—
743C2×D3—34no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—128no—
754C2×D3—128no—
755C2×D3—128no—
756C3×C4—22no—
757C3×C4—24no—
758C3×C4—22no—
759C3×C4—24no—
760C3×C4—22no—
761C3×C4—34no—
762C3×C4—42no—
763C3×C4—42no—
764C3×C4—64no—
765C3×C4—64no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4D3×#4114yes—
769Dic3—24no—
770Dic3—24no—
771Dic3—22no—
772Dic3—22no—
773Dic3—34no—
774Dic3—62no—
775Dic3—62no—
776Dic3—64no—
777Dic3—62no—
778Dic3—64no—
779Dic3—122no—
780Dic3—122no—
781Dic3D3×#4114yes—
782C32C2×#55611yescharacteristic, complemented, Sylow
783C23—32no—
784C23—91no—
785C23—91no—
786C23—182no—
787C23—182no—
788C23—182no—
789C23—182no—
790C23—182no—
791C23—182no—
792C23C22×D3211yescharacteristic
793Q8—68no—
794Q8—64no—
795Q8—188no—
796Q8—184no—
797D4—64no—
798D4—184no—
799C2×C4—22no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—34no—
804C2×C4—34no—
805C2×C4—64no—
806C2×C4—94no—
807C2×C4—91no—
808C2×C4—94no—
809C2×C4—92no—
810C2×C4—91no—
811C2×C4—92no—
812C2×C4—182no—
813C2×C4—182no—
814C2×C4—184no—
815C2×C4—184no—
816C2×C4—182no—
817C2×C4—184no—
818C2×C4—184no—
819C2×C4—182no—
820C2×C4—184no—
821C2×C4—182no—
822C2×C4—182no—
823C2×C4C22×D3212yes—
824C2×C4C22×D3211yescharacteristic
825C2×C4C22×D3212yes—
826C2×C4C22×D3211yescharacteristic
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—122no—
833C2×C3C2×D3×#4112yes—
834C2×C3C2×D3×#4112yes—
835C2×C3D3×2−1+412yes—
836D3—38no—
837D3—42no—
838D3—64no—
839D3—122no—
840D3—122no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—92no—
848C22—92no—
849C22—92no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—364no—
854C22—364no—
855C22C23×D3211yescharacteristic
856C4—21no—
857C4—22no—
858C4—22no—
859C4—34no—
860C4—62no—
861C4—64no—
862C4—64no—
863C4—62no—
864C4—92no—
865C4—181no—
866C4—182no—
867C4—182no—
868C4#6430612yes—
869C3—21no—
870C3D3×#55612yescomplemented
871C2—41no—
872C2—94no—
873C2—122no—
874C2—361no—
875C2C2×#6430611yescharacteristic
876C2D32×#4111yescharacteristic
877C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC2×#3811C22
hypercenter#117D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#117C2semidirect
2. C3×#5533C2semidirect
4. #10594925C2semidirect
5. #10594841C2semidirect
6. #10594631C2semidirect
7. #10594602C2semidirect
8. #10594565C2semidirect
9. #10594557C2semidirect
10. #10594374C2semidirect
11. #10594363C2semidirect
13. #10594154C2semidirect
14. #10594145C2semidirect
15. #10594020C2semidirect
16. #10593940C2semidirect
17. C4×#3797C2semidirect
24. C32×#117C22semidirect
25. #64135C22semidirect
26. #64101C22semidirect
27. #64101C22semidirect
31. #64086C22semidirect
32. #64081C22semidirect
35. C3×#924C22semidirect
36. C3×#897C22semidirect
37. C3×#892C22semidirect
38. C3×#888C22semidirect
39. C3×#887C22semidirect
41. C3×#879C22semidirect
42. C3×#876C22semidirect
43. C3×C4×Dic6C22semidirect
44. #63982C22semidirect
49. #63956C22semidirect
53. #63918C22semidirect
54. C4×#627C22semidirect
59. #63899C22semidirect
68. #63877C22semidirect
69. #63871C22semidirect
70. #63868C22semidirect
71. #63865C22semidirect
72. #63862C22semidirect
73. #63862C22semidirect
74. #63862C22semidirect
75. #63856C22semidirect
77. #63848C22semidirect
78. #63843C22semidirect
79. Dic3×Dic6C22semidirect
80. #63841C22semidirect
81. #63839C22semidirect
82. #63838C22semidirect
83. #63837C22semidirect
104. #5533D3semidirect
196. C3×#117C2×D3semidirect
211. #924C2×D3semidirect
219. #897C2×D3semidirect
228. #892C2×D3semidirect
241. #888C2×D3semidirect
246. #887C2×D3semidirect
265. #879C2×D3semidirect
272. #876C2×D3semidirect
288. C4×Dic6C2×D3semidirect
552. #117D32semidirect
655. C3⋊D3#556semidirect
782. C32C2×#556semidirect
870. C3D3×#556semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
C3×#55332
C4×#38112
#105949252
#105948412
#105946312
#105946022
#105945652
#105945572
#105943742
#105943632
#105942882
#105941542
#105941452
#105940202
#105939402
C4×#37972
D3×#5563