Finite Group Databasebeta

← #11903087

Subgroups — #11903087

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#125C211yesmaximal, characteristic, complemented
2C3×#5694C212yesmaximal, complemented
3#10594656C212yesmaximal, complemented
4#10594631C211yesmaximal, characteristic, complemented
5#10594631C211yesmaximal, characteristic, complemented
6#10594608C212yesmaximal
7#10594602C212yesmaximal, complemented
8#10594602C211yesmaximal, characteristic, complemented
9D32×C4⋊C4C211yesmaximal, characteristic, complemented
10#10594551C212yesmaximal, complemented
11#10594482C212yesmaximal, complemented
12#10594456C212yesmaximal, complemented
13#10594429C214yesmaximal, complemented
14#10594409C214yesmaximal, complemented
15C4×#3802C211yesmaximal, characteristic
16#10593917C212yesmaximal, complemented
17C4×#3797C211yesmaximal, characteristic, complemented
18D3×#552—32nomaximal
19C2×#3802C2211yescharacteristic
20C2×C4×D32C2212yes—
21C2×C4×D32C2211yescharacteristic
22C2×C4×D32C2211yescharacteristic
23C2×#3797C2211yescharacteristic
24C32×#125C2211yescharacteristic, complemented
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2212yes—
28C4⋊C4×C3⋊D3C2212yes—
29#64099C2211yescharacteristic, complemented
30#64099C2211yescharacteristic, complemented
31#64098C2212yescomplemented
32#64098C2212yescomplemented
33C42×C3⋊D3C2211yescharacteristic
34#64079C2211yescharacteristic, complemented
35C3×#898C2214yescomplemented
36C3×#897C2212yescomplemented
37C3×#897C2212yescomplemented
38C3×#894C2214yes—
39C3×#892C2214yescomplemented
40C3×#892C2212yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#890C2214yescomplemented
43C3×C4×D12C2212yes—
44C3×C4×Dic6C2212yescomplemented
45#63921C2211yescharacteristic
46#63921C2212yes—
47#63921C2212yes—
48#63921C2212yes—
49#63921C2211yescharacteristic
50C4×#627C2212yescomplemented
51#63905C2214yes—
52#63902C2212yes—
53C4×#625C2212yes—
54#63900C2211yescharacteristic
55#63900C2212yes—
56#63900C2212yes—
57#63900C2211yescharacteristic
58#63899C2214yescomplemented
59#63899C2214yescomplemented
60#63898C2212yes—
61#63891C2214yes—
62D3×C4⋊Dic3C2212yescomplemented
63#63884C2214yes—
64#63883C2212yes—
65#63883C2212yes—
66C4×#624C2212yes—
67C4×#624C2212yes—
68#63877C2214yescomplemented
69#63877C2214yescomplemented
70#63877C2214yescomplemented
71D3×Dic3⋊C4C2214yescomplemented
72#63869C2214yescomplemented
73#63861C2214yescomplemented
74#63859C2214yescomplemented
75#63858C2214yescomplemented
76#63856C2212yescomplemented
77#63856C2212yescomplemented
78#63847C2214yescomplemented
79#63847C2214yescomplemented
80#63843C2212yescomplemented
81#63841C2212yescomplemented
82#63841C2214yescomplemented
83#63838C2212yescomplemented
84C3×#552—32no—
85#5708—34no—
86D3×#126—34no—
87#5694D312yescomplemented
88#5693—34no—
89D3×#125—32no—
90D3×#125—34no—
91D3×#125—61no—
92D3×#123—34no—
93#5650—34no—
94#5642—32no—
95#5639—32no—
96D3×C22⋊Q8—32no—
97D3×C22⋊Q8—32no—
98#5581—32no—
99C4×D3×Q8—32no—
100C4×D3×D4—32no—
101#5541—32no—
102#5531—34no—
103#5529—32no—
104D3×#117—32no—
105D3×#117—34no—
106#5513—32no—
107C2×D3×C4⋊C4—32no—
108C22×D32C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C3×D12C2312yes—
116C2×C3×C4×D3C2314yes—
117C2×C3×C4×D3C2312yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×Dic6C2312yes—
120C2×#627C2312yes—
121C2×#625C2312yes—
122C2×#624C2312yes—
123C2×#624C2312yes—
124C2×#624C2311yescharacteristic
125C2×#624C2311yescharacteristic
126C2×D3×Dic3C2312yes—
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2312yes—
129#3802—24no—
130C4×D32—28no—
131C4×D32—24no—
132C4×D32—24no—
133#3797—24no—
134C32×C4⋊C4C2312yes—
135C32×C4⋊C4C2311yescharacteristic
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2312yes—
138C32×C42C2311yescharacteristic
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2312yes—
142C4⋊(C3⋊Dic3)C2312yes—
143#3750C2312yes—
144#3750C2312yes—
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2311yescharacteristic
151C4×C3⋊Dic3C2311yescharacteristic
152C3×(C2×D3)⋊C4C2312yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2314yes—
160C3×C4⋊Dic3C2312yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×C4×Dic3C2314yes—
164C3×C4×Dic3C2314yes—
165#3724C2312yes—
166#3724C2314yes—
167#3724C2312yes—
168#3724C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2312yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2312yes—
176Dic32C2314yes—
177Dic32C2314yes—
178C2×#552—91noSylow
179C2×D3×Q8—32no—
180C2×D3×D4—32no—
181C22×C4×D3—34no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C3×#126—34no—
185C3×#125—21no—
186C3×#125—34no—
187C3×#125C2×D312yescomplemented
188C3×#123—34no—
189C3×C22⋊Q8—32no—
190C3×C22⋊Q8—32no—
191C3×C4×Q8—32no—
192C3×C4×D4—32no—
193C3×#117—32no—
194C3×#117—34no—
195C2×C3×C4⋊C4—32no—
196#946—32no—
197#946—32no—
198Q8×Dic3—32no—
199#935—34no—
200D4×Dic3—32no—
201#929—34no—
202C4×#67—32no—
203C4×#67—32no—
204#926—32no—
205#926—34no—
206C2×C4⋊Dic3—32no—
207#924—32no—
208#924—32no—
209C2×Dic3⋊C4—34no—
210#898—34no—
211#898—34no—
212#898C2×D314yescomplemented
213#897C2×D312yescomplemented
214#897C2×D312yescomplemented
215#896—34no—
216#896—34no—
217#894—34no—
218#894C2×D314yes—
219#893—32no—
220#892—34no—
221#892—32no—
222#892C2×D312yescomplemented
223#892C2×D314yescomplemented
224D3×C4⋊C4—34no—
225D3×C4⋊C4—32no—
226D3×C4⋊C4—34no—
227D3×C4⋊C4—34no—
228D3×C4⋊C4—32no—
229D3×C4⋊C4—32no—
230D3×C4⋊C4—32no—
231D3×C4⋊C4—34no—
232D3×C4⋊C4—34no—
233D3×C4⋊C4—32no—
234D3×C4⋊C4—34no—
235D3×C4⋊C4—34no—
236D3×C4⋊C4—61no—
237D3×C4⋊C4—61no—
238D3×C4⋊C4—62no—
239D3×C4⋊C4—62no—
240D3×C4⋊C4C2×D312yescomplemented
241#890—32no—
242#890—32no—
243#890—34no—
244#890—61no—
245#890—61no—
246#890C2×D314yescomplemented
247#889—34no—
248#889—34no—
249#889—34no—
250#889—34no—
251#889—34no—
252#889—34no—
253#889—62no—
254#889—62no—
255#887—32no—
256#887—34no—
257#886—34no—
258#883—34no—
259#883—34no—
260#67⋊C4—32no—
261#67⋊C4—32no—
262D3×C22⋊C4—34no—
263D3×C22⋊C4—34no—
264D3×C22⋊C4—34no—
265D3×C22⋊C4—32no—
266D3×C22⋊C4—32no—
267#879—34no—
268#879—34no—
269#879—34no—
270#878—34no—
271#878—34no—
272#877—34no—
273#877—34no—
274#877—34no—
275#876—34no—
276C4×D12C2×D312yes—
277#872—34no—
278#872—34no—
279#872—34no—
280C42×D3—32no—
281C42×D3—34no—
282C42×D3—34no—
283C42×D3—61no—
284#870—32no—
285#870—34no—
286#870—61no—
287C4×Dic6—34no—
288C4×Dic6C2×D312yescomplemented
289C22×C3⋊D3C2411yescharacteristic
290C22×C3×D3C2412yes—
291C22×C3×D3C2412yes—
292C2×D32—22no—
293C2×D32—22no—
294C2×D32—22no—
295C2×D32—22no—
296C2×D32—22no—
297C2×D32#4114yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2412yes—
300C2×C32×C4C2411yescharacteristic
301C2×C32×C4C2412yes—
302C2×C32×C4C2411yescharacteristic
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308C4×C3⋊D3—24no—
309C4×C3⋊D3—22no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—24no—
312C4×C3⋊D3#4114yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C3×D12—24no—
318C3×C4×D3—28no—
319C3×C4×D3—24no—
320C3×C4×D3—24no—
321C3×Dic6—24no—
322#627—24no—
323#625—24no—
324#624—24no—
325#624—22no—
326#624—22no—
327#624—24no—
328D3×Dic3—28no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331#552—32no—
332#552—92no—
333#552—92no—
334#552—94no—
335#552—92no—
336#552—94no—
337C2×#126—92no—
338C2×#125—92no—
339C2×#125—91no—
340C2×#123—92no—
341C2×C22⋊Q8—91no—
342C2×C22⋊Q8—91no—
343C2×C4×Q8—91no—
344C2×C4×D4—91no—
345C2×#117—91no—
346C2×#117—92no—
347C22×C4⋊C4—91no—
348C23×D3—32no—
349C23×D3—32no—
350C2×C3×Q8—32no—
351C2×C3×D4—32no—
352C22×C3×C4—34no—
353C22×C3×C4—32no—
354C22×C3×C4—32no—
355C2×#67—32no—
356C2×#67—32no—
357C22×Dic3—32no—
358C22×Dic3—34no—
359C22×Dic3—32no—
360D3×Q8—68no—
361D3×D4—68no—
362C2×D12C22×D312yes—
363C2×C4×D3—32no—
364C2×C4×D3—32no—
365C2×C4×D3—34no—
366C2×C4×D3—32no—
367C2×C4×D3—32no—
368C2×C4×D3—34no—
369C2×C4×D3—32no—
370C2×C4×D3—34no—
371C2×C4×D3—32no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—32no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—68no—
381C2×C4×D3—68no—
382C2×C4×D3—616no—
383C2×C4×D3C22×D312yes—
384C2×C4×D3C22×D312yes—
385C2×C4×D3C22×D314yes—
386C2×Dic6—34no—
387C2×Dic6C22×D312yes—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—32no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4C22×D314yes—
399C3×C4⋊C4C22×D314yes—
400C3×C4⋊C4C22×D312yes—
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—32no—
407C3×C42—21no—
408C3×C42—34no—
409C3×C42—34no—
410C3×C42C22×D312yes—
411#217—32no—
412#217—34no—
413#217—34no—
414#217—34no—
415#217—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—32no—
421(C2×D3)⋊C4C22×D312yes—
422(C2×D3)⋊C4C22×D314yes—
423(C2×D3)⋊C4C22×D314yes—
424(C2×D3)⋊C4C22×D312yes—
425(C2×D3)⋊C4C22×D314yes—
426C4⋊Dic3—34no—
427C4⋊Dic3—32no—
428C4⋊Dic3—32no—
429C4⋊Dic3—34no—
430C4⋊Dic3—34no—
431C4⋊Dic3—34no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—62no—
435C4⋊Dic3—62no—
436C4⋊Dic3C22×D312yes—
437C4⋊Dic3C22×D314yes—
438C4⋊Dic3C22×D312yes—
439C4⋊Dic3C22×D314yes—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—32no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—32no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4—62no—
460Dic3⋊C4—62no—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463C4×Dic3—32no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—61no—
471C4×Dic3—61no—
472C4×Dic3—61no—
473C4×Dic3C22×D314yes—
474C4×Dic3C22×D314yes—
475C22×C32C2511yescharacteristic
476C2×C3⋊D3C2×#4112yes—
477C2×C3⋊D3C2×#4112yes—
478C2×C3⋊D32−1+412yes—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3C2×#4114yes—
485D32—28no—
486D32—44no—
487C32×C4—22no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—22no—
491C32×C4C2×#4112yes—
492C3⋊Dic3—22no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—22no—
496C3⋊Dic3C2×#4112yes—
497C3×Dic3—22no—
498C3×Dic3—22no—
499C3×Dic3—24no—
500C3×Dic3—24no—
501C22×Q8—91no—
502C22×D4—91no—
503C23×C4—92no—
504C23×C4—91no—
505C23×C4—91no—
506#126—34no—
507#126—94no—
508#126—94no—
509#126—94no—
510#125—34no—
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
520#123—34no—
521#123—94no—
522#123—94no—
523#123—94no—
524C22⋊Q8—32no—
525C22⋊Q8—32no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528C22⋊Q8—92no—
529C22⋊Q8—92no—
530C4×Q8—32no—
531C4×Q8—92no—
532C4×Q8—92no—
533C4×Q8—92no—
534C4×D4—32no—
535C4×D4—92no—
536C4×D4—92no—
537C4×D4—92no—
538#117—32no—
539#117—34no—
540#117—94no—
541#117—94no—
542#117—94no—
543#117—92no—
544#117—94no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—92no—
548C2×C4⋊C4—92no—
549C2×C4⋊C4—91no—
550C2×C4⋊C4—92no—
551C2×C4⋊C4—92no—
552C2×C4⋊C4—94no—
553C2×C4⋊C4—92no—
554C2×C4⋊C4—91no—
555C2×C4⋊C4—91no—
556C2×C4⋊C4—92no—
557C2×C4⋊C4—92no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—92no—
560C2×C22⋊C4—92no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—92no—
563C2×C42—92no—
564C2×C42—92no—
565C2×C42—91no—
566C23×C3—32no—
567C23×C3—32no—
568C22×D3—32no—
569C22×D3—38no—
570C22×D3—61no—
571C22×D3—64no—
572C22×D3—64no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3C23×D312yes—
577C22×D3C23×D312yes—
578C3×Q8—64no—
579C3×D4—64no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—34no—
586C2×C3×C4—32no—
587C2×C3×C4—34no—
588C2×C3×C4—32no—
589C2×C3×C4—68no—
590C2×C3×C4—64no—
591C2×C3×C4—64no—
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D314yes—
595C2×C3×C4C23×D314yes—
596C2×C3×C4C23×D312yes—
597#67—64no—
598#67—64no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—34no—
603C2×Dic3—34no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—64no—
610C2×Dic3—64no—
611C2×Dic3—68no—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D314yes—
614C2×Dic3C23×D314yes—
615C2×Dic3C23×D312yes—
616D12—24no—
617C4×D3—28no—
618C4×D3—24no—
619C4×D3—24no—
620C4×D3—38no—
621C4×D3—64no—
622C4×D3—64no—
623C4×D3—64no—
624C4×D3—68no—
625C4×D3—68no—
626C4×D3—64no—
627C4×D3—64no—
628C4×D3—64no—
629C4×D3—68no—
630C4×D3—68no—
631C4×D3—64no—
632C4×D3—68no—
633C4×D3—124no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—124no—
637Dic6—24no—
638Dic6—68no—
639C2×C32C22×#4111yescharacteristic
640C2×C32C22×#4111yescharacteristic
641C2×C32C2×2−1+411yescharacteristic
642C3⋊D3#55214yescomplemented
643C3×D3—24no—
644C3×D3—42no—
645C24—91no—
646C24—91no—
647C2×Q8—32no—
648C2×Q8—92no—
649C2×Q8—184no—
650C2×D4—32no—
651C2×D4—92no—
652C2×D4—184no—
653C22×C4—34no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—91no—
657C22×C4—92no—
658C22×C4—92no—
659C22×C4—91no—
660C22×C4—94no—
661C22×C4—92no—
662C22×C4—92no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—92no—
666C22×C4—91no—
667C22×C4—92no—
668C22×C4—184no—
669C22×C4—184no—
670C22×C4—188no—
671C4⋊C4—32no—
672C4⋊C4—34no—
673C4⋊C4—34no—
674C4⋊C4—32no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—92no—
678C4⋊C4—94no—
679C4⋊C4—94no—
680C4⋊C4—92no—
681C4⋊C4—94no—
682C4⋊C4—94no—
683C4⋊C4—92no—
684C4⋊C4—91no—
685C4⋊C4—92no—
686C4⋊C4—91no—
687C4⋊C4—92no—
688C4⋊C4—92no—
689C4⋊C4—92no—
690C4⋊C4—92no—
691C4⋊C4—92no—
692C4⋊C4—92no—
693C4⋊C4C2×D3211yescharacteristic
694C4⋊C4C2×D3211yescharacteristic
695C4⋊C4C2×D3212yes—
696C4⋊C4C2×D3212yes—
697C22⋊C4—32no—
698C22⋊C4—34no—
699C22⋊C4—34no—
700C22⋊C4—32no—
701C22⋊C4—34no—
702C22⋊C4—92no—
703C22⋊C4—94no—
704C22⋊C4—94no—
705C22⋊C4—92no—
706C22⋊C4—94no—
707C42—34no—
708C42—34no—
709C42—94no—
710C42—94no—
711C42—91no—
712C42—91no—
713C42—91no—
714C42C2×D3211yescharacteristic
715C22×C3—21no—
716C22×C3—34no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3C24×D312yes—
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—34no—
729C2×D3—34no—
730C2×D3—34no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—616no—
735C2×D3—128no—
736C2×D3D3×#4114yes—
737C3×C4—24no—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—24no—
741C3×C4—22no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—42no—
746C3×C4—64no—
747C3×C4—62no—
748C3×C4—62no—
749C3×C4—64no—
750C3×C4D3×#4114yes—
751Dic3—24no—
752Dic3—22no—
753Dic3—22no—
754Dic3—24no—
755Dic3—34no—
756Dic3—62no—
757Dic3—64no—
758Dic3—62no—
759Dic3—62no—
760Dic3—64no—
761Dic3—122no—
762Dic3—121no—
763Dic3—121no—
764Dic3—122no—
765C32C2×#55211yescharacteristic, complemented, Sylow
766C23—32no—
767C23—32no—
768C23—94no—
769C23—91no—
770C23—182no—
771C23—182no—
772C23—182no—
773C23—182no—
774C23—182no—
775Q8—64no—
776Q8—184no—
777D4—64no—
778D4—184no—
779C2×C4—32no—
780C2×C4—34no—
781C2×C4—34no—
782C2×C4—32no—
783C2×C4—68no—
784C2×C4—64no—
785C2×C4—64no—
786C2×C4—91no—
787C2×C4—94no—
788C2×C4—91no—
789C2×C4—92no—
790C2×C4—91no—
791C2×C4—92no—
792C2×C4—184no—
793C2×C4—182no—
794C2×C4—182no—
795C2×C4—184no—
796C2×C4—182no—
797C2×C4—182no—
798C2×C4—184no—
799C2×C4—184no—
800C2×C4—184no—
801C2×C4—184no—
802C2×C4—188no—
803C2×C4C22×D3211yescharacteristic
804C2×C4C22×D3212yes—
805C2×C4C22×D3211yescharacteristic
806C2×C4C22×D3212yes—
807C2×C4C22×D3211yescharacteristic
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—64no—
812C2×C3—122no—
813C2×C3C2×D3×#4112yes—
814C2×C3C2×D3×#4112yes—
815C2×C3D3×2−1+412yes—
816D3—24no—
817D3—38no—
818D3—42no—
819D3—64no—
820C22—34no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—62no—
826C22—92no—
827C22—92no—
828C22—92no—
829C22—188no—
830C22—364no—
831C22C23×D3211yescharacteristic
832C4—22no—
833C4—21no—
834C4—21no—
835C4—22no—
836C4—62no—
837C4—62no—
838C4—64no—
839C4—64no—
840C4—92no—
841C4—182no—
842C4—181no—
843C4—181no—
844C4—182no—
845C4#6431912yes—
846C3—21no—
847C3D3×#55212yescomplemented
848C2—64no—
849C2—94no—
850C2—122no—
851C2C2×#6431911yescharacteristic
852C2D32×#4111yescharacteristic
853C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
prime radicalC2×#3802C22
hypercenter#125D32
hypocenterC32C2×#552
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×#5694C2semidirect
3. #10594656C2semidirect
4. #10594631C2semidirect
5. #10594631C2semidirect
7. #10594602C2semidirect
8. #10594602C2semidirect
9. D32×C4⋊C4C2semidirect
10. #10594551C2semidirect
11. #10594482C2semidirect
12. #10594456C2semidirect
13. #10594429C2semidirect
14. #10594409C2semidirect
16. #10593917C2semidirect
17. C4×#3797C2semidirect
24. C32×#125C22semidirect
29. #64099C22semidirect
30. #64099C22semidirect
31. #64098C22semidirect
32. #64098C22semidirect
34. #64079C22semidirect
35. C3×#898C22semidirect
36. C3×#897C22semidirect
37. C3×#897C22semidirect
39. C3×#892C22semidirect
40. C3×#892C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#890C22semidirect
44. C3×C4×Dic6C22semidirect
50. C4×#627C22semidirect
58. #63899C22semidirect
59. #63899C22semidirect
62. D3×C4⋊Dic3C22semidirect
68. #63877C22semidirect
69. #63877C22semidirect
70. #63877C22semidirect
71. D3×Dic3⋊C4C22semidirect
72. #63869C22semidirect
73. #63861C22semidirect
74. #63859C22semidirect
75. #63858C22semidirect
76. #63856C22semidirect
77. #63856C22semidirect
78. #63847C22semidirect
79. #63847C22semidirect
80. #63843C22semidirect
81. #63841C22semidirect
82. #63841C22semidirect
83. #63838C22semidirect
87. #5694D3semidirect
187. C3×#125C2×D3semidirect
212. #898C2×D3semidirect
213. #897C2×D3semidirect
214. #897C2×D3semidirect
222. #892C2×D3semidirect
223. #892C2×D3semidirect
240. D3×C4⋊C4C2×D3semidirect
246. #890C2×D3semidirect
288. C4×Dic6C2×D3semidirect
519. #125D32semidirect
642. C3⋊D3#552semidirect
765. C32C2×#552semidirect
847. C3D3×#552semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
C3×#56942
#105946562
#105946312
#105946082
#105946022
D32×C4⋊C42
#105945512
#105944822
#105944562
#105944292
#105944092
C4×#38022
#105939172
C4×#37972
D3×#5523