Finite Group Databasebeta

← #11900081

Subgroups — #11900081

Order 1152.

3445 conjugacy classes of subgroups.

The subgroup lattice has 735 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic, complemented
3C3×#5523C212yesmaximal, complemented
4#10594986C212yesmaximal, complemented
5C2×#63900C211yesmaximal, characteristic, complemented
6#10594602C212yesmaximal, complemented
7D32×C4⋊C4C212yesmaximal, complemented
8#10594511C212yesmaximal, complemented
9#10594509C212yesmaximal, complemented
10#10594255C214yesmaximal, complemented
11#10594051C214yesmaximal, complemented
12C4×#3802C212yesmaximal, complemented
13C4×#3797C212yesmaximal, complemented
14#10593889C214yesmaximal, complemented
15D3×#520—32nomaximal
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#235C2212yes—
18C2×#3811C2212yes—
19C22×#624C2212yes—
20C2×#3805C2212yes—
21#64306C4116yescomplemented
22C2×#3802C2211yescharacteristic
23C2×C4×D32C2214yes—
24C2×C4×D32C2212yes—
25C2×#3798C2212yes—
26C2×#3797C2211yescharacteristic
27C2×#3796C2212yes—
28C32×#117C2211yescharacteristic, complemented
29#64135C2211yescharacteristic, complemented
30#64101C2211yescharacteristic, complemented
31#64101C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34C22⋊C4×C3⋊D3C2212yes—
35#64086C2212yescomplemented
36#64081C2212yescomplemented
37C42×C3⋊D3C2212yes—
38C2×C3×C4⋊Dic3C2212yescomplemented
39C3×#892C2214yescomplemented
40C3×D3×C4⋊C4C2214yescomplemented
41C3×#67⋊C4C2218yescomplemented
42C3×C4×D12C2214yescomplemented
43C3×C4×Dic6C2214yescomplemented
44Dic3×#67C2218yescomplemented
45C2×#3724C2212yescomplemented
46#63921C2214yes—
47C4×#627C2214yescomplemented
48#63904C2218yescomplemented
49#63902C2214yescomplemented
50C4×#625C2214yescomplemented
51#63900C2212yes—
52#63900C2212yes—
53#63900C2212yescomplemented
54#63900C2212yescomplemented
55#63898C2214yescomplemented
56D3×C4⋊Dic3C2214yescomplemented
57#63883C2214yes—
58C4×#624C2214yes—
59#63880C2218yescomplemented
60#63877C2218yescomplemented
61D3×Dic3⋊C4C2218yescomplemented
62#63843C2214yescomplemented
63#63841C2214yescomplemented
64#63838C2214yescomplemented
65C2×D3×#41—32no—
66C3×#520—32no—
67#5827—32no—
68#5574—34no—
69C4×D3×Q8—34no—
70#5546—38no—
71#5546—34no—
72C4×D3×D4—38no—
73C4×D3×D4—34no—
74#5523—34no—
75#5523D312yescomplemented
76D3×#117—32no—
77D3×#117—34no—
78D3×#117—61no—
79#5504—32no—
80#5504—34no—
81C2×D3×C4⋊C4—32no—
82C2×D3×C4⋊C4—34no—
83C23×C3⋊D3C2311yescharacteristic
84C22×D32C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4×C3⋊D3C2×C418yescomplemented
88C2×C4×C3⋊D3C2312yes—
89C2×C4×C3⋊D3C2312yes—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×#67C2314yes—
95C22×C3×Dic3C2314yes—
96C3×#235C2×C4116yescomplemented
97C2×C3×D12C2312yes—
98C2×C3×C4×D3C2318yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×Dic6C2312yes—
101#3811C2×C4116yescomplemented
102C2×#627C2312yes—
103C2×#626C2314yes—
104C2×#625C2312yes—
105C2×#624—44no—
106C2×#624C2314yes—
107C2×#624C2314yes—
108C2×#624C2312yes—
109#3805C2×C4116yescomplemented
110C2×D3×Dic3C2318yes—
111C2×D3×Dic3C2314yes—
112#3802C2×C418yescomplemented
113C4×D32—48no—
114C4×D32C2×C4116yescomplemented
115#3798C2×C4116yescomplemented
116#3797C2×C418yescomplemented
117#3796C2×C4116yescomplemented
118C32×C4⋊C4C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4C2312yes—
121C32×C42C2312yes—
122#3757C2312yes—
123#3752C2312yes—
124#3752C2312yes—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750C2312yes—
128#3750C2312yes—
129C4×C3⋊Dic3C2312yes—
130C4×C3⋊Dic3C2312yes—
131C4×C3⋊Dic3C2312yes—
132C3×(C2×D3)⋊C4C2318yes—
133C3×C4⋊Dic3C2314yes—
134C3×C4⋊Dic3C2314yes—
135C3×Dic3⋊C4C2318yes—
136C3×C4×Dic3C2318yes—
137#3724C2314yes—
138#3724C2314yes—
139Dic3⋊Dic3C2318yes—
140(C2×D3)⋊Dic3C2318yes—
141Dic32C2318yes—
142C2×#520—91noSylow
143C2×C3×#41—32no—
144D3×#41—332no—
145C2×#239—32no—
146C2×D3×Q8—32no—
147C2×#237—34no—
148C2×#237—32no—
149C2×D3×D4—34no—
150C2×D3×D4—32no—
151C2×#235—34no—
152C2×#235C2×D312yes—
153C22×C4×D3—32no—
154C22×C4×D3—34no—
155C22×C4×D3—34no—
156C22×C4×D3—38no—
157C22×C4×D3—61no—
158C3×C4×Q8—34no—
159C3×C4×D4—38no—
160C3×C4×D4—34no—
161C3×#117—21no—
162C3×#117—34no—
163C3×#117C2×D312yescomplemented
164C2×C3×C4⋊C4—32no—
165C2×C3×C4⋊C4—34no—
166Q8×Dic3—34no—
167D4×Dic3—38no—
168D4×Dic3—34no—
169C4×#67—38no—
170C4×#67—38no—
171C4×#67—38no—
172#926—32no—
173#926—34no—
174#926—61no—
175C2×C4⋊Dic3—34no—
176C2×C4⋊Dic3C2×D312yescomplemented
177C2×Dic3⋊C4—34no—
178C2×Dic3⋊C4—38no—
179#893—34no—
180#893—38no—
181#892—34no—
182#892—32no—
183#892—32no—
184#892—61no—
185#892—61no—
186#892C2×D314yescomplemented
187D3×C4⋊C4—34no—
188D3×C4⋊C4—38no—
189D3×C4⋊C4—32no—
190D3×C4⋊C4—32no—
191D3×C4⋊C4—34no—
192D3×C4⋊C4—34no—
193D3×C4⋊C4—34no—
194D3×C4⋊C4—34no—
195D3×C4⋊C4—38no—
196D3×C4⋊C4—61no—
197D3×C4⋊C4—61no—
198D3×C4⋊C4C2×D314yescomplemented
199#887—34no—
200#887—38no—
201#67⋊C4—38no—
202#67⋊C4—38no—
203#67⋊C4C2×D318yescomplemented
204D3×C22⋊C4—34no—
205D3×C22⋊C4—38no—
206D3×C22⋊C4—62no—
207#877—34no—
208#877—38no—
209#877—62no—
210C4×D12—38no—
211C4×D12C2×D314yescomplemented
212#872—34no—
213#872—38no—
214#872—62no—
215C42×D3—34no—
216C42×D3—38no—
217C42×D3—62no—
218C4×Dic6—38no—
219C4×Dic6C2×D314yescomplemented
220C23×C32C2411yescharacteristic
221C22×C3⋊D3—22no—
222C22×C3⋊D3—22no—
223C22×C3⋊D3C22×C414yes—
224C22×C3⋊D3C2411yescharacteristic
225C22×C3⋊D3C2411yescharacteristic
226C22×C3×D3C2414yes—
227C2×D32—24no—
228C2×D32—24no—
229C2×D32C22×C418yes—
230C2×C32×C4C22×C414yescomplemented
231C2×C32×C4C2412yes—
232C2×C32×C4C2412yes—
233C2×C32×C4C2411yescharacteristic
234C2×C32×C4C2411yescharacteristic
235C2×C3⋊Dic3C22×C414yescomplemented
236C2×C3⋊Dic3C2412yes—
237C2×C3⋊Dic3C2412yes—
238C2×C3⋊Dic3C2411yescharacteristic
239C2×C3⋊Dic3C2411yescharacteristic
240C4×C3⋊D3—24no—
241C4×C3⋊D3—24no—
242C4×C3⋊D3C22×C414yes—
243C4×C3⋊D3C22×C414yes—
244C4×C3⋊D3C22×C414yescomplemented
245C4×C3⋊D3C22×C414yescomplemented
246C3×#67C22×C4116yescomplemented
247C2×C3×Dic3—44no—
248C2×C3×Dic3C2418yes—
249C2×C3×Dic3C2414yes—
250C3×D12C22×C418yescomplemented
251C3×C4×D3—48no—
252C3×C4×D3C22×C4116yescomplemented
253C3×Dic6C22×C418yescomplemented
254#627C22×C418yescomplemented
255#626C22×C4116yescomplemented
256#625C22×C418yescomplemented
257#624—28no—
258#624—44no—
259#624C22×C418yes—
260D3×Dic3—48no—
261D3×Dic3C22×C4116yescomplemented
262C22×#41—91no—
263#520—32no—
264#520—92no—
265#520—92no—
266#520—92no—
267#520—94no—
268#520—94no—
269C2×C4×Q8—92no—
270C2×C4×D4—94no—
271C2×C4×D4—92no—
272C2×#117—92no—
273C2×#117—91no—
274C22×C4⋊C4—91no—
275C22×C4⋊C4—92no—
276C23×D3—32no—
277C23×D3—34no—
278C23×D3—61no—
279C3×#41—316no—
280C2×C3×Q8—32no—
281C2×C3×D4—34no—
282C2×C3×D4—32no—
283C22×C3×C4—21no—
284C22×C3×C4—34no—
285C22×C3×C4—34no—
286C22×C3×C4—38no—
287C22×C3×C4C22×D312yes—
288C2×#67—34no—
289C2×#67—34no—
290C2×#67C22×D314yes—
291C22×Dic3—32no—
292C22×Dic3—34no—
293C22×Dic3—38no—
294C22×Dic3—61no—
295C22×Dic3C22×D314yes—
296#239—316no—
297D3×Q8—316no—
298#237—332no—
299#237—316no—
300D3×D4—332no—
301D3×D4—316no—
302#235—332no—
303#235C4×D3116yescomplemented
304C2×D12—34no—
305C2×D12C22×D312yes—
306C2×C4×D3—34no—
307C2×C4×D3—316no—
308C2×C4×D3—32no—
309C2×C4×D3—32no—
310C2×C4×D3—32no—
311C2×C4×D3—32no—
312C2×C4×D3—34no—
313C2×C4×D3—332no—
314C2×C4×D3—34no—
315C2×C4×D3—34no—
316C2×C4×D3—38no—
317C2×C4×D3—38no—
318C2×C4×D3—38no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—68no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—1216no—
327C2×C4×D3—128no—
328C2×C4×D3C22×D318yes—
329C2×C4×D3C22×D314yes—
330C2×Dic6—34no—
331C2×Dic6C22×D312yes—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—38no—
335C3×C4⋊C4—34no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4C22×D312yes—
338C3×C4⋊C4C22×D312yes—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—38no—
341C3×C22⋊C4C22×D314yes—
342C3×C42—22no—
343C3×C42—38no—
344C3×C42C22×D314yes—
345#217—34no—
346#217—38no—
347#217—62no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4C22×D318yes—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—38no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3C22×D314yes—
360C4⋊Dic3C22×D314yes—
361Dic3⋊C4—34no—
362Dic3⋊C4—34no—
363Dic3⋊C4—38no—
364Dic3⋊C4—38no—
365Dic3⋊C4—38no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4C22×D318yes—
369C4×Dic3—34no—
370C4×Dic3—34no—
371C4×Dic3—34no—
372C4×Dic3—38no—
373C4×Dic3—38no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3C22×D318yes—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32C23×C412yes—
381C22×C32C2511yescharacteristic
382C2×C3⋊D3—21no—
383C2×C3⋊D3—21no—
384C2×C3⋊D3—28no—
385C2×C3⋊D3C23×C412yes—
386C2×C3⋊D3C23×C412yes—
387C2×C3⋊D3H(5,𝔽2)12yes—
388C2×C3⋊D32−1+412yes—
389C2×C3×D3—24no—
390C2×C3×D3—24no—
391C2×C3×D3C23×C418yes—
392D32—216no—
393C32×C4—22no—
394C32×C4—22no—
395C32×C4C23×C412yes—
396C32×C4C23×C412yes—
397C3⋊Dic3—22no—
398C3⋊Dic3—22no—
399C3⋊Dic3C23×C412yes—
400C3⋊Dic3C23×C412yes—
401C3×Dic3—28no—
402C3×Dic3C23×C418yes—
403C2×#41—32no—
404C2×#41—92no—
405C2×#41—92no—
406C2×#41—92no—
407C2×#41—916no—
408C22×Q8—91no—
409C22×D4—92no—
410C22×D4—91no—
411C23×C4—92no—
412C23×C4—92no—
413C23×C4—94no—
414C23×C4—91no—
415C4×Q8—34no—
416C4×Q8—94no—
417C4×Q8—94no—
418C4×Q8—94no—
419C4×D4—38no—
420C4×D4—34no—
421C4×D4—98no—
422C4×D4—94no—
423C4×D4—98no—
424C4×D4—94no—
425C4×D4—94no—
426C4×D4—98no—
427#117—34no—
428#117—98no—
429#117—94no—
430#117—91no—
431#117—91no—
432#117—91no—
433#117—92no—
434#117—92no—
435#117D3211yescharacteristic, complemented
436C2×C4⋊C4—32no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—92no—
439C2×C4⋊C4—94no—
440C2×C4⋊C4—92no—
441C2×C4⋊C4—92no—
442C2×C4⋊C4—92no—
443C2×C4⋊C4—98no—
444C2×C4⋊C4—94no—
445C2×C4⋊C4—92no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448C2×C22⋊C4—94no—
449C2×C22⋊C4—92no—
450C2×C42—94no—
451C2×C42—92no—
452C23×C3—21no—
453C23×C3—34no—
454C23×C3C23×D312yes—
455C22×D3—32no—
456C22×D3—38no—
457C22×D3—32no—
458C22×D3—316no—
459C22×D3—61no—
460C22×D3—64no—
461C22×D3—61no—
462C22×D3—68no—
463C22×D3—68no—
464C22×D3—64no—
465C22×D3—64no—
466C22×D3—122no—
467C22×D3—122no—
468C22×D3C23×D314yes—
469C3×Q8—38no—
470C3×D4—316no—
471C3×D4—38no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—24no—
477C2×C3×C4—34no—
478C2×C3×C4—316no—
479C2×C3×C4—38no—
480C2×C3×C4—128no—
481C2×C3×C4—124no—
482C2×C3×C4C2×C4×D318yescomplemented
483C2×C3×C4C23×D314yes—
484C2×C3×C4C23×D314yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487#67—316no—
488#67—316no—
489#67C2×C4×D3116yescomplemented
490C2×Dic3—38no—
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—316no—
494C2×Dic3—34no—
495C2×Dic3—34no—
496C2×Dic3—44no—
497C2×Dic3—64no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—128no—
503C2×Dic3C23×D318yes—
504C2×Dic3C23×D314yes—
505D12—316no—
506D12C2×C4×D318yescomplemented
507C4×D3—316no—
508C4×D3—38no—
509C4×D3—38no—
510C4×D3—38no—
511C4×D3—38no—
512C4×D3—316no—
513C4×D3—48no—
514C4×D3—64no—
515C4×D3—64no—
516C4×D3—64no—
517C4×D3—64no—
518C4×D3—616no—
519C4×D3—68no—
520C4×D3—68no—
521C4×D3—124no—
522C4×D3—124no—
523C4×D3—128no—
524C4×D3—128no—
525C4×D3C2×C4×D3116yescomplemented
526Dic6—316no—
527Dic6C2×C4×D318yescomplemented
528C2×C32—22no—
529C2×C32C24×C411yescharacteristic
530C2×C32C2×H(5,𝔽2)11yescharacteristic
531C2×C32C2×2−1+411yescharacteristic
532C3⋊D3—22no—
533C3⋊D3#52014yescomplemented
534C3×D3—28no—
535C24—92no—
536C24—91no—
537#41—316no—
538#41—916no—
539#41—916no—
540#41—916no—
541C2×Q8—32no—
542C2×Q8—92no—
543C2×Q8—98no—
544C2×D4—34no—
545C2×D4—32no—
546C2×D4—94no—
547C2×D4—916no—
548C2×D4—98no—
549C2×D4—92no—
550C22×C4—34no—
551C22×C4—34no—
552C22×C4—38no—
553C22×C4—92no—
554C22×C4—916no—
555C22×C4—94no—
556C22×C4—94no—
557C22×C4—94no—
558C22×C4—98no—
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—98no—
565C22×C4—92no—
566C22×C4—92no—
567C22×C4—368no—
568C22×C4—364no—
569C22×C4C2×D3211yescharacteristic
570C4⋊C4—34no—
571C4⋊C4—38no—
572C4⋊C4—34no—
573C4⋊C4—94no—
574C4⋊C4—94no—
575C4⋊C4—98no—
576C4⋊C4—92no—
577C4⋊C4—91no—
578C4⋊C4—92no—
579C4⋊C4—91no—
580C4⋊C4C2×D3211yescharacteristic
581C4⋊C4C2×D3211yescharacteristic
582C22⋊C4—38no—
583C22⋊C4—98no—
584C22⋊C4—92no—
585C22⋊C4—92no—
586C22⋊C4—92no—
587C22⋊C4C2×D3212yes—
588C42—38no—
589C42—98no—
590C42—92no—
591C42—92no—
592C42—92no—
593C42C2×D3212yes—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—21no—
598C22×C3—38no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3C22×C4×D314yes—
604C22×C3C24×D312yes—
605C2×D3—24no—
606C2×D3—24no—
607C2×D3—34no—
608C2×D3—34no—
609C2×D3—34no—
610C2×D3—34no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—632no—
616C2×D3—616no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—128no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3C22×C4×D318yes—
623C3×C4—24no—
624C3×C4—24no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—38no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—68no—
631C3×C4C22×C4×D314yes—
632C3×C4C22×C4×D314yes—
633Dic3—28no—
634Dic3—34no—
635Dic3—34no—
636Dic3—62no—
637Dic3—62no—
638Dic3—64no—
639Dic3—64no—
640Dic3—122no—
641Dic3—122no—
642Dic3C22×C4×D318yes—
643C32C2×#52011yescharacteristic, complemented, Sylow
644C23—34no—
645C23—98no—
646C23—91no—
647C23—94no—
648C23—91no—
649C23—182no—
650C23—182no—
651C23—184no—
652C23—184no—
653C23C22×D3211yescharacteristic
654Q8—38no—
655Q8—98no—
656D4—316no—
657D4—38no—
658D4—916no—
659D4—98no—
660C2×C4—34no—
661C2×C4—316no—
662C2×C4—38no—
663C2×C4—98no—
664C2×C4—916no—
665C2×C4—94no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—94no—
669C2×C4—94no—
670C2×C4—94no—
671C2×C4—94no—
672C2×C4—92no—
673C2×C4—92no—
674C2×C4—128no—
675C2×C4—124no—
676C2×C4—184no—
677C2×C4—184no—
678C2×C4—188no—
679C2×C4—364no—
680C2×C4—368no—
681C2×C4C4×D3214yescomplemented
682C2×C4C22×D3212yes—
683C2×C4C22×D3212yes—
684C2×C4C22×D3211yescharacteristic
685C2×C4C22×D3211yescharacteristic
686C2×C3—24no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—42no—
691C2×C3—68no—
692C2×C3C23×C4×D312yes—
693C2×C3D3×H(5,𝔽2)12yes—
694C2×C3D3×2−1+412yes—
695D3—28no—
696D3—38no—
697D3—64no—
698D3—64no—
699D3—122no—
700C22—21no—
701C22—21no—
702C22—38no—
703C22—64no—
704C22—64no—
705C22—92no—
706C22—92no—
707C22—92no—
708C22—92no—
709C22—188no—
710C22—1816no—
711C22—181no—
712C22—181no—
713C22C2×C4×D3212yes—
714C22C23×D3211yescharacteristic
715C4—22no—
716C4—22no—
717C4—38no—
718C4—68no—
719C4—92no—
720C4—92no—
721C4—182no—
722C4—182no—
723C4C2×C4×D3212yes—
724C4C2×C4×D3212yes—
725C3—21no—
726C3D3×#52012yescomplemented
727C2—22no—
728C2—68no—
729C2—94no—
730C2—182no—
731C2C22×C4×D3211yescharacteristic
732C2#1059669211yescharacteristic
733C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC2×#64306C2
hypercenter#117D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#117C2semidirect
3. C3×#5523C2semidirect
4. #10594986C2semidirect
5. C2×#63900C2semidirect
6. #10594602C2semidirect
7. D32×C4⋊C4C2semidirect
8. #10594511C2semidirect
9. #10594509C2semidirect
10. #10594255C2semidirect
11. #10594051C2semidirect
12. C4×#3802C2semidirect
13. C4×#3797C2semidirect
14. #10593889C2semidirect
21. #64306C4semidirect
28. C32×#117C22semidirect
29. #64135C22semidirect
30. #64101C22semidirect
31. #64101C22semidirect
35. #64086C22semidirect
36. #64081C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C3×#892C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C3×#67⋊C4C22semidirect
42. C3×C4×D12C22semidirect
43. C3×C4×Dic6C22semidirect
44. Dic3×#67C22semidirect
45. C2×#3724C22semidirect
47. C4×#627C22semidirect
48. #63904C22semidirect
49. #63902C22semidirect
50. C4×#625C22semidirect
53. #63900C22semidirect
54. #63900C22semidirect
55. #63898C22semidirect
56. D3×C4⋊Dic3C22semidirect
59. #63880C22semidirect
60. #63877C22semidirect
61. D3×Dic3⋊C4C22semidirect
62. #63843C22semidirect
63. #63841C22semidirect
64. #63838C22semidirect
75. #5523D3semidirect
87. C2×C4×C3⋊D3C2×C4semidirect
96. C3×#235C2×C4semidirect
101. #3811C2×C4semidirect
109. #3805C2×C4semidirect
112. #3802C2×C4semidirect
114. C4×D32C2×C4semidirect
115. #3798C2×C4semidirect
116. #3797C2×C4semidirect
117. #3796C2×C4semidirect
163. C3×#117C2×D3semidirect
176. C2×C4⋊Dic3C2×D3semidirect
186. #892C2×D3semidirect
198. D3×C4⋊C4C2×D3semidirect
203. #67⋊C4C2×D3semidirect
211. C4×D12C2×D3semidirect
219. C4×Dic6C2×D3semidirect
230. C2×C32×C4C22×C4semidirect
235. C2×C3⋊Dic3C22×C4semidirect
244. C4×C3⋊D3C22×C4semidirect
245. C4×C3⋊D3C22×C4semidirect
246. C3×#67C22×C4semidirect
250. C3×D12C22×C4semidirect
252. C3×C4×D3C22×C4semidirect
253. C3×Dic6C22×C4semidirect
254. #627C22×C4semidirect
255. #626C22×C4semidirect
256. #625C22×C4semidirect
261. D3×Dic3C22×C4semidirect
303. #235C4×D3semidirect
435. #117D32semidirect
482. C2×C3×C4C2×C4×D3semidirect
489. #67C2×C4×D3semidirect
506. D12C2×C4×D3semidirect
525. C4×D3C2×C4×D3semidirect
527. Dic6C2×C4×D3semidirect
533. C3⋊D3#520semidirect
643. C32C2×#520semidirect
681. C2×C4C4×D32semidirect
726. C3D3×#520semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C3⋊D3×#1172
C3×#55232
#105949862
C2×#639002
#105946022
D32×C4⋊C42
#105945112
#105945092
#105942552
#105940512
C4×#38022
C4×#37972
#105938892
D3×#5203