Finite Group Databasebeta

← D3×#5517 #11900829

Subgroups — D3×#5517 #11900829

Order 1152.

2447 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
1#10595988C211yesmaximal, characteristic, complemented
2C3×D3×#117C211yesmaximal, characteristic
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595050C211yesmaximal, characteristic, complemented
5#10595049C211yesmaximal, characteristic, complemented
6D3×#926C211yesmaximal, characteristic
7C2×C4×D3×Dic3C211yesmaximal, characteristic
8#10594477C212yesmaximal, complemented
9#10594445C212yesmaximal, complemented
10D3×#890C212yesmaximal, complemented
11D3×#888C212yesmaximal, complemented
12D3×#878C214yesmaximal
13#10594029C214yesmaximal, complemented
14#10593926C214yesmaximal, complemented
15C4×D3×Dic6C214yesmaximal, complemented
16D3×#533—31nomaximal
17C2×#5517—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×D3×Dic6C2214yes—
21C32×#117C2211yescharacteristic
22#64135C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64099C2212yescomplemented
25#64097C2212yescomplemented
26#64087C2214yes—
27C4×#634C2214yescomplemented
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#892C2212yes—
32C3×D3×C4⋊C4C2212yes—
33C3×#890C2212yescomplemented
34C3×#888C2212yescomplemented
35C3×D3×C22⋊C4C2212yes—
36C3×#878C2214yes—
37C3×#877C2212yes—
38C3×#872C2212yes—
39C3×C42×D3C2212yes—
40C3×C4×Dic6C2214yescomplemented
41#63982C2214yes—
42D3×#217C2212yes—
43#63964C2214yes—
44#63955C2212yes—
45C2×Dic32C2212yes—
46#63919C2212yescomplemented
47#63918C2212yescomplemented
48C4×#627C2214yescomplemented
49C4×#627C2214yescomplemented
50#63899C2214yes—
51#63896C2214yes—
52#63893C2214yes—
53D3×C4⋊Dic3C2214yes—
54D3×C4⋊Dic3C2212yes—
55#63887C2214yes—
56D3×Dic3⋊C4C2214yes—
57D3×Dic3⋊C4C2214yes—
58C4×D3×Dic3C2211yescharacteristic
59C4×D3×Dic3C2212yes—
60C4×D3×Dic3C2211yescharacteristic
61C4×D3×Dic3C2212yes—
62C4×D3×Dic3C2211yescharacteristic
63C4×D3×Dic3C2211yescharacteristic
64C4×D3×Dic3C2212yes—
65#63872C2212yescomplemented
66#63869C2212yescomplemented
67#63855C2212yes—
68#63846C2214yescomplemented
69#63845C2214yescomplemented
70#63844C2214yescomplemented
71Dic3×Dic6C2214yescomplemented
72#63841C2212yes—
73#63840C2214yescomplemented
74#63839C2214yescomplemented
75#63837C2214yescomplemented
76#63837C2214yescomplemented
77C3×#533—31no—
78C2×C3×#117—31no—
79C2×#926—31no—
80C22×C4×Dic3—31no—
81#5728—32no—
82D3×C4⋊Q8—32no—
83#5688—32no—
84D3×#125—32no—
85D3×C22⋊Q8—34no—
86#5622—34no—
87#5578—34no—
88C4×D3×Q8—34no—
89D3×#117—31no—
90D3×#117D311yescharacteristic
91#5517—31no—
92#5517—31no—
93#5517—31no—
94#5517—31no—
95#5517—31no—
96#5517—32no—
97#5517—32no—
98#5517—34no—
99#5517—34no—
100#5517—61no—
101#5517D311yescharacteristic, direct product factor
102C2×#890—32no—
103C2×#888—32no—
104C2×#878—34no—
105C2×C42×D3—31no—
106#5470—31no—
107C2×C4×Dic6—34no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2312yes—
111C2×#634C2314yes—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3Q818yescomplemented
115C2×C3×C4×D3C2314yes—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2314yes—
121C2×#627C2314yes—
122C2×#627C2314yes—
123C2×D3×Dic3—28no—
124C2×D3×Dic3C2314yes—
125C2×D3×Dic3C2312yes—
126C2×D3×Dic3C2312yes—
127C2×D3×Dic3C2312yes—
128C2×D3×Dic3C2312yes—
129D3×Dic6—216no—
130C32×C4⋊C4C2312yes—
131C32×C22⋊C4C2312yes—
132C32×C42C2312yes—
133#3757C2312yes—
134C4⋊(C3⋊Dic3)C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2314yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2312yes—
139C4×C3⋊Dic3C2312yes—
140C4×C3⋊Dic3C2311yescharacteristic
141C4×C3⋊Dic3C2311yescharacteristic
142C3×#217C2312yes—
143C3×#217C2312yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×C4⋊Dic3C2312yes—
147C3×C4⋊Dic3C2312yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2312yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157#3724C2314yes—
158#3724C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165Dic32C2314yes—
166Dic32C2312yes—
167Dic32C2312yes—
168Dic32C2312yes—
169Dic32C2312yes—
170C2×#533—91noSylow
171C23×C3×C4—31no—
172C23×Dic3—32no—
173C2×D3×Q8—34no—
174C22×C4×D3—32no—
175C22×C4×D3C2×D311yescharacteristic
176C22×Dic6—34no—
177C3×C4⋊Q8—32no—
178C3×#125—32no—
179C3×C22⋊Q8—34no—
180C3×C4×Q8—34no—
181C3×#117—21no—
182C3×#117—31no—
183C3×#117—31no—
184C3×#117—32no—
185C3×#117—32no—
186C3×#117—32no—
187C3×#117C2×D311yescharacteristic
188C3×#117C2×D311yescharacteristic
189C2×C3×C4⋊C4—32no—
190C2×C3×C22⋊C4—32no—
191C2×C3×C42—31no—
192C2×C3×C42—32no—
193C2×#217—32no—
194#946—34no—
195Q8×Dic3—34no—
196#944—34no—
197#926—31no—
198#926—31no—
199#926—32no—
200#926—32no—
201#926—32no—
202#926—61no—
203#926C2×D311yescharacteristic
204#926C2×D311yescharacteristic
205C2×C4⋊Dic3—34no—
206C2×C4⋊Dic3—32no—
207#924—34no—
208C2×Dic3⋊C4—34no—
209C2×Dic3⋊C4—34no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—32no—
213C2×C4×Dic3—32no—
214C2×C4×Dic3—32no—
215C2×C4×Dic3—32no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—32no—
219C2×C4×Dic3—31no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3—61no—
222C2×C4×Dic3C2×D311yescharacteristic
223#897—34no—
224#896—34no—
225#896—34no—
226#892—32no—
227#892C2×D312yes—
228D3×C4⋊C4—32no—
229D3×C4⋊C4—34no—
230D3×C4⋊C4—34no—
231D3×C4⋊C4—34no—
232D3×C4⋊C4C2×D312yes—
233#890—32no—
234#890—32no—
235#890—32no—
236#890—34no—
237#890—32no—
238#890—34no—
239#890—32no—
240#890—62no—
241#890C2×D312yescomplemented
242#889—34no—
243#889—34no—
244#888—34no—
245#888—32no—
246#888—32no—
247#888—32no—
248#888—32no—
249#888—34no—
250#888—34no—
251#888—32no—
252#888—62no—
253#888C2×D312yescomplemented
254#887—34no—
255#887—34no—
256#887—34no—
257D3×C22⋊C4—32no—
258D3×C22⋊C4C2×D312yes—
259#878—34no—
260#878—34no—
261#878—34no—
262#878—34no—
263#878—34no—
264#878—34no—
265#878—34no—
266#878—34no—
267#878—34no—
268#878—64no—
269#878C2×D314yes—
270#877—32no—
271#877C2×D312yes—
272#872—32no—
273#872C2×D312yes—
274C42×D3—31no—
275C42×D3—31no—
276C42×D3—31no—
277C42×D3—31no—
278C42×D3—32no—
279C42×D3—32no—
280C42×D3—32no—
281C42×D3C2×D312yes—
282#870—32no—
283#869—32no—
284C4×Dic6—34no—
285C4×Dic6—34no—
286C4×Dic6—34no—
287C4×Dic6—34no—
288C4×Dic6—34no—
289C4×Dic6—34no—
290C4×Dic6—34no—
291C4×Dic6—34no—
292C4×Dic6—34no—
293C4×Dic6—34no—
294C4×Dic6—64no—
295C4×Dic6C2×D314yescomplemented
296C23×C32C2411yescharacteristic
297C22×C3×D3—24no—
298C22×C3×D3C2×Q814yes—
299C22×C3×D3C2411yescharacteristic
300C22×C3×D3C2411yescharacteristic
301C2×C32×C4C2×Q814yescomplemented
302C2×C32×C4C2414yes—
303C2×C32×C4C2411yescharacteristic
304C2×C32×C4C2411yescharacteristic
305C2×C3⋊Dic3—24no—
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2414yes—
308C2×C3⋊Dic3C2412yes—
309#634—28no—
310C2×C3×Dic3—24no—
311C2×C3×Dic3C2×Q814yescomplemented
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2414yes—
315C2×C3×Dic3C2411yescharacteristic
316C2×C3×Dic3C2411yescharacteristic
317C2×C3×Dic3C2412yes—
318C3×C4×D3—28no—
319C3×C4×D3C2×Q814yes—
320C3×C4×D3C2×Q814yes—
321C3×C4×D3C2×Q814yescomplemented
322C3×C4×D3C2×Q814yescomplemented
323C3×Dic6—28no—
324#627—28no—
325#627—28no—
326D3×Dic3—28no—
327D3×Dic3—24no—
328D3×Dic3—24no—
329D3×Dic3—24no—
330D3×Dic3#4118yes—
331#533—31no—
332#533—91no—
333#533—91no—
334#533—94no—
335#533—94no—
336#533—92no—
337#533—92no—
338#533—91no—
339C2×C4⋊Q8—92no—
340C2×#125—92no—
341C2×C22⋊Q8—94no—
342C2×C4×Q8—94no—
343C2×#117—31no—
344C2×#117—91no—
345C22×C42—91no—
346C24×C3—31no—
347C23×D3C22×D311yescharacteristic
348C2×C3×Q8—34no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—38no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—32no—
357C22×C3×C4—34no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×Dic3—32no—
361C22×Dic3—32no—
362C22×Dic3—32no—
363C22×Dic3—32no—
364C22×Dic3—32no—
365C22×Dic3—32no—
366C22×Dic3—34no—
367C22×Dic3—62no—
368C22×Dic3—68no—
369C22×Dic3C22×D312yes—
370C22×Dic3C22×D311yescharacteristic
371D3×Q8—616no—
372C2×C4×D3—32no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—34no—
377C2×C4×D3—68no—
378C2×C4×D3Dic618yescomplemented
379C2×C4×D3C22×D314yes—
380C2×C4×D3C22×D311yescharacteristic
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—34no—
385C2×Dic6—34no—
386C2×Dic6—34no—
387C2×Dic6—34no—
388C2×Dic6—34no—
389C2×Dic6—34no—
390C2×Dic6—64no—
391C2×Dic6—616no—
392C2×Dic6C22×D314yes—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—32no—
399C3×C4⋊C4—32no—
400C3×C4⋊C4C22×D312yes—
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—32no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4C22×D312yes—
407C3×C22⋊C4C22×D312yes—
408C3×C42—22no—
409C3×C42—34no—
410C3×C42—32no—
411C3×C42—32no—
412C3×C42—32no—
413C3×C42—31no—
414C3×C42—31no—
415C3×C42C22×D312yes—
416C3×C42C22×D312yes—
417#217—32no—
418#217—32no—
419#217—34no—
420#217—62no—
421#217C22×D312yes—
422#217C22×D312yes—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4C22×D314yes—
425C4⋊Dic3—34no—
426C4⋊Dic3—34no—
427C4⋊Dic3—32no—
428C4⋊Dic3—32no—
429C4⋊Dic3—34no—
430C4⋊Dic3—34no—
431C4⋊Dic3—34no—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—64no—
435C4⋊Dic3—62no—
436C4⋊Dic3C22×D314yes—
437C4⋊Dic3C22×D312yes—
438C4⋊Dic3C22×D312yes—
439Dic3⋊C4—34no—
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—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—64no—
453Dic3⋊C4—64no—
454Dic3⋊C4C22×D314yes—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D314yes—
457C4×Dic3—32no—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—32no—
461C4×Dic3—31no—
462C4×Dic3—31no—
463C4×Dic3—31no—
464C4×Dic3—31no—
465C4×Dic3—32no—
466C4×Dic3—32no—
467C4×Dic3—34no—
468C4×Dic3—32no—
469C4×Dic3—32no—
470C4×Dic3—32no—
471C4×Dic3—32no—
472C4×Dic3—34no—
473C4×Dic3—32no—
474C4×Dic3—32no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C4×Dic3—61no—
478C4×Dic3—61no—
479C4×Dic3C22×D312yes—
480C4×Dic3C22×D312yes—
481C4×Dic3C22×D312yes—
482C4×Dic3C22×D314yes—
483C4×Dic3C22×D311yescharacteristic
484C4×Dic3C22×D311yescharacteristic
485C22×C32—22no—
486C22×C32C22×Q812yes—
487C22×C32C2511yescharacteristic
488C2×C3×D3—22no—
489C2×C3×D3—28no—
490C2×C3×D3C22×Q812yes—
491C2×C3×D3C22×Q812yes—
492C2×C3×D3C2×#4114yes—
493C32×C4—24no—
494C32×C4C22×Q812yes—
495C32×C4C22×Q812yes—
496C3⋊Dic3—22no—
497C3⋊Dic3—24no—
498C3⋊Dic3C2×#4114yes—
499C3×Dic3—22no—
500C3×Dic3—24no—
501C3×Dic3—24no—
502C3×Dic3C22×Q812yes—
503C3×Dic3C22×Q812yes—
504C3×Dic3C2×#4114yes—
505C22×Q8—94no—
506C23×C4—31no—
507C23×C4—92no—
508C4⋊Q8—32no—
509C4⋊Q8—92no—
510C4⋊Q8—94no—
511C4⋊Q8—92no—
512C4⋊Q8—94no—
513C4⋊Q8—92no—
514#125—32no—
515#125—92no—
516#125—94no—
517#125—94no—
518#125—92no—
519#125—92no—
520C22⋊Q8—34no—
521C22⋊Q8—94no—
522C22⋊Q8—94no—
523C22⋊Q8—94no—
524C22⋊Q8—94no—
525C22⋊Q8—94no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528C4×Q8—34no—
529C4×Q8—94no—
530C4×Q8—94no—
531C4×Q8—94no—
532C4×Q8—94no—
533C4×Q8—94no—
534C4×Q8—94no—
535C4×Q8—94no—
536#117—31no—
537#117—31no—
538#117—32no—
539#117—32no—
540#117—32no—
541#117—92no—
542#117—92no—
543#117—92no—
544#117—91no—
545#117D3211yescharacteristic
546C2×C4⋊C4—32no—
547C2×C4⋊C4—92no—
548C2×C4⋊C4—94no—
549C2×C4⋊C4—94no—
550C2×C4⋊C4—94no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—92no—
553C2×C42—31no—
554C2×C42—32no—
555C2×C42—92no—
556C2×C42—92no—
557C2×C42—91no—
558C2×C42—91no—
559C2×C42—91no—
560C2×C42—91no—
561C2×C42—92no—
562C2×C42—92no—
563C2×C42—91no—
564C23×C3—21no—
565C23×C3—31no—
566C23×C3—34no—
567C23×C3—31no—
568C23×C3—64no—
569C23×C3C23×D311yescharacteristic
570C23×C3C23×D311yescharacteristic
571C22×D3—24no—
572C22×D3C2×Dic614yes—
573C22×D3C23×D311yescharacteristic
574C22×D3C23×D311yescharacteristic
575C3×Q8—68no—
576C2×C3×C4—21no—
577C2×C3×C4—24no—
578C2×C3×C4—21no—
579C2×C3×C4—24no—
580C2×C3×C4—34no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—32no—
584C2×C3×C4—34no—
585C2×C3×C4—34no—
586C2×C3×C4—34no—
587C2×C3×C4—34no—
588C2×C3×C4—32no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—68no—
592C2×C3×C4—64no—
593C2×C3×C4C2×Dic614yescomplemented
594C2×C3×C4D3×Q814yescomplemented
595C2×C3×C4C23×D314yes—
596C2×C3×C4C23×D314yes—
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×Dic3—24no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—38no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—34no—
608C2×Dic3—34no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—64no—
612C2×Dic3—64no—
613C2×Dic3—68no—
614C2×Dic3—64no—
615C2×Dic3—64no—
616C2×Dic3—64no—
617C2×Dic3—64no—
618C2×Dic3—124no—
619C2×Dic3C2×Dic614yescomplemented
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D314yes—
622C2×Dic3C23×D314yes—
623C2×Dic3C23×D311yescharacteristic
624C2×Dic3C23×D311yescharacteristic
625C2×Dic3C23×D312yes—
626C4×D3—28no—
627C4×D3—38no—
628C4×D3—64no—
629C4×D3—64no—
630C4×D3—64no—
631C4×D3—68no—
632C4×D3C2×Dic614yes—
633C4×D3C2×Dic614yes—
634C4×D3C2×Dic614yescomplemented
635C4×D3C2×Dic614yescomplemented
636Dic6—28no—
637Dic6—68no—
638Dic6—68no—
639Dic6—68no—
640Dic6—68no—
641Dic6—68no—
642Dic6—68no—
643Dic6—128no—
644C2×C32—22no—
645C2×C32C23×Q811yescharacteristic
646C2×C32C22×#4112yes—
647C3×D3—22no—
648C3×D3#53314yescomplemented
649C24—31no—
650C2×Q8—34no—
651C2×Q8—94no—
652C2×Q8—94no—
653C2×Q8—94no—
654C2×Q8—1816no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—38no—
661C22×C4—32no—
662C22×C4—34no—
663C22×C4—92no—
664C22×C4—92no—
665C22×C4—92no—
666C22×C4—92no—
667C22×C4—94no—
668C22×C4—92no—
669C22×C4—188no—
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—34no—
672C4⋊C4—32no—
673C4⋊C4—32no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—94no—
678C4⋊C4—94no—
679C4⋊C4—94no—
680C4⋊C4—94no—
681C4⋊C4—94no—
682C4⋊C4—94no—
683C4⋊C4—94no—
684C4⋊C4—92no—
685C4⋊C4—94no—
686C4⋊C4—94no—
687C4⋊C4—94no—
688C4⋊C4C2×D3212yes—
689C22⋊C4—32no—
690C22⋊C4—32no—
691C22⋊C4—34no—
692C22⋊C4—94no—
693C22⋊C4—92no—
694C22⋊C4C2×D3212yes—
695C42—31no—
696C42—31no—
697C42—34no—
698C42—32no—
699C42—32no—
700C42—32no—
701C42—92no—
702C42—92no—
703C42—92no—
704C42—92no—
705C42—94no—
706C42—91no—
707C42—91no—
708C42—92no—
709C42—92no—
710C42C2×D3212yes—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—32no—
716C22×C3—34no—
717C22×C3—32no—
718C22×C3—42no—
719C22×C3—68no—
720C22×C3—62no—
721C22×C3C22×Dic612yes—
722C22×C3C2×D3×Q812yes—
723C22×C3C24×D311yescharacteristic
724C22×C3C24×D311yescharacteristic
725C2×D3—22no—
726C2×D3—28no—
727C2×D3C22×Dic612yes—
728C2×D3C22×Dic612yes—
729C2×D3D3×#4114yes—
730C3×C4—24no—
731C3×C4—24no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—32no—
735C3×C4—32no—
736C3×C4—34no—
737C3×C4—44no—
738C3×C4—64no—
739C3×C4—64no—
740C3×C4—62no—
741C3×C4C22×Dic612yes—
742C3×C4C22×Dic612yes—
743C3×C4C2×D3×Q812yes—
744C3×C4C2×D3×Q812yes—
745Dic3—24no—
746Dic3—24no—
747Dic3—22no—
748Dic3—34no—
749Dic3—34no—
750Dic3—64no—
751Dic3—64no—
752Dic3—64no—
753Dic3—62no—
754Dic3—62no—
755Dic3—124no—
756Dic3—122no—
757Dic3C22×Dic612yes—
758Dic3C22×Dic612yes—
759Dic3D3×#4114yes—
760C32C2×#53311yescharacteristic, complemented, Sylow
761C23—31no—
762C23—34no—
763C23—31no—
764C23—64no—
765C23C22×D3211yescharacteristic
766Q8—68no—
767Q8—188no—
768Q8—188no—
769Q8—188no—
770C2×C4—34no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—31no—
774C2×C4—34no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—32no—
779C2×C4—34no—
780C2×C4—34no—
781C2×C4—68no—
782C2×C4—64no—
783C2×C4—98no—
784C2×C4—92no—
785C2×C4—92no—
786C2×C4—94no—
787C2×C4—184no—
788C2×C4—184no—
789C2×C4—184no—
790C2×C4—188no—
791C2×C4—184no—
792C2×C4D3×Dic614yescomplemented
793C2×C4C22×D3214yes—
794C2×C4C22×D3211yescharacteristic
795C2×C4C22×D3211yescharacteristic
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—22no—
800C2×C3—34no—
801C2×C3—42no—
802C2×C3—62no—
803C2×C3C23×Dic611yescharacteristic
804C2×C3C22×D3×Q811yescharacteristic
805C2×C3C2×D3×#4112yes—
806C2×C3C2×D3×#4112yes—
807D3—22no—
808D3#551714yesdirect product factor
809C22—22no—
810C22—32no—
811C22—34no—
812C22—32no—
813C22—68no—
814C22—62no—
815C22C2×D3×Dic612yes—
816C22C23×D3211yescharacteristic
817C4—24no—
818C4—32no—
819C4—32no—
820C4—34no—
821C4—62no—
822C4—64no—
823C4—64no—
824C4—94no—
825C4—182no—
826C4—184no—
827C4C2×D3×Dic612yes—
828C4C2×D3×Dic612yes—
829C3—21no—
830C3C2×#551711yescharacteristic, complemented
831C3D3×#53311yescharacteristic, complemented
832C2—22no—
833C2—34no—
834C2—62no—
835C2C22×D3×Dic611yescharacteristic
836C2D32×#4112yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
prime radicalC23×C3×D3C23
hypercenter#117D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
3. C3×#5517C2semidirect
4. #10595050C2semidirect
5. #10595049C2semidirect
8. #10594477C2semidirect
9. #10594445C2semidirect
10. D3×#890C2semidirect
11. D3×#888C2semidirect
13. #10594029C2semidirect
14. #10593926C2semidirect
15. C4×D3×Dic6C2semidirect
24. #64099C22semidirect
25. #64097C22semidirect
27. C4×#634C22semidirect
33. C3×#890C22semidirect
34. C3×#888C22semidirect
40. C3×C4×Dic6C22semidirect
46. #63919C22semidirect
47. #63918C22semidirect
48. C4×#627C22semidirect
49. C4×#627C22semidirect
65. #63872C22semidirect
66. #63869C22semidirect
68. #63846C22semidirect
69. #63845C22semidirect
70. #63844C22semidirect
71. Dic3×Dic6C22semidirect
73. #63840C22semidirect
74. #63839C22semidirect
75. #63837C22semidirect
76. #63837C22semidirect
101. #5517D3direct (N × H)
114. C2×C3×C4×D3Q8semidirect
241. #890C2×D3semidirect
253. #888C2×D3semidirect
295. C4×Dic6C2×D3semidirect
301. C2×C32×C4C2×Q8semidirect
311. C2×C3×Dic3C2×Q8semidirect
321. C3×C4×D3C2×Q8semidirect
322. C3×C4×D3C2×Q8semidirect
378. C2×C4×D3Dic6semidirect
593. C2×C3×C4C2×Dic6semidirect
594. C2×C3×C4D3×Q8semidirect
619. C2×Dic3C2×Dic6semidirect
634. C4×D3C2×Dic6semidirect
635. C4×D3C2×Dic6semidirect
648. C3×D3#533semidirect
760. C32C2×#533semidirect
792. C2×C4D3×Dic6semidirect
808. D3#5517direct (N × H)
830. C3C2×#5517semidirect
831. C3D3×#533semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×D3×#1172
C3×#55172
#105950502
#105950492
D3×#9262
C2×C4×D3×Dic32
#105944772
#105944452
D3×#8902
D3×#8882
D3×#8782
#105940292
#105939262
C4×D3×Dic62
D3×#5333
C2×#55173