Finite Group Databasebeta

← D3×#5688 #11900861

Subgroups — D3×#5688 #11900861

Order 1152.

2447 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596159C211yesmaximal, characteristic, complemented
2C3×#5688C211yesmaximal, characteristic, complemented
3C3×D3×#125C211yesmaximal, characteristic, complemented
4D3×#896C214yesmaximal
5D3×#892C212yesmaximal
6#10594477C212yesmaximal, complemented
7#10594448C212yesmaximal, complemented
8#10594398C214yesmaximal, complemented
9#10594388C214yesmaximal, complemented
10D3×#888C212yesmaximal, complemented
11D3×#887C214yesmaximal, complemented
12C42×D32C211yesmaximal, characteristic
13D3×#870C211yesmaximal, characteristic, complemented
14#10593874C211yesmaximal, characteristic, complemented
15#10593854C211yesmaximal, characteristic, complemented
16D3×#533—31nomaximal
17C2×#5688—31nomaximal
18C2×C4×D32C2212yes—
19C2×C4×D32C2211yescharacteristic
20C2×D3×Dic6C2214yes—
21C32×#125C2211yescharacteristic, complemented
22#64105C2214yes—
23#64101C2212yes—
24#64097C2212yescomplemented
25#64096C2214yescomplemented
26C42×C3⋊D3C2211yescharacteristic
27#64079C2211yescharacteristic, complemented
28C3×#896C2214yes—
29C3×#892C2212yes—
30C3×D3×C4⋊C4C2212yes—
31C3×D3×C4⋊C4C2214yes—
32C3×#890C2212yescomplemented
33C3×#889C2214yescomplemented
34C3×#888C2212yescomplemented
35C3×#887C2214yescomplemented
36C3×C42×D3C2211yescharacteristic
37C3×C42×D3C2211yescharacteristic
38C3×#870C2211yescharacteristic, complemented
39C3×#870C2211yescharacteristic, complemented
40D3×(C2×D3)⋊C4C2214yes—
41#63919C2212yescomplemented
42#63918C2212yescomplemented
43#63899C2214yes—
44#63896C2214yes—
45#63895C2214yes—
46D3×C4⋊Dic3C2212yes—
47#63888C2214yes—
48C4×#624C2212yes—
49C4×#624C2211yescharacteristic
50#63878C2214yes—
51D3×Dic3⋊C4C2214yes—
52D3×Dic3⋊C4C2214yes—
53C4×D3×Dic3C2214yes—
54C4×D3×Dic3C2212yes—
55C4×D3×Dic3C2211yescharacteristic
56C4×D3×Dic3C2212yes—
57C4×D3×Dic3C2211yescharacteristic
58#63869C2212yescomplemented
59#63867C2214yescomplemented
60#63865C2214yes—
61#63851C2214yes—
62#63849C2212yes—
63#63844C2214yescomplemented
64#63843C2214yescomplemented
65#63841C2212yes—
66#63840C2214yescomplemented
67#63839C2214yescomplemented
68#63838C2214yescomplemented
69#63838C2214yescomplemented
70#63837C2214yescomplemented
71#63837C2214yescomplemented
72#63836C2214yes—
73C3×#533—31no—
74C2×C3×#125—31no—
75#5728—32no—
76D3×C4⋊Q8—32no—
77#5688—31no—
78#5688—31no—
79#5688—34no—
80#5688—32no—
81#5688—32no—
82#5688—34no—
83#5688—31no—
84#5688—31no—
85#5688—31no—
86#5688—61no—
87#5688D311yescharacteristic, direct product factor
88D3×#125—31no—
89D3×#125D311yescharacteristic, complemented
90D3×C22⋊Q8—34no—
91#5622—34no—
92#5578—34no—
93C4×D3×Q8—34no—
94D3×#117—32no—
95#5517—32no—
96C2×#896—34no—
97C2×#892—32no—
98C2×#888—32no—
99C2×#887—34no—
100C2×C42×D3—31no—
101C2×C42×D3—31no—
102#5470—31no—
103C2×#870—31no—
104C22×D32C2311yescharacteristic
105C2×C4×C3⋊D3C2312yes—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2314yes—
108C2×C3×C4×D3C2314yes—
109C2×C3×C4×D3C2312yes—
110C2×C3×C4×D3C2312yes—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2314yes—
114C2×#627C2314yes—
115C2×#627C2314yes—
116C2×#624C2312yes—
117C2×#624C2311yescharacteristic
118C2×D3×Dic3C2314yes—
119C2×D3×Dic3C2312yes—
120C2×D3×Dic3C2311yescharacteristic
121C2×D3×Dic3C2311yescharacteristic
122C2×D3×Dic3C2312yes—
123C4×D32—28no—
124C4×D32Q818yescomplemented
125D3×Dic6—216no—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2312yes—
128C32×C42C2311yescharacteristic
129#3752C2314yes—
130C4⋊(C3⋊Dic3)C2312yes—
131#3750C2314yes—
132#3750C2314yes—
133C4×C3⋊Dic3C2312yes—
134C4×C3⋊Dic3C2311yescharacteristic
135C4×C3⋊Dic3C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2312yes—
138C3×C4⋊Dic3C2314yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2312yes—
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2312yes—
149C3×C4×Dic3C2311yescharacteristic
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158Dic32C2312yes—
159Dic32C2314yes—
160Dic32C2312yes—
161Dic32C2312yes—
162C2×#533—91noSylow
163C2×D3×Q8—34no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—32no—
167C22×C4×D3—32no—
168C22×Dic6—34no—
169C3×C4⋊Q8—32no—
170C3×#125—21no—
171C3×#125—34no—
172C3×#125—32no—
173C3×#125—31no—
174C3×#125—31no—
175C3×#125C2×D311yescharacteristic, complemented
176C3×#125C2×D311yescharacteristic, complemented
177C3×C22⋊Q8—34no—
178C3×C4×Q8—34no—
179C3×#117—32no—
180C2×C3×C4⋊C4—34no—
181C2×C3×C4⋊C4—32no—
182C2×C3×C42—31no—
183C2×C3×C42—31no—
184#946—34no—
185Q8×Dic3—34no—
186#944—34no—
187C2×(C2×D3)⋊C4—34no—
188#926—32no—
189C2×C4⋊Dic3—32no—
190#924—34no—
191C2×Dic3⋊C4—34no—
192C2×Dic3⋊C4—34no—
193C2×C4×Dic3—32no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—32no—
197C2×C4×Dic3—34no—
198#897—34no—
199#896—34no—
200#896—34no—
201#896—34no—
202#896—34no—
203#896—34no—
204#896—34no—
205#896—34no—
206#896—34no—
207#896—34no—
208#896—64no—
209#896C2×D314yes—
210#892—32no—
211#892—32no—
212#892—32no—
213#892—34no—
214#892—32no—
215#892—32no—
216#892—34no—
217#892—62no—
218#892C2×D312yes—
219D3×C4⋊C4—32no—
220D3×C4⋊C4—34no—
221D3×C4⋊C4—34no—
222D3×C4⋊C4C2×D312yes—
223D3×C4⋊C4C2×D314yes—
224#890—32no—
225#890C2×D312yescomplemented
226#889—34no—
227#889C2×D314yescomplemented
228#888—34no—
229#888—32no—
230#888—32no—
231#888—32no—
232#888—32no—
233#888—34no—
234#888—34no—
235#888—32no—
236#888—62no—
237#888C2×D312yescomplemented
238#887—34no—
239#887—34no—
240#887—34no—
241#887—34no—
242#887—34no—
243#887—34no—
244#887—34no—
245#887—34no—
246#887—34no—
247#887—34no—
248#887—64no—
249#887C2×D314yescomplemented
250D3×C22⋊C4—34no—
251#878—34no—
252#878—34no—
253#877—34no—
254#872—34no—
255C42×D3—32no—
256C42×D3—31no—
257C42×D3—31no—
258C42×D3—32no—
259C42×D3—34no—
260C42×D3—31no—
261C42×D3—31no—
262C42×D3—31no—
263C42×D3—32no—
264C42×D3—31no—
265C42×D3—32no—
266C42×D3—61no—
267C42×D3C2×D311yescharacteristic
268C42×D3C2×D311yescharacteristic
269#870—31no—
270#870—31no—
271#870—32no—
272#870—34no—
273#870—61no—
274#870C2×D311yescharacteristic, complemented
275#870C2×D311yescharacteristic, complemented
276#869—32no—
277C4×Dic6—34no—
278C4×Dic6—34no—
279C4×Dic6—34no—
280C22×C3⋊D3C2411yescharacteristic
281C22×C3×D3C2411yescharacteristic
282C22×C3×D3C2411yescharacteristic
283C2×D32—24no—
284C2×D32C2×Q814yes—
285C2×C32×C4C2412yes—
286C2×C32×C4C2414yes—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3C2414yes—
289C2×C3⋊Dic3C2411yescharacteristic
290C2×C3⋊Dic3C2412yes—
291C4×C3⋊D3—24no—
292C4×C3⋊D3C2×Q814yescomplemented
293#634—28no—
294C2×C3×Dic3C2414yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2414yes—
297C2×C3×Dic3C2411yescharacteristic
298C2×C3×Dic3C2411yescharacteristic
299C2×C3×Dic3C2412yes—
300C3×C4×D3—28no—
301C3×C4×D3—24no—
302C3×C4×D3—24no—
303C3×C4×D3C2×Q814yes—
304C3×C4×D3C2×Q814yescomplemented
305C3×Dic6—28no—
306#627—28no—
307#627—28no—
308#624—24no—
309#624C2×Q814yescomplemented
310D3×Dic3—28no—
311D3×Dic3—24no—
312D3×Dic3C2×Q814yes—
313D3×Dic3C2×Q814yescomplemented
314D3×Dic3#4118yes—
315#533—31no—
316#533—91no—
317#533—92no—
318#533—94no—
319#533—94no—
320#533—91no—
321#533—92no—
322#533—91no—
323C2×C4⋊Q8—92no—
324C2×#125—31no—
325C2×#125—91no—
326C2×C22⋊Q8—94no—
327C2×C4×Q8—94no—
328C2×#117—92no—
329C22×C42—91no—
330C23×D3—31no—
331C23×D3—31no—
332C2×C3×Q8—34no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—32no—
336C22×C3×C4—34no—
337C22×C3×C4—32no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—32no—
341C22×Dic3—32no—
342C22×Dic3—34no—
343D3×Q8—616no—
344C2×C4×D3—31no—
345C2×C4×D3—32no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—38no—
352C2×C4×D3—38no—
353C2×C4×D3—32no—
354C2×C4×D3—34no—
355C2×C4×D3—32no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×C4×D3—32no—
359C2×C4×D3—61no—
360C2×C4×D3—62no—
361C2×C4×D3—68no—
362C2×C4×D3—68no—
363C2×C4×D3C22×D312yes—
364C2×C4×D3C22×D312yes—
365C2×C4×D3C22×D314yes—
366C2×C4×D3C22×D311yescharacteristic
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—34no—
369C2×Dic6—34no—
370C2×Dic6—34no—
371C2×Dic6—34no—
372C2×Dic6—34no—
373C2×Dic6—34no—
374C2×Dic6—64no—
375C2×Dic6—616no—
376C2×Dic6C22×D314yes—
377C3×C4⋊C4—24no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—34no—
385C3×C4⋊C4—32no—
386C3×C4⋊C4—32no—
387C3×C4⋊C4C22×D314yes—
388C3×C4⋊C4C22×D314yes—
389C3×C4⋊C4C22×D312yes—
390C3×C4⋊C4C22×D312yes—
391C3×C22⋊C4—34no—
392C3×C42—21no—
393C3×C42—32no—
394C3×C42—34no—
395C3×C42—31no—
396C3×C42—32no—
397C3×C42—31no—
398C3×C42C22×D311yescharacteristic
399C3×C42C22×D311yescharacteristic
400#217—34no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—64no—
407(C2×D3)⋊C4C22×D314yes—
408C4⋊Dic3—32no—
409C4⋊Dic3—32no—
410C4⋊Dic3—34no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—62no—
414C4⋊Dic3C22×D314yes—
415C4⋊Dic3C22×D312yes—
416C4⋊Dic3C22×D312yes—
417Dic3⋊C4—34no—
418Dic3⋊C4—34no—
419Dic3⋊C4—34no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—64no—
429Dic3⋊C4—64no—
430Dic3⋊C4C22×D314yes—
431Dic3⋊C4C22×D314yes—
432Dic3⋊C4C22×D314yes—
433Dic3⋊C4C22×D314yes—
434Dic3⋊C4C22×D314yes—
435C4×Dic3—32no—
436C4×Dic3—32no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—34no—
440C4×Dic3—34no—
441C4×Dic3—32no—
442C4×Dic3—34no—
443C4×Dic3—32no—
444C4×Dic3—32no—
445C4×Dic3—32no—
446C4×Dic3—32no—
447C4×Dic3—32no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3—62no—
452C4×Dic3—61no—
453C4×Dic3—64no—
454C4×Dic3C22×D312yes—
455C4×Dic3C22×D311yescharacteristic
456C4×Dic3C22×D312yes—
457C4×Dic3C22×D311yescharacteristic
458C4×Dic3C22×D314yes—
459C22×C32C2511yescharacteristic
460C2×C3⋊D3—22no—
461C2×C3⋊D3C22×Q812yes—
462C2×C3×D3—22no—
463C2×C3×D3C22×Q812yes—
464C2×C3×D3C22×Q812yes—
465C2×C3×D3C2×#4114yes—
466D32—28no—
467C32×C4—24no—
468C32×C4—22no—
469C32×C4C22×Q812yes—
470C3⋊Dic3—24no—
471C3⋊Dic3C22×Q812yes—
472C3⋊Dic3C2×#4114yes—
473C3×Dic3—22no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3C22×Q812yes—
477C3×Dic3C22×Q812yes—
478C3×Dic3C2×#4114yes—
479C22×Q8—94no—
480C23×C4—91no—
481C23×C4—92no—
482C4⋊Q8—32no—
483C4⋊Q8—92no—
484C4⋊Q8—94no—
485C4⋊Q8—92no—
486C4⋊Q8—94no—
487C4⋊Q8—92no—
488#125—34no—
489#125—32no—
490#125—31no—
491#125—31no—
492#125—94no—
493#125—92no—
494#125—91no—
495#125D3211yescharacteristic, complemented
496C22⋊Q8—34no—
497C22⋊Q8—94no—
498C22⋊Q8—94no—
499C22⋊Q8—94no—
500C22⋊Q8—94no—
501C22⋊Q8—94no—
502C22⋊Q8—94no—
503C22⋊Q8—94no—
504C4×Q8—34no—
505C4×Q8—94no—
506C4×Q8—94no—
507C4×Q8—94no—
508C4×Q8—94no—
509C4×Q8—94no—
510C4×Q8—94no—
511C4×Q8—94no—
512#117—32no—
513#117—94no—
514#117—94no—
515#117—92no—
516#117—92no—
517#117—92no—
518C2×C4⋊C4—32no—
519C2×C4⋊C4—34no—
520C2×C4⋊C4—92no—
521C2×C4⋊C4—94no—
522C2×C4⋊C4—94no—
523C2×C22⋊C4—94no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—92no—
527C2×C42—91no—
528C2×C42—94no—
529C2×C42—92no—
530C2×C42—91no—
531C2×C42—91no—
532C2×C42—92no—
533C2×C42—91no—
534C23×C3—31no—
535C23×C3—31no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—34no—
539C22×D3—34no—
540C22×D3—61no—
541C22×D3—64no—
542C22×D3—64no—
543C22×D3C23×D311yescharacteristic
544C22×D3C23×D311yescharacteristic
545C3×Q8—68no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—24no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—32no—
552C2×C3×C4—34no—
553C2×C3×C4—34no—
554C2×C3×C4—32no—
555C2×C3×C4—34no—
556C2×C3×C4—34no—
557C2×C3×C4—64no—
558C2×C3×C4—68no—
559C2×C3×C4—64no—
560C2×C3×C4C23×D312yes—
561C2×C3×C4C23×D312yes—
562C2×C3×C4C23×D314yes—
563C2×C3×C4C23×D314yes—
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—34no—
571C2×Dic3—34no—
572C2×Dic3—38no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—61no—
576C2×Dic3—62no—
577C2×Dic3—64no—
578C2×Dic3—64no—
579C2×Dic3—68no—
580C2×Dic3C23×D312yes—
581C2×Dic3C23×D314yes—
582C2×Dic3C23×D314yes—
583C2×Dic3C23×D311yescharacteristic
584C2×Dic3C23×D311yescharacteristic
585C2×Dic3C23×D312yes—
586C4×D3—24no—
587C4×D3—28no—
588C4×D3—24no—
589C4×D3—34no—
590C4×D3—34no—
591C4×D3—38no—
592C4×D3—34no—
593C4×D3—34no—
594C4×D3—34no—
595C4×D3—34no—
596C4×D3—64no—
597C4×D3—64no—
598C4×D3—64no—
599C4×D3—64no—
600C4×D3—64no—
601C4×D3—68no—
602C4×D3—64no—
603C4×D3—124no—
604C4×D3D3×Q814yes—
605C4×D3D3×Q814yescomplemented
606Dic6—28no—
607Dic6—68no—
608Dic6—68no—
609Dic6—68no—
610Dic6—68no—
611Dic6—68no—
612Dic6—68no—
613Dic6—128no—
614C2×C32C23×Q811yescharacteristic
615C2×C32C22×#4112yes—
616C3⋊D3—22no—
617C3×D3—22no—
618C3×D3#53314yescomplemented
619C24—91no—
620C2×Q8—34no—
621C2×Q8—94no—
622C2×Q8—94no—
623C2×Q8—94no—
624C2×Q8—1816no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—32no—
628C22×C4—32no—
629C22×C4—34no—
630C22×C4—91no—
631C22×C4—98no—
632C22×C4—92no—
633C22×C4—91no—
634C22×C4—92no—
635C22×C4—91no—
636C22×C4—92no—
637C22×C4—94no—
638C22×C4—91no—
639C22×C4—92no—
640C22×C4—188no—
641C4⋊C4—34no—
642C4⋊C4—32no—
643C4⋊C4—34no—
644C4⋊C4—34no—
645C4⋊C4—34no—
646C4⋊C4—32no—
647C4⋊C4—34no—
648C4⋊C4—34no—
649C4⋊C4—94no—
650C4⋊C4—94no—
651C4⋊C4—94no—
652C4⋊C4—94no—
653C4⋊C4—94no—
654C4⋊C4—92no—
655C4⋊C4—94no—
656C4⋊C4—94no—
657C4⋊C4C2×D3212yes—
658C4⋊C4C2×D3214yes—
659C22⋊C4—34no—
660C22⋊C4—94no—
661C22⋊C4—94no—
662C22⋊C4—94no—
663C42—32no—
664C42—32no—
665C42—31no—
666C42—31no—
667C42—34no—
668C42—92no—
669C42—92no—
670C42—92no—
671C42—94no—
672C42—94no—
673C42—92no—
674C42—91no—
675C42—94no—
676C42C2×D3211yescharacteristic
677C22×C3—21no—
678C22×C3—32no—
679C22×C3—34no—
680C22×C3—32no—
681C22×C3—62no—
682C22×C3C24×D311yescharacteristic
683C22×C3C24×D311yescharacteristic
684C2×D3—22no—
685C2×D3—32no—
686C2×D3—32no—
687C2×D3—62no—
688C2×D3—68no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—68no—
692C2×D3—122no—
693C2×D3C2×D3×Q812yes—
694C2×D3C2×D3×Q812yes—
695C2×D3D3×#4114yes—
696C3×C4—24no—
697C3×C4—24no—
698C3×C4—22no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—32no—
702C3×C4—32no—
703C3×C4—34no—
704C3×C4—44no—
705C3×C4—42no—
706C3×C4—64no—
707C3×C4—64no—
708C3×C4—62no—
709C3×C4C2×D3×Q812yes—
710C3×C4C2×D3×Q812yes—
711Dic3—24no—
712Dic3—24no—
713Dic3—22no—
714Dic3—32no—
715Dic3—32no—
716Dic3—34no—
717Dic3—34no—
718Dic3—64no—
719Dic3—62no—
720Dic3—64no—
721Dic3—64no—
722Dic3—124no—
723Dic3C2×D3×Q812yes—
724Dic3C2×D3×Q812yes—
725Dic3D3×#4114yes—
726C32C2×#53311yescharacteristic, complemented, Sylow
727C23—31no—
728C23—31no—
729C23—94no—
730C23—91no—
731C23—184no—
732Q8—68no—
733Q8—188no—
734Q8—188no—
735Q8—188no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—32no—
739C2×C4—34no—
740C2×C4—34no—
741C2×C4—32no—
742C2×C4—34no—
743C2×C4—34no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—68no—
747C2×C4—94no—
748C2×C4—94no—
749C2×C4—94no—
750C2×C4—98no—
751C2×C4—91no—
752C2×C4—92no—
753C2×C4—94no—
754C2×C4—94no—
755C2×C4—184no—
756C2×C4—184no—
757C2×C4—184no—
758C2×C4—188no—
759C2×C4C22×D3212yes—
760C2×C4C22×D3214yes—
761C2×C4C22×D3211yescharacteristic
762C2×C3—21no—
763C2×C3—22no—
764C2×C3—34no—
765C2×C3—62no—
766C2×C3C22×D3×Q811yescharacteristic
767C2×C3C22×D3×Q811yescharacteristic
768C2×C3C2×D3×#4112yes—
769C2×C3C2×D3×#4112yes—
770D3—22no—
771D3—62no—
772D3—62no—
773D3—122no—
774D3#568814yesdirect product factor
775C22—32no—
776C22—34no—
777C22—32no—
778C22—62no—
779C22—92no—
780C22—188no—
781C22—182no—
782C22C23×D3211yescharacteristic
783C4—22no—
784C4—24no—
785C4—32no—
786C4—32no—
787C4—34no—
788C4—62no—
789C4—64no—
790C4—64no—
791C4—92no—
792C4—94no—
793C4—184no—
794C4D32×Q812yes—
795C3—21no—
796C3C2×#568811yescharacteristic, complemented
797C3D3×#53311yescharacteristic, complemented
798C2—34no—
799C2—62no—
800C2—182no—
801C2C2×D32×Q811yescharacteristic
802C2D32×#4112yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
prime radicalC22×D32C23
hypercenter#125D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596159C2semidirect
2. C3×#5688C2semidirect
3. C3×D3×#125C2semidirect
6. #10594477C2semidirect
7. #10594448C2semidirect
8. #10594398C2semidirect
9. #10594388C2semidirect
10. D3×#888C2semidirect
11. D3×#887C2semidirect
13. D3×#870C2semidirect
14. #10593874C2semidirect
15. #10593854C2semidirect
21. C32×#125C22semidirect
24. #64097C22semidirect
25. #64096C22semidirect
27. #64079C22semidirect
32. C3×#890C22semidirect
33. C3×#889C22semidirect
34. C3×#888C22semidirect
35. C3×#887C22semidirect
38. C3×#870C22semidirect
39. C3×#870C22semidirect
41. #63919C22semidirect
42. #63918C22semidirect
58. #63869C22semidirect
59. #63867C22semidirect
63. #63844C22semidirect
64. #63843C22semidirect
66. #63840C22semidirect
67. #63839C22semidirect
68. #63838C22semidirect
69. #63838C22semidirect
70. #63837C22semidirect
71. #63837C22semidirect
87. #5688D3direct (N × H)
89. D3×#125D3semidirect
124. C4×D32Q8semidirect
175. C3×#125C2×D3semidirect
176. C3×#125C2×D3semidirect
225. #890C2×D3semidirect
227. #889C2×D3semidirect
237. #888C2×D3semidirect
249. #887C2×D3semidirect
274. #870C2×D3semidirect
275. #870C2×D3semidirect
292. C4×C3⋊D3C2×Q8semidirect
304. C3×C4×D3C2×Q8semidirect
309. #624C2×Q8semidirect
313. D3×Dic3C2×Q8semidirect
495. #125D32semidirect
605. C4×D3D3×Q8semidirect
618. C3×D3#533semidirect
726. C32C2×#533semidirect
774. D3#5688direct (N × H)
796. C3C2×#5688semidirect
797. C3D3×#533semidirect

Maximal subgroups

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

subgroupindex
#105961592
C3×#56882
C3×D3×#1252
D3×#8962
D3×#8922
#105944772
#105944482
#105943982
#105943882
D3×#8882
D3×#8872
C42×D322
D3×#8702
#105938742
#105938542
D3×#5333
C2×#56883