Finite Group Databasebeta

← D3×#5519 #11901900

Subgroups — D3×#5519 #11901900

Order 1152.

2263 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595990C211yesmaximal, characteristic, complemented
2C3×D3×#117C211yesmaximal, characteristic
3C3×#5519C211yesmaximal, characteristic, complemented
4#10595052C211yesmaximal, characteristic, complemented
5#10595051C211yesmaximal, characteristic, complemented
6D3×#926C211yesmaximal, characteristic
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic
8#10594505C212yesmaximal, complemented
9#10594502C212yesmaximal, complemented
10D3×#890C212yesmaximal, complemented
11D3×#888C212yesmaximal, complemented
12D3×#878C214yesmaximal
13#10594035C214yesmaximal, complemented
14#10593959C212yesmaximal, complemented
15#10593954C212yesmaximal, complemented
16D3×#870C212yesmaximal, complemented
17D3×#869C212yesmaximal, complemented
18D3×#544—31nomaximal
19C2×#5519—31nomaximal
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×D3×Dic6C2214yes—
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64099C2212yescomplemented
27#64097C2212yescomplemented
28#64087C2214yes—
29#64079C2212yescomplemented
30#64078C2212yescomplemented
31C3×#926C2211yescharacteristic
32C3×#926C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#892C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890C2212yescomplemented
39C3×#888C2212yescomplemented
40C3×D3×C22⋊C4C2212yes—
41C3×#878C2214yes—
42C3×#877C2212yes—
43C3×#872C2212yes—
44C3×C42×D3C2212yes—
45C3×#870C2212yescomplemented
46C3×#869C2212yescomplemented
47#63982C2214yes—
48D3×#217C2212yes—
49C2×Dic3⋊Dic3C2212yes—
50#63964C2214yes—
51#63955C2212yes—
52#63919C2212yescomplemented
53#63918C2212yescomplemented
54#63918C2212yescomplemented
55#63918C2212yescomplemented
56#63918C2214yescomplemented
57#63899C2214yes—
58#63896C2214yes—
59#63893C2214yes—
60D3×C4⋊Dic3C2214yes—
61D3×C4⋊Dic3C2212yes—
62D3×C4⋊Dic3C2212yes—
63D3×C4⋊Dic3C2212yes—
64D3×C4⋊Dic3C2212yes—
65D3×C4⋊Dic3C2211yescharacteristic
66D3×C4⋊Dic3C2211yescharacteristic
67#63887C2214yes—
68D3×Dic3⋊C4C2214yes—
69D3×Dic3⋊C4C2214yes—
70C4×D3×Dic3C2212yes—
71#63872C2212yescomplemented
72#63869C2212yescomplemented
73#63869C2212yescomplemented
74#63869C2212yescomplemented
75#63867C2214yescomplemented
76#63867C2214yescomplemented
77#63866C2214yescomplemented
78#63855C2212yes—
79#63846C2214yescomplemented
80#63845C2214yescomplemented
81#63841C2211yescharacteristic
82#63841C2211yescharacteristic
83#63840C2214yescomplemented
84#63839C2214yescomplemented
85C3×#544—31no—
86C2×C3×#117—31no—
87C2×#926—31no—
88C22×C4⋊Dic3—31no—
89#5729—32no—
90#5729—32no—
91D3×C4⋊Q8—32no—
92D3×C4⋊Q8—32no—
93#5689—32no—
94#5689—32no—
95D3×#125—32no—
96D3×#125—32no—
97D3×C22⋊Q8—34no—
98#5623—34no—
99D3×#117—31no—
100D3×#117D311yescharacteristic
101#5519—31no—
102#5519—31no—
103#5519—31no—
104#5519—31no—
105#5519—31no—
106#5519—32no—
107#5519—32no—
108#5519—34no—
109#5519—32no—
110#5519—32no—
111#5519—61no—
112#5519D311yescharacteristic, direct product factor
113C2×D3×C4⋊C4—31no—
114#5500—31no—
115C2×#890—32no—
116C2×#888—32no—
117C2×#878—34no—
118C2×#870—32no—
119C2×#869—32no—
120C23×C3×D3C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C3⋊Dic3C2312yes—
123C2×#634C2314yes—
124C22×C3×Dic3C2312yes—
125C22×C3×Dic3C2311yescharacteristic
126C2×C3×C4×D3Q818yescomplemented
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6C2314yes—
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×D3×Dic3—44no—
137C2×D3×Dic3C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152#3750C2314yes—
153#3750C2314yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2312yes—
156C3×#217C2312yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×C4⋊Dic3C2314yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188C2×#544—91noSylow
189C23×C3×C4—31no—
190C23×Dic3—32no—
191C2×D3×Q8—34no—
192C22×C4×D3—32no—
193C22×C4×D3C2×D311yescharacteristic
194C22×Dic6—34no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—32no—
197C3×#125—32no—
198C3×#125—32no—
199C3×C22⋊Q8—34no—
200C3×#117—21no—
201C3×#117—31no—
202C3×#117—31no—
203C3×#117—31no—
204C3×#117—31no—
205C3×#117—32no—
206C3×#117—32no—
207C3×#117C2×D311yescharacteristic
208C3×#117C2×D311yescharacteristic
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C22⋊C4—32no—
213C2×C3×C42—32no—
214C2×#217—32no—
215#946—34no—
216#944—34no—
217#944—34no—
218#926—31no—
219#926—31no—
220#926—32no—
221#926—31no—
222#926—31no—
223#926—32no—
224#926—61no—
225#926C2×D311yescharacteristic
226#926C2×D311yescharacteristic
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—32no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—32no—
232C2×C4⋊Dic3—34no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—32no—
235C2×C4⋊Dic3—32no—
236C2×C4⋊Dic3—32no—
237C2×C4⋊Dic3—61no—
238C2×C4⋊Dic3C2×D311yescharacteristic
239#924—34no—
240C2×Dic3⋊C4—32no—
241C2×Dic3⋊C4—34no—
242C2×Dic3⋊C4—34no—
243C2×C4×Dic3—32no—
244#897—34no—
245#896—34no—
246#896—34no—
247#892—31no—
248#892—31no—
249#892C2×D311yescharacteristic
250#892C2×D311yescharacteristic
251D3×C4⋊C4—34no—
252D3×C4⋊C4—31no—
253D3×C4⋊C4—32no—
254D3×C4⋊C4—32no—
255D3×C4⋊C4—34no—
256D3×C4⋊C4—34no—
257D3×C4⋊C4—32no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—31no—
260D3×C4⋊C4C2×D311yescharacteristic
261D3×C4⋊C4C2×D311yescharacteristic
262#890—32no—
263#890—32no—
264#890—32no—
265#890—34no—
266#890—32no—
267#890—34no—
268#890—32no—
269#890—32no—
270#890—32no—
271#890—62no—
272#890C2×D312yescomplemented
273#889—34no—
274#889—34no—
275#889—34no—
276#889—34no—
277#888—34no—
278#888—32no—
279#888—32no—
280#888—32no—
281#888—32no—
282#888—34no—
283#888—34no—
284#888—32no—
285#888—34no—
286#888—32no—
287#888—32no—
288#888—62no—
289#888C2×D312yescomplemented
290D3×C22⋊C4—32no—
291D3×C22⋊C4C2×D312yes—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—64no—
302#878C2×D314yes—
303#877—32no—
304#877C2×D312yes—
305#872—32no—
306#872C2×D312yes—
307C42×D3—32no—
308C42×D3C2×D312yes—
309#870—32no—
310#870—32no—
311#870—32no—
312#870—32no—
313#870—32no—
314#870—34no—
315#870—34no—
316#870—62no—
317#870C2×D312yescomplemented
318#869—34no—
319#869—32no—
320#869—32no—
321#869—32no—
322#869—32no—
323#869—32no—
324#869—34no—
325#869—62no—
326#869C2×D312yescomplemented
327C23×C32C2411yescharacteristic
328C22×C3×D3—22no—
329C22×C3×D3—22no—
330C22×C3×D3C2×Q814yes—
331C22×C3×D3C2411yescharacteristic
332C22×C3×D3C2411yescharacteristic
333C2×C32×C4C2×Q814yescomplemented
334C2×C32×C4C2412yes—
335C2×C32×C4C2412yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C3⋊Dic3—42no—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2414yes—
342#634—44no—
343C2×C3×Dic3—42no—
344C2×C3×Dic3C2×Q814yescomplemented
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2411yescharacteristic
352C3×C4×D3—24no—
353C3×C4×D3—24no—
354C3×C4×D3C2×Q814yes—
355C3×C4×D3C2×Q814yes—
356C3×C4×D3C2×Q814yescomplemented
357C3×C4×D3C2×Q814yescomplemented
358C3×Dic6—44no—
359#627—44no—
360#627—44no—
361D3×Dic3—24no—
362D3×Dic3—28no—
363D3×Dic3—24no—
364D3×Dic3—44no—
365#544—31no—
366#544—91no—
367#544—91no—
368#544—94no—
369#544—92no—
370#544—92no—
371#544—92no—
372#544—92no—
373#544—91no—
374C2×C4⋊Q8—92no—
375C2×C4⋊Q8—92no—
376C2×#125—92no—
377C2×#125—92no—
378C2×C22⋊Q8—94no—
379C2×#117—31no—
380C2×#117—91no—
381C22×C4⋊C4—91no—
382C24×C3—31no—
383C23×D3C22×D311yescharacteristic
384C2×C3×Q8—34no—
385C22×C3×C4—21no—
386C22×C3×C4—31no—
387C22×C3×C4—38no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—32no—
393C22×C3×C4—32no—
394C22×C3×C4—32no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×Dic3—32no—
398C22×Dic3—32no—
399C22×Dic3—32no—
400C22×Dic3—32no—
401C22×Dic3—34no—
402C22×Dic3—34no—
403C22×Dic3—62no—
404C22×Dic3—124no—
405C22×Dic3C22×D312yes—
406C22×Dic3C22×D311yescharacteristic
407D3×Q8—128no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—124no—
413C2×C4×D3Dic618yescomplemented
414C2×C4×D3C22×D312yes—
415C2×C4×D3C22×D312yes—
416C2×C4×D3C22×D311yescharacteristic
417C2×C4×D3C22×D311yescharacteristic
418C2×C4×D3C22×D311yescharacteristic
419C2×C4×D3C22×D311yescharacteristic
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—34no—
426C2×Dic6—64no—
427C2×Dic6—128no—
428C2×Dic6C22×D314yes—
429C3×C4⋊C4—21no—
430C3×C4⋊C4—21no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C4⋊C4C22×D311yescharacteristic
444C3×C4⋊C4C22×D311yescharacteristic
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C22⋊C4—22no—
447C3×C22⋊C4—32no—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4C22×D312yes—
452C3×C22⋊C4C22×D312yes—
453C3×C42—22no—
454C3×C42—32no—
455C3×C42—32no—
456C3×C42—32no—
457C3×C42—32no—
458C3×C42C22×D312yes—
459C3×C42C22×D312yes—
460#217—32no—
461#217—32no—
462#217—32no—
463#217—32no—
464#217—62no—
465#217C22×D312yes—
466#217C22×D312yes—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4C22×D312yes—
470(C2×D3)⋊C4C22×D312yes—
471C4⋊Dic3—31no—
472C4⋊Dic3—32no—
473C4⋊Dic3—34no—
474C4⋊Dic3—31no—
475C4⋊Dic3—32no—
476C4⋊Dic3—32no—
477C4⋊Dic3—34no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—32no—
481C4⋊Dic3—32no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—32no—
487C4⋊Dic3—34no—
488C4⋊Dic3—34no—
489C4⋊Dic3—61no—
490C4⋊Dic3—62no—
491C4⋊Dic3—64no—
492C4⋊Dic3—61no—
493C4⋊Dic3—62no—
494C4⋊Dic3C22×D311yescharacteristic
495C4⋊Dic3C22×D311yescharacteristic
496C4⋊Dic3C22×D312yes—
497C4⋊Dic3C22×D314yes—
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D312yes—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—64no—
518Dic3⋊C4—64no—
519Dic3⋊C4C22×D314yes—
520Dic3⋊C4C22×D314yes—
521Dic3⋊C4C22×D312yes—
522Dic3⋊C4C22×D312yes—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—62no—
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D312yes—
534C22×C32—21no—
535C22×C32—21no—
536C22×C32C22×Q812yes—
537C22×C32C2511yescharacteristic
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—28no—
541C2×C3×D3C22×Q812yes—
542C2×C3×D3C22×Q812yes—
543C2×C3×D3H(5,𝔽2)12yes—
544C2×C3×D32−1+412yes—
545C32×C4—22no—
546C32×C4—22no—
547C32×C4C22×Q812yes—
548C32×C4C22×Q812yes—
549C3⋊Dic3—24no—
550C3⋊Dic3—22no—
551C3⋊Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3C22×Q812yes—
558C3×Dic3C22×Q812yes—
559C22×Q8—94no—
560C23×C4—31no—
561C23×C4—92no—
562C4⋊Q8—32no—
563C4⋊Q8—32no—
564C4⋊Q8—92no—
565C4⋊Q8—92no—
566C4⋊Q8—94no—
567C4⋊Q8—92no—
568C4⋊Q8—94no—
569C4⋊Q8—94no—
570C4⋊Q8—92no—
571C4⋊Q8—94no—
572C4⋊Q8—92no—
573C4⋊Q8—92no—
574#125—32no—
575#125—32no—
576#125—94no—
577#125—94no—
578#125—92no—
579#125—92no—
580#125—92no—
581#125—94no—
582#125—94no—
583#125—92no—
584#125—92no—
585#125—92no—
586C22⋊Q8—34no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594#117—31no—
595#117—31no—
596#117—31no—
597#117—31no—
598#117—32no—
599#117—32no—
600#117—92no—
601#117—92no—
602#117—91no—
603#117—91no—
604#117—91no—
605#117D3211yescharacteristic
606C2×C4⋊C4—31no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—31no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—92no—
611C2×C4⋊C4—92no—
612C2×C4⋊C4—92no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—94no—
616C2×C4⋊C4—94no—
617C2×C4⋊C4—94no—
618C2×C4⋊C4—92no—
619C2×C4⋊C4—91no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—92no—
622C2×C42—32no—
623C2×C42—92no—
624C23×C3—21no—
625C23×C3—31no—
626C23×C3—34no—
627C23×C3—31no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3C23×D311yescharacteristic
631C23×C3C23×D311yescharacteristic
632C22×D3—22no—
633C22×D3—22no—
634C22×D3C2×Dic614yes—
635C22×D3C23×D311yescharacteristic
636C22×D3C23×D311yescharacteristic
637C3×Q8—124no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—24no—
643C2×C3×C4—34no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—34no—
647C2×C3×C4—34no—
648C2×C3×C4—34no—
649C2×C3×C4—34no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—34no—
654C2×C3×C4—32no—
655C2×C3×C4—64no—
656C2×C3×C4—64no—
657C2×C3×C4—122no—
658C2×C3×C4C2×Dic614yescomplemented
659C2×C3×C4D3×Q814yescomplemented
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—34no—
673C2×Dic3—34no—
674C2×Dic3—42no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—64no—
678C2×Dic3—64no—
679C2×Dic3—68no—
680C2×Dic3—64no—
681C2×Dic3—124no—
682C2×Dic3—122no—
683C2×Dic3—122no—
684C2×Dic3—242no—
685C2×Dic3C2×Dic614yescomplemented
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D314yes—
691C2×Dic3C23×D311yescharacteristic
692C2×Dic3C23×D311yescharacteristic
693C4×D3—24no—
694C4×D3—24no—
695C4×D3—68no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—124no—
699C4×D3C2×Dic614yes—
700C4×D3C2×Dic614yes—
701C4×D3C2×Dic614yescomplemented
702C4×D3C2×Dic614yescomplemented
703Dic6—44no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708Dic6—124no—
709Dic6—124no—
710Dic6—244no—
711C2×C32—22no—
712C2×C32C23×Q811yescharacteristic
713C2×C32C2×H(5,𝔽2)11yescharacteristic
714C2×C32C2×2−1+411yescharacteristic
715C3×D3—22no—
716C3×D3#54414yescomplemented
717C24—31no—
718C2×Q8—34no—
719C2×Q8—94no—
720C2×Q8—94no—
721C2×Q8—94no—
722C2×Q8—368no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—38no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—92no—
733C22×C4—92no—
734C22×C4—94no—
735C22×C4—94no—
736C22×C4—92no—
737C22×C4—364no—
738C22×C4C2×D3211yescharacteristic
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—32no—
742C4⋊C4—31no—
743C4⋊C4—32no—
744C4⋊C4—31no—
745C4⋊C4—31no—
746C4⋊C4—31no—
747C4⋊C4—34no—
748C4⋊C4—34no—
749C4⋊C4—34no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—92no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—92no—
761C4⋊C4—92no—
762C4⋊C4—91no—
763C4⋊C4—91no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—94no—
767C4⋊C4C2×D3211yescharacteristic
768C4⋊C4C2×D3211yescharacteristic
769C22⋊C4—32no—
770C22⋊C4—32no—
771C22⋊C4—32no—
772C22⋊C4—32no—
773C22⋊C4—92no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4C2×D3212yes—
777C42—32no—
778C42—32no—
779C42—32no—
780C42—32no—
781C42—92no—
782C42—92no—
783C42—92no—
784C42C2×D3212yes—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—22no—
790C22×C3—21no—
791C22×C3—32no—
792C22×C3—32no—
793C22×C3—32no—
794C22×C3—32no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—68no—
798C22×C3—61no—
799C22×C3—61no—
800C22×C3C22×Dic612yes—
801C22×C3C2×D3×Q812yes—
802C22×C3C24×D311yescharacteristic
803C22×C3C24×D311yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—28no—
807C2×D3C22×Dic612yes—
808C2×D3C22×Dic612yes—
809C2×D3#100912yes—
810C2×D3#101012yes—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—32no—
818C3×C4—32no—
819C3×C4—42no—
820C3×C4—42no—
821C3×C4—62no—
822C3×C4—64no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4C22×Dic612yes—
827C3×C4C22×Dic612yes—
828C3×C4C2×D3×Q812yes—
829C3×C4C2×D3×Q812yes—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—24no—
834Dic3—22no—
835Dic3—62no—
836Dic3—64no—
837Dic3—62no—
838Dic3—62no—
839Dic3—64no—
840Dic3—62no—
841Dic3—122no—
842Dic3—124no—
843Dic3—122no—
844Dic3C22×Dic612yes—
845Dic3C22×Dic612yes—
846C32C2×#54411yescharacteristic, complemented, Sylow
847C23—31no—
848C23—34no—
849C23—31no—
850C23—62no—
851C23—62no—
852C23C22×D3211yescharacteristic
853Q8—124no—
854Q8—364no—
855Q8—364no—
856Q8—364no—
857C2×C4—34no—
858C2×C4—31no—
859C2×C4—31no—
860C2×C4—34no—
861C2×C4—34no—
862C2×C4—34no—
863C2×C4—34no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—34no—
869C2×C4—64no—
870C2×C4—64no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—94no—
874C2×C4—122no—
875C2×C4—188no—
876C2×C4—184no—
877C2×C4—184no—
878C2×C4—364no—
879C2×C4—362no—
880C2×C4D3×Dic614yescomplemented
881C2×C4C22×D3212yes—
882C2×C4C22×D3212yes—
883C2×C4C22×D3211yescharacteristic
884C2×C4C22×D3211yescharacteristic
885C2×C3—22no—
886C2×C3—22no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—34no—
891C2×C3—42no—
892C2×C3—62no—
893C2×C3C23×Dic611yescharacteristic
894C2×C3C22×D3×Q811yescharacteristic
895C2×C3C2×#100911yescharacteristic
896C2×C3C2×#101011yescharacteristic
897C2×C3D3×H(5,𝔽2)11yescharacteristic
898C2×C3D3×2−1+411yescharacteristic
899D3—22no—
900D3#551914yesdirect product factor
901C22—21no—
902C22—21no—
903C22—32no—
904C22—32no—
905C22—32no—
906C22—32no—
907C22—68no—
908C22—61no—
909C22—61no—
910C22C2×D3×Dic612yes—
911C22C23×D3211yescharacteristic
912C4—22no—
913C4—22no—
914C4—32no—
915C4—32no—
916C4—62no—
917C4—64no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—184no—
922C4—182no—
923C4—182no—
924C4C2×D3×Dic612yes—
925C4C2×D3×Dic612yes—
926C3—21no—
927C3C2×#551911yescharacteristic, complemented
928C3D3×#54411yescharacteristic, complemented
929C2—22no—
930C2—34no—
931C2—62no—
932C2C22×D3×Dic611yescharacteristic
933C2D3×#100911yescharacteristic
934C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC23×C3×D3C23
hypercenter#117D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595990C2semidirect
3. C3×#5519C2semidirect
4. #10595052C2semidirect
5. #10595051C2semidirect
8. #10594505C2semidirect
9. #10594502C2semidirect
10. D3×#890C2semidirect
11. D3×#888C2semidirect
13. #10594035C2semidirect
14. #10593959C2semidirect
15. #10593954C2semidirect
16. D3×#870C2semidirect
17. D3×#869C2semidirect
26. #64099C22semidirect
27. #64097C22semidirect
29. #64079C22semidirect
30. #64078C22semidirect
38. C3×#890C22semidirect
39. C3×#888C22semidirect
45. C3×#870C22semidirect
46. C3×#869C22semidirect
52. #63919C22semidirect
53. #63918C22semidirect
54. #63918C22semidirect
55. #63918C22semidirect
56. #63918C22semidirect
71. #63872C22semidirect
72. #63869C22semidirect
73. #63869C22semidirect
74. #63869C22semidirect
75. #63867C22semidirect
76. #63867C22semidirect
77. #63866C22semidirect
79. #63846C22semidirect
80. #63845C22semidirect
83. #63840C22semidirect
84. #63839C22semidirect
112. #5519D3direct (N × H)
126. C2×C3×C4×D3Q8semidirect
272. #890C2×D3semidirect
289. #888C2×D3semidirect
317. #870C2×D3semidirect
326. #869C2×D3semidirect
333. C2×C32×C4C2×Q8semidirect
344. C2×C3×Dic3C2×Q8semidirect
356. C3×C4×D3C2×Q8semidirect
357. C3×C4×D3C2×Q8semidirect
413. C2×C4×D3Dic6semidirect
658. C2×C3×C4C2×Dic6semidirect
659. C2×C3×C4D3×Q8semidirect
685. C2×Dic3C2×Dic6semidirect
701. C4×D3C2×Dic6semidirect
702. C4×D3C2×Dic6semidirect
716. C3×D3#544semidirect
846. C32C2×#544semidirect
880. C2×C4D3×Dic6semidirect
900. D3#5519direct (N × H)
927. C3C2×#5519semidirect
928. C3D3×#544semidirect

Maximal subgroups

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

subgroupindex
#105959902
C3×D3×#1172
C3×#55192
#105950522
#105950512
D3×#9262
C2×D3×C4⋊Dic32
#105945052
#105945022
D3×#8902
D3×#8882
D3×#8782
#105940352
#105939592
#105939542
D3×#8702
D3×#8692
D3×#5443
C2×#55193