Finite Group Databasebeta

← #11906230

Subgroups — #11906230

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C3×#5519C211yesmaximal, characteristic, complemented
4#10595051C211yesmaximal, characteristic, complemented
5#10595050C211yesmaximal, characteristic, complemented
6#10594982C211yesmaximal, characteristic
7C2×#63898C211yesmaximal, characteristic
8#10594485C212yesmaximal, complemented
9#10594460C212yesmaximal, complemented
10#10594452C212yesmaximal, complemented
11#10594376C212yesmaximal, complemented
12#10594170C214yesmaximal, complemented
13D3×#878C214yesmaximal, complemented
14#10593956C212yesmaximal, complemented
15#10593941C212yesmaximal, complemented
16#10593941C212yesmaximal, complemented
17#10593904C212yesmaximal, complemented
18#86599—31nomaximal
19#85860—31nomaximal
20C22×C3×D12C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×D3×Dic6C2214yescomplemented
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64099C2211yescharacteristic, complemented
27#64099C2211yescharacteristic, complemented
28#64097C2211yescharacteristic, complemented
29#64097C2211yescharacteristic, complemented
30#64087C2212yes—
31#64087C2212yes—
32C4×#634C2212yescomplemented
33C4×#634C2212yescomplemented
34C3×#926C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#893C2212yes—
38C3×#893C2212yes—
39C3×#890C2212yescomplemented
40C3×#888C2212yescomplemented
41C3×D3×C22⋊C4C2214yes—
42C3×#878C2214yes—
43C3×C4×D12C2212yes—
44C3×C4×D12C2212yes—
45C3×#870C2212yescomplemented
46C3×#869C2212yescomplemented
47#63982C2212yes—
48#63982C2212yes—
49D3×#217C2214yes—
50#63964C2214yes—
51C2×(C2×D3)⋊Dic3C2212yes—
52#63919C2211yescharacteristic, complemented
53#63919C2212yescomplemented
54#63919C2211yescharacteristic, complemented
55#63918C2212yescomplemented
56C4×#627C2212yescomplemented
57C4×#627C2212yescomplemented
58#63899C2214yescomplemented
59#63899C2214yescomplemented
60#63898C2212yes—
61#63898C2212yes—
62#63898C2212yes—
63#63898C2212yes—
64#63898C2212yes—
65#63898C2212yes—
66#63896C2214yescomplemented
67#63896C2214yescomplemented
68#63893C2214yescomplemented
69#63893C2214yescomplemented
70Dic3×D12C2212yes—
71Dic3×D12C2212yes—
72D3×C4⋊Dic3C2214yescomplemented
73#63887C2214yescomplemented
74#63887C2214yescomplemented
75D3×Dic3⋊C4C2214yescomplemented
76D3×Dic3⋊C4C2214yescomplemented
77#63872C2211yescharacteristic, complemented
78#63872C2212yescomplemented
79#63872C2211yescharacteristic, complemented
80#63869C2212yescomplemented
81#63857C2214yescomplemented
82#63856C2214yescomplemented
83#63851C2214yescomplemented
84#63851C2214yescomplemented
85C3×#544—31no—
86C3×#518—31no—
87#5798—31no—
88C2×D4×Dic3—31no—
89#5730—32no—
90#5730—32no—
91#5727—32no—
92#5727—32no—
93#5690—32no—
94#5690—32no—
95#5690—32no—
96#5690—32no—
97#5634—34no—
98D3×C22⋊Q8—34no—
99#5543—32no—
100#5543—32no—
101#5539—32no—
102#5539—32no—
103#5539—32no—
104#5539—32no—
105D4×Dic6—32no—
106D4×Dic6—32no—
107#5521—31no—
108#5521D311yescharacteristic
109#5519—31no—
110#5519D311yescharacteristic, complemented
111#5517—31no—
112#5517—31no—
113#5517—31no—
114#5517—31no—
115#5517—61no—
116C2×#893—31no—
117#5500—31no—
118#5483—34no—
119C2×#878—34no—
120C23×C3×D3C2312yes—
121C22×C32×C4C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C2×#634C2312yes—
125C2×#634C2312yes—
126C22×C3×Dic3C2312yes—
127C2×C3×D12Q818yescomplemented
128C2×C3×D12C2312yes—
129C2×C3×D12C2312yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×C4×D3C2314yes—
132C2×C3×Dic6C2314yes—
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#627C2312yes—
136C2×D3×Dic3—44no—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151#3750C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2312yes—
155C4×C3⋊Dic3C2311yescharacteristic
156C4×C3⋊Dic3C2312yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C3×#217C2312yes—
161C3×#217C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2311yescharacteristic
170C3×C4⋊Dic3C2311yescharacteristic
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2312yes—
175#3724C2312yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188#3501—91noSylow
189C22×C3×D4—31no—
190C23×Dic3—32no—
191C2×D3×Q8—34no—
192C22×D12C2×D311yescharacteristic
193C22×C4×D3—32no—
194C22×Dic6—34no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—32no—
197C3×#125—32no—
198C3×#125—32no—
199C3×C22⋊Q8—34no—
200C3×C4×D4—32no—
201C3×C4×D4—32no—
202C3×C4×D4—32no—
203C3×C4×D4—32no—
204C3×#117—21no—
205C3×#117—31no—
206C3×#117—31no—
207C3×#117C2×D311yescharacteristic
208C3×#117C2×D311yescharacteristic
209C2×C3×C4⋊C4—31no—
210C2×C3×C22⋊C4—34no—
211C2×#217—32no—
212C2×#217—34no—
213#946—34no—
214#946—34no—
215#946—34no—
216D4×Dic3—32no—
217D4×Dic3—32no—
218D4×Dic3—32no—
219D4×Dic3—32no—
220D4×Dic3—32no—
221D4×Dic3—32no—
222D4×Dic3—32no—
223D4×Dic3—32no—
224C2×(C2×D3)⋊C4—32no—
225#926—31no—
226#926—31no—
227#926—61no—
228#926C2×D311yescharacteristic
229#926C2×D311yescharacteristic
230C2×C4⋊Dic3—34no—
231C2×C4⋊Dic3C2×D311yescharacteristic
232#924—34no—
233#924—34no—
234#924—34no—
235#924—34no—
236#924—34no—
237C2×Dic3⋊C4—34no—
238C2×Dic3⋊C4—34no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—61no—
242#897—34no—
243#897—34no—
244#897—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#896—34no—
251#893—32no—
252#893—32no—
253#893—32no—
254#893—32no—
255#893—32no—
256#893—32no—
257#893C2×D312yes—
258#893C2×D312yes—
259D3×C4⋊C4—34no—
260D3×C4⋊C4—34no—
261D3×C4⋊C4—34no—
262#890—31no—
263#890—31no—
264#890—31no—
265#890—31no—
266#890—31no—
267#890—32no—
268#890—31no—
269#890—31no—
270#890—31no—
271#890—32no—
272#890—32no—
273#890—61no—
274#890—61no—
275#890C2×D312yescomplemented
276#888—31no—
277#888—31no—
278#888—31no—
279#888—31no—
280#888—31no—
281#888—32no—
282#888—31no—
283#888—31no—
284#888—31no—
285#888—32no—
286#888—32no—
287#888—61no—
288#888—61no—
289#888C2×D312yescomplemented
290D3×C22⋊C4—34no—
291D3×C22⋊C4C2×D314yes—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—32no—
296#878—32no—
297#878—32no—
298#878—32no—
299#878—32no—
300#878—32no—
301#878—32no—
302#878—32no—
303#878—34no—
304#878—34no—
305#878—34no—
306#878—34no—
307#878—34no—
308#878—34no—
309#878—62no—
310#878—62no—
311#878C2×D314yes—
312C4×D12—32no—
313C4×D12—32no—
314C4×D12C2×D312yes—
315C4×D12C2×D312yes—
316#870—32no—
317#870C2×D312yescomplemented
318#869—32no—
319#869C2×D312yescomplemented
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6—32no—
328C4×Dic6—62no—
329C4×Dic6—62no—
330C23×C32C2411yescharacteristic
331C22×C3×D3—42no—
332C22×C3×D3—42no—
333C22×C3×D3C2×Q818yescomplemented
334C22×C3×D3C2414yes—
335C2×C32×C4C2×Q814yescomplemented
336C2×C32×C4C2412yes—
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—41no—
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2411yescharacteristic
347C2×C3⋊Dic3C2411yescharacteristic
348#634—24no—
349#634—42no—
350C2×C3×Dic3—42no—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C3×D12C2×Q818yescomplemented
357C3×D12C2×Q818yescomplemented
358C3×C4×D3—44no—
359C3×C4×D3—44no—
360C3×Dic6—44no—
361#627—24no—
362#627—44no—
363#627—42no—
364D3×Dic3—28no—
365D3×Dic3—44no—
366D3×Dic3—44no—
367D3×Dic3—44no—
368#554—92no—
369#554—92no—
370#554—92no—
371#554—92no—
372#554—92no—
373#554—92no—
374D4×Q8—92no—
375D4×Q8—92no—
376#544—31no—
377#544—91no—
378#543—94no—
379#533—91no—
380#533—91no—
381C2×C22⋊Q8—94no—
382#518—31no—
383#518—91no—
384C2×C4×D4—91no—
385C24×C3—32no—
386C23×D3C22×D312yes—
387C2×C3×Q8—34no—
388C2×C3×D4—38no—
389C2×C3×D4—32no—
390C2×C3×D4—32no—
391C22×C3×C4—21no—
392C22×C3×C4—32no—
393C22×C3×C4—34no—
394C22×C3×C4—34no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—34no—
402C22×Dic3—34no—
403C22×Dic3—34no—
404C22×Dic3—34no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—124no—
408C22×Dic3C22×D312yes—
409D3×Q8—128no—
410C2×D12Dic618yescomplemented
411C2×D12C22×D312yes—
412C2×D12C22×D312yes—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—124no—
418C2×C4×D3C22×D314yes—
419C2×C4×D3C22×D314yes—
420C2×Dic6—32no—
421C2×Dic6—32no—
422C2×Dic6—32no—
423C2×Dic6—32no—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—32no—
427C2×Dic6—32no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—62no—
431C2×Dic6—62no—
432C2×Dic6—128no—
433C2×Dic6C22×D314yes—
434C3×C4⋊C4—21no—
435C3×C4⋊C4—21no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—34no—
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C4⋊C4C22×D311yescharacteristic
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C4⋊C4C22×D311yescharacteristic
449C3×C22⋊C4—22no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4C22×D312yes—
455C3×C22⋊C4C22×D312yes—
456C3×C42—22no—
457C3×C42—32no—
458C3×C42—32no—
459C3×C42C22×D312yes—
460C3×C42C22×D312yes—
461#217—32no—
462#217—32no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217—34no—
467#217—62no—
468#217C22×D312yes—
469#217C22×D312yes—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4C22×D314yes—
475(C2×D3)⋊C4C22×D314yes—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—32no—
485C4⋊Dic3—32no—
486C4⋊Dic3—32no—
487C4⋊Dic3—32no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—62no—
491C4⋊Dic3—62no—
492C4⋊Dic3—61no—
493C4⋊Dic3—61no—
494C4⋊Dic3C22×D312yes—
495C4⋊Dic3C22×D311yescharacteristic
496C4⋊Dic3C22×D312yes—
497C4⋊Dic3C22×D314yes—
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D311yescharacteristic
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—62no—
522Dic3⋊C4—62no—
523Dic3⋊C4—62no—
524Dic3⋊C4—62no—
525Dic3⋊C4C22×D314yes—
526Dic3⋊C4C22×D314yes—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—61no—
538C4×Dic3—61no—
539C4×Dic3—62no—
540C4×Dic3—61no—
541C4×Dic3—61no—
542C4×Dic3C22×D312yes—
543C4×Dic3C22×D312yes—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32C22×Q812yes—
547C22×C32C2511yescharacteristic
548C2×C3×D3—24no—
549C2×C3×D3—24no—
550C2×C3×D3—48no—
551C2×C3×D3C22×Q818yes—
552C32×C4—22no—
553C32×C4—22no—
554C32×C4C22×Q812yes—
555C32×C4C22×Q812yes—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3—22no—
559C3⋊Dic3—22no—
560C3⋊Dic3—21no—
561C3⋊Dic3H(5,𝔽2)12yes—
562C3×Dic3—24no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—22no—
567C22×Q8—94no—
568C22×D4—31no—
569C23×C4—92no—
570C4⋊Q8—32no—
571C4⋊Q8—32no—
572C4⋊Q8—92no—
573C4⋊Q8—91no—
574C4⋊Q8—91no—
575C4⋊Q8—92no—
576C4⋊Q8—91no—
577C4⋊Q8—91no—
578#125—32no—
579#125—32no—
580#125—92no—
581#125—91no—
582#125—91no—
583#125—92no—
584#125—91no—
585#125—91no—
586C22⋊Q8—34no—
587C22⋊Q8—92no—
588C22⋊Q8—92no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×D4—32no—
609C4×D4—32no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—92no—
618C4×D4—92no—
619C4×D4—92no—
620#117—31no—
621#117—31no—
622#117—91no—
623#117D3211yescharacteristic
624C2×C4⋊C4—31no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—94no—
627C2×C4⋊C4—94no—
628C2×C22⋊C4—34no—
629C2×C22⋊C4—94no—
630C2×C22⋊C4—92no—
631C2×C42—91no—
632C23×C3—21no—
633C23×C3—34no—
634C23×C3—38no—
635C23×C3—122no—
636C23×C3—122no—
637C23×C3C23×D311yescharacteristic
638C23×C3C23×D311yescharacteristic
639C22×D3—42no—
640C22×D3—42no—
641C22×D3C2×Dic618yescomplemented
642C22×D3C23×D314yes—
643C3×Q8—124no—
644C3×D4—38no—
645C3×D4—38no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—24no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—34no—
656C2×C3×C4—124no—
657C2×C3×C4—124no—
658C2×C3×C4—122no—
659C2×C3×C4C2×Dic614yescomplemented
660C2×C3×C4D3×Q814yescomplemented
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—42no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—68no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—122no—
692C2×Dic3—124no—
693C2×Dic3—124no—
694C2×Dic3—124no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—122no—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D314yes—
703D12C2×Dic618yescomplemented
704D12C2×Dic618yescomplemented
705C4×D3—44no—
706C4×D3—44no—
707C4×D3—68no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—124no—
711Dic6—44no—
712Dic6—64no—
713Dic6—64no—
714Dic6—64no—
715Dic6—64no—
716Dic6—124no—
717Dic6—122no—
718Dic6—122no—
719Dic6—124no—
720Dic6—124no—
721Dic6—122no—
722Dic6—122no—
723Dic6—124no—
724C2×C32—22no—
725C2×C32C23×Q811yescharacteristic
726C2×C32C2×H(5,𝔽2)11yescharacteristic
727C2×C32#58511yescharacteristic
728C3×D3—28no—
729C24—32no—
730C2×Q8—34no—
731C2×Q8—92no—
732C2×Q8—92no—
733C2×Q8—94no—
734C2×Q8—92no—
735C2×Q8—92no—
736C2×Q8—368no—
737C2×D4—32no—
738C2×D4—32no—
739C2×D4—38no—
740C22×C4—32no—
741C22×C4—34no—
742C22×C4—34no—
743C22×C4—94no—
744C22×C4—94no—
745C22×C4—94no—
746C22×C4—94no—
747C22×C4—91no—
748C22×C4—91no—
749C22×C4—364no—
750C22×C4C2×D3211yescharacteristic
751C4⋊C4—32no—
752C4⋊C4—32no—
753C4⋊C4—34no—
754C4⋊C4—34no—
755C4⋊C4—34no—
756C4⋊C4—31no—
757C4⋊C4—31no—
758C4⋊C4—31no—
759C4⋊C4—31no—
760C4⋊C4—92no—
761C4⋊C4—92no—
762C4⋊C4—92no—
763C4⋊C4—94no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—92no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4—92no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—92no—
775C4⋊C4—92no—
776C4⋊C4—92no—
777C4⋊C4C2×D3211yescharacteristic
778C4⋊C4C2×D3211yescharacteristic
779C22⋊C4—32no—
780C22⋊C4—32no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—92no—
788C22⋊C4C2×D3212yes—
789C42—32no—
790C42—32no—
791C42—91no—
792C42—91no—
793C42—91no—
794C42—91no—
795C42—92no—
796C42C2×D3212yes—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—22no—
802C22×C3—21no—
803C22×C3—38no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—64no—
807C22×C3—64no—
808C22×C3—128no—
809C22×C3C22×Dic612yes—
810C22×C3C2×D3×Q812yes—
811C22×C3C24×D311yescharacteristic
812C22×C3C24×D311yescharacteristic
813C2×D3—24no—
814C2×D3—24no—
815C2×D3—48no—
816C2×D3C22×Dic618yes—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—64no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4C22×Dic612yes—
831C3×C4C22×Dic612yes—
832C3×C4C2×D3×Q812yes—
833C3×C4C2×D3×Q812yes—
834Dic3—22no—
835Dic3—24no—
836Dic3—22no—
837Dic3—22no—
838Dic3—22no—
839Dic3—32no—
840Dic3—32no—
841Dic3—62no—
842Dic3—62no—
843Dic3—62no—
844Dic3—62no—
845Dic3—61no—
846Dic3—61no—
847Dic3—61no—
848Dic3—61no—
849Dic3—62no—
850Dic3—61no—
851Dic3—61no—
852Dic3—62no—
853Dic3—122no—
854Dic3—122no—
855Dic3—121no—
856Dic3—121no—
857C32#350111yescharacteristic, complemented, Sylow
858C23—34no—
859C23—38no—
860C23—122no—
861C23—122no—
862C23C22×D3211yescharacteristic
863Q8—124no—
864Q8—184no—
865Q8—184no—
866Q8—362no—
867Q8—364no—
868Q8—362no—
869D4—38no—
870D4—38no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—34no—
876C2×C4—91no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—91no—
880C2×C4—92no—
881C2×C4—92no—
882C2×C4—124no—
883C2×C4—124no—
884C2×C4—122no—
885C2×C4—188no—
886C2×C4—182no—
887C2×C4—364no—
888C2×C4—364no—
889C2×C4—364no—
890C2×C4—361no—
891C2×C4D3×Dic614yescomplemented
892C2×C4C22×D3212yes—
893C2×C4C22×D3212yes—
894C2×C4C22×D3211yescharacteristic
895C2×C4C22×D3211yescharacteristic
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—42no—
902C2×C3—68no—
903C2×C3C23×Dic611yescharacteristic
904C2×C3C22×D3×Q811yescharacteristic
905C2×C3D3×H(5,𝔽2)11yescharacteristic
906C2×C3D3×H(5,𝔽2)11yescharacteristic
907C2×C3#596611yescharacteristic
908C2×C3#596811yescharacteristic
909D3—28no—
910C22—21no—
911C22—21no—
912C22—38no—
913C22—64no—
914C22—64no—
915C22—128no—
916C22C2×D3×Dic612yes—
917C22C23×D3211yescharacteristic
918C4—22no—
919C4—22no—
920C4—62no—
921C4—64no—
922C4—62no—
923C4—62no—
924C4—62no—
925C4—92no—
926C4—181no—
927C4—182no—
928C4—182no—
929C4—181no—
930C4—181no—
931C4C2×D3×Dic612yes—
932C4C2×D3×Dic612yes—
933C3—21no—
934C3#8586011yescharacteristic, complemented
935C3#8659911yescharacteristic, complemented
936C2—22no—
937C2—68no—
938C2C22×D3×Dic611yescharacteristic
939C2#1059669211yescharacteristic
940C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
3. C3×#5519C2semidirect
4. #10595051C2semidirect
5. #10595050C2semidirect
8. #10594485C2semidirect
9. #10594460C2semidirect
10. #10594452C2semidirect
11. #10594376C2semidirect
12. #10594170C2semidirect
13. D3×#878C2semidirect
14. #10593956C2semidirect
15. #10593941C2semidirect
16. #10593941C2semidirect
17. #10593904C2semidirect
22. C2×D3×Dic6C22semidirect
26. #64099C22semidirect
27. #64099C22semidirect
28. #64097C22semidirect
29. #64097C22semidirect
32. C4×#634C22semidirect
33. C4×#634C22semidirect
39. C3×#890C22semidirect
40. C3×#888C22semidirect
45. C3×#870C22semidirect
46. C3×#869C22semidirect
52. #63919C22semidirect
53. #63919C22semidirect
54. #63919C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. C4×#627C22semidirect
58. #63899C22semidirect
59. #63899C22semidirect
66. #63896C22semidirect
67. #63896C22semidirect
68. #63893C22semidirect
69. #63893C22semidirect
72. D3×C4⋊Dic3C22semidirect
73. #63887C22semidirect
74. #63887C22semidirect
75. D3×Dic3⋊C4C22semidirect
76. D3×Dic3⋊C4C22semidirect
77. #63872C22semidirect
78. #63872C22semidirect
79. #63872C22semidirect
80. #63869C22semidirect
81. #63857C22semidirect
82. #63856C22semidirect
83. #63851C22semidirect
84. #63851C22semidirect
110. #5519D3semidirect
127. C2×C3×D12Q8semidirect
275. #890C2×D3semidirect
289. #888C2×D3semidirect
317. #870C2×D3semidirect
319. #869C2×D3semidirect
333. C22×C3×D3C2×Q8semidirect
335. C2×C32×C4C2×Q8semidirect
356. C3×D12C2×Q8semidirect
357. C3×D12C2×Q8semidirect
410. C2×D12Dic6semidirect
641. C22×D3C2×Dic6semidirect
659. C2×C3×C4C2×Dic6semidirect
660. C2×C3×C4D3×Q8semidirect
703. D12C2×Dic6semidirect
704. D12C2×Dic6semidirect
857. C32#3501semidirect
891. C2×C4D3×Dic6semidirect
934. C3#85860semidirect
935. C3#86599semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×#55212
C3×#55192
#105950512
#105950502
#105949822
C2×#638982
#105944852
#105944602
#105944522
#105943762
#105941702
D3×#8782
#105939562
#105939412
#105939042
#865993
#858603