Finite Group Databasebeta

← #10800532

Subgroups — #10800532

Order 768.

1222 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5649C211yesmaximal, characteristic
2Dic3×#117C211yesmaximal, characteristic, complemented
3#74051C211yesmaximal, characteristic, complemented
4C3×#1899C211yesmaximal, characteristic, complemented
5#71705C211yesmaximal, characteristic, complemented
6#71595C211yesmaximal, characteristic, complemented
7#70030C212yesmaximal
8Dic3×#99C212yesmaximal, complemented
9#69535C211yesmaximal, characteristic, complemented
10#68955C212yesmaximal, complemented
11#68952C212yesmaximal, complemented
12#21421—31nomaximal, Sylow
13C2×C3×#123C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C2×#939C2211yescharacteristic
16C2×D4×Dic3C2211yescharacteristic
17C2×#929C2211yescharacteristic
18C2×#926C2211yescharacteristic
19C22×C4×Dic3C2211yescharacteristic
20#5649—21no—
21#5649—21no—
22#5649—21no—
23#5649—21no—
24#5649—21no—
25#5649—21no—
26#5649—21no—
27#5649—21no—
28C2×#898C411yescharacteristic, complemented
29C2×#892C411yescharacteristic, complemented
30C2×#889C411yescharacteristic, complemented
31C2×#887C411yescharacteristic, complemented
32C2×#885C411yescharacteristic, complemented
33C2×#67⋊C4C411yescharacteristic, complemented
34C2×#67⋊C4C2211yescharacteristic
35C2×#879C411yescharacteristic, complemented
36C2×#878C2211yescharacteristic
37C2×#877C411yescharacteristic, complemented
38C2×C3×#99C2212yes—
39C3×#381C2211yescharacteristic
40C2×#834C2212yes—
41#5211C2211yescharacteristic
42Dic3×C4⋊C4—21no—
43Dic3×C4⋊C4—21no—
44C2×#806C2212yes—
45C2×#806C2212yes—
46#4942C2212yes—
47Dic3×C22⋊C4C2212yes—
48Dic3×C22⋊C4C2212yes—
49Dic3×C22⋊C4C2212yes—
50#4932—21no—
51C42×Dic3—21no—
52#4651—21no—
53#4650—21no—
54#4649—21no—
55#4648—21no—
56C3×#342C2212yes—
57#4527C2212yes—
58#4527C2212yes—
59#4526C2212yes—
60C2×#529—31no—
61#2283—31no—
62C4×#117—31no—
63#1996—32no—
64#1964—32no—
65#1899—31no—
66#1899—31no—
67#1899—31no—
68#1899D311yescharacteristic, complemented
69C4×#99—32no—
70C4×#99—32no—
71C22×C3×D4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C22×#67C2×C411yescharacteristic
74C22×#67C2311yescharacteristic
75C23×Dic3C2×C411yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C22×C4×D3C2×C411yescharacteristic
79C22×Dic6C2×C411yescharacteristic
80C3×#123—21no—
81C3×#123—21no—
82C3×#123—21no—
83C3×#123—21no—
84C3×#117—24no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×C411yescharacteristic
87C2×C3×C4⋊C4C2×C411yescharacteristic
88C2×C3×C22⋊C4C2×C411yescharacteristic
89C2×C3×C22⋊C4C2×C411yescharacteristic
90C2×C3×C22⋊C4C2312yes—
91C2×C3×C22⋊C4C2311yescharacteristic
92C2×C3×C22⋊C4C2312yes—
93C2×C3×C42—21no—
94C2×#217C2×C411yescharacteristic
95C2×#217C2×C411yescharacteristic
96C2×#217C2312yes—
97C2×#217C2311yescharacteristic
98C2×#217C2312yes—
99#939—21no—
100#939—21no—
101#939—21no—
102#939—21no—
103D4×Dic3—21no—
104D4×Dic3—21no—
105D4×Dic3—21no—
106D4×Dic3—21no—
107#929—21no—
108#929—21no—
109#929—21no—
110#929—21no—
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112C2×(C2×D3)⋊C4C2×C411yescharacteristic
113C2×(C2×D3)⋊C4C2×C411yescharacteristic
114C2×(C2×D3)⋊C4C2×C411yescharacteristic
115#926—24no—
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3C2×C411yescharacteristic
118C2×C4⋊Dic3C2×C411yescharacteristic
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4C2×C411yescharacteristic
121C2×Dic3⋊C4C2×C411yescharacteristic
122C2×Dic3⋊C4C2×C411yescharacteristic
123C2×Dic3⋊C4C2×C411yescharacteristic
124C2×Dic3⋊C4C2×C411yescharacteristic
125C2×Dic3⋊C4C2×C411yescharacteristic
126C2×C4×Dic3—21no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
130C2×C4×Dic3C2×C411yescharacteristic
131C2×C4×Dic3C2×C411yescharacteristic
132C2×C4×Dic3C2×C411yescharacteristic
133C2×C4×Dic3C2×C411yescharacteristic
134C2×C4×Dic3C2×C411yescharacteristic
135C2×C4×Dic3C2×C411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3D411yescharacteristic
141C2×C4×Dic3D411yescharacteristic
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144#898—21no—
145#898—21no—
146#898—21no—
147#898—21no—
148#892—21no—
149#892—21no—
150#892—21no—
151#892—21no—
152#889—21no—
153#889—21no—
154#889—21no—
155#889—21no—
156#887—21no—
157#887—21no—
158#887—21no—
159#887—21no—
160#885—21no—
161#885—21no—
162#885—21no—
163#885—21no—
164#67⋊C4—21no—
165#67⋊C4—21no—
166#67⋊C4—21no—
167#67⋊C4—21no—
168#67⋊C4—21no—
169#67⋊C4—21no—
170#67⋊C4—21no—
171#67⋊C4—21no—
172#879—21no—
173#879—21no—
174#879—21no—
175#879—21no—
176#878—21no—
177#878—21no—
178#878—21no—
179#878—21no—
180#877—21no—
181#877—21no—
182#877—21no—
183#877—21no—
184C3×#99—24no—
185C3×#95—21no—
186C3×#95—21no—
187#834—24no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194#806—24no—
195#806—24no—
196#529—61no—
197#529—61no—
198#529—61no—
199#529—61no—
200#529—61no—
201#529—61no—
202#529—61no—
203#529—61no—
204C2×#126—31no—
205C2×#126—31no—
206C2×#125—31no—
207C2×#124—31no—
208C2×#123—31no—
209C2×#123C2×D311yescharacteristic
210C2×C22⋊Q8—31no—
211C2×#121—31no—
212C2×C4×Q8—31no—
213C2×C4×D4—31no—
214C2×C4×D4—31no—
215C2×C4×D4—31no—
216C2×#117—31no—
217C2×#117—31no—
218C2×#117—31no—
219C2×#117C2×D311yescharacteristic
220C22×C42—31no—
221C2×#99—32no—
222C2×#99—32no—
223C2×#99—32no—
224C2×#99C2×D312yes—
225#383—61no—
226#382—61no—
227#381—31no—
228#381C2×D311yescharacteristic
229#380—32no—
230C4×C4⋊C4—61no—
231C4×C4⋊C4—61no—
232C4×C4⋊C4—61no—
233C4×C22⋊C4—32no—
234C4×C22⋊C4—32no—
235C4×C22⋊C4—32no—
236#376—61no—
237#376—61no—
238C43—61no—
239#342—32no—
240#342—32no—
241#342—32no—
242#342C2×D312yes—
243C24×C3C22×C411yescharacteristic
244C24×C3C2411yescharacteristic
245C23×D3C22×C411yescharacteristic
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—22no—
249C2×C3×D4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C411yescharacteristic
258C22×C3×C4C22×C411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—22no—
266C2×#67—22no—
267C2×#67—21no—
268C2×#67—21no—
269C2×#67—42no—
270C22×Dic3—22no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—22no—
274C22×Dic3—42no—
275C22×Dic3—42no—
276C22×Dic3—42no—
277C22×Dic3C22×C411yescharacteristic
278C22×Dic3C22×C411yescharacteristic
279C22×Dic3C22×C411yescharacteristic
280C22×Dic3C22×C411yescharacteristic
281C22×Dic3C22×C411yescharacteristic
282C22×Dic3C22×C411yescharacteristic
283C22×Dic3C22×C411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286C22×Dic3C2×D411yescharacteristic
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C22×Dic3C2×D411yescharacteristic
291C22×Dic3C2×D411yescharacteristic
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—42no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—42no—
298C3×C4⋊C4—24no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4#4114yes—
313C3×C42—24no—
314#217—21no—
315#217—21no—
316#217—22no—
317#217—21no—
318#217—21no—
319#217—21no—
320#217—21no—
321#217—22no—
322#217—22no—
323#217#4114yes—
324(C2×D3)⋊C4—21no—
325(C2×D3)⋊C4—21no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332C4⋊Dic3—24no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—44no—
350C4×Dic3—24no—
351C4×Dic3—21no—
352C4×Dic3—21no—
353C4×Dic3—21no—
354C4×Dic3—21no—
355C4×Dic3—44no—
356C4×Dic3—44no—
357C4×Dic3—44no—
358C4×Dic3C22⋊C411yescharacteristic
359C4×Dic3C22⋊C411yescharacteristic
360C4×Dic3C22⋊C411yescharacteristic
361C4×Dic3C22⋊C411yescharacteristic
362C4×Dic3C22⋊C411yescharacteristic
363C4×Dic3C22⋊C411yescharacteristic
364C4×Dic3C22⋊C411yescharacteristic
365C4×Dic3C22⋊C411yescharacteristic
366C4×Dic3C22⋊C411yescharacteristic
367C4×Dic3C22⋊C411yescharacteristic
368C4×Dic3C22⋊C411yescharacteristic
369C4×Dic3C22⋊C411yescharacteristic
370C4×Dic3C22⋊C411yescharacteristic
371C4×Dic3C22⋊C411yescharacteristic
372C4×Dic3C22⋊C411yescharacteristic
373C4×Dic3C22⋊C411yescharacteristic
374C22×Q8—31no—
375C22×D4—31no—
376C22×D4—31no—
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4C22×D311yescharacteristic
383#126—61no—
384#126—61no—
385#126—61no—
386#126—61no—
387#126—61no—
388#126—61no—
389#126—61no—
390#126—61no—
391#125—61no—
392#125—61no—
393#125—61no—
394#125—61no—
395#124—61no—
396#124—61no—
397#124—61no—
398#124—61no—
399#123—21no—
400#123—21no—
401#123—21no—
402#123—21no—
403#123—61no—
404#123—61no—
405#123—61no—
406#123—61no—
407C22⋊Q8—61no—
408C22⋊Q8—61no—
409C22⋊Q8—61no—
410C22⋊Q8—61no—
411#121—61no—
412#121—61no—
413#121—61no—
414#121—61no—
415C4×Q8—61no—
416C4×Q8—61no—
417C4×Q8—61no—
418C4×Q8—61no—
419C4×D4—61no—
420C4×D4—61no—
421C4×D4—61no—
422C4×D4—61no—
423C4×D4—61no—
424C4×D4—61no—
425C4×D4—61no—
426C4×D4—61no—
427C4×D4—61no—
428C4×D4—61no—
429C4×D4—61no—
430C4×D4—61no—
431#117—24no—
432#117—61no—
433#117—61no—
434#117—61no—
435#117—61no—
436#117—61no—
437#117—61no—
438#117—61no—
439#117—61no—
440#117—64no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—31no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—61no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4C4×D311yescharacteristic
453C2×C4⋊C4C4×D311yescharacteristic
454C2×C22⋊C4—32no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—32no—
463C2×C22⋊C4C4×D311yescharacteristic
464C2×C22⋊C4C4×D311yescharacteristic
465C2×C22⋊C4C22×D312yes—
466C2×C22⋊C4C22×D311yescharacteristic
467C2×C22⋊C4C22×D312yes—
468C2×C42—21no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—31no—
474C2×C42—31no—
475C2×C42—31no—
476C2×C42—31no—
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—31no—
480C2×C42—31no—
481C2×C42—31no—
482C2×C42—31no—
483C2×C42—61no—
484C2×C42—62no—
485C2×C42—62no—
486C2×C42—62no—
487#99—24no—
488#99—64no—
489#99—64no—
490#99—64no—
491#95—21no—
492#95—21no—
493#95—62no—
494#95—62no—
495#95—62no—
496#95—62no—
497#95—61no—
498#95—61no—
499C23×C3—21no—
500C23×C3—22no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3C23×C411yescharacteristic
506C23×C3C22×D411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C2×#4112yes—
509C23×C3C2×#4112yes—
510C22×D3—21no—
511C22×D3—22no—
512C22×D3—41no—
513C22×D3—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—42no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—24no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537C2×C3×C4C2×C22⋊C411yescharacteristic
538C2×C3×C4C2×C22⋊C411yescharacteristic
539C2×C3×C4C2×C22⋊C411yescharacteristic
540C2×C3×C4C2×C22⋊C411yescharacteristic
541#67—42no—
542#67—41no—
543#67—41no—
544#67—42no—
545#67—42no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—22no—
556C2×Dic3—24no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—42no—
564C2×Dic3—42no—
565C2×Dic3—42no—
566C2×Dic3—42no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—42no—
570C2×Dic3—42no—
571C2×Dic3—42no—
572C2×Dic3C2×C22⋊C411yescharacteristic
573C2×Dic3C2×C22⋊C411yescharacteristic
574C2×Dic3C2×C22⋊C411yescharacteristic
575C2×Dic3C2×C22⋊C411yescharacteristic
576C2×Dic3C2×C22⋊C411yescharacteristic
577C2×Dic3C2×C22⋊C411yescharacteristic
578C2×Dic3C2×C22⋊C411yescharacteristic
579C2×Dic3C2×C22⋊C411yescharacteristic
580C4×D3—42no—
581C4×D3—42no—
582Dic6—42no—
583Dic6—42no—
584C24—31no—
585C24C2×C4×D311yescharacteristic
586C24C23×D311yescharacteristic
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—122no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—62no—
600C2×D4—122no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—122no—
627C22×C4—122no—
628C22×C4—122no—
629C22×C4—122no—
630C22×C4C2×C4×D311yescharacteristic
631C22×C4C2×C4×D311yescharacteristic
632C22×C4C2×C4×D311yescharacteristic
633C22×C4C2×C4×D311yescharacteristic
634C22×C4C2×C4×D311yescharacteristic
635C22×C4D3×D411yescharacteristic
636C22×C4D3×D411yescharacteristic
637C22×C4D3×D411yescharacteristic
638C22×C4D3×D411yescharacteristic
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—64no—
657C4⋊C4—61no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—124no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—34no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C22⋊C4—61no—
681C22⋊C4—61no—
682C22⋊C4—62no—
683C22⋊C4—61no—
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—62no—
688C22⋊C4—62no—
689C22⋊C4#23714yes—
690C42—24no—
691C42—31no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—31no—
697C42—31no—
698C42—31no—
699C42—31no—
700C42—31no—
701C42—31no—
702C42—31no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42—31no—
707C42—61no—
708C42—61no—
709C42—61no—
710C42—61no—
711C42—64no—
712C42—124no—
713C42—124no—
714C42—124no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—82no—
727C22×C3C22×C22⋊C411yescharacteristic
728C22×C3C4×#4112yes—
729C22×C3#52511yescharacteristic
730C22×C3#52511yescharacteristic
731C22×C3#53212yes—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—82no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—44no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—82no—
745Dic3—21no—
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—21no—
750Dic3—21no—
751Dic3—44no—
752Dic3—41no—
753Dic3—41no—
754Dic3—41no—
755Dic3—82no—
756Dic3#41012yes—
757Dic3#41012yes—
758C23—21no—
759C23—22no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—61no—
765C23—62no—
766C23—121no—
767C23—121no—
768C23C22×C4×D311yescharacteristic
769C23C2×D3×D411yescharacteristic
770C23C2×D3×D411yescharacteristic
771C23C2×#23712yes—
772C23D3×#4112yes—
773Q8—122no—
774Q8—122no—
775D4—41no—
776D4—41no—
777D4—42no—
778D4—122no—
779D4—122no—
780D4—121no—
781D4—121no—
782D4—122no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—64no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—62no—
822C2×C4—122no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4D3×C22⋊C411yescharacteristic
840C2×C4D3×C22⋊C411yescharacteristic
841C2×C4D3×C22⋊C411yescharacteristic
842C2×C4D3×C22⋊C411yescharacteristic
843C2×C3—21no—
844C2×C3—22no—
845C2×C3—21no—
846C2×C3—22no—
847C2×C3—81no—
848C2×C3#229711yescharacteristic
849C2×C3C2×#41011yescharacteristic
850C2×C3C2×#41011yescharacteristic
851D3—81no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—82no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—242no—
868C22C2×D3×C22⋊C411yescharacteristic
869C22C4×#23712yes—
870C22#558611yescharacteristic
871C22#559612yes—
872C22#565611yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—32no—
878C4—32no—
879C4—44no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—61no—
884C4—61no—
885C4—61no—
886C4—61no—
887C4—61no—
888C4—61no—
889C4—82no—
890C4—124no—
891C4—121no—
892C4—121no—
893C4—121no—
894C4—242no—
895C3#2142111yescharacteristic, complemented, Sylow
896C2—21no—
897C2—22no—
898C2—21no—
899C2—22no—
900C2—81no—
901C2—241no—
902C2#7465811yescharacteristic
903C2D3×#41011yescharacteristic
904C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1899C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#939C22
cosocleC24×C3C24
hypercenter#1899D3
hypocenterC3#21421
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. Dic3×#117C2semidirect
3. #74051C2semidirect
4. C3×#1899C2semidirect
5. #71705C2semidirect
6. #71595C2semidirect
8. Dic3×#99C2semidirect
9. #69535C2semidirect
10. #68955C2semidirect
11. #68952C2semidirect
28. C2×#898C4semidirect
29. C2×#892C4semidirect
30. C2×#889C4semidirect
31. C2×#887C4semidirect
32. C2×#885C4semidirect
33. C2×#67⋊C4C4semidirect
35. C2×#879C4semidirect
37. C2×#877C4semidirect
68. #1899D3semidirect
895. C3#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#56492
Dic3×#1172
#740512
C3×#18992
#717052
#715952
#700302
Dic3×#992
#695352
#689552
#689522
#214213