Finite Group Databasebeta

← #10826954

Subgroups — #10826954

Order 768.

1928 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5606C211yesmaximal, characteristic
3C2×#5173C211yesmaximal, characteristic, complemented
4C2×#5170C211yesmaximal, characteristic, complemented
5C2×#4809C211yesmaximal, characteristic, complemented
6C2×#4783C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#70269C211yesmaximal, characteristic, complemented
11#70200C211yesmaximal, characteristic, complemented
12#69964C211yesmaximal, characteristic, complemented
13#69955C211yesmaximal, characteristic, complemented
14#68879C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23922—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C22×#216C2211yescharacteristic, complemented
25C2×#938C2211yescharacteristic
26C2×#937—21no—
27C2×D4×Dic3—21no—
28C22×#214C2211yescharacteristic, complemented
29C2×#924C2211yescharacteristic
30C2×#924C2211yescharacteristic
31C22×Dic12C2211yescharacteristic, complemented
32D3×C22⋊Q8—24no—
33D3×C22⋊Q8—24no—
34#5606—24no—
35#5606—24no—
36C2×#897C2211yescharacteristic
37C2×#897C2211yescharacteristic
38C2×#896—21no—
39C2×#892C2211yescharacteristic
40C2×D3×C4⋊C4—21no—
41C2×D3×C4⋊C4C2211yescharacteristic
42C2×#883—21no—
43C2×#67⋊C4—21no—
44C2×D3×C22⋊C4—21no—
45C2×#878—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×#835C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#830C2211yescharacteristic
52#5173—24no—
53#5170—24no—
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×(C2×D3)⋊C8C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×#816C2211yescharacteristic, complemented
59C2×#816C2211yescharacteristic, complemented
60C2×#810C2211yescharacteristic, complemented
61C2×#810C2211yescharacteristic, complemented
62#4809—24no—
63#4783—24no—
64C3×#340C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C22×C22⋊Q8—31no—
70C2×#452—31no—
71C2×#452—31no—
72C2×#451—31no—
73C2×#448—31no—
74#2001—31no—
75#2001—31no—
76#2000—31no—
77#2000D311yescharacteristic, complemented
78#1874—31no—
79#1873—31no—
80#1873—31no—
81#1872—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—21no—
89C22×#67—21no—
90C23×Dic3—21no—
91C23×Dic3D411yescharacteristic
92C2×D3×Q8—22no—
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—22no—
96C2×D3×Q8—41no—
97C2×D3×Q8—41no—
98C2×#237—22no—
99C2×#237—22no—
100C2×#237—22no—
101C2×#237—22no—
102C2×#237—41no—
103C2×#237—41no—
104C22×C4×D3—21no—
105C22×C4×D3—21no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3D411yescharacteristic
113C22×C4×D3D411yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×Dic6—21no—
117C22×Dic6C2311yescharacteristic
118C22×Dic6C2311yescharacteristic
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—41no—
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×#121—22no—
127C3×#121—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136#946—22no—
137#946D414yescomplemented
138C2×#216—22no—
139C2×#216—22no—
140C2×#216—41no—
141#938—22no—
142#938D414yes—
143#937—28no—
144D4×Dic3—28no—
145C2×#214—22no—
146C2×#214—22no—
147C2×#214—41no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156#924—22no—
157#924—22no—
158#924—22no—
159#924—22no—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×Dic3⋊C4—21no—
164C2×C4×Dic3—21no—
165C22×C3⋊C8C2311yescharacteristic
166C22×C3⋊C8C2311yescharacteristic
167C2×Dic12—22no—
168C2×Dic12—22no—
169C2×Dic12—41no—
170#897—22no—
171#897—22no—
172#897D414yes—
173#897D414yescomplemented
174#896—28no—
175#892—22no—
176#892—22no—
177D3×C4⋊C4—28no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180#883—28no—
181#67⋊C4—28no—
182D3×C22⋊C4—28no—
183#878—28no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—41no—
187#835—22no—
188#832—22no—
189#830—41no—
190(C2×D3)⋊C8—22no—
191(C2×D3)⋊C8—22no—
192(C2×D3)⋊C8—22no—
193(C2×D3)⋊C8—22no—
194#816—22no—
195#816—22no—
196#810—22no—
197#810—22no—
198C22×#41—31no—
199C23×Q8—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×Q16—31no—
203C22×SD16—31no—
204C22×SD16C2×D311yescharacteristic, complemented
205#525—64no—
206#525—64no—
207C2×#123—61no—
208C2×C22⋊Q8—31no—
209C2×C22⋊Q8—31no—
210C2×C22⋊Q8—31no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—61no—
214C2×C22⋊Q8—61no—
215C2×C22⋊Q8—64no—
216C2×C22⋊Q8—64no—
217C2×C22⋊Q8C2×D311yescharacteristic
218C2×#121—31no—
219C2×#121C2×D311yescharacteristic
220C2×#120—61no—
221C2×C4×D4—61no—
222C2×C4×D4—61no—
223C2×#117—31no—
224C22×C4⋊C4—31no—
225C22×C4⋊C4—61no—
226C22×C22⋊C4—61no—
227#452—64no—
228#452—64no—
229#451—64no—
230#448—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103—31no—
234C2×#103—31no—
235C2×#103—31no—
236C2×#103C2×D311yescharacteristic, complemented
237C2×#102—31no—
238C2×#102C2×D311yescharacteristic, complemented
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245#340—31no—
246#340—31no—
247#340—31no—
248#340C2×D311yescharacteristic, complemented
249C24×C3—21no—
250C24×C3C2×D411yescharacteristic
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—41no—
257C23×D3—41no—
258C23×D3C2×D411yescharacteristic
259C23×D3C2×D411yescharacteristic
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8C2×D412yes—
266C2×C3×D4—24no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4C2×D412yes—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—42no—
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—42no—
292C22×Dic3—24no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—41no—
300C22×Dic3—42no—
301C22×Dic3—42no—
302C22×Dic3C2×D411yescharacteristic
303C22×Dic3C2×D411yescharacteristic
304D3×Q8—44no—
305D3×Q8—44no—
306D3×Q8—44no—
307D3×Q8—44no—
308#237—44no—
309#237—44no—
310#237—44no—
311#237—44no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3—22no—
325C2×C4×D3—22no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C2×C4×D3—44no—
329C2×C4×D3—44no—
330C2×C4×D3—41no—
331C2×C4×D3—41no—
332C2×C4×D3—42no—
333C2×C4×D3—42no—
334C2×C4×D3—42no—
335C2×C4×D3—42no—
336C2×C4×D3C2×D412yes—
337C2×C4×D3C2×D412yes—
338C2×C4×D3C2×D412yes—
339C2×C4×D3C2×D412yes—
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—21no—
343C2×Dic6—21no—
344C2×Dic6—21no—
345C2×Dic6—21no—
346C2×Dic6—21no—
347C2×Dic6—21no—
348C2×Dic6—24no—
349C2×Dic6—21no—
350C2×Dic6—21no—
351C2×Dic6—42no—
352C2×Dic6—42no—
353C2×Dic6C2×D412yes—
354C2×Dic6C2×D412yes—
355C3×SD16—44no—
356C2×C3×C8—21no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C3×C4⋊C4—24no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4C2×D412yes—
366C3×C4⋊C4C2×D412yes—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—24no—
369#217—24no—
370#217—24no—
371#217—24no—
372#216—44no—
373#214—44no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—24no—
381C4⋊Dic3—24no—
382C4⋊Dic3C2×D412yes—
383C4⋊Dic3C2×D412yes—
384Dic3⋊C4—24no—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388C4×Dic3—24no—
389C2×C3⋊C8—21no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395Dic12—44no—
396C25—31no—
397C2×#41—62no—
398C2×#41—62no—
399C2×#41—62no—
400C2×#41—62no—
401C2×#41—121no—
402C2×#41—121no—
403C22×Q8—31no—
404C22×Q8—31no—
405C22×Q8—61no—
406C22×Q8—62no—
407C22×Q8—62no—
408C22×Q8—62no—
409C22×Q8—62no—
410C22×Q8—121no—
411C22×Q8—121no—
412C22×Q8C22×D311yescharacteristic
413C22×D4—21no—
414C22×D4—61no—
415C22×D4—61no—
416C22×D4C22×D311yescharacteristic
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—61no—
427C23×C4—61no—
428C23×C4—61no—
429C23×C4—121no—
430C23×C4—121no—
431C23×C4C22×D311yescharacteristic
432C2×Q16—62no—
433C2×Q16—62no—
434C2×Q16—62no—
435C2×Q16—62no—
436C2×Q16—121no—
437C2×Q16—121no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—41no—
441C2×SD16—62no—
442C2×SD16—62no—
443C2×SD16—121no—
444C22×C8—31no—
445C22×C8—31no—
446C22×C8C22×D311yescharacteristic
447C22×C8C22×D311yescharacteristic
448#123—68no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—34no—
452C22⋊Q8—34no—
453C22⋊Q8—34no—
454C22⋊Q8—68no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—68no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8—62no—
463#121—22no—
464#121—22no—
465#121—34no—
466#121—62no—
467#120—68no—
468C4×D4—68no—
469C4×D4—68no—
470#117—62no—
471#117—62no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—68no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4—61no—
479C2×C4⋊C4—61no—
480C2×C4⋊C4—61no—
481C2×C4⋊C4—61no—
482C2×C4⋊C4—61no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—68no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C42—61no—
497#103—22no—
498#103—62no—
499#103—62no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—22no—
504#102—62no—
505C22⋊C8—41no—
506C22⋊C8—62no—
507C22⋊C8—62no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—121no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—22no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3#13712yes—
525C23×C3C22×D411yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—28no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3—44no—
541C22×D3—44no—
542C22×D3—44no—
543C22×D3#12012yes—
544C22×D3#12012yes—
545C22×D3#13512yes—
546C22×D3#13712yes—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—48no—
554C3×D4—41no—
555C3×D4—41no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—21no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4H(5,𝔽2)11yescharacteristic
577C2×C3×C4H(5,𝔽2)11yescharacteristic
578#67—48no—
579#67—48no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—44no—
589C2×Dic3—48no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3#12012yes—
599C2×Dic3#12012yes—
600C4×D3—22no—
601C4×D3—22no—
602C4×D3—22no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—44no—
609C4×D3—44no—
610C4×D3—48no—
611C4×D3—48no—
612Dic6—22no—
613Dic6—22no—
614Dic6—22no—
615Dic6—22no—
616Dic6—48no—
617Dic6—41no—
618Dic6—41no—
619Dic6—41no—
620Dic6—41no—
621C3×C8—41no—
622C3×C8—41no—
623C3⋊C8—41no—
624C3⋊C8—41no—
625C24—21no—
626C24—31no—
627C24—31no—
628C24—62no—
629C24—62no—
630C24—62no—
631C24—62no—
632C24—62no—
633C24—121no—
634C24—121no—
635C24D3×D411yescharacteristic
636#41—124no—
637#41—124no—
638#41—124no—
639#41—124no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—32no—
646C2×Q8—32no—
647C2×Q8—64no—
648C2×Q8—61no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—61no—
652C2×Q8—61no—
653C2×Q8—61no—
654C2×Q8—61no—
655C2×Q8—61no—
656C2×Q8—61no—
657C2×Q8—61no—
658C2×Q8—122no—
659C2×Q8—122no—
660C2×Q8—124no—
661C2×Q8—124no—
662C2×Q8—124no—
663C2×Q8—124no—
664C2×Q8D3×D412yes—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—64no—
674C2×D4—64no—
675C2×D4—122no—
676C2×D4—122no—
677C2×D4—122no—
678C2×D4—122no—
679C2×D4D3×D412yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—32no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—64no—
700C22×C4—64no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—64no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—121no—
717C22×C4—121no—
718C22×C4—122no—
719C22×C4—124no—
720C22×C4—124no—
721C22×C4—124no—
722C22×C4—124no—
723C22×C4—122no—
724C22×C4—122no—
725C22×C4—122no—
726C22×C4—122no—
727C22×C4—121no—
728C22×C4—122no—
729C22×C4D3×D411yescharacteristic
730C22×C4C23×D311yescharacteristic
731Q16—124no—
732Q16—124no—
733SD16—44no—
734SD16—124no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—61no—
742C2×C8—61no—
743C2×C8—61no—
744C2×C8—61no—
745C2×C8—61no—
746C2×C8—61no—
747C4⋊C4—24no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—32no—
751C4⋊C4—32no—
752C4⋊C4—64no—
753C4⋊C4—64no—
754C4⋊C4—64no—
755C4⋊C4—64no—
756C4⋊C4—64no—
757C4⋊C4—64no—
758C4⋊C4—61no—
759C4⋊C4—61no—
760C4⋊C4D3×D412yes—
761C4⋊C4D3×D412yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—64no—
765C22⋊C4—64no—
766C22⋊C4—64no—
767C22⋊C4—64no—
768C22⋊C4—64no—
769C22⋊C4—64no—
770C22⋊C4—64no—
771C42—64no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3C2×#12011yescharacteristic
787C22×C3C2×#12011yescharacteristic
788C22×C3#53411yescharacteristic
789C22×C3C2×#13511yescharacteristic
790C22×C3C2×#13711yescharacteristic
791C22×C3C2×#13711yescharacteristic
792C22×C3#57511yescharacteristic
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—416no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—41no—
806C2×D3—41no—
807C2×D3#45214yescomplemented
808C3×C4—42no—
809C3×C4—41no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4D4211yescharacteristic
813C3×C4D4211yescharacteristic
814C3×C4D4211yescharacteristic
815C3×C4D4211yescharacteristic
816Dic3—22no—
817Dic3—22no—
818Dic3—42no—
819Dic3—42no—
820Dic3—42no—
821Dic3—42no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—22no—
829C23—32no—
830C23—32no—
831C23—32no—
832C23—32no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—68no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—124no—
851C23—124no—
852C23—124no—
853C23—124no—
854C23—124no—
855C23—124no—
856C23#91512yes—
857C23C2×D3×D411yescharacteristic
858Q8—22no—
859Q8—22no—
860Q8—41no—
861Q8—41no—
862Q8—62no—
863Q8—62no—
864Q8—62no—
865Q8—62no—
866Q8—128no—
867Q8—121no—
868Q8—121no—
869Q8—121no—
870Q8—121no—
871D4—22no—
872D4—22no—
873D4—48no—
874D4—41no—
875D4—41no—
876D4—128no—
877D4—128no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—124no—
913C2×C4—124no—
914C2×C4—128no—
915C2×C4—128no—
916C2×C4—124no—
917C2×C4—128no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4C2×D3×D411yescharacteristic
927C2×C4C2×D3×D411yescharacteristic
928C2×C4C2×D3×D411yescharacteristic
929C2×C4C2×D3×D411yescharacteristic
930C2×C4#100411yescharacteristic
931C2×C4#100911yescharacteristic
932C8—41no—
933C8—41no—
934C8—121no—
935C8—121no—
936C2×C3—42no—
937C2×C3—82no—
938C2×C3#240311yescharacteristic
939C2×C3C2×#45211yescharacteristic
940C2×C3#300211yescharacteristic
941C2×C3#300411yescharacteristic
942C2×C3#300711yescharacteristic
943C2×C3#319011yescharacteristic
944C2×C3#319611yescharacteristic
945D3—24no—
946D3—42no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—34no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—1216no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22D3×#12011yescharacteristic
977C22D3×#12011yescharacteristic
978C22#560511yescharacteristic
979C22C2×#91511yescharacteristic
980C22D3×#13511yescharacteristic
981C22#577311yescharacteristic
982C22D3×#13711yescharacteristic
983C4—42no—
984C4—41no—
985C4—42no—
986C4—42no—
987C4—62no—
988C4—62no—
989C4—122no—
990C4—122no—
991C4—122no—
992C4—122no—
993C4#559011yescharacteristic
994C4#560911yescharacteristic
995C4#560911yescharacteristic
996C4#571711yescharacteristic
997C3#2392211yescharacteristic, complemented, Sylow
998C2—42no—
999C2—64no—
1000C2—82no—
1001C2—122no—
1002C2#7675311yescharacteristic
1003C2#8003911yescharacteristic
1004C2#8008211yescharacteristic
1005C2#8014711yescharacteristic
1006C2D3×#45211yescharacteristic
1007C2#8066511yescharacteristic
1008C2#8081311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5606C2
hypercenter#2000D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×D3×C22⋊Q8C2semidirect
3. C2×#5173C2semidirect
4. C2×#5170C2semidirect
5. C2×#4809C2semidirect
6. C2×#4783C2semidirect
7. C3×#2000C2semidirect
8. #71700C2semidirect
9. #71685C2semidirect
10. #70269C2semidirect
11. #70200C2semidirect
12. #69964C2semidirect
13. #69955C2semidirect
14. #68879C2semidirect
15. #68878C2semidirect
20. C22×C3×SD16C22semidirect
24. C22×#216C22semidirect
28. C22×#214C22semidirect
31. C22×Dic12C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#102C22semidirect
49. C2×#835C22semidirect
50. C2×#832C22semidirect
58. C2×#816C22semidirect
59. C2×#816C22semidirect
60. C2×#810C22semidirect
61. C2×#810C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
77. #2000D3semidirect
137. #946D4semidirect
173. #897D4semidirect
204. C22×SD16C2×D3semidirect
236. C2×#103C2×D3semidirect
238. C2×#102C2×D3semidirect
248. #340C2×D3semidirect
807. C2×D3#452semidirect
997. C3#23922semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C2×#56062
C2×#51732
C2×#51702
C2×#48092
C2×#47832
C3×#20002
#717002
#716852
#702692
#702002
#699642
#699552
#688792
#688782
#239223