Finite Group Databasebeta

← #10826960

Subgroups — #10826960

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×#5627C211yesmaximal, characteristic
3C2×#5187C211yesmaximal, characteristic, complemented
4C2×#5186C211yesmaximal, characteristic, complemented
5C2×#4808C211yesmaximal, characteristic, complemented
6C2×#4806C211yesmaximal, characteristic, complemented
7C3×#2001C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#70269C211yesmaximal, characteristic, complemented
11#70268C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13#69955C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68879C211yesmaximal, characteristic, complemented
16#23922—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C22×#216C2211yescharacteristic, complemented
26C22×#215C2211yescharacteristic, complemented
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×#204C2211yescharacteristic, complemented
30#5627—24no—
31#5627—24no—
32D3×C22⋊Q8—24no—
33D3×C22⋊Q8—24no—
34C2×#897C2211yescharacteristic
35C2×#896—21no—
36C2×#895C2211yescharacteristic
37C2×#894—21no—
38C2×#893—21no—
39C2×#892C2211yescharacteristic
40C2×D3×C4⋊C4—21no—
41C2×D3×C4⋊C4C2211yescharacteristic
42C2×#882—21no—
43C2×#67⋊C4—21no—
44C2×D3×C22⋊C4—21no—
45C2×#878—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×#835C2211yescharacteristic, complemented
50C2×#835C2211yescharacteristic, complemented
51C2×#830C2211yescharacteristic
52#5187—24no—
53#5186—24no—
54C2×#821C2211yescharacteristic, complemented
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×(C2×D3)⋊C8C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×(C2×D3)⋊C8C2211yescharacteristic
59C2×#816C2211yescharacteristic, complemented
60C2×#810C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic, complemented
62#4808—24no—
63#4806—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#2001D311yescharacteristic, complemented
76#2000—31no—
77#2000—31no—
78#1874—31no—
79#1873—31no—
80#1873—31no—
81#1872—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C23×Dic3D411yescharacteristic
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—22no—
93C2×#239—41no—
94C2×#239—41no—
95C2×D3×Q8—22no—
96C2×D3×Q8—22no—
97C2×D3×Q8—22no—
98C2×D3×Q8—22no—
99C2×D3×Q8—41no—
100C2×D3×Q8—41no—
101C22×D12—21no—
102C22×D12—21no—
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3D411yescharacteristic
114C22×C4×D3D411yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×Dic6—21no—
118C22×Dic6C2311yescharacteristic
119C2×C3×Q16—22no—
120C2×C3×Q16—22no—
121C2×C3×Q16—41no—
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—22no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×#217—21no—
135#946—22no—
136#946—22no—
137#946D414yes—
138#946D414yescomplemented
139C2×#216—22no—
140C2×#216—22no—
141C2×#216—41no—
142C2×#215—22no—
143C2×#215—22no—
144C2×#215—41no—
145#930—22no—
146#930—22no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156#924—22no—
157#924—22no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—21no—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×C4×Dic3—21no—
163C22×C3⋊C8C2311yescharacteristic
164C22×C3⋊C8C2311yescharacteristic
165C2×#204—22no—
166C2×#204—22no—
167C2×#204—41no—
168#897—22no—
169#897D414yescomplemented
170#896—28no—
171#895—22no—
172#895D414yes—
173#894—28no—
174#893—28no—
175#892—22no—
176#892—22no—
177D3×C4⋊C4—28no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180#882—28no—
181#67⋊C4—28no—
182D3×C22⋊C4—28no—
183#878—28no—
184C3×#103—22no—
185C3×#103—22no—
186C3×C22⋊C8—41no—
187#835—22no—
188#835—22no—
189#830—41no—
190#821—22no—
191(C2×D3)⋊C8—22no—
192(C2×D3)⋊C8—22no—
193(C2×D3)⋊C8—22no—
194(C2×D3)⋊C8—22no—
195#816—22no—
196#810—22no—
197#809—22no—
198C22×#41—31no—
199C23×Q8—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×Q16C2×D311yescharacteristic, complemented
203C22×SD16—31no—
204C22×SD16—31no—
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—61no—
213C2×C22⋊Q8—61no—
214C2×C22⋊Q8—64no—
215C2×C22⋊Q8—64no—
216C2×C22⋊Q8C2×D311yescharacteristic
217C2×C22⋊Q8C2×D311yescharacteristic
218C2×#121—31no—
219C2×#121—31no—
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×#103C2×D311yescharacteristic, complemented
236C2×#103C2×D311yescharacteristic, complemented
237C2×#102—31no—
238C2×#102—31no—
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×C3C2×D411yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—21no—
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×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8C2×D412yes—
271C2×C3×Q8C2×D412yes—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—42no—
286C2×#67—42no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—41no—
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295#239—44no—
296#239—44no—
297#239—44no—
298#239—44no—
299D3×Q8—44no—
300D3×Q8—44no—
301D3×Q8—44no—
302D3×Q8—44no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—21no—
307C2×D12—24no—
308C2×D12—24no—
309C2×D12—21no—
310C2×D12—42no—
311C2×D12—42no—
312C2×D12—42no—
313C2×D12—42no—
314C2×D12C2×D412yes—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—24no—
324C2×C4×D3—24no—
325C2×C4×D3—24no—
326C2×C4×D3—22no—
327C2×C4×D3—22no—
328C2×C4×D3—22no—
329C2×C4×D3—22no—
330C2×C4×D3—44no—
331C2×C4×D3—44no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—41no—
335C2×C4×D3—41no—
336C2×C4×D3—42no—
337C2×C4×D3—42no—
338C2×C4×D3—42no—
339C2×C4×D3—42no—
340C2×C4×D3—42no—
341C2×C4×D3—42no—
342C2×C4×D3C2×D412yes—
343C2×C4×D3C2×D412yes—
344C2×C4×D3C2×D412yes—
345C2×C4×D3C2×D412yes—
346C2×Dic6—21no—
347C2×Dic6—21no—
348C2×Dic6—21no—
349C2×Dic6—21no—
350C2×Dic6—24no—
351C2×Dic6—21no—
352C2×Dic6—42no—
353C2×Dic6—42no—
354C2×Dic6C2×D412yes—
355C3×Q16—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—24no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4C2×D412yes—
367C3×C4⋊C4C2×D412yes—
368C3×C22⋊C4—24no—
369C3×C22⋊C4—24no—
370#217—24no—
371#216—44no—
372#215—44no—
373(C2×D3)⋊C4—24no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
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—
395#204—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—61no—
405C22×Q8—62no—
406C22×Q8—62no—
407C22×Q8—62no—
408C22×Q8—62no—
409C22×Q8—121no—
410C22×Q8—121no—
411C22×Q8C22×D311yescharacteristic
412C22×Q8C22×D311yescharacteristic
413C22×D4—31no—
414C22×D4—61no—
415C22×D4—61no—
416C22×D4—61no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—61no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—61no—
428C23×C4—61no—
429C23×C4—121no—
430C23×C4—121no—
431C23×C4C22×D311yescharacteristic
432C2×Q16—22no—
433C2×Q16—22no—
434C2×Q16—41no—
435C2×Q16—62no—
436C2×Q16—62no—
437C2×Q16—121no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—121no—
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—22no—
452C22⋊Q8—22no—
453C22⋊Q8—34no—
454C22⋊Q8—34no—
455C22⋊Q8—34no—
456C22⋊Q8—68no—
457C22⋊Q8—62no—
458C22⋊Q8—68no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8—62no—
463#121—34no—
464#121—62no—
465#121—62no—
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—21no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—68no—
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—22no—
499#103—62no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—62no—
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#13712yes—
518C23×C3C22×D411yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—28no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—22no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3#12012yes—
544C22×D3#12012yes—
545C22×D3#13512yes—
546C22×D3#13712yes—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8—22no—
550C3×Q8—22no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—41no—
555C2×C3×C4—22no—
556C2×C3×C4—21no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
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×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D411yescharacteristic
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4H(5,𝔽2)11yescharacteristic
579C2×C3×C4H(5,𝔽2)11yescharacteristic
580#67—48no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—44no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3#12012yes—
596C2×Dic3#12012yes—
597D12—22no—
598D12—22no—
599D12—48no—
600D12—48no—
601D12—41no—
602D12—41no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—22no—
611C4×D3—44no—
612C4×D3—44no—
613C4×D3—48no—
614C4×D3—48no—
615C4×D3—48no—
616Dic6—22no—
617Dic6—22no—
618Dic6—48no—
619Dic6—41no—
620Dic6—41no—
621C3×C8—41no—
622C3×C8—41no—
623C3⋊C8—41no—
624C3⋊C8—41no—
625C24—31no—
626C24—31no—
627C24—62no—
628C24—62no—
629C24—62no—
630C24—62no—
631C24—62no—
632C24—61no—
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—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—32no—
651C2×Q8—64no—
652C2×Q8—61no—
653C2×Q8—61no—
654C2×Q8—61no—
655C2×Q8—61no—
656C2×Q8—61no—
657C2×Q8—122no—
658C2×Q8—122no—
659C2×Q8—124no—
660C2×Q8—124no—
661C2×Q8—124no—
662C2×Q8—124no—
663C2×Q8D3×D412yes—
664C2×Q8D3×D412yes—
665C2×D4—32no—
666C2×D4—64no—
667C2×D4—64no—
668C2×D4—64no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—122no—
675C2×D4—122no—
676C2×D4—122no—
677C2×D4—122no—
678C2×D4—122no—
679C2×D4—122no—
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—21no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—64no—
701C22×C4—64no—
702C22×C4—64no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
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—122no—
728C22×C4—121no—
729C22×C4D3×D411yescharacteristic
730C22×C4C23×D311yescharacteristic
731Q16—44no—
732Q16—124no—
733SD16—124no—
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—24no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—32no—
752C4⋊C4—32no—
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×C3C2×#12011yescharacteristic
780C22×C3C2×#12011yescharacteristic
781C22×C3#53411yescharacteristic
782C22×C3C2×#13511yescharacteristic
783C22×C3C2×#13711yescharacteristic
784C22×C3C2×#13711yescharacteristic
785C22×C3#57511yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—416no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—42no—
801C2×D3—42no—
802C2×D3—42no—
803C2×D3—81no—
804C2×D3—81no—
805C2×D3—81no—
806C2×D3—81no—
807C2×D3#45214yescomplemented
808C3×C4—42no—
809C3×C4—41no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4D4211yescharacteristic
814C3×C4D4211yescharacteristic
815C3×C4D4211yescharacteristic
816C3×C4D4211yescharacteristic
817Dic3—22no—
818Dic3—22no—
819Dic3—42no—
820Dic3—42no—
821Dic3—42no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—32no—
829C23—32no—
830C23—32no—
831C23—32no—
832C23—68no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—62no—
844C23—124no—
845C23—124no—
846C23—124no—
847C23—124no—
848C23—124no—
849C23—124no—
850C23—121no—
851C23—121no—
852C23—121no—
853C23—121no—
854C23—121no—
855C23—121no—
856C23#91812yes—
857C23C2×D3×D411yescharacteristic
858Q8—22no—
859Q8—22no—
860Q8—22no—
861Q8—22no—
862Q8—41no—
863Q8—41no—
864Q8—41no—
865Q8—41no—
866Q8—62no—
867Q8—62no—
868Q8—128no—
869Q8—121no—
870Q8—121no—
871D4—62no—
872D4—62no—
873D4—128no—
874D4—128no—
875D4—128no—
876D4—121no—
877D4—121no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—32no—
886C2×C4—32no—
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—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
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—62no—
913C2×C4—62no—
914C2×C4—124no—
915C2×C4—124no—
916C2×C4—128no—
917C2×C4—128no—
918C2×C4—128no—
919C2×C4—124no—
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#240311yescharacteristic
938C2×C3C2×#45211yescharacteristic
939C2×C3#300211yescharacteristic
940C2×C3#300411yescharacteristic
941C2×C3#300711yescharacteristic
942C2×C3#319011yescharacteristic
943C2×C3#319611yescharacteristic
944D3—24no—
945D3—42no—
946D3—82no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—34no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—1216no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—122no—
970C22—122no—
971C22—122no—
972C22—241no—
973C22—241no—
974C22—241no—
975C22—241no—
976C22D3×#12011yescharacteristic
977C22D3×#12011yescharacteristic
978C22#560511yescharacteristic
979C22C2×#91811yescharacteristic
980C22D3×#13511yescharacteristic
981C22D3×#13711yescharacteristic
982C22#577711yescharacteristic
983C4—42no—
984C4—42no—
985C4—41no—
986C4—42no—
987C4—42no—
988C4—62no—
989C4—62no—
990C4—122no—
991C4—122no—
992C4—122no—
993C4#559011yescharacteristic
994C4#560911yescharacteristic
995C4#560911yescharacteristic
996C4#571711yescharacteristic
997C3#2392211yescharacteristic, complemented, Sylow
998C2—42no—
999C2—64no—
1000C2—122no—
1001C2—242no—
1002C2#7675311yescharacteristic
1003C2#8018311yescharacteristic
1004C2#8018411yescharacteristic
1005C2D3×#45211yescharacteristic
1006C2#8022611yescharacteristic
1007C2#8076411yescharacteristic
1008C2#8090911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC2×#5627C2
hypercenter#2001D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C2×D3×C22⋊Q8C2semidirect
3. C2×#5187C2semidirect
4. C2×#5186C2semidirect
5. C2×#4808C2semidirect
6. C2×#4806C2semidirect
7. C3×#2001C2semidirect
8. #71700C2semidirect
9. #71699C2semidirect
10. #70269C2semidirect
11. #70268C2semidirect
12. #69962C2semidirect
13. #69955C2semidirect
14. #68880C2semidirect
15. #68879C2semidirect
20. C22×C3×Q16C22semidirect
25. C22×#216C22semidirect
26. C22×#215C22semidirect
29. C22×#204C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#103C22semidirect
49. C2×#835C22semidirect
50. C2×#835C22semidirect
54. C2×#821C22semidirect
59. C2×#816C22semidirect
60. C2×#810C22semidirect
61. C2×#809C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
75. #2001D3semidirect
138. #946D4semidirect
169. #897D4semidirect
202. C22×Q16C2×D3semidirect
235. C2×#103C2×D3semidirect
236. C2×#103C2×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×#56272
C2×#51872
C2×#51862
C2×#48082
C2×#48062
C3×#20012
#717002
#716992
#702692
#702682
#699622
#699552
#688802
#688792
#239223