Finite Group Databasebeta

← #10826957

Subgroups — #10826957

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×#5828C211yesmaximal, characteristic
2C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C2×#5239C211yesmaximal, characteristic, complemented
5C2×#5186C211yesmaximal, characteristic, complemented
6C2×#5170C211yesmaximal, characteristic, complemented
7#72071C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71693C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70268C211yesmaximal, characteristic, complemented
12#70205C211yesmaximal, characteristic, complemented
13#70200C211yesmaximal, characteristic, complemented
14#69955C211yesmaximal, characteristic, complemented
15#69931C211yesmaximal, characteristic, complemented
16#23922—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic, complemented
21C22×C3×SD16C2211yescharacteristic, complemented
22C2×C3×C22⋊Q8C2211yescharacteristic
23#5828—24no—
24#5828—24no—
25C2×#946C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C2×#946C2211yescharacteristic
28C22×#216C2211yescharacteristic, complemented
29C2×#938C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#937—21no—
32C2×#935—21no—
33C22×#214C2211yescharacteristic, complemented
34C2×C4×#67—21no—
35C2×C4×#67—21no—
36C2×#926C2211yescharacteristic
37C2×#924C2211yescharacteristic
38D3×C22⋊Q8—24no—
39D3×C22⋊Q8—24no—
40C2×#897C2211yescharacteristic
41C2×#896—21no—
42C2×D3×C4⋊C4—21no—
43C2×D3×C4⋊C4C2211yescharacteristic
44C2×D3×C22⋊C4—21no—
45C2×#878—21no—
46C3×#452—24no—
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×C22⋊C8C2211yescharacteristic
50#5239—24no—
51C2×#835C2211yescharacteristic, complemented
52C2×#835C2211yescharacteristic, complemented
53C2×#835C2211yescharacteristic, complemented
54C2×#832C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic
56#5186—24no—
57#5170—24no—
58C2×(C2×D3)⋊C8C2211yescharacteristic
59C2×(C2×D3)⋊C8C2211yescharacteristic
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×(C2×D3)⋊C8C2211yescharacteristic
62C2×#816C2211yescharacteristic, complemented
63C2×#816C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C22×C22⋊Q8—31no—
70C2×#452—31no—
71C2×#452D311yescharacteristic, complemented
72C2×#451—31no—
73C2×#448—31no—
74#2001—31no—
75#2001—31no—
76#2000—31no—
77#2000—31no—
78#1874—31no—
79#1873—31no—
80#1873—31no—
81#1872—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C22×#67—21no—
98C23×Dic3D411yescharacteristic
99C2×D3×Q8—22no—
100C2×D3×Q8—22no—
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—41no—
104C2×D3×Q8—41no—
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—
122C2×C3×SD16—22no—
123C2×C3×SD16—22no—
124C2×C3×SD16—41no—
125C22×C3×C8C2311yescharacteristic
126C22×C3×C8C2311yescharacteristic
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8D414yescomplemented
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136#946—22no—
137#946—22no—
138#946—22no—
139#946—22no—
140#946—22no—
141#946D414yes—
142C2×#216—22no—
143C2×#216—22no—
144C2×#216—41no—
145#938—22no—
146#938—22no—
147#938—22no—
148#938D414yes—
149#937—28no—
150#935—28no—
151C2×#214—22no—
152C2×#214—22no—
153C2×#214—41no—
154C4×#67—28no—
155C4×#67—28no—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160#926—22no—
161#926—22no—
162C2×C4⋊Dic3—21no—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166#924—22no—
167#924D414yescomplemented
168C2×Dic3⋊C4—21no—
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4—21no—
173C2×C4×Dic3—21no—
174C22×C3⋊C8C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176#897—22no—
177#897—22no—
178#896—28no—
179D3×C4⋊C4—28no—
180D3×C4⋊C4—22no—
181D3×C4⋊C4—22no—
182D3×C22⋊C4—28no—
183#878—28no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#835—22no—
189#835—22no—
190#832—22no—
191#830—22no—
192(C2×D3)⋊C8—22no—
193(C2×D3)⋊C8—22no—
194(C2×D3)⋊C8—41no—
195(C2×D3)⋊C8—41no—
196#816—22no—
197#816—22no—
198C22×#41C2×D311yescharacteristic
199C23×Q8—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×Q16C2×D311yescharacteristic, complemented
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×#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—24no—
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#340—31no—
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
260C3×#41—44no—
261C3×#41—44no—
262C3×#41—44no—
263C3×#41—44no—
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×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8C2×D412yes—
275C2×C3×Q8C2×D412yes—
276C2×C3×D4—24no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4C2×D412yes—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—24no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2411yescharacteristic
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—42no—
302C2×#67—42no—
303C2×#67—42no—
304C2×#67—42no—
305C22×Dic3—22no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—22no—
311C22×Dic3—41no—
312C22×Dic3C2×D411yescharacteristic
313C22×Dic3C2×D411yescharacteristic
314D3×Q8—44no—
315D3×Q8—44no—
316D3×Q8—44no—
317D3×Q8—44no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—22no—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—22no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—41no—
339C2×C4×D3—41no—
340C2×C4×D3—42no—
341C2×C4×D3—42no—
342C2×C4×D3—42no—
343C2×C4×D3—42no—
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—
356C3×SD16—44no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4C2×D412yes—
366C3×C22⋊C4—24no—
367#217—24no—
368#217—24no—
369#217—24no—
370#217—24no—
371#216—44no—
372#214—44no—
373(C2×D3)⋊C4—24no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377C4⋊Dic3—24no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C2×D412yes—
382C4⋊Dic3C2×D412yes—
383C4⋊Dic3C2×D412yes—
384Dic3⋊C4—24no—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389C4×Dic3—24no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C25—31no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—41no—
402C2×#41—41no—
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—21no—
414C22×D4—61no—
415C22×D4—61no—
416C22×D4C22×D311yescharacteristic
417C23×C4—21no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—61no—
426C23×C4—61no—
427C23×C4—62no—
428C23×C4—62no—
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—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—34no—
451C22⋊Q8—34no—
452C22⋊Q8—68no—
453C22⋊Q8—62no—
454C22⋊Q8—68no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8#6714yescomplemented
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—31no—
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—61no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—68no—
488C2×C22⋊C4—61no—
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—22no—
506C22⋊C8—62no—
507C22⋊C8—62no—
508C22⋊C8—62no—
509C22⋊C8—121no—
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#12012yes—
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#13512yes—
545C22×D3#13712yes—
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—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—48no—
558C3×D4—41no—
559C3×D4—41no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—48no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4#12012yes—
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4H(5,𝔽2)11yescharacteristic
582C2×C3×C4H(5,𝔽2)11yescharacteristic
583#67—48no—
584#67—48no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—22no—
593C2×Dic3—21no—
594C2×Dic3—44no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3#12012yes—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—44no—
609C4×D3—44no—
610C4×D3—48no—
611C4×D3—48no—
612C4×D3—41no—
613C4×D3—41no—
614C4×D3—41no—
615C4×D3—41no—
616Dic6—22no—
617Dic6—22no—
618Dic6—48no—
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—44no—
637#41—44no—
638#41—44no—
639#41—44no—
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×Q8C2×#6712yes—
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—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—31no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—31no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—62no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—62no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—62no—
709C22×C4—62no—
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—124no—
719C22×C4—124no—
720C22×C4—124no—
721C22×C4—124no—
722C22×C4—122no—
723C22×C4—122no—
724C22×C4—122no—
725C22×C4—122no—
726C22×C4—121no—
727C22×C4D3×D411yescharacteristic
728C22×C4D3×D412yes—
729C22×C4C2×#6712yes—
730C22×C4C23×D311yescharacteristic
731Q16—44no—
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—32no—
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⋊C4—61no—
761C4⋊C4C2×#6712yes—
762C22⋊C4—24no—
763C22⋊C4—64no—
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—22no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4D4211yescharacteristic
813C3×C4D4211yescharacteristic
814C3×C4D4211yescharacteristic
815C3×C4D4211yescharacteristic
816Dic3—22no—
817Dic3—42no—
818Dic3—41no—
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#93712yes—
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—22no—
872D4—22no—
873D4—48no—
874D4—41no—
875D4—41no—
876D4—128no—
877D4—128no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—32no—
888C2×C4—48no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—61no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—124no—
909C2×C4—124no—
910C2×C4—128no—
911C2×C4—128no—
912C2×C4—124no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4#93712yes—
926C2×C4C2×D3×D411yescharacteristic
927C2×C4C2×D3×D411yescharacteristic
928C2×C4C2×D3×D411yescharacteristic
929C2×C4#100411yescharacteristic
930C2×C4#100411yescharacteristic
931C2×C4C22×#6711yescharacteristic
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
977C22#558911yescharacteristic
978C22D3×#13511yescharacteristic
979C22#576811yescharacteristic
980C22D3×#13711yescharacteristic
981C22D3×#13711yescharacteristic
982C22C2×#93711yescharacteristic
983C4—22no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—62no—
988C4—122no—
989C4—122no—
990C4—121no—
991C4—122no—
992C4—122no—
993C4#559011yescharacteristic
994C4#559011yescharacteristic
995C4D4×#6711yescharacteristic
996C4D4×#6711yescharacteristic
997C3#2392211yescharacteristic, complemented, Sylow
998C2—42no—
999C2—64no—
1000C2—82no—
1001C2—122no—
1002C2D3×#45211yescharacteristic
1003C2#8022811yescharacteristic
1004C2#8023311yescharacteristic
1005C2#8023511yescharacteristic
1006C2#8260411yescharacteristic
1007C2#8391111yescharacteristic
1008C2#8397911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC2×#5828C2
hypercenterC2×#452D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×D3×C22⋊Q8C2semidirect
3. C2×C3×#452C2semidirect
4. C2×#5239C2semidirect
5. C2×#5186C2semidirect
6. C2×#5170C2semidirect
7. #72071C2semidirect
8. #72054C2semidirect
9. #71693C2semidirect
10. #70273C2semidirect
11. #70268C2semidirect
12. #70205C2semidirect
13. #70200C2semidirect
14. #69955C2semidirect
15. #69931C2semidirect
20. C22×C3×Q16C22semidirect
21. C22×C3×SD16C22semidirect
28. C22×#216C22semidirect
33. C22×#214C22semidirect
47. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
51. C2×#835C22semidirect
52. C2×#835C22semidirect
53. C2×#835C22semidirect
54. C2×#832C22semidirect
62. C2×#816C22semidirect
63. C2×#816C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
71. C2×#452D3semidirect
128. C3×C22⋊Q8D4semidirect
167. #924D4semidirect
202. C22×Q16C2×D3semidirect
204. C22×SD16C2×D3semidirect
236. C2×#103C2×D3semidirect
238. C2×#102C2×D3semidirect
462. C22⋊Q8#67semidirect
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×#58282
C2×D3×C22⋊Q82
C2×C3×#4522
C2×#52392
C2×#51862
C2×#51702
#720712
#720542
#716932
#702732
#702682
#702052
#702002
#699552
#699312
#239223