Finite Group Databasebeta

← #10826963

Subgroups — #10826963

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×#5524C211yesmaximal, characteristic
3C2×#5047C211yesmaximal, characteristic, complemented
4C2×#4809C211yesmaximal, characteristic, complemented
5C2×#4806C211yesmaximal, characteristic, complemented
6C2×#4733C211yesmaximal, characteristic, complemented
7C3×#1873C211yesmaximal, characteristic, complemented
8#71585C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#69955C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23922—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#216C2211yescharacteristic, complemented
24C22×#215C2211yescharacteristic, complemented
25C2×#924C2211yescharacteristic
26C22×Dic12C2211yescharacteristic, complemented
27C22×#204C2211yescharacteristic, complemented
28D3×C22⋊Q8—24no—
29D3×C22⋊Q8—24no—
30#5524—24no—
31#5524—24no—
32C2×#897C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×#896—21no—
36C2×#895C2211yescharacteristic
37C2×#895C2211yescharacteristic
38C2×D3×C4⋊C4—21no—
39C2×D3×C4⋊C4C2211yescharacteristic
40C2×#886—21no—
41C2×#882—21no—
42C2×D3×C22⋊C4—21no—
43C2×#878—21no—
44C2×C4×D12—21no—
45C2×C4×D12—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×#830C2211yescharacteristic
50C2×#821C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×#816C2211yescharacteristic, complemented
56#5047—24no—
57C2×#810C2211yescharacteristic, complemented
58C2×#810C2211yescharacteristic, complemented
59C2×#810C2211yescharacteristic, complemented
60C2×#809C2211yescharacteristic, complemented
61#4809—24no—
62#4806—24no—
63#4733—24no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, 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#2000—31no—
78#1874—31no—
79#1873—31no—
80#1873D311yescharacteristic, complemented
81#1872—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C23×Dic3D411yescharacteristic
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—22no—
92C2×D3×Q8—41no—
93C2×D3×Q8—41no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—41no—
99C2×#235—41no—
100C22×D12—21no—
101C22×D12—21no—
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×C4×D3—21no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—21no—
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
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8D414yescomplemented
123C3×#117—22no—
124C3×#117—22no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C42—21no—
132C2×#217—21no—
133#946—22no—
134#946—22no—
135C2×#216—22no—
136C2×#216—22no—
137C2×#216—41no—
138C2×#215—22no—
139C2×#215—22no—
140C2×#215—41no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×C4⋊Dic3—21no—
148C2×C4⋊Dic3—21no—
149C2×C4⋊Dic3—21no—
150C2×C4⋊Dic3C2311yescharacteristic
151#924—22no—
152#924D414yescomplemented
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4—21no—
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C2×Dic12—22no—
159C2×Dic12—22no—
160C2×Dic12—41no—
161C2×#204—22no—
162C2×#204—22no—
163C2×#204—41no—
164#897—22no—
165#897—22no—
166#897—22no—
167#897—22no—
168#897—22no—
169#897D414yes—
170#896—28no—
171#895—22no—
172#895—22no—
173#895—22no—
174#895D414yes—
175D3×C4⋊C4—28no—
176D3×C4⋊C4—22no—
177D3×C4⋊C4—22no—
178#886—28no—
179#882—28no—
180D3×C22⋊C4—28no—
181#878—28no—
182C4×D12—28no—
183C4×D12—28no—
184C3×#103—22no—
185C3×#103—22no—
186C3×C22⋊C8—22no—
187#830—22no—
188#821—22no—
189(C2×D3)⋊C8—22no—
190(C2×D3)⋊C8—22no—
191(C2×D3)⋊C8—41no—
192(C2×D3)⋊C8—41no—
193#816—22no—
194#810—22no—
195#810—22no—
196#810—22no—
197#809—22no—
198C22×#41—31no—
199C23×Q8—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×Q16—31no—
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—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×#117C2×D311yescharacteristic
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#340C2×D311yescharacteristic, complemented
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×Q8C2×D412yes—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2411yescharacteristic
278C2×#67—24no—
279C2×#67—42no—
280C2×#67—42no—
281C22×Dic3—22no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—22no—
286C22×Dic3—41no—
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289D3×Q8—44no—
290D3×Q8—44no—
291D3×Q8—44no—
292D3×Q8—44no—
293#235—44no—
294#235—44no—
295#235—44no—
296#235—44no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—24no—
302C2×D12—24no—
303C2×D12—21no—
304C2×D12—42no—
305C2×D12—42no—
306C2×D12—42no—
307C2×D12—42no—
308C2×D12C2×D412yes—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
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×D3—42no—
337C2×C4×D3—42no—
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—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C3×C4⋊C4—24no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4C2×D412yes—
366C3×C4⋊C4C2×D412yes—
367C3×C4⋊C4C2×D412yes—
368C3×C22⋊C4—24no—
369C3×C22⋊C4—24no—
370C3×C42—24no—
371#217—24no—
372#216—44no—
373#215—44no—
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—
379(C2×D3)⋊C4—24no—
380C4⋊Dic3—24no—
381C4⋊Dic3—24no—
382C4⋊Dic3—21no—
383C4⋊Dic3—24no—
384C4⋊Dic3C2×D412yes—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8—21no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394Dic12—44no—
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—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—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—62no—
423C23×C4—62no—
424C23×C4—61no—
425C23×C4—61no—
426C23×C4—62no—
427C23×C4—61no—
428C23×C4—62no—
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—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—34no—
451C22⋊Q8—34no—
452C22⋊Q8—68no—
453C22⋊Q8—62no—
454C22⋊Q8—62no—
455C22⋊Q8—62no—
456C22⋊Q8—68no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8D1214yescomplemented
463#121—34no—
464#121—62no—
465#121—62no—
466#121—62no—
467#120—68no—
468C4×D4—68no—
469C4×D4—68no—
470#117—22no—
471#117—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—68no—
476C2×C4⋊C4—61no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4—61no—
479C2×C4⋊C4—61no—
480C2×C4⋊C4—61no—
481C2×C4⋊C4—61no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4C22×D311yescharacteristic
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—21no—
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—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#12012yes—
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#13512yes—
545C22×D3#13712yes—
546C22×D3#13712yes—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8—41no—
550C3×Q8—41no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—41no—
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#12012yes—
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4H(5,𝔽2)11yescharacteristic
575C2×C3×C4H(5,𝔽2)11yescharacteristic
576#67—48no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—22no—
580C2×Dic3—21no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—44no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3#12012yes—
593D12—22no—
594D12—22no—
595D12—48no—
596D12—48no—
597D12—41no—
598D12—41no—
599C4×D3—22no—
600C4×D3—22no—
601C4×D3—22no—
602C4×D3—22no—
603C4×D3—44no—
604C4×D3—44no—
605C4×D3—48no—
606C4×D3—48no—
607C4×D3—48no—
608C4×D3—41no—
609C4×D3—41no—
610C4×D3—41no—
611C4×D3—41no—
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—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—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×Q8C2×D1212yes—
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—31no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—31no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—64no—
697C22×C4—62no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—121no—
715C22×C4—121no—
716C22×C4—124no—
717C22×C4—124no—
718C22×C4—124no—
719C22×C4—124no—
720C22×C4—122no—
721C22×C4—122no—
722C22×C4—122no—
723C22×C4—122no—
724C22×C4—122no—
725C22×C4—121no—
726C22×C4—122no—
727C22×C4C2×D1212yes—
728C22×C4D3×D411yescharacteristic
729C22×C4D3×D412yes—
730C22×C4C23×D311yescharacteristic
731Q16—124no—
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—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
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⋊C4C2×D1212yes—
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—24no—
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—22no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4D4211yescharacteristic
814C3×C4D4211yescharacteristic
815C3×C4D4211yescharacteristic
816C3×C4D4211yescharacteristic
817Dic3—22no—
818Dic3—42no—
819Dic3—42no—
820Dic3—41no—
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#88212yes—
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—62no—
872D4—62no—
873D4—128no—
874D4—128no—
875D4—128no—
876D4—121no—
877D4—121no—
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—22no—
888C2×C4—32no—
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—61no—
898C2×C4—61no—
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—62no—
909C2×C4—124no—
910C2×C4—124no—
911C2×C4—128no—
912C2×C4—128no—
913C2×C4—128no—
914C2×C4—124no—
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#88212yes—
926C2×C4C22×D1211yescharacteristic
927C2×C4C2×D3×D411yescharacteristic
928C2×C4C2×D3×D411yescharacteristic
929C2×C4C2×D3×D411yescharacteristic
930C2×C4#100911yescharacteristic
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—
976C22C2×#88211yescharacteristic
977C22D3×#12011yescharacteristic
978C22#565311yescharacteristic
979C22D3×#13511yescharacteristic
980C22#576811yescharacteristic
981C22D3×#13711yescharacteristic
982C22D3×#13711yescharacteristic
983C4—22no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—62no—
989C4—121no—
990C4—122no—
991C4—122no—
992C4—122no—
993C4D4×D1211yescharacteristic
994C4D4×D1211yescharacteristic
995C4#560911yescharacteristic
996C4#560911yescharacteristic
997C3#2392211yescharacteristic, complemented, Sylow
998C2—42no—
999C2—64no—
1000C2—122no—
1001C2—242no—
1002C2#7488411yescharacteristic
1003C2#7883311yescharacteristic
1004C2#7895811yescharacteristic
1005C2D3×#45211yescharacteristic
1006C2#8022811yescharacteristic
1007C2#8152211yescharacteristic
1008C2#8152311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
prime radicalC2×#5524C2
hypercenter#1873D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
1. C2×D3×C22⋊Q8C2semidirect
3. C2×#5047C2semidirect
4. C2×#4809C2semidirect
5. C2×#4806C2semidirect
6. C2×#4733C2semidirect
7. C3×#1873C2semidirect
8. #71585C2semidirect
9. #70273C2semidirect
10. #70272C2semidirect
11. #69955C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
23. C22×#216C22semidirect
24. C22×#215C22semidirect
26. C22×Dic12C22semidirect
27. C22×#204C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#103C22semidirect
50. C2×#821C22semidirect
55. C2×#816C22semidirect
57. C2×#810C22semidirect
58. C2×#810C22semidirect
59. C2×#810C22semidirect
60. C2×#809C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
80. #1873D3semidirect
122. C3×C22⋊Q8D4semidirect
152. #924D4semidirect
235. C2×#103C2×D3semidirect
236. C2×#103C2×D3semidirect
247. #340C2×D3semidirect
248. #340C2×D3semidirect
462. C22⋊Q8D12semidirect
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×#55242
C2×#50472
C2×#48092
C2×#48062
C2×#47332
C3×#18732
#715852
#702732
#702722
#699552
#688882
#688872
#688802
#688782
#239223