Finite Group Databasebeta

← #10826352

Subgroups — #10826352

Order 768.

1888 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic, complemented
2C2×#5630C211yesmaximal, characteristic
3#82751C211yesmaximal, characteristic, complemented
4C2×#5046C211yesmaximal, characteristic, complemented
5C2×#4806C211yesmaximal, characteristic, complemented
6C2×#4731C211yesmaximal, characteristic, complemented
7C3×#2001C211yesmaximal, characteristic, complemented
8#72072C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#70278C211yesmaximal, characteristic, complemented
11#70276C211yesmaximal, characteristic, complemented
12#70267C211yesmaximal, characteristic, complemented
13#69958C211yesmaximal, characteristic, complemented
14#68896C211yesmaximal, characteristic, complemented
15#68885C211yesmaximal, characteristic, complemented
16#23862—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic, complemented
19C23×D12C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×#947C2211yescharacteristic
24C22×#216C2211yescharacteristic, complemented
25C22×#215C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C2×#918—24no—
30C2×#918—24no—
31C2×#918—24no—
32C22×#204C2211yescharacteristic
33C22×#204C2211yescharacteristic
34C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35#5630—24no—
36#5630—24no—
37C2×#895—21no—
38C2×#895C2211yescharacteristic
39C2×#894—21no—
40C2×#893C2211yescharacteristic
41C2×#882—21no—
42C2×D3×C22⋊C4—21no—
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×C22⋊C8C2211yescharacteristic
46#5229C2211yescharacteristic, complemented
47C2×#835C2211yescharacteristic, complemented
48C2×#830C2211yescharacteristic
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52#5046—24no—
53#4989—21no—
54#4987C2211yescharacteristic, complemented
55#4979—21no—
56#4973C2211yescharacteristic, complemented
57C2×#810C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60#4956—21no—
61#4947—21no—
62#4806—24no—
63#4731—24no—
64C3×#340C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C22×#137—31no—
69C2×#546—31no—
70C2×#448—31no—
71C2×#450—31no—
72C2×#450—31no—
73#2409—31no—
74#2015—31no—
75#2015—31no—
76#2001—31no—
77#2001D311yescharacteristic, complemented
78#1895—31no—
79#1877—31no—
80#1877—31no—
81#1870—31no—
82#1788—31no—
83C24×D3—21no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67D411yescharacteristic
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—41no—
92C2×#239—41no—
93C2×#239D414yes—
94C2×D3×Q8—22no—
95C2×D3×Q8—22no—
96C2×D3×Q8—22no—
97C2×D3×Q8—22no—
98C2×D3×Q8—41no—
99C2×D3×Q8—41no—
100C22×D12—21no—
101C22×D12—21no—
102C22×D12—21no—
103C22×D12—22no—
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12C2311yescharacteristic
110C22×D12C2311yescharacteristic
111C22×C4×D3—21no—
112C22×C4×D3—21no—
113C22×C4×D3—21no—
114C22×C4×D3C2311yescharacteristic
115C22×Dic6—21no—
116C22×Dic6C2311yescharacteristic
117C2×C3×Q16—22no—
118C2×C3×Q16—22no—
119C2×C3×Q16—22no—
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—41no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×#217—21no—
133C2×#217D411yescharacteristic
134#947—22no—
135#947—22no—
136C2×#216—22no—
137C2×#216—22no—
138C2×#216—22no—
139C2×#215—22no—
140C2×#215—22no—
141C2×#215—22no—
142C2×#215—22no—
143C2×#215—41no—
144C2×#215D414yescomplemented
145C4×#67—22no—
146C4×#67—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)⋊C4D411yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154#924—22no—
155#924—41no—
156C2×Dic3⋊C4—21no—
157C2×Dic3⋊C4D411yescharacteristic
158C2×C4×Dic3C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161#918—232no—
162C2×#204—22no—
163C2×#204—22no—
164C2×#204—22no—
165C2×#204—22no—
166C2×#204—41no—
167C2×#204D414yescomplemented
168C2×ΓL(1,𝔽25)—22no—
169C2×ΓL(1,𝔽25)—22no—
170C2×ΓL(1,𝔽25)—22no—
171#895—28no—
172#895—22no—
173#895D414yes—
174#894—28no—
175#893—22no—
176#893—22no—
177#882—28no—
178D3×C22⋊C4—28no—
179C3×#103—22no—
180C3×#103—41no—
181C3×C22⋊C8—22no—
182#835—41no—
183C3⋊#95—21no—
184C3⋊#95—21no—
185C3⋊#95—21no—
186C3⋊#95—21no—
187C3⋊#95—21no—
188#830—22no—
189#821—22no—
190#821—22no—
191(C2×D3)⋊C8—22no—
192#810—22no—
193#809—22no—
194#809—22no—
195C22×#41—31no—
196C23×Q8—31no—
197C23×D4—31no—
198C2×#137—64no—
199C2×#137—64no—
200C2×#137—64no—
201C22×Q16—31no—
202C22×Q16C2×D311yescharacteristic, complemented
203C22×SD16—31no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×M16—31no—
208#546—64no—
209#546—64no—
210C2×#124—31no—
211C2×#123—61no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8C2×D311yescharacteristic
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—31no—
216C2×#121—61no—
217C2×#120—61no—
218C2×C4×D4—31no—
219C2×C4×D4—31no—
220C22×C22⋊C4—61no—
221#450—64no—
222#450—64no—
223#448—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103C2×D311yescharacteristic, complemented
227C2×#103C2×D311yescharacteristic, complemented
228C2×#102—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—31no—
234C2×C22⋊C8C2×D311yescharacteristic
235#395—61no—
236#393—61no—
237#391—31no—
238#391—31no—
239#386—61no—
240#385—61no—
241#380—31no—
242#340—31no—
243#340C2×D311yescharacteristic, complemented
244#336—31no—
245#336—31no—
246C24×C3C2×D411yescharacteristic
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—24no—
250C23×D3—42no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3—42no—
254C23×D3—81no—
255C23×D3—81no—
256C23×D3C2×D411yescharacteristic
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
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×Q8C2×D412yes—
268C2×C3×Q8C2×D412yes—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—22no—
282C2×#67—22no—
283C2×#67—41no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3C2×D411yescharacteristic
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289#239—28no—
290#239—44no—
291#239—44no—
292#239—44no—
293D3×Q8—28no—
294D3×Q8—44no—
295D3×Q8—44no—
296D3×Q8—44no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—24no—
305C2×D12—24no—
306C2×D12—21no—
307C2×D12—24no—
308C2×D12—44no—
309C2×D12—44no—
310C2×D12—44no—
311C2×D12—42no—
312C2×D12—42no—
313C2×D12—42no—
314C2×D12—42no—
315C2×D12—44no—
316C2×D12—81no—
317C2×D12—81no—
318C2×D12C2×D412yes—
319C2×D12C2×D412yes—
320C2×D12C2×D412yes—
321C2×D12C2×D412yes—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—42no—
329C2×C4×D3—42no—
330C2×C4×D3—42no—
331C2×C4×D3—42no—
332C2×C4×D3—42no—
333C2×C4×D3—81no—
334C2×C4×D3—81no—
335C2×C4×D3C2×D412yes—
336C2×C4×D3C2×D412yes—
337C2×Dic6—21no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—42no—
343C2×Dic6—42no—
344C2×Dic6—42no—
345C2×Dic6C2×D412yes—
346C3×Q16—28no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8C2×D412yes—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—42no—
358C3×C4⋊C4C2×D412yes—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—42no—
361#217—22no—
362#217—42no—
363#216—28no—
364#215—28no—
365#215—44no—
366(C2×D3)⋊C4—24no—
367(C2×D3)⋊C4—24no—
368(C2×D3)⋊C4—24no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—24no—
371(C2×D3)⋊C4—42no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374Dic3⋊C4—22no—
375Dic3⋊C4—42no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C2×C3⋊C8—21no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8—21no—
382C2×C3⋊C8—21no—
383C2×C3⋊C8C2×D412yes—
384#204—28no—
385#204—44no—
386ΓL(1,𝔽25)—28no—
387C25—61no—
388C2×#41—34no—
389C2×#41—62no—
390C2×#41—62no—
391C2×#41—62no—
392C2×#41—121no—
393C2×#41—121no—
394C22×Q8—31no—
395C22×Q8—61no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×Q8—121no—
401C22×Q8—121no—
402C22×Q8C22×D311yescharacteristic
403C22×Q8C22×D311yescharacteristic
404C22×D4—31no—
405C22×D4—31no—
406C22×D4—31no—
407C22×D4—62no—
408C22×D4—62no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—61no—
412C22×D4—61no—
413C22×D4—61no—
414C22×D4—121no—
415C22×D4—121no—
416C23×C4—31no—
417C23×C4—61no—
418C23×C4—61no—
419C23×C4—61no—
420C23×C4C22×D311yescharacteristic
421#137—632no—
422C2×Q16—22no—
423C2×Q16—22no—
424C2×Q16—22no—
425C2×Q16—62no—
426C2×Q16—62no—
427C2×Q16—62no—
428C2×SD16—34no—
429C2×SD16—34no—
430C2×SD16—62no—
431C2×SD16—62no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—62no—
435C2×SD16—62no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—121no—
439C2×SD16—121no—
440C2×M16—62no—
441C2×M16—62no—
442C2×M16—62no—
443C22×C8—31no—
444C22×C8—31no—
445C22×C8C22×D311yescharacteristic
446C22×C8C22×D311yescharacteristic
447#124—62no—
448#124—62no—
449#123—68no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—41no—
454C22⋊Q8—62no—
455C22⋊Q8—121no—
456#121—34no—
457#121—62no—
458#121—68no—
459#120—68no—
460C4×D4—62no—
461C4×D4—62no—
462C4×D4—62no—
463C4×D4—62no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—61no—
469C2×C4⋊C4C22×D311yescharacteristic
470C2×C4⋊C4C22×D311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—68no—
476C2×C22⋊C4—61no—
477C2×C22⋊C4—61no—
478C2×C22⋊C4—61no—
479C2×C22⋊C4—61no—
480C2×C22⋊C4—61no—
481C2×C22⋊C4—61no—
482C2×C42—31no—
483#103—22no—
484#103—41no—
485#103—62no—
486#103—121no—
487#102—62no—
488#102—62no—
489#102—62no—
490#102—62no—
491C22⋊C8—22no—
492C22⋊C8—62no—
493C22⋊C8—62no—
494#95—61no—
495#95—61no—
496#95—61no—
497#95—61no—
498#95—61no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3#13712yescomplemented
506C23×C3C22×D411yescharacteristic
507C22×D3—22no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—22no—
517C22×D3—48no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—48no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—84no—
530C22×D3—84no—
531C22×D3—84no—
532C22×D3—84no—
533C22×D3—84no—
534C22×D3#12012yes—
535C3×Q8—22no—
536C3×Q8—22no—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×Q8—41no—
542C3×Q8—41no—
543C2×C3×C4—21no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4H(5,𝔽2)11yescharacteristic
567C2×C3×C4H(5,𝔽2)11yescharacteristic
568#67—44no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—22no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3#12012yes—
584D12—22no—
585D12—22no—
586D12—22no—
587D12—22no—
588D12—22no—
589D12—48no—
590D12—48no—
591D12—41no—
592D12—41no—
593D12—84no—
594D12#12014yes—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—22no—
598C4×D3—22no—
599C4×D3—48no—
600C4×D3—48no—
601C4×D3—84no—
602Dic6—22no—
603Dic6—22no—
604Dic6—48no—
605Dic6—41no—
606Dic6—41no—
607C3×C8—22no—
608C3×C8—41no—
609C3⋊C8—22no—
610C3⋊C8—41no—
611C24—31no—
612C24—64no—
613C24—61no—
614C24—61no—
615C24—122no—
616C24—122no—
617C24—122no—
618C24—122no—
619C24—241no—
620C24—241no—
621C24D3×D411yescharacteristic
622#41—68no—
623#41—124no—
624#41—124no—
625#41—124no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—32no—
637C2×Q8—61no—
638C2×Q8—68no—
639C2×Q8—61no—
640C2×Q8—61no—
641C2×Q8—61no—
642C2×Q8—61no—
643C2×Q8—122no—
644C2×Q8—122no—
645C2×Q8—122no—
646C2×Q8—124no—
647C2×Q8—124no—
648C2×Q8—124no—
649C2×Q8D3×D412yes—
650C2×Q8D3×D412yes—
651C2×D4—32no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—32no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—122no—
669C2×D4—122no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C2×D4—124no—
674C2×D4—122no—
675C2×D4—122no—
676C2×D4—121no—
677C2×D4—241no—
678C2×D4—241no—
679C22×C4—21no—
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—32no—
691C22×C4—32no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—122no—
703C22×C4—122no—
704C22×C4—122no—
705C22×C4—122no—
706C22×C4—122no—
707C22×C4—241no—
708C22×C4—241no—
709C22×C4D3×D411yescharacteristic
710C22×C4C23×D311yescharacteristic
711Q16—28no—
712Q16—68no—
713SD16—68no—
714SD16—68no—
715SD16—124no—
716SD16—124no—
717M16—68no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—32no—
724C2×C8—61no—
725C2×C8—61no—
726C2×C8—61no—
727C2×C8—61no—
728C2×C8—61no—
729C2×C8D3×D412yes—
730C4⋊C4—24no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—62no—
736C4⋊C4—61no—
737C4⋊C4—61no—
738C4⋊C4—122no—
739C4⋊C4D3×D412yes—
740C22⋊C4—24no—
741C22⋊C4—42no—
742C22⋊C4—64no—
743C22⋊C4—62no—
744C22⋊C4—64no—
745C22⋊C4—64no—
746C22⋊C4—64no—
747C22⋊C4—62no—
748C22⋊C4—122no—
749C22⋊C4—122no—
750C42—61no—
751C42—61no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3C2×#12011yescharacteristic
760C22×C3D4211yescharacteristic
761C22×C3D4211yescharacteristic
762C22×C3C2×#13711yescharacteristic
763C22×C3#57511yescharacteristic
764C22×C3#57711yescharacteristic
765C22×C3#57711yescharacteristic
766C2×D3—22no—
767C2×D3—24no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—42no—
775C2×D3—42no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—42no—
779C2×D3—42no—
780C2×D3—42no—
781C2×D3—42no—
782C2×D3—42no—
783C2×D3—816no—
784C2×D3—81no—
785C2×D3—81no—
786C2×D3—81no—
787C2×D3—81no—
788C3×C4—42no—
789C3×C4—42no—
790C3×C4—41no—
791C3×C4—42no—
792C3×C4—81no—
793C3×C4C2×#12011yescharacteristic
794C3×C4#53411yescharacteristic
795C3×C4D4211yescharacteristic
796C3×C4D4211yescharacteristic
797Dic3—22no—
798Dic3—42no—
799Dic3—41no—
800Dic3—41no—
801Dic3—81no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—32no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—62no—
814C23—61no—
815C23—62no—
816C23—61no—
817C23—62no—
818C23—62no—
819C23—128no—
820C23—128no—
821C23—121no—
822C23—121no—
823C23—121no—
824C23—121no—
825C23—121no—
826C23—121no—
827C23—121no—
828C23—121no—
829C23—121no—
830C23—121no—
831C23—244no—
832C23—244no—
833C23—244no—
834C23—244no—
835C23—244no—
836C23#91812yescomplemented
837C23C2×D3×D411yescharacteristic
838Q8—22no—
839Q8—22no—
840Q8—22no—
841Q8—22no—
842Q8—41no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—62no—
847Q8—62no—
848Q8—128no—
849Q8—121no—
850Q8—121no—
851D4—34no—
852D4—62no—
853D4—62no—
854D4—62no—
855D4—62no—
856D4—62no—
857D4—128no—
858D4—128no—
859D4—124no—
860D4—121no—
861D4—121no—
862D4—244no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—32no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—62no—
896C2×C4—128no—
897C2×C4—128no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—244no—
904C2×C4C2×D3×D411yescharacteristic
905C2×C4C2×D3×D411yescharacteristic
906C2×C4C2×D3×D411yescharacteristic
907C2×C4C2×D3×D411yescharacteristic
908C2×C4#100411yescharacteristic
909C2×C4#100911yescharacteristic
910C8—22no—
911C8—41no—
912C8—62no—
913C8—121no—
914C2×C3—42no—
915C2×C3#240311yescharacteristic
916C2×C3#300711yescharacteristic
917C2×C3#300911yescharacteristic
918C2×C3#326611yescharacteristic
919C2×C3#326611yescharacteristic
920C2×C3#327511yescharacteristic
921C2×C3#327511yescharacteristic
922D3—42no—
923D3—44no—
924D3—82no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—64no—
936C22—121no—
937C22—122no—
938C22—122no—
939C22—121no—
940C22—122no—
941C22—122no—
942C22—121no—
943C22—122no—
944C22—121no—
945C22—122no—
946C22—122no—
947C22—122no—
948C22—122no—
949C22—2416no—
950C22—241no—
951C22—241no—
952C22—241no—
953C22—241no—
954C22D3×#12011yescharacteristic
955C22#559011yescharacteristic
956C22#560911yescharacteristic
957C22C2×#91811yescharacteristic
958C22#577011yescharacteristic
959C22#577711yescharacteristic
960C22#577811yescharacteristic
961C4—42no—
962C4—41no—
963C4—42no—
964C4—42no—
965C4—62no—
966C4—81no—
967C4—121no—
968C4—121no—
969C4—122no—
970C4—241no—
971C4D3×#12011yescharacteristic
972C4#560511yescharacteristic
973C4#560911yescharacteristic
974C4#571711yescharacteristic
975C3#2386211yescharacteristic, complemented, Sylow
976C2—42no—
977C2—122no—
978C2—124no—
979C2—242no—
980C2#7675311yescharacteristic
981C2#8018411yescharacteristic
982C2#8020411yescharacteristic
983C2#8022911yescharacteristic
984C2#8026811yescharacteristic
985C2#8077111yescharacteristic
986C2#8092211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC2×#5630C2
hypercenter#2001D3
hypocenterC3#23862
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. C22×#918C2semidirect
3. #82751C2semidirect
4. C2×#5046C2semidirect
5. C2×#4806C2semidirect
6. C2×#4731C2semidirect
7. C3×#2001C2semidirect
8. #72072C2semidirect
9. #71700C2semidirect
10. #70278C2semidirect
11. #70276C2semidirect
12. #70267C2semidirect
13. #69958C2semidirect
14. #68896C2semidirect
15. #68885C2semidirect
18. C22×D3×Q8C22semidirect
20. C22×C3×Q16C22semidirect
24. C22×#216C22semidirect
34. C22×ΓL(1,𝔽25)C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
46. #5229C22semidirect
47. C2×#835C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
54. #4987C22semidirect
56. #4973C22semidirect
57. C2×#810C22semidirect
64. C3×#340C22semidirect
65. #4550C22semidirect
66. #4550C22semidirect
67. #4529C22semidirect
77. #2001D3semidirect
144. C2×#215D4semidirect
167. C2×#204D4semidirect
202. C22×Q16C2×D3semidirect
226. C2×#103C2×D3semidirect
227. C2×#103C2×D3semidirect
243. #340C2×D3semidirect
505. C23×C3#137semidirect
836. C23#918semidirect
975. C3#23862semidirect

Maximal subgroups

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

subgroupindex
C22×#9182
C2×#56302
#827512
C2×#50462
C2×#48062
C2×#47312
C3×#20012
#720722
#717002
#702782
#702762
#702672
#699582
#688962
#688852
#238623