Finite Group Databasebeta

← #10830629

Subgroups — #10830629

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5676C211yesmaximal, characteristic, complemented
2C2×#5057C211yesmaximal, characteristic, complemented
3C2×#4810C211yesmaximal, characteristic, complemented
4C2×#4773C211yesmaximal, characteristic, complemented
5C2×C4×D24C211yesmaximal, characteristic, complemented
6#74239C211yesmaximal, characteristic, complemented
7C3×#1958C211yesmaximal, characteristic, complemented
8#70272C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70244C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#70175C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic, complemented
15#69556C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#215C2211yescharacteristic, complemented
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C22×D24C2211yescharacteristic
25#5676—24no—
26#5676—24no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic, complemented
29C2×#884—21no—
30C2×#883—21no—
31C2×#882—21no—
32C2×D3×C22⋊C4—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic, complemented
41C3×#382C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
49C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C2×#818C2211yescharacteristic, complemented
51#5057—24no—
52#4987C2211yescharacteristic
53#4987C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57#4810—24no—
58#4773—24no—
59C4×D24—24no—
60#4674—21no—
61#4671—21no—
62#4665—21no—
63#4665—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958D311yescharacteristic, complemented
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—41no—
97C2×D3×D4—41no—
98C22×D12—21no—
99C22×D12—21no—
100C22×D12—21no—
101C22×D12D411yescharacteristic
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×#124—22no—
112C3×#124D414yescomplemented
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#217—21no—
119#946—22no—
120#946—22no—
121C2×#215—22no—
122C2×#215—22no—
123C2×#215—41no—
124#938—22no—
125#938—22no—
126C2×#213—22no—
127C2×#213—22no—
128C2×#213—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4D411yescharacteristic
137C2×(C2×D3)⋊C4D411yescharacteristic
138C2×C4⋊Dic3D411yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×Dic3⋊C4—21no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C2×D24—22no—
145C2×D24—22no—
146C2×D24D414yescomplemented
147#895—22no—
148#895—22no—
149#895—41no—
150#895—41no—
151#884—28no—
152#883—28no—
153#882—28no—
154D3×C22⋊C4—28no—
155C4×D12—22no—
156C4×D12—22no—
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12D414yescomplemented
161C3×#103—22no—
162C3×#103—41no—
163C3×#102—22no—
164C3×#102—41no—
165C3×C4×C8—22no—
166C3×#95—21no—
167C3×#95—21no—
168#835—22no—
169#832—22no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#821—22no—
173#821—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177(C2×D3)⋊C8—41no—
178#818—22no—
179#809—22no—
180#809—22no—
181C4⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124C2×D311yescharacteristic
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103C2×D311yescharacteristic, complemented
209C2×#103C2×D311yescharacteristic, complemented
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8C2×D311yescharacteristic, complemented
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382C2×D311yescharacteristic, complemented
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C23×D3C2×D411yescharacteristic
242C23×D3C2×D411yescharacteristic
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8C2×D412yes—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4C2×D412yes—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C2×#67—24no—
262C2×#67—24no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—81no—
266C2×#67—81no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#239—44no—
272#239—44no—
273#239—44no—
274#239—44no—
275D3×D4—44no—
276D3×D4—44no—
277D3×D4—44no—
278D3×D4—44no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—24no—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—21no—
290C2×D12—41no—
291C2×D12—42no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—81no—
298C2×D12—81no—
299C2×D12C2×D412yes—
300C2×D12C2×D412yes—
301C2×D12C2×D412yes—
302C2×D12#4112yes—
303C2×C4×D3—24no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—24no—
317C2×C4×D3—42no—
318C2×C4×D3—42no—
319C2×C4×D3—42no—
320C2×C4×D3—81no—
321C2×C4×D3—81no—
322C2×C4×D3—81no—
323C2×C4×D3—81no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8C2×D412yes—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—24no—
336C3×C42C2×D412yes—
337C3×C42C2×D412yes—
338#217—24no—
339#215—44no—
340#213—44no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—42no—
348(C2×D3)⋊C4—81no—
349(C2×D3)⋊C4—81no—
350C4⋊Dic3—22no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3C2×D412yes—
355Dic3⋊C4—24no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362D24—28no—
363C25—61no—
364C2×#41—62no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—121no—
369C2×#41—121no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—31no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—62no—
381C22×D4—61no—
382C22×D4—62no—
383C22×D4—121no—
384C22×D4—121no—
385C22×D4C22×D311yescharacteristic
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4—61no—
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
394C2×D8—34no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—22no—
405#124D1214yescomplemented
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—68no—
410#121—62no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—34no—
418C4×D4—62no—
419C4×D4—62no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—61no—
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—68no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—62no—
445#103—22no—
446#103—41no—
447#103—62no—
448#102—22no—
449#102—41no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—62no—
455C22⋊C8—62no—
456C22⋊C8—62no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C4×C8—22no—
460#95—21no—
461#95—21no—
462#95—61no—
463#95—61no—
464C23×C3—22no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3C22×D411yescharacteristic
472C22×D3—21no—
473C22×D3—22no—
474C22×D3—21no—
475C22×D3—22no—
476C22×D3—21no—
477C22×D3—22no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—22no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—48no—
490C22×D3—48no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—84no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3#13512yes—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—41no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4#12012yes—
529C2×C3×C4#12012yes—
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C2×#4111yescharacteristic
534C2×C3×C4H(5,𝔽2)11yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536#67—48no—
537#67—84no—
538C2×Dic3—21no—
539C2×Dic3—22no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550D12—22no—
551D12—22no—
552D12—22no—
553D12—22no—
554D12—22no—
555D12—44no—
556D12—48no—
557D12—41no—
558D12—41no—
559D12—84no—
560D12—84no—
561D12#12114yes—
562C4×D3—48no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—41no—
571C4×D3—84no—
572C4×D3—84no—
573C3×C8—22no—
574C3×C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—21no—
578C24—31no—
579C24—31no—
580C24—64no—
581C24—61no—
582C24—61no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—122no—
587C24—241no—
588C24—241no—
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8C2×D1212yes—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—32no—
605C2×D4—32no—
606C2×D4—32no—
607C2×D4—32no—
608C2×D4—62no—
609C2×D4—64no—
610C2×D4—64no—
611C2×D4—64no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—121no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—122no—
630C2×D4—124no—
631C2×D4—124no—
632C2×D4—124no—
633C2×D4—124no—
634C2×D4—241no—
635C2×D4—241no—
636C2×D4—241no—
637C2×D4—241no—
638C2×D4C2×D1212yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—64no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—64no—
659C22×C4—61no—
660C22×C4—122no—
661C22×C4—122no—
662C22×C4—122no—
663C22×C4—241no—
664C22×C4—241no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4D3×D411yescharacteristic
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8D3×D412yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—32no—
690C4⋊C4—64no—
691C4⋊C4—62no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—62no—
700C22⋊C4—62no—
701C22⋊C4—64no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42C2×D1212yes—
708C42D3×D412yes—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3C2×#12011yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3C2×#13511yescharacteristic
720C22×C3#57511yescharacteristic
721C22×C3#57611yescharacteristic
722C22×C3#57611yescharacteristic
723C2×D3—24no—
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—41no—
736C2×D3—42no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—816no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4C2×#12111yescharacteristic
758C3×C4#53511yescharacteristic
759C3×C4D4211yescharacteristic
760C3×C4#54611yescharacteristic
761Dic3—41no—
762Dic3—41no—
763Dic3—42no—
764Dic3—81no—
765C23—22no—
766C23—32no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—61no—
774C23—62no—
775C23—61no—
776C23—62no—
777C23—61no—
778C23—62no—
779C23—61no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—62no—
784C23—61no—
785C23—61no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—128no—
791C23—128no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23—244no—
807C23C2×D3×D411yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—34no—
815D4—41no—
816D4—41no—
817D4—62no—
818D4—62no—
819D4—62no—
820D4—62no—
821D4—62no—
822D4—124no—
823D4—128no—
824D4—128no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4—244no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—62no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—128no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—244no—
865C2×C4—244no—
866C2×C4#88212yes—
867C2×C4#88212yes—
868C2×C4C22×D1211yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4D3×#4111yescharacteristic
873C2×C4#100911yescharacteristic
874C8—22no—
875C8—41no—
876C8—121no—
877C8—121no—
878C2×C3—82no—
879C2×C3#240811yescharacteristic
880C2×C3#300211yescharacteristic
881C2×C3#300811yescharacteristic
882C2×C3#327311yescharacteristic
883C2×C3#328011yescharacteristic
884C2×C3#329711yescharacteristic
885C2×C3#332211yescharacteristic
886D3—42no—
887D3—44no—
888D3—81no—
889D3—82no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—64no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—121no—
902C22—121no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—121no—
908C22—122no—
909C22—121no—
910C22—122no—
911C22—121no—
912C22—122no—
913C22—121no—
914C22—122no—
915C22—122no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—2416no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22C2×#88211yescharacteristic
927C22#567611yescharacteristic
928C22#571711yescharacteristic
929C22D3×#13511yescharacteristic
930C22#576811yescharacteristic
931C22#576911yescharacteristic
932C22#576911yescharacteristic
933C4—22no—
934C4—22no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—121no—
939C4—121no—
940C4—122no—
941C4—241no—
942C4D4×D1211yescharacteristic
943C4#555411yescharacteristic
944C4D3×#12111yescharacteristic
945C4#560711yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—82no—
948C2—122no—
949C2—124no—
950C2—241no—
951C2—242no—
952C2#7643611yescharacteristic
953C2#7883311yescharacteristic
954C2#7883411yescharacteristic
955C2#8165311yescharacteristic
956C2#8165611yescharacteristic
957C2#8182911yescharacteristic
958C2#8183111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1958C2
socleC23×C3C22×D4
hypercenter#1958D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
1. C2×#5676C2semidirect
2. C2×#5057C2semidirect
3. C2×#4810C2semidirect
4. C2×#4773C2semidirect
5. C2×C4×D24C2semidirect
6. #74239C2semidirect
7. C3×#1958C2semidirect
8. #70272C2semidirect
9. #70267C2semidirect
10. #70244C2semidirect
11. #70204C2semidirect
12. #70198C2semidirect
13. #70175C2semidirect
14. #69787C2semidirect
15. #69556C2semidirect
21. C22×#215C22semidirect
28. C2×#895C22semidirect
35. C2×C4×D12C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
40. C2×C3×C4×C8C22semidirect
41. C3×#382C22semidirect
42. C2×#835C22semidirect
45. C2×#821C22semidirect
48. C2×(C2×D3)⋊C8C22semidirect
49. C2×(C2×D3)⋊C8C22semidirect
50. C2×#818C22semidirect
53. #4987C22semidirect
56. C2×C4⋊(C3⋊C8)C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
76. #1958D3semidirect
112. C3×#124D4semidirect
146. C2×D24D4semidirect
160. C4×D12D4semidirect
208. C2×#103C2×D3semidirect
209. C2×#103C2×D3semidirect
221. C2×C4×C8C2×D3semidirect
226. #382C2×D3semidirect
405. #124D12semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#56762
C2×#50572
C2×#48102
C2×#47732
C2×C4×D242
#742392
C3×#19582
#702722
#702672
#702442
#702042
#701982
#701752
#697872
#695562
#242453