Finite Group Databasebeta

← #10827369

Subgroups — #10827369

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5514C211yesmaximal, characteristic, complemented
2#82812C211yesmaximal, characteristic, complemented
3C2×#4810C211yesmaximal, characteristic, complemented
4C2×#4804C211yesmaximal, characteristic, complemented
5C3×#1872C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic, complemented
7#71560C211yesmaximal, characteristic, complemented
8#70276C211yesmaximal, characteristic, complemented
9#70232C211yesmaximal, characteristic, complemented
10#69961C211yesmaximal, characteristic, complemented
11#69957C211yesmaximal, characteristic, complemented
12#68899C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68813C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#930—21no—
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×C4×#67—21no—
25C2×C4×#67C2211yescharacteristic
26C22×D24C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5514—24no—
29#5514—24no—
30C2×#898—21no—
31C2×#895C2211yescharacteristic
32C2×#894—21no—
33C2×#893C2211yescharacteristic
34C2×#892C2211yescharacteristic
35C2×#890C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45#4991—21no—
46#4989—21no—
47#4988C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4960—21no—
53#4956—21no—
54#4810—24no—
55#4804—24no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872D311yescharacteristic, complemented
77#1869—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—41no—
90C2×#239—41no—
91C22×D12—21no—
92C22×D12—21no—
93C22×D12C2311yescharacteristic
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217D411yescharacteristic
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—41no—
114#930—28no—
115#930—22no—
116#930—22no—
117#930—22no—
118#930—41no—
119C4×#67—28no—
120C4×#67—22no—
121C4×#67—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4D411yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—41no—
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146#898—28no—
147#895—22no—
148#895D414yescomplemented
149#894—28no—
150#893—22no—
151#893—22no—
152#892—22no—
153#892D414yescomplemented
154#890—22no—
155#890—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×C22⋊C8—41no—
159#835—22no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—41no—
164#821—22no—
165#821—41no—
166(C2×D3)⋊C8—22no—
167#809—22no—
168#809—22no—
169#809—41no—
170C22×#41—31no—
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8C2×D311yescharacteristic
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4C2×D311yescharacteristic
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—24no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—22no—
244C2×#67—22no—
245C2×#67—41no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—81no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256#239—28no—
257#239—44no—
258#239—44no—
259#239—44no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—24no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—42no—
274C2×D12—81no—
275C2×D12—81no—
276C2×D12C2×D412yes—
277C2×D12#4112yes—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—24no—
283C2×C4×D3—42no—
284C2×C4×D3—42no—
285C2×C4×D3—42no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3C2×D412yes—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C22⋊C4—42no—
305#217—22no—
306#215—44no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—81no—
315(C2×D3)⋊C4—81no—
316C4⋊Dic3—24no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3C2×D412yes—
321Dic3⋊C4—24no—
322Dic3⋊C4—22no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C4×Dic3—24no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332D24—44no—
333D3×C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4—61no—
348C23×C4—21no—
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—62no—
362C22×C8—121no—
363C22×C8—121no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—22no—
371C22⋊Q8—41no—
372#121—34no—
373#121—62no—
374#121—62no—
375#121—62no—
376#121—68no—
377#121—62no—
378#121—121no—
379C4×D4—62no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—68no—
383C4×D4—62no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C42—31no—
410C2×C42—61no—
411#103—22no—
412#103—22no—
413#103—62no—
414#102—62no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—41no—
420C22⋊C8—62no—
421C22⋊C8—121no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3#13512yes—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#12012yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—84no—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484#67—44no—
485#67—48no—
486#67—84no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3#12012yes—
502D12—22no—
503D12—22no—
504D12—22no—
505D12—22no—
506D12—48no—
507D12—41no—
508D12—41no—
509D12—41no—
510D12—41no—
511D12—84no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—48no—
517C4×D3—84no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—31no—
523C24—61no—
524C24—61no—
525C24D3×D411yescharacteristic
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23512yes—
536C2×D4—32no—
537C2×D4—32no—
538C2×D4—64no—
539C2×D4—62no—
540C2×D4—64no—
541C2×D4—62no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—121no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—31no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—64no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—241no—
592C22×C4—241no—
593C22×C4D3×D411yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—32no—
616C4⋊C4—42no—
617C4⋊C4—62no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4D3×D412yes—
624C4⋊C4D3×D412yes—
625C22⋊C4—42no—
626C22⋊C4—64no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—62no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—64no—
637C42—61no—
638C42—61no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3C2×#12011yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3C2×#13511yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57611yescharacteristic
652C22×C3#57711yescharacteristic
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—81no—
679C3×C4#52511yescharacteristic
680C3×C4#53511yescharacteristic
681C3×C4#54611yescharacteristic
682C3×C4#54611yescharacteristic
683Dic3—22no—
684Dic3—41no—
685Dic3—42no—
686Dic3—41no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—32no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—62no—
702C23—62no—
703C23—121no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23#91912yes—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—62no—
722D4—62no—
723D4—62no—
724D4—62no—
725D4—128no—
726D4—124no—
727D4—128no—
728D4—121no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—32no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—84no—
768C2×C4—128no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—244no—
775C2×C4C2×#23511yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×D3×D411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4D3×#4111yescharacteristic
780C2×C4#100911yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3#240411yescharacteristic
787C2×C3#300211yescharacteristic
788C2×C3#301211yescharacteristic
789C2×C3#329711yescharacteristic
790C2×C3#330111yescharacteristic
791C2×C3#330711yescharacteristic
792C2×C3#330911yescharacteristic
793D3—42no—
794D3—82no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—62no—
804C22—62no—
805C22—62no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—122no—
816C22—241no—
817C22—241no—
818C22—241no—
819C22—241no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22#549011yescharacteristic
825C22D3×#12011yescharacteristic
826C22#565411yescharacteristic
827C22#576211yescharacteristic
828C22C2×#91911yescharacteristic
829C22#577411yescharacteristic
830C22#577711yescharacteristic
831C4—42no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—62no—
836C4—81no—
837C4—121no—
838C4—121no—
839C4—122no—
840C4—241no—
841C4#554711yescharacteristic
842C4#555011yescharacteristic
843C4#560711yescharacteristic
844C4#561211yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—122no—
848C2—242no—
849C2—242no—
850C2#7488611yescharacteristic
851C2#7880811yescharacteristic
852C2#7889711yescharacteristic
853C2#8014911yescharacteristic
854C2#8018211yescharacteristic
855C2#8143211yescharacteristic
856C2#8148511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1872C2
socleC23×C3C22×D4
hypercenter#1872D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×#5514C2semidirect
2. #82812C2semidirect
3. C2×#4810C2semidirect
4. C2×#4804C2semidirect
5. C3×#1872C2semidirect
6. #71699C2semidirect
7. #71560C2semidirect
8. #70276C2semidirect
9. #70232C2semidirect
10. #69961C2semidirect
11. #69957C2semidirect
12. #68899C2semidirect
13. #68897C2semidirect
14. #68883C2semidirect
15. #68813C2semidirect
76. #1872D3semidirect
148. #895D4semidirect
153. #892D4semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#55142
#828122
C2×#48102
C2×#48042
C3×#18722
#716992
#715602
#702762
#702322
#699612
#699572
#688992
#688972
#688832
#688132
#239623