Finite Group Databasebeta

← #10827358

Subgroups — #10827358

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×#5614C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3#84097C211yesmaximal, characteristic, complemented
4C2×#5233C211yesmaximal, characteristic, complemented
5#72054C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7#72043C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71681C211yesmaximal, characteristic, complemented
10#70268C211yesmaximal, characteristic, complemented
11#70232C211yesmaximal, characteristic, complemented
12#70200C211yesmaximal, characteristic, complemented
13#70164C211yesmaximal, characteristic, complemented
14#69952C211yesmaximal, characteristic, complemented
15#69926C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#938—21no—
23C2×#938C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#935—21no—
26C2×D4×Dic3C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C2×#926C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30#5614—24no—
31#5614—24no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890C2211yescharacteristic
34C2×#67⋊C4—21no—
35C2×#879—21no—
36C3×#449—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5233—24no—
41#5229C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5222—21no—
46#5221C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51#5213—21no—
52#5212C2211yescharacteristic
53#5210—21no—
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#449D311yescharacteristic, complemented
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#1872—31no—
77#1869—31no—
78#1825—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C22×#67—21no—
93C22×#67—21no—
94C22×#67D411yescharacteristic
95C23×Dic3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—41no—
101C2×C3×D8—22no—
102C2×C3×D8—22no—
103C2×C3×D8—41no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×#121—22no—
107C3×#121D414yescomplemented
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118#946—22no—
119#946—41no—
120#938—28no—
121#938—22no—
122#938—22no—
123#938—22no—
124#938—41no—
125#935—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128C4×#67—22no—
129C4×#67—22no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132#926—22no—
133#926D414yescomplemented
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×C4×Dic3—21no—
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8—22no—
146C22×C3⋊C8—41no—
147C22×C3⋊C8—41no—
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152#890—22no—
153#890—22no—
154#67⋊C4—28no—
155#879—28no—
156C3×#103—22no—
157C3×#102—22no—
158C3×C22⋊C8—22no—
159#835—22no—
160#835—22no—
161#832—22no—
162#832—22no—
163#832—41no—
164#832—41no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170C22×#41C2×D311yescharacteristic
171C22×SD16C2×D311yescharacteristic
172C22×D8C2×D311yescharacteristic
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—24no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
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#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3C2×D411yescharacteristic
220C23×D3C2×D411yescharacteristic
221C3×#41—28no—
222C3×#41—44no—
223C3×#41—44no—
224C3×#41—44no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8#4112yes—
231C2×C3×D4—24no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—81no—
246C2×C3×D4—81no—
247C2×C3×D4C2×D412yes—
248C2×C3×D4#4112yes—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2411yescharacteristic
262C2×#67—24no—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—41no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—81no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—24no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—81no—
277C22×Dic3—81no—
278C22×Dic3C2×D411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—24no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C3×SD16—44no—
291C3×D8—44no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4C2×D412yes—
300C3×C22⋊C4—24no—
301#217—24no—
302#217—24no—
303#217—24no—
304#217—22no—
305#217—42no—
306#217—42no—
307#217—81no—
308#217—81no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—42no—
311C4⋊Dic3—24no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3C2×D412yes—
319C4⋊Dic3C2×D412yes—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—22no—
323Dic3⋊C4—42no—
324C4×Dic3—24no—
325C4×Dic3—21no—
326C4×Dic3—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—44no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—41no—
339C2×#41—41no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4C22×D311yescharacteristic
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353C2×SD16—22no—
354C2×SD16—22no—
355C2×SD16—41no—
356C2×D8—22no—
357C2×D8—22no—
358C2×D8—41no—
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—62no—
371C22⋊Q8—121no—
372#121—22no—
373#121—62no—
374#121—68no—
375#121—62no—
376#121—62no—
377#121—121no—
378#121#6714yescomplemented
379C4×D4—68no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—62no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—61no—
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—62no—
413#103—62no—
414#102—22no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—22no—
420C22⋊C8—121no—
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—22no—
432C23×C3—22no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3#12012yes—
446C23×C3C22×D411yescharacteristic
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3#13512yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—48no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—84no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—48no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4#12012yes—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4H(5,𝔽2)11yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488#67—44no—
489#67—48no—
490#67—84no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—84no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—41no—
517C4×D3—84no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—21no—
524C24—31no—
525C24D3×D411yescharacteristic
526#41—28no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23712yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—62no—
551C2×D4—64no—
552C2×D4—62no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—121no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4#23712yes—
562C2×D4C2×#6712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—64no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—64no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4D3×D411yescharacteristic
592C22×C4D3×D412yes—
593C22×C4C2×#6712yes—
594C22×C4C23×D311yescharacteristic
595SD16—44no—
596D8—44no—
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—21no—
611C4⋊C4—32no—
612C4⋊C4—32no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—62no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—122no—
624C4⋊C4C2×#6712yes—
625C22⋊C4—24no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—62no—
629C22⋊C4—64no—
630C22⋊C4—62no—
631C22⋊C4—122no—
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×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3C2×#12011yescharacteristic
661C22×C3#54611yescharacteristic
662C22×C3#54611yescharacteristic
663C22×C3C2×#13511yescharacteristic
664C22×C3#57511yescharacteristic
665C22×C3#57611yescharacteristic
666C22×C3#57711yescharacteristic
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—22no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C3×C4—22no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4#52511yescharacteristic
678C3×C4#53511yescharacteristic
679C3×C4#54611yescharacteristic
680C3×C4#54611yescharacteristic
681Dic3—41no—
682Dic3—41no—
683Dic3—42no—
684Dic3—42no—
685Dic3—41no—
686Dic3—81no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—22no—
696C23—32no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23#93712yes—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—124no—
732D4—128no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—244no—
773C2×C4—244no—
774C2×C4#93712yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×#23711yescharacteristic
777C2×C4C2×#23711yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4#100411yescharacteristic
780C2×C4C22×#6711yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—82no—
787C2×C3—82no—
788C2×C3#240411yescharacteristic
789C2×C3#300211yescharacteristic
790C2×C3#301211yescharacteristic
791C2×C3#329711yescharacteristic
792C2×C3#330111yescharacteristic
793C2×C3#330711yescharacteristic
794C2×C3#330911yescharacteristic
795D3—42no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—62no—
810C22—62no—
811C22—62no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22#559111yescharacteristic
825C22#559111yescharacteristic
826C22D3×#13511yescharacteristic
827C22#576811yescharacteristic
828C22#577411yescharacteristic
829C22#577511yescharacteristic
830C22C2×#93711yescharacteristic
831C4—22no—
832C4—42no—
833C4—42no—
834C4—121no—
835C4—121no—
836C4—122no—
837C4—121no—
838C4—122no—
839C4—241no—
840C4—241no—
841C4#558611yescharacteristic
842C4#559211yescharacteristic
843C4#580611yescharacteristic
844C4#580611yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—82no—
848C2—82no—
849C2—122no—
850C2#8010211yescharacteristic
851C2#8010311yescharacteristic
852C2#8010711yescharacteristic
853C2#8011011yescharacteristic
854C2#8258111yescharacteristic
855C2#8391111yescharacteristic
856C2#8394911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5614C2semidirect
2. C2×C3×#449C2semidirect
3. #84097C2semidirect
4. C2×#5233C2semidirect
5. #72054C2semidirect
6. #72047C2semidirect
7. #72043C2semidirect
8. #72037C2semidirect
9. #71681C2semidirect
10. #70268C2semidirect
11. #70232C2semidirect
12. #70200C2semidirect
13. #70164C2semidirect
14. #69952C2semidirect
15. #69926C2semidirect
65. C2×#449D3semidirect
107. C3×#121D4semidirect
133. #926D4semidirect
378. #121#67semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#56142
C2×C3×#4492
#840972
C2×#52332
#720542
#720472
#720432
#720372
#716812
#702682
#702322
#702002
#701642
#699522
#699262
#239623