Finite Group Databasebeta

← #25107944

Subgroups — #25107944

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583032C211yesmaximal, characteristic
2#19137290C211yesmaximal, characteristic, complemented
3#19137175C211yesmaximal, characteristic, complemented
4#19135468C211yesmaximal, characteristic, complemented
5#19135458C211yesmaximal, characteristic, complemented
6#19135293C211yesmaximal, characteristic, complemented
7#19135279C211yesmaximal, characteristic, complemented
8#19135220C211yesmaximal, characteristic, complemented
9#19135213C211yesmaximal, characteristic, complemented
10#19134941C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic, complemented
20C2×#13063284C2211yescharacteristic
21#14583032C418yescomplemented
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063235C2211yescharacteristic, complemented
32C2×C8×Dic43C2211yescharacteristic, complemented
33#14582802—21no—
34#14582802C2211yescharacteristic, complemented
35#14582801—21no—
36#14582801—21no—
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582798C2211yescharacteristic, complemented
42#14582792—21no—
43#14582779—21no—
44#14582774—21no—
45#14582759C2211yescharacteristic
46#14582754—21no—
47#14582754—21no—
48C4⋊C4×Dic43C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#121×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic, complemented
56C2×#102×C43C2211yescharacteristic, complemented
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172—21no—
62C22×D172—22no—
63C22×D172—41no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172—41no—
67C22×D172C2×C414yescomplemented
68C22×D172C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C23×Dic43—21no—
71C2×#10621882—41no—
72C2×#10621882—41no—
73C2×#10621882—41no—
74C2×#10621882—41no—
75C2×#10621882C2×C414yes—
76C2×#10621882C2×C414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79D4×Dic43—41no—
80D4×Dic43—41no—
81#13063284—41no—
82#13063284—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063258—41no—
106#13063256—41no—
107#13063247—41no—
108#13063247—41no—
109#13063247—41no—
110#13063247—41no—
111#13063245C2×C414yescomplemented
112#13063245C2×C414yescomplemented
113C22⋊(C43⋊C8)C2×C414yescomplemented
114#13063235—41no—
115C8×Dic43—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#121×C43—22no—
125#121×C43C2×C414yes—
126#117×C43—41no—
127#117×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134#102×C43—41no—
135#102×C43—41no—
136C22⋊C8×C43—22no—
137C24×C43—21no—
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43—81no—
148C2×D4×C43—21no—
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C2×D4×C43C22×C412yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C22×C412yes—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—42no—
171C22×Dic43—81no—
172C22×Dic43—81no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C2×D172—24no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—44no—
189C2×D172—44no—
190C2×D172—44no—
191C2×D172—44no—
192C2×D172—42no—
193C2×D172—42no—
194C2×D172C22×C412yes—
195C2×D172C22×C412yes—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43C22×C412yes—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—42no—
210C42×C43—42no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213C22⋊Dic43—42no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43—81no—
217#10621882—44no—
218#10621882—44no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4—81no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—41no—
232C4⋊Dic43—41no—
233C4⋊Dic43—81no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C4×D412yes—
259C23×C43C22×D411yescharacteristic
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—48no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—84no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C4×D412yes—
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—22no—
331D172—48no—
332D172—41no—
333D172—41no—
334D172—41no—
335D172—41no—
336C8×C43—41no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—22no—
340#22056—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43C2×C4×D411yescharacteristic
356C22×C43#53411yescharacteristic
357C22×C43#53511yescharacteristic
358C22×C43#57611yescharacteristic
359C22×C43#57611yescharacteristic
360C22×C43#57611yescharacteristic
361C22×C43#57711yescharacteristic
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—816no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—22no—
378C4×C43—42no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43#51811yescharacteristic
382C4×C43#51811yescharacteristic
383C4×C43#53811yescharacteristic
384C4×C43#53811yescharacteristic
385Dic43—41no—
386Dic43—41no—
387Dic43—41no—
388Dic43—41no—
389Dic43—81no—
390Dic43—81no—
391C2×#447—431no—
392#2324—431no—
393#2309—431no—
394#1972—431no—
395#1970—431no—
396#1936—431no—
397#1934—431no—
398#1926—431no—
399#1925—431no—
400#1879—431no—
401#1879—431no—
402#1875D4311yescharacteristic, complemented
403#1854—431no—
404#1786—431no—
405#1750—431no—
406C2×C43—42no—
407C2×C43—82no—
408C2×C43#232111yescharacteristic
409C2×C43#294611yescharacteristic
410C2×C43#294811yescharacteristic
411C2×C43#319811yescharacteristic
412C2×C43#319911yescharacteristic
413C2×C43#322011yescharacteristic
414C2×C43#322411yescharacteristic
415D43—82no—
416D43—82no—
417C23×D4—431no—
418C22×D8—431no—
419C22×D8—431no—
420C2×#121C2×D4311yescharacteristic
421C2×C4×D4—431no—
422C2×#117—431no—
423C2×#117C2×D4311yescharacteristic
424#447—438no—
425C2×#107—431no—
426C2×#106—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102C2×D4311yescharacteristic, complemented
434C2×#102C2×D4311yescharacteristic, complemented
435C2×C22⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
439#390—431no—
440#390—431no—
441#390—431no—
442#390—431no—
443#390—431no—
444#390—861no—
445#390—861no—
446#390—861no—
447#389—431no—
448#388—861no—
449#386—861no—
450#385—861no—
451#380—431no—
452#379—861no—
453#379—861no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340C2×D4311yescharacteristic, complemented
458#340C2×D4311yescharacteristic, complemented
459#336—431no—
460#336—431no—
461C43#2205611yescharacteristic, complemented, Sylow
462C25—861no—
463C22×D4—21no—
464C22×D4—434no—
465C22×D4—431no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—862no—
469C22×D4—1721no—
470C22×D4—1721no—
471C22×D4—1721no—
472C22×D4—1721no—
473C22×D4C22×D4311yescharacteristic
474C23×C4—861no—
475C23×C4C22×D4311yescharacteristic
476C2×D8—434no—
477C2×D8—434no—
478C2×D8—1721no—
479C2×D8—1721no—
480C2×D8—1721no—
481C2×D8—1721no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—22no—
487#121C4×D4314yes—
488C4×D4—1721no—
489C4×D4—1721no—
490#117—41no—
491#117—41no—
492#117—1721no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—21no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—861no—
522#107—1721no—
523#106—1721no—
524#102—41no—
525#102—41no—
526#102—434no—
527#102—434no—
528#102—1721no—
529#102—1721no—
530#102—1721no—
531#102—1721no—
532C22⋊C8—22no—
533C22⋊C8—434no—
534#97—1721no—
535C4×C8—1721no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—864no—
541C24—861no—
542C24—861no—
543C24—3441no—
544C24—3441no—
545C24—3441no—
546C24—3441no—
547C24—1722no—
548C24—1722no—
549C24D4×D4311yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—432no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4—1722no—
574C2×D4—1722no—
575C2×D4—1724no—
576C2×D4—1724no—
577C2×D4C2×C4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—1722no—
594C22×C4C2×C4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4#1062190012yes—
597C22×C4C23×D4311yescharacteristic
598D8—1724no—
599D8—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—3441no—
622C4⋊C4—1721no—
623C4⋊C4—1721no—
624C4⋊C4C2×C4×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—42no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—1721no—
639C22⋊C4—1721no—
640C22⋊C4—1722no—
641C42—42no—
642C42—861no—
643C42—861no—
644C42—861no—
645C42—861no—
646C42—3441no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—862no—
661C23—862no—
662C23—3444no—
663C23—3444no—
664C23—3444no—
665C23—3444no—
666C23—3444no—
667C23—3444no—
668C23—1728no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23(C22⋊D43)⋊C412yes—
682C23C2×D4×D4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—862no—
689D4—862no—
690D4—862no—
691D4—862no—
692D4—1728no—
693D4—1721no—
694D4—1721no—
695D4—1721no—
696D4—1721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—3444no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4(C22⋊D43)⋊C412yes—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337111yescharacteristic
737C2×C4#1306337111yescharacteristic
738C8—41no—
739C8—41no—
740C8—862no—
741C8—862no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—34416no—
757C22—3441no—
758C22—3441no—
759C22—3441no—
760C22—3441no—
761C22—3441no—
762C22—3441no—
763C22—3441no—
764C22—3441no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22C2×(C22⋊D43)⋊C411yescharacteristic
772C22#1458346011yescharacteristic
773C22#1458346411yescharacteristic
774C22#1458370111yescharacteristic
775C22#1458370311yescharacteristic
776C22#1458370311yescharacteristic
777C22#1458370611yescharacteristic
778C4—22no—
779C4—42no—
780C4—81no—
781C4—81no—
782C4—3441no—
783C4—3441no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4#1458337111yescharacteristic
789C4#1458337111yescharacteristic
790C4#1458348611yescharacteristic
791C4#1458348611yescharacteristic
792C2—42no—
793C2—82no—
794C2—3442no—
795C2—3442no—
796C2#1913725811yescharacteristic
797C2#1914343011yescharacteristic
798C2#1914344311yescharacteristic
799C2#1914544511yescharacteristic
800C2#1914545911yescharacteristic
801C2#1914564311yescharacteristic
802C2#1914568711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#1875D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. #19137290C2semidirect
3. #19137175C2semidirect
4. #19135468C2semidirect
5. #19135458C2semidirect
6. #19135293C2semidirect
7. #19135279C2semidirect
8. #19135220C2semidirect
9. #19135213C2semidirect
10. #19134941C2semidirect
11. #19134941C2semidirect
12. #19134794C2semidirect
13. #19134527C2semidirect
14. #19134363C2semidirect
15. C43×#1875C2semidirect
19. C2×D4×Dic43C22semidirect
21. #14583032C4semidirect
22. C2×#13063258C22semidirect
23. C2×#13063256C22semidirect
31. C2×#13063235C22semidirect
32. C2×C8×Dic43C22semidirect
34. #14582802C22semidirect
41. #14582798C22semidirect
48. C4⋊C4×Dic43C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
55. C2×#102×C43C22semidirect
56. C2×#102×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
67. C22×D172C2×C4semidirect
111. #13063245C2×C4semidirect
112. #13063245C2×C4semidirect
113. C22⋊(C43⋊C8)C2×C4semidirect
402. #1875D43semidirect
433. C2×#102C2×D43semidirect
434. C2×#102C2×D43semidirect
457. #340C2×D43semidirect
458. #340C2×D43semidirect
461. C43#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
#191372902
#191371752
#191354682
#191354582
#191352932
#191352792
#191352202
#191352132
#191349412
#191347942
#191345272
#191343632
C43×#18752
#2205643