Finite Group Databasebeta

← #25107935

Subgroups — #25107935

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×#14583031C211yesmaximal, characteristic
2#19137282C211yesmaximal, characteristic, complemented
3#19137174C211yesmaximal, characteristic, complemented
4#19135472C211yesmaximal, characteristic, complemented
5#19135458C211yesmaximal, characteristic, complemented
6#19135290C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135212C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134914C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21#14583031C418yescomplemented
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063257C2211yescharacteristic, complemented
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063235C2211yescharacteristic, complemented
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic, complemented
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582799—21no—
39#14582799—21no—
40#14582799—21no—
41#14582795C2211yescharacteristic, complemented
42#14582793—21no—
43#14582778—21no—
44#14582772—21no—
45#14582756C2211yescharacteristic
46#14582754—21no—
47#14582754—21no—
48C4×C4⋊Dic43C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic, complemented
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C2×D4×D43—22no—
65C2×D4×D43—41no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43—41no—
69C2×D4×D43C2×C414yescomplemented
70C22×C4×D43C2311yescharacteristic
71C2×#10621882—41no—
72C2×#10621882—41no—
73C2×#10621882C2×C414yes—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063296—22no—
77#13063296C2×C414yes—
78#13063283—41no—
79#13063283—41no—
80#13063282—41no—
81#13063282—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
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)⋊C4D411yescharacteristic
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104#13063258—41no—
105#13063257—41no—
106#13063247—41no—
107#13063247C2×C414yescomplemented
108#13063246—41no—
109#13063246—41no—
110#13063246C2×C414yescomplemented
111#13063245—41no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8C2×C414yescomplemented
114#13063235—41no—
115C8×Dic43—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C2×D8×C43—41no—
123C2×D8×C43—41no—
124C2×D8×C43C2×C414yes—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C4×D4×C43—41no—
128C4×D4×C43—41no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#102×C43—41no—
136#102×C43—41no—
137C24×C43—21no—
138C24×C43—21no—
139C23×D43—21no—
140C23×D43—24no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—81no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C22×C412yes—
159C2×D4×C43C22×C412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—42no—
163C22×C4×C43—81no—
164C22×C4×C43—81no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—42no—
171C2×C22⋊D43—42no—
172C2×C22⋊D43—81no—
173C2×C22⋊D43—81no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180D4×D43—44no—
181D4×D43—44no—
182D4×D43—44no—
183D4×D43—44no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172C22×C412yes—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43C22×C412yes—
195C2×C4×D43#4112yes—
196D8×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43C22×C412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C42×C43—21no—
211C42×C43—21no—
212C22⋊Dic43—24no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43—81no—
217#10621882—44no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—42no—
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—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—41no—
233Dic43⋊C4—41no—
234Dic43⋊C4—81no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8C22×C412yes—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43C22×D411yescharacteristic
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—22no—
267C22×D43—48no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—84no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43C4×D412yes—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
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×C43—84no—
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
308C22⋊D43—48no—
309C22⋊D43—84no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43C4×D412yes—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#22056—431nomaximal, Sylow
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
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—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—816no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43#51811yescharacteristic
382C4×C43#51811yescharacteristic
383C4×C43#53811yescharacteristic
384C4×C43#53811yescharacteristic
385Dic43—22no—
386Dic43—41no—
387Dic43—41no—
388Dic43—42no—
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#1879D4311yescharacteristic, complemented
402#1875—431no—
403#1854—431no—
404#1786—431no—
405#1750—431no—
406C2×C43—82no—
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—42no—
416D43—82no—
417C23×D4—431no—
418C22×D8—431no—
419C22×D8C2×D4311yescharacteristic
420C2×#121—431no—
421C2×C4×D4C2×D4311yescharacteristic, complemented
422C2×#117—431no—
423C2×#117—431no—
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
434C2×#102C2×D4311yescharacteristic, complemented
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×#97—431no—
438C2×C4×C8—431no—
439#390—431no—
440#390—431no—
441#390—431no—
442#390—431no—
443#390—861no—
444#390—861no—
445#390—861no—
446#390C2×D4311yescharacteristic
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#340—431no—
458#340C2×D4311yescharacteristic, complemented
459#336—431no—
460#336C2×D4311yescharacteristic, complemented
461C43#2205611yescharacteristic, complemented, Sylow
462C25—861no—
463C22×D4—434no—
464C22×D4—431no—
465C22×D4—862no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—1721no—
469C22×D4—1721no—
470C22×D4—1721no—
471C22×D4—1721no—
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—21no—
475C23×C4—431no—
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—434no—
479C2×D8—1721no—
480C2×D8—1721no—
481C2×D8C4×D4314yes—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—434no—
487#121—862no—
488C4×D4—41no—
489C4×D4—41no—
490#117—1721no—
491#117—1721no—
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—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
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—431no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42C22×D4311yescharacteristic
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—434no—
533C22⋊C8—862no—
534#97—1721no—
535C4×C8—1721no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—21no—
541C24—431no—
542C24—864no—
543C24—861no—
544C24—3441no—
545C24—3441no—
546C24—3441no—
547C24—3441no—
548C24—1722no—
549C24—1722no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—432no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—3441no—
569C2×D4—3441no—
570C2×D4—1724no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4—1724no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4C2×C4×D4312yes—
577C2×D4C2×C4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—431no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598D8—44no—
599D8—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8C2×C4×D4312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4—1721no—
624C4⋊C4—1721no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—864no—
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—21no—
642C42—21no—
643C42—861no—
644C42—861no—
645C42—3441no—
646C42—1722no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—432no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—862no—
669C23—3444no—
670C23—3444no—
671C23—3444no—
672C23—3444no—
673C23—3444no—
674C23—3444no—
675C23—1728no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23C2×D4×D4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—862no—
692D4—862no—
693D4—3444no—
694D4—1728no—
695D4—1721no—
696D4—1721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—432no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337011yescharacteristic
737C2×C4#1306337111yescharacteristic
738C8—22no—
739C8—41no—
740C8—862no—
741C8—1721no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—34416no—
760C22—3441no—
761C22—3441no—
762C22—3441no—
763C22—3441no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1721no—
768C22—1721no—
769C22—1721no—
770C22—1721no—
771C22C4×D4×D4311yescharacteristic
772C22#1458345911yescharacteristic
773C22#1458346511yescharacteristic
774C22#1458370011yescharacteristic
775C22#1458370311yescharacteristic
776C22#1458370311yescharacteristic
777C22#1458370611yescharacteristic
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—862no—
783C4—3441no—
784C4—3441no—
785C4—1722no—
786C4—1721no—
787C4—1721no—
788C4#1458337111yescharacteristic
789C4#1458337211yescharacteristic
790C4#1458348111yescharacteristic
791C4#1458348511yescharacteristic
792C2—82no—
793C2—82no—
794C2—3442no—
795C2—1722no—
796C2#1913725111yescharacteristic
797C2#1914342011yescharacteristic
798C2#1914344411yescharacteristic
799C2#1914544611yescharacteristic
800C2#1914545811yescharacteristic
801C2#1914564411yescharacteristic
802C2#1914568811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #19137282C2semidirect
3. #19137174C2semidirect
4. #19135472C2semidirect
5. #19135458C2semidirect
6. #19135290C2semidirect
7. #19135275C2semidirect
8. #19135223C2semidirect
9. #19135212C2semidirect
10. #19134943C2semidirect
11. #19134914C2semidirect
12. #19134795C2semidirect
13. #19134524C2semidirect
14. #19134360C2semidirect
15. C43×#1879C2semidirect
21. #14583031C4semidirect
22. C2×#13063258C22semidirect
23. C2×#13063257C22semidirect
28. C2×#13063246C22semidirect
32. C2×#13063235C22semidirect
33. C2×C8×Dic43C22semidirect
35. #14582802C22semidirect
41. #14582795C22semidirect
48. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582654C22semidirect
54. C2×C4×D4×C43C22semidirect
56. C2×#102×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
69. C2×D4×D43C2×C4semidirect
107. #13063247C2×C4semidirect
110. #13063246C2×C4semidirect
113. (C2×D43)⋊C8C2×C4semidirect
401. #1879D43semidirect
421. C2×C4×D4C2×D43semidirect
434. C2×#102C2×D43semidirect
458. #340C2×D43semidirect
460. #336C2×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×#145830312
#191372822
#191371742
#191354722
#191354582
#191352902
#191352752
#191352232
#191352122
#191349432
#191349142
#191347952
#191345242
#191343602
C43×#18792
#2205643