Finite Group Databasebeta

← #25116911

Subgroups — #25116911

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583032C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4#19137615C211yesmaximal, characteristic, complemented
5#19137415C211yesmaximal, characteristic, complemented
6#19135468C211yesmaximal, characteristic, complemented
7#19135293C211yesmaximal, characteristic, complemented
8#19135220C211yesmaximal, characteristic, complemented
9#19134941C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134857C211yesmaximal, characteristic, complemented
12#19134787C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134371C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×D4×Dic43—21no—
20C2×D4×Dic43C2211yescharacteristic, complemented
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C2×C22⋊C4×D43—21no—
25#14583032C418yescomplemented
26#14583008—24no—
27C2×#13063256C2211yescharacteristic, complemented
28C2×#13063256C2211yescharacteristic, complemented
29C2×#13063247—24no—
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063235C2211yescharacteristic, complemented
38C2×#13063235C2211yescharacteristic, complemented
39#14582802C2211yescharacteristic, complemented
40#14582800C2211yescharacteristic
41#14582800C2211yescharacteristic
42#14582798C2211yescharacteristic, complemented
43#14582792—21no—
44#14582779—21no—
45#14582777—21no—
46#14582777—21no—
47#14582774—21no—
48#14582754—21no—
49C4⋊C4×Dic43C2211yescharacteristic, complemented
50C4×C22⋊Dic43C2211yescharacteristic
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C23×C8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic, complemented
58C2×#102×C43C2211yescharacteristic, complemented
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2×C414yescomplemented
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C23×Dic43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C2×#10621882—22no—
77C2×#10621882—22no—
78C2×#10621882—41no—
79C2×#10621882—41no—
80C2×#10621882C2×C414yescomplemented
81C2×#10621882C2×C414yescomplemented
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84D4×Dic43—22no—
85D4×Dic43—41no—
86D4×Dic43—44no—
87#13063287—22no—
88#13063287—22no—
89#13063287—41no—
90#13063287—41no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—41no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×C22⋊Dic43D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C22⋊C4×D43—44no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112#13063256—22no—
113#13063256—41no—
114#13063247—22no—
115#13063247—22no—
116#13063247—22no—
117#13063247D414yescomplemented
118#13063245C2×C414yescomplemented
119#13063245C2×C414yescomplemented
120C22⋊(C43⋊C8)C2×C414yescomplemented
121#13063235—22no—
122#13063235—41no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95D411yescharacteristic
126C43⋊#95D411yescharacteristic
127C22×D4×C43—21no—
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43—22no—
131C22×C8×C43—22no—
132C22×C8×C43—41no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135#121×C43—22no—
136#121×C43C2×C414yescomplemented
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142#102×C43—22no—
143#102×C43—41no—
144#95×C43—21no—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—24no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—42no—
154C23×D43—81no—
155C23×D43—81no—
156C2×D4×C43—21no—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43C22×C412yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—42no—
179C22×Dic43—42no—
180C22×Dic43—42no—
181C22×Dic43—42no—
182C22×Dic43—81no—
183C22×Dic43—81no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—24no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—28no—
198C2×D172—42no—
199C2×D172—42no—
200C2×D172—44no—
201C2×D172—44no—
202C2×D172—44no—
203C2×D172C22×C412yes—
204C2×D172C22×C412yes—
205C2×D172C2×D412yes—
206C2×D172#4112yes—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—81no—
212C2×C4×D43—81no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—44no—
219C2×C8×C43C2×D412yes—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C22×C412yes—
226C22⋊C4×C43—24no—
227C22⋊C4×C43—42no—
228C22⋊Dic43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43—42no—
231C22⋊Dic43—42no—
232C22⋊Dic43—81no—
233#10621882—28no—
234#10621882—44no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240(C2×D43)⋊C4—81no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—42no—
245C4⋊Dic43—42no—
246C4⋊Dic43C2×D412yes—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—42no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257C2×C43⋊C8C22×C412yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43C4×D412yes—
270C23×C43AGL(1,ℤ/8)12yes—
271C23×C43AGL(1,ℤ/8)12yes—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—48no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—48no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43—84no—
292C22×D43—84no—
293C22×D43—84no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—48no—
297D4×C43—41no—
298D4×C43—41no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—22no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—84no—
340C2×Dic43—84no—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—48no—
347D172—41no—
348D172—41no—
349D172C4×D414yescomplemented
350C4×D43—84no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—41no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356#22858—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43#44214yescomplemented
371C22×C43C2×C4×D411yescharacteristic
372C22×C43D4211yescharacteristic
373C22×C43#54611yescharacteristic
374C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C43#57611yescharacteristic
377C22×C43#57711yescharacteristic
378C2×D43—24no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—816no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43—81no—
393C4×C43—22no—
394C4×C43—42no—
395C4×C43—81no—
396C4×C43—81no—
397C4×C43C2×C4×D411yescharacteristic
398C4×C43#51811yescharacteristic
399C4×C43#54611yescharacteristic
400C4×C43#55111yescharacteristic
401Dic43—41no—
402Dic43—42no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102—431no—
410#2361—431no—
411D4×C22⋊C4—431no—
412#1972—431no—
413#1936—431no—
414#1926—431no—
415#1893D4311yescharacteristic, complemented
416#1879—431no—
417#1879—431no—
418#1864—431no—
419#1853—431no—
420#1762—431no—
421#1752—431no—
422C2×C43—24no—
423C2×C43—82no—
424C2×C43#235811yescharacteristic
425C2×C43C2×#44211yescharacteristic
426C2×C43#294611yescharacteristic
427C2×C43#326411yescharacteristic
428C2×C43#326511yescharacteristic
429C2×C43#330611yescharacteristic
430C2×C43#331811yescharacteristic
431D43—44no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8—431no—
436C23×C8C2×D4311yescharacteristic
437C2×#121C2×D4311yescharacteristic
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—864no—
455C2×#102C2×D4311yescharacteristic, complemented
456C2×#102C2×D4311yescharacteristic, complemented
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97—431no—
460#390—431no—
461#390—431no—
462#390—431no—
463#389—431no—
464#388—861no—
465#386—861no—
466#386—861no—
467#386—861no—
468#385—861no—
469#380C2×D4311yescharacteristic
470#379—861no—
471C4×C4⋊C4—431no—
472C4×C22⋊C4—431no—
473#340—431no—
474#340—431no—
475#340C2×D4311yescharacteristic, complemented
476#340C2×D4311yescharacteristic, complemented
477#336—431no—
478#336—431no—
479C43#2285811yescharacteristic, complemented, Sylow
480C25—861no—
481C22×D4—21no—
482C22×D4—434no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—861no—
488C22×D4—862no—
489C22×D4—1721no—
490C22×D4—1721no—
491C22×D4C22×D4311yescharacteristic
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—862no—
500C2×D8—862no—
501C2×D8—1721no—
502C2×D8—1721no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—22no—
511#121C4×D4314yescomplemented
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—862no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—1721no—
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—1724no—
542C2×C42—431no—
543C2×C42—431no—
544C2×C42—861no—
545#106—862no—
546#106—1721no—
547#102—22no—
548#102—41no—
549#102—434no—
550#102—434no—
551#102—434no—
552#102—862no—
553#102—862no—
554#102—862no—
555C22⋊C8—434no—
556#97—862no—
557#97—1721no—
558#95—21no—
559#95—431no—
560#95—431no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—861no—
565C24—864no—
566C24—861no—
567C24—3441no—
568C24—3441no—
569C24—1722no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24D4×D4311yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—432no—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—868no—
587C2×D4—864no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—1724no—
597C2×D4—1724no—
598C2×D4—1724no—
599C2×D4—1722no—
600C2×D4—1722no—
601C2×D4C2×C4×D4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4C2×C4×D4312yes—
628C22×C4D4×D4311yescharacteristic
629C22×C4#1062190012yes—
630C22×C4C23×D4311yescharacteristic
631D8—868no—
632D8—1724no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—432no—
640C2×C8—432no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8D4×D4312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—432no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—1722no—
656C4⋊C4—1722no—
657C4⋊C4C2×C4×D4312yes—
658C22⋊C4—24no—
659C22⋊C4—42no—
660C22⋊C4—862no—
661C22⋊C4—862no—
662C22⋊C4—3441no—
663C22⋊C4—3441no—
664C22⋊C4—3441no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—861no—
672C42—861no—
673C42—861no—
674C42—861no—
675C42—1722no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—3444no—
692C23—3444no—
693C23—3444no—
694C23—3444no—
695C23—3444no—
696C23—1728no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1728no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23(C22⋊D43)⋊C412yes—
709C23#1306334912yes—
710C23#1306335212yes—
711C23C2×D4×D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—434no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—862no—
722D4—862no—
723D4—1728no—
724D4—1721no—
725D4—1721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—862no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—3444no—
757C2×C4—3444no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4(C22⋊D43)⋊C412yes—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4311yescharacteristic
767C2×C4C2×#1062190011yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337111yescharacteristic
770C8—22no—
771C8—41no—
772C8—862no—
773C8—862no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—864no—
788C22—34416no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—3441no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22#1458300814yescomplemented
803C22C2×(C22⋊D43)⋊C411yescharacteristic
804C22#1458353311yescharacteristic
805C22#1458353811yescharacteristic
806C22C2×#1306334911yescharacteristic
807C22C2×#1306335211yescharacteristic
808C22#1458370111yescharacteristic
809C22#1458370611yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—81no—
814C4—3441no—
815C4—1721no—
816C4—1721no—
817C4—1722no—
818C4—1721no—
819C4—1721no—
820C4C4×D4×D4311yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458353611yescharacteristic
823C4#1458357211yescharacteristic
824C2—24no—
825C2—82no—
826C2—3442no—
827C2—1724no—
828C2#1913757511yescharacteristic
829C2C2×#1458300811yescharacteristic
830C2#1914343011yescharacteristic
831C2#1914607211yescharacteristic
832C2#1914608711yescharacteristic
833C2#1914656211yescharacteristic
834C2#1914674211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. C22×#13063247C2semidirect
4. #19137615C2semidirect
5. #19137415C2semidirect
6. #19135468C2semidirect
7. #19135293C2semidirect
8. #19135220C2semidirect
9. #19134941C2semidirect
10. #19134940C2semidirect
11. #19134857C2semidirect
12. #19134787C2semidirect
13. #19134419C2semidirect
14. #19134371C2semidirect
15. C43×#1893C2semidirect
20. C2×D4×Dic43C22semidirect
25. #14583032C4semidirect
27. C2×#13063256C22semidirect
28. C2×#13063256C22semidirect
37. C2×#13063235C22semidirect
38. C2×#13063235C22semidirect
39. #14582802C22semidirect
42. #14582798C22semidirect
49. C4⋊C4×Dic43C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
57. C2×#102×C43C22semidirect
58. C2×#102×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
69. C22×D172C2×C4semidirect
80. C2×#10621882C2×C4semidirect
81. C2×#10621882C2×C4semidirect
117. #13063247D4semidirect
118. #13063245C2×C4semidirect
119. #13063245C2×C4semidirect
120. C22⋊(C43⋊C8)C2×C4semidirect
136. #121×C43C2×C4semidirect
349. D172C4×D4semidirect
370. C22×C43#442semidirect
415. #1893D43semidirect
455. C2×#102C2×D43semidirect
456. C2×#102C2×D43semidirect
475. #340C2×D43semidirect
476. #340C2×D43semidirect
479. C43#22858semidirect
511. #121C4×D43semidirect
802. C22#14583008semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
C2×#145830082
C22×#130632472
#191376152
#191374152
#191354682
#191352932
#191352202
#191349412
#191349402
#191348572
#191347872
#191344192
#191343712
C43×#18932
#2285843