Finite Group Databasebeta

← #25116907

Subgroups — #25116907

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×#14583035C211yesmaximal, characteristic
2C2×#14583010C211yesmaximal, characteristic, complemented
3C22×#13063245C211yesmaximal, characteristic, complemented
4#19137611C211yesmaximal, characteristic, complemented
5#19137415C211yesmaximal, characteristic, complemented
6#19135469C211yesmaximal, characteristic, complemented
7#19135290C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19135021C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134944C211yesmaximal, characteristic, complemented
12#19134853C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C43×#1853C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic, complemented
24C2×C4×C22⋊D43—21no—
25C2×C22⋊C4×D43—21no—
26#14583035C418yescomplemented
27#14583010—24no—
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245—24no—
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic, complemented
36C2×#13063245C2211yescharacteristic, complemented
37C2×#13063235C2211yescharacteristic, complemented
38C2×#13063235C2211yescharacteristic, complemented
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582800C2211yescharacteristic, complemented
42#14582795C2211yescharacteristic, complemented
43#14582789—21no—
44#14582778—21no—
45#14582777—21no—
46#14582777—21no—
47#14582770—21no—
48#14582754—21no—
49C4⋊C4×Dic43C2211yescharacteristic, complemented
50C4×C22⋊Dic43C2211yescharacteristic
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic, complemented
57C2×#106×C43C2211yescharacteristic, complemented
58C2×C22⋊C8×C43C2211yescharacteristic
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
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C2×D344—22no—
78C2×D344—22no—
79C2×D344—41no—
80C2×D344—41no—
81C2×D344C2×C414yescomplemented
82C2×D344C2×C414yescomplemented
83C22×C43⋊C8—22no—
84C22×C43⋊C8—22no—
85C22×C43⋊C8—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063299—22no—
89#13063299C2×C414yescomplemented
90#13063287—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287—41no—
94#13063287—41no—
95#13063287—41no—
96C4×C22⋊D43—44no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43D411yescharacteristic
100C2×C22⋊Dic43D411yescharacteristic
101C2×(C2×D43)⋊C4—21no—
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—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C22⋊C4×D43—44no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063247C2×C414yescomplemented
116#13063247C2×C414yescomplemented
117#13063245—22no—
118#13063245—22no—
119#13063245—22no—
120#13063245—22no—
121#13063245—41no—
122#13063245D414yescomplemented
123#13063235—22no—
124#13063235—41no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95D411yescharacteristic
128C43⋊#95D411yescharacteristic
129C23×C4×C43—21no—
130C23×C4×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—41no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141#106×C43—22no—
142#106×C43—41no—
143C22⋊C8×C43C2×C414yescomplemented
144#95×C43—21no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
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—
156C22×C4×C43—21no—
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×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—81no—
167C22×C4×C43C22×C412yes—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43#4112yes—
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—42no—
173C2×C22⋊D43—42no—
174C22×Dic43—21no—
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—24no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—28no—
194C2×D172—42no—
195C2×D172—42no—
196C2×D172—44no—
197C2×D172—44no—
198C2×D172—44no—
199C2×D172C22×C412yes—
200C2×D172C22×C412yes—
201C2×D172C22×C412yes—
202C2×D172C2×D412yes—
203C2×D172#4112yes—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—81no—
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×C43C22×C412yes—
218C2×C8×C43C22×C412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43C2×D412yes—
228C22⋊C4×C43—42no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—42no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—81no—
239(C2×D43)⋊C4—81no—
240(C2×D43)⋊C4—81no—
241C4⋊Dic43—21no—
242C4⋊Dic43C22×C412yes—
243Dic43⋊C4—42no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—42no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—44no—
255C2×C43⋊C8C2×D412yes—
256D344—28no—
257D344—44no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43C4×D412yes—
263C23×C43AGL(1,ℤ/8)12yes—
264C23×C43AGL(1,ℤ/8)12yes—
265C23×C43C22×D411yescharacteristic
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—48no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
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—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
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—84no—
313C2×C4×C43C4×D412yes—
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C22⋊D43—48no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
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—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—48no—
344D172—41no—
345D172—41no—
346D172—41no—
347D172—41no—
348D172C4×D414yescomplemented
349C4×D43—84no—
350C4×D43—84no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#22858—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43#44214yescomplemented
364C22×C43C2×C4×D411yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43#54611yescharacteristic
367C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C43#57611yescharacteristic
370C22×C43#57711yescharacteristic
371C2×D43—24no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—816no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
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×C43—81no—
398C4×C43C2×C4×D411yescharacteristic
399C4×C43#51811yescharacteristic
400C4×C43#54611yescharacteristic
401C4×C43#55111yescharacteristic
402Dic43—42no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43—41no—
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#1893—431no—
416#1879—431no—
417#1879—431no—
418#1864—431no—
419#1853D4311yescharacteristic, complemented
420#1762—431no—
421#1752—431no—
422C2×C43—24no—
423C2×C43#235811yescharacteristic
424C2×C43C2×#44211yescharacteristic
425C2×C43#294611yescharacteristic
426C2×C43#326411yescharacteristic
427C2×C43#326511yescharacteristic
428C2×C43#330611yescharacteristic
429C2×C43#331811yescharacteristic
430D43—44no—
431D43—82no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8—431no—
436C23×C8—431no—
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106C2×D4311yescharacteristic, complemented
447C2×#106C2×D4311yescharacteristic, complemented
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—864no—
457C2×C22⋊C8C2×D4311yescharacteristic
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—434no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—861no—
488C22×D4—861no—
489C22×D4—862no—
490C22×D4—1721no—
491C22×D4—1721no—
492C23×C4—21no—
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—431no—
504C22×C8—431no—
505C22×C8—862no—
506C22×C8—862no—
507C22×C8—1721no—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—434no—
511#121—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—861no—
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—22no—
546#106—41no—
547#102—434no—
548#102—434no—
549#102—434no—
550#102—862no—
551#102—862no—
552#102—862no—
553#102—862no—
554#102—1721no—
555C22⋊C8C4×D4314yescomplemented
556#97—862no—
557#97—1721no—
558#95—21no—
559#95—431no—
560#95—431no—
561#95—861no—
562#95—861no—
563C24—861no—
564C24—864no—
565C24—861no—
566C24—861no—
567C24—3441no—
568C24—3441no—
569C24—1722no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24D4×D4311yescharacteristic
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—432no—
577C2×D4—432no—
578C2×D4—432no—
579C2×D4—868no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—1724no—
596C2×D4—1724no—
597C2×D4—1724no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4—1722no—
601C2×D4—1722no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—861no—
618C22×C4—3441no—
619C22×C4—3441no—
620C22×C4—3441no—
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#1062190212yes—
630C22×C4C23×D4311yescharacteristic
631D8—868no—
632D8—1724no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—432no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—1724no—
644C2×C8C2×C4×D4312yes—
645C2×C8C2×C4×D4312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—42no—
654C4⋊C4—432no—
655C4⋊C4—861no—
656C4⋊C4—1722no—
657C4⋊C4D4×D4312yes—
658C22⋊C4—42no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—864no—
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—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—3444no—
686C23—3444no—
687C23—3444no—
688C23—3444no—
689C23—3444no—
690C23—1728no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1728no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23#1306328712yes—
709C23#1306335212yes—
710C23#1306335212yes—
711C23C2×D4×D4311yescharacteristic
712D4—434no—
713D4—862no—
714D4—862no—
715D4—862no—
716D4—862no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—1728no—
721D4—1728no—
722D4—1721no—
723D4—1721no—
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—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—3444no—
759C2×C4—3444no—
760C2×C4—3444no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4#1306328712yes—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4311yescharacteristic
767C2×C4C2×#1062190211yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337111yescharacteristic
770C8—22no—
771C8—22no—
772C8—862no—
773C8—1721no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—864no—
781C22—34416no—
782C22—3441no—
783C22—3441no—
784C22—3441no—
785C22—3441no—
786C22—3441no—
787C22—3441no—
788C22—3441no—
789C22—3441no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22#1458301014yescomplemented
803C22C2×#1306328711yescharacteristic
804C22#1458353111yescharacteristic
805C22#1458354111yescharacteristic
806C22C2×#1306335211yescharacteristic
807C22C2×#1306335211yescharacteristic
808C22#1458370311yescharacteristic
809C22#1458370811yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4—1722no—
819C4—1721no—
820C4C4×D4×D4311yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458354011yescharacteristic
823C4#1458357611yescharacteristic
824C2—24no—
825C2—3442no—
826C2—3442no—
827C2—1724no—
828C2#1913757111yescharacteristic
829C2C2×#1458301011yescharacteristic
830C2#1914342511yescharacteristic
831C2#1914607911yescharacteristic
832C2#1914608311yescharacteristic
833C2#1914655411yescharacteristic
834C2#1914673411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1853C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1853D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#14583010C2semidirect
3. C22×#13063245C2semidirect
4. #19137611C2semidirect
5. #19137415C2semidirect
6. #19135469C2semidirect
7. #19135290C2semidirect
8. #19135221C2semidirect
9. #19135021C2semidirect
10. #19134944C2semidirect
11. #19134944C2semidirect
12. #19134853C2semidirect
13. #19134419C2semidirect
14. #19134374C2semidirect
15. C43×#1853C2semidirect
23. C2×#13063287C22semidirect
26. #14583035C4semidirect
35. C2×#13063245C22semidirect
36. C2×#13063245C22semidirect
37. C2×#13063235C22semidirect
38. C2×#13063235C22semidirect
41. #14582800C22semidirect
42. #14582795C22semidirect
49. C4⋊C4×Dic43C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
56. C2×#106×C43C22semidirect
57. C2×#106×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
69. C22×D172C2×C4semidirect
81. C2×D344C2×C4semidirect
82. C2×D344C2×C4semidirect
89. #13063299C2×C4semidirect
115. #13063247C2×C4semidirect
116. #13063247C2×C4semidirect
122. #13063245D4semidirect
143. C22⋊C8×C43C2×C4semidirect
348. D172C4×D4semidirect
363. C22×C43#442semidirect
419. #1853D43semidirect
446. C2×#106C2×D43semidirect
447. C2×#106C2×D43semidirect
475. #340C2×D43semidirect
476. #340C2×D43semidirect
479. C43#22858semidirect
555. C22⋊C8C4×D43semidirect
802. C22#14583010semidirect

Maximal subgroups

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

subgroupindex
C2×#145830352
C2×#145830102
C22×#130632452
#191376112
#191374152
#191354692
#191352902
#191352212
#191350212
#191349442
#191348532
#191344192
#191343742
C43×#18532
#2285843