Finite Group Databasebeta

← #25269522

Subgroups — #25269522

Order 11008.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583487C212yesmaximal, complemented
2#19142947C211yesmaximal, characteristic, complemented
3#19142940C211yesmaximal, characteristic, complemented
4#19142877C212yesmaximal, complemented
5#19140523C212yesmaximal, complemented
6#19140329C212yesmaximal, complemented
7#19139718C214yesmaximal, complemented
8#19139688C214yesmaximal, complemented
9#19139017C212yesmaximal, complemented
10#19138958C212yesmaximal, complemented
11#19138183C212yesmaximal, complemented
12#19138109C212yesmaximal, complemented
13#19137298C212yesmaximal, complemented
14C4×#13063299C212yesmaximal, complemented
15C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16#14583487—216no—
17C2×#13063325C2211yescharacteristic, complemented
18C2×#13063322C2211yescharacteristic, complemented
19C2×#13063318C2214yes—
20C2×#13063311C2214yes—
21C2×#13063307C2214yes—
22C2×#13063304C2212yes—
23C2×#13063299C2212yes—
24C2×#13063299C2212yes—
25C2×#13063299C2212yes—
26C2×#13063299C2212yes—
27C2×#13063299C2212yes—
28C2×#13063298C2214yes—
29C2×#13063294C2214yes—
30C2×C4×D172C2212yescomplemented
31C2×C4×C22⋊D43C2214yes—
32#14582839C2214yescomplemented
33#14582826C2214yescomplemented
34#14582824C2214yes—
35#14582817C2214yescomplemented
36#14582815C2214yes—
37#14582815C2214yes—
38#14582812C2214yescomplemented
39#14582808C2214yes—
40#14582805C2212yescomplemented
41#14582801C2212yescomplemented
42#14582801C2212yescomplemented
43#14582801C2212yescomplemented
44#14582801C2212yescomplemented
45#14582797C2212yescomplemented
46#14582797C2212yescomplemented
47#14582797C2212yescomplemented
48#14582791C2214yescomplemented
49#14582790C2214yescomplemented
50#14582784C2214yescomplemented
51#14582778C2214yes—
52#14582778C2214yes—
53#14582778C2214yes—
54#14582778C2214yes—
55#14582777C2214yescomplemented
56#14582773C2214yescomplemented
57#14582769C2211yescharacteristic, complemented
58#14582769C2211yescharacteristic, complemented
59#14582759C2212yes—
60#14582759C2212yes—
61#14582759C2212yes—
62#14582759C2212yes—
63C4×C4⋊Dic43C2212yescomplemented
64C4×(C2×D43)⋊C4C2214yescomplemented
65C24×C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C42×C43C2211yescharacteristic
69C22×C42×C43C2211yescharacteristic
70C4×C22⋊C4×C43C2212yes—
71C4×C22⋊C4×C43C2212yes—
72C4×C22⋊C4×C43C2212yes—
73C4×C22⋊C4×C43C2212yes—
74C2×#95×C43C2211yescharacteristic
75C2×#95×C43C2211yescharacteristic
76C22×Dic86C2312yes—
77C22×D172C2312yes—
78C22×D172C2312yes—
79C22×D172C2312yes—
80C22×C22⋊D43C2314yes—
81C22×C22⋊D43C2314yes—
82C22×C22⋊D43C2314yes—
83C22×C4×D43C2314yes—
84#13063325—42no—
85#13063322—42no—
86#13063318—216no—
87#13063311—216no—
88#13063307—216no—
89#13063304—28no—
90#13063299—28no—
91#13063299—28no—
92#13063299—28no—
93#13063299—44no—
94#13063299—44no—
95#13063298—216no—
96#13063294—216no—
97C4×D172—44no—
98C4×C22⋊D43—216no—
99C2×C4⋊Dic43C2312yes—
100C2×C4⋊Dic43C2312yes—
101C2×C4⋊Dic43C2312yes—
102C2×C4⋊Dic43C2312yes—
103C2×C4⋊Dic43C2312yes—
104C2×C4⋊Dic43C2312yes—
105C2×C4⋊Dic43C2312yes—
106C2×C4⋊Dic43C2312yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×C22⋊Dic43C2314yes—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C25×C43C2311yescharacteristic
128C23×C4×C43—24no—
129C23×C4×C43—42no—
130C23×C4×C43—42no—
131C23×C4×C43C2312yes—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2312yes—
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—24no—
140C2×C22⋊C4×C43D418yescomplemented
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2312yes—
143C2×C22⋊C4×C43C2312yes—
144C2×C22⋊C4×C43C2312yes—
145C2×C42×C43—42no—
146C2×C42×C43—42no—
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2312yes—
149C2×C42×C43C2311yescharacteristic
150C2×C42×C43C2312yes—
151C2×C42×C43C2311yescharacteristic
152C2×C42×C43C2311yescharacteristic
153#95×C43C2312yes—
154#95×C43C2312yes—
155#95×C43C2312yes—
156#95×C43C2312yes—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—41no—
160C24×C43—41no—
161C24×C43—41no—
162C24×C43—41no—
163C24×C43C2×D414yes—
164C24×C43C2412yes—
165C24×C43C2411yescharacteristic
166C23×D43C2414yes—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—24no—
170C22×C4×C43—24no—
171C22×C4×C43—24no—
172C22×C4×C43—24no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43—41no—
187C22×C4×C43—416no—
188C22×C4×C43C2×D414yes—
189C22×C4×C43C2×D414yes—
190C22×C4×C43#4114yes—
191C22×C4×C43#4114yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—28no—
202C2×C22⋊D43—28no—
203C2×C22⋊D43—28no—
204C2×C22⋊D43—28no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C22×Dic43C2414yes—
211C22×Dic43C2414yes—
212C22×Dic43C2414yes—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—24no—
216C2×D172—24no—
217C2×D172—24no—
218C2×D172—42no—
219C2×D172—42no—
220C2×D172—42no—
221C2×D172—42no—
222C2×C4×D43—28no—
223C2×C4×D43—44no—
224C2×C4×D43—44no—
225C2×Dic86—24no—
226C2×Dic86—42no—
227C2×Dic86—42no—
228C22⋊C4×C43—24no—
229C22⋊C4×C43—24no—
230C22⋊C4×C43C2×D418yes—
231C22⋊C4×C43C2×D418yes—
232C42×C43—24no—
233C42×C43—22no—
234C42×C43—22no—
235C42×C43—41no—
236C42×C43—41no—
237C42×C43—42no—
238C22⋊Dic43—28no—
239C22⋊Dic43—28no—
240C22⋊Dic43—28no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—28no—
244(C2×D43)⋊C4—28no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4—44no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43—42no—
256C4⋊Dic43—42no—
257Dic43⋊C4—28no—
258Dic43⋊C4—28no—
259C4×Dic43—28no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—28no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—44no—
272C23×C43—44no—
273C23×C43—44no—
274C23×C43—44no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43C22×D414yes—
278C23×C43C22×D412yes—
279C23×C43C2×#4112yes—
280C23×C43C2×#4112yes—
281C23×C43C2511yescharacteristic
282C22×D43—24no—
283C22×D43—24no—
284C22×D43—24no—
285C22×D43—24no—
286C22×D43—24no—
287C22×D43—24no—
288C22×D43—24no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—28no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—44no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43—48no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43—48no—
315C2×C4×C43C22×D414yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C2×#4112yes—
319C2×C4×C43C2×#4112yes—
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2×#4112yes—
322C2×C4×C43H(5,𝔽2)12yes—
323C2×C4×C43H(5,𝔽2)12yes—
324C22⋊D43—416no—
325C22⋊D43—88no—
326C22⋊D43—88no—
327C2×Dic43—24no—
328C2×Dic43—24no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—24no—
334C2×Dic43—24no—
335C2×Dic43—24no—
336D172—48no—
337D172—84no—
338D172—84no—
339C4×D43—88no—
340Dic86—84no—
341#35005—431nomaximal, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—416no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43#53214yes—
357C22×C43C23×D411yescharacteristic
358C22×C43C22×#4111yescharacteristic
359C22×C43C22×#4111yescharacteristic
360C22×C43C2×H(5,𝔽2)11yescharacteristic
361C22×C43C2×H(5,𝔽2)11yescharacteristic
362C22×C43#58511yescharacteristic
363C22×C43#58511yescharacteristic
364C2×D43—44no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43—44no—
370C2×D43—44no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—24no—
374C4×C43—22no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43#53814yescomplemented
380Dic43—44no—
381Dic43—44no—
382Dic43—44no—
383C2×#538—432no—
384#2857—431no—
385#2856—431no—
386#2847—432no—
387#2639—432no—
388#2617—432no—
389#2559—434no—
390#2557—434no—
391#2496—432no—
392#2491—432no—
393#2428—432no—
394#2422—432no—
395#2325—432no—
396C4×#121—432no—
397C2×C4×C22⋊C4D4311yescharacteristic, complemented
398C2×C43—24no—
399C2×C43—44no—
400C2×C43C2×#53211yescharacteristic
401C2×C43C2×#53811yescharacteristic
402C2×C43#345511yescharacteristic
403C2×C43#349611yescharacteristic
404C2×C43#349611yescharacteristic
405C2×C43#350511yescharacteristic
406C2×C43#350611yescharacteristic
407D43—84no—
408C24×C4C2×D4311yescharacteristic
409#538—8616no—
410C2×C4⋊Q8—431no—
411C2×#127—431no—
412C2×#126—434no—
413C2×#124—434no—
414C2×#123—434no—
415C2×C22⋊Q8—432no—
416C2×#121—432no—
417C2×#121—432no—
418C2×#121—432no—
419C2×#121—432no—
420C2×#121—432no—
421C2×#121—434no—
422C2×#120—434no—
423C2×C4×D4—434no—
424C2×C4×D4—432no—
425C22×C22⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4C2×D4311yescharacteristic
427C22×C42C2×D4311yescharacteristic
428C22×C42C2×D4311yescharacteristic
429#400—434no—
430#397—434no—
431#397—434no—
432#394—434no—
433#394—434no—
434#394—434no—
435#393—434no—
436#392—434no—
437#391—432no—
438#390—432no—
439#390—432no—
440#390—432no—
441#390—432no—
442#389—432no—
443#389—432no—
444#389—432no—
445#388—434no—
446#388—434no—
447#387—434no—
448#386—434no—
449#386—434no—
450#386—434no—
451#386—434no—
452#386—434no—
453#385—434no—
454#384—431no—
455#384—431no—
456#380—432no—
457#380—432no—
458#380—432no—
459#380—432no—
460C4×C4⋊C4—432no—
461C4×C22⋊C4—434no—
462C4×C22⋊C4C2×D4312yes—
463C4×C22⋊C4C2×D4312yes—
464C4×C22⋊C4C2×D4312yes—
465C4×C22⋊C4C2×D4312yes—
466C2×#95C2×D4311yescharacteristic
467C2×#95C2×D4311yescharacteristic
468C43#3500511yescharacteristic, complemented, Sylow
469C25C22×D4311yescharacteristic
470C22×Q8—432no—
471C22×D4—434no—
472C22×D4—434no—
473C22×D4—434no—
474C22×D4—432no—
475C22×D4—432no—
476C22×D4—432no—
477C23×C4—24no—
478C23×C4—42no—
479C23×C4—42no—
480C23×C4—434no—
481C23×C4C22×D4312yes—
482C23×C4C22×D4311yescharacteristic
483C23×C4C22×D4311yescharacteristic
484C23×C4C22×D4311yescharacteristic
485C23×C4C22×D4312yes—
486C23×C4C22×D4311yescharacteristic
487C23×C4C22×D4311yescharacteristic
488C23×C4C22×D4311yescharacteristic
489C4⋊Q8—1722no—
490#127—1722no—
491#126—8616no—
492#124—8616no—
493#123—8616no—
494C22⋊Q8—868no—
495#121—868no—
496#121—868no—
497#121—868no—
498#121—8616no—
499#121—1724no—
500#121—1724no—
501#120—8616no—
502C4×D4—8616no—
503C4×D4—1724no—
504C2×C4⋊C4—432no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—432no—
508C2×C4⋊C4—432no—
509C2×C4⋊C4—432no—
510C2×C4⋊C4—432no—
511C2×C4⋊C4—432no—
512C2×C4⋊C4—432no—
513C2×C4⋊C4—432no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—434no—
524C2×C22⋊C4—434no—
525C2×C22⋊C4—434no—
526C2×C22⋊C4D17218yescomplemented
527C2×C22⋊C4C22×D4312yes—
528C2×C22⋊C4C22×D4312yes—
529C2×C22⋊C4C22×D4312yes—
530C2×C22⋊C4C22×D4312yes—
531C2×C42—42no—
532C2×C42—42no—
533C2×C42—434no—
534C2×C42C22×D4312yes—
535C2×C42C22×D4311yescharacteristic
536C2×C42C22×D4311yescharacteristic
537C2×C42C22×D4312yes—
538C2×C42C22×D4311yescharacteristic
539C2×C42C22×D4311yescharacteristic
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95C22×D4312yes—
547#95C22×D4312yes—
548#95C22×D4312yes—
549#95C22×D4312yes—
550C24—22no—
551C24—22no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—41no—
556C24—434no—
557C24C2×D17214yes—
558C24C23×D4312yes—
559C24C23×D4311yescharacteristic
560C2×Q8—864no—
561C2×Q8—1722no—
562C2×Q8—1722no—
563C2×D4—868no—
564C2×D4—868no—
565C2×D4—868no—
566C2×D4—868no—
567C2×D4—868no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—864no—
573C2×D4—1722no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4—1722no—
577C2×D4—1724no—
578C2×D4—1724no—
579C2×D4—1724no—
580C2×D4—1724no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—416no—
602C22×C4—434no—
603C22×C4—434no—
604C22×C4—434no—
605C22×C4—868no—
606C22×C4—1724no—
607C22×C4—1724no—
608C22×C4C2×D17214yes—
609C22×C4C2×D17214yes—
610C22×C4#1062189814yes—
611C22×C4#1062189814yes—
612C22×C4C23×D4312yes—
613C22×C4C23×D4312yes—
614C22×C4C23×D4312yes—
615C22×C4C23×D4311yescharacteristic
616C22×C4C23×D4311yescharacteristic
617C22×C4C23×D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620C22×C4C23×D4311yescharacteristic
621C4⋊C4—868no—
622C4⋊C4—868no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—1722no—
630C4⋊C4—1722no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—868no—
634C22⋊C4—868no—
635C22⋊C4—868no—
636C22⋊C4—868no—
637C22⋊C4—868no—
638C22⋊C4—868no—
639C22⋊C4—868no—
640C22⋊C4—1724no—
641C22⋊C4—1724no—
642C22⋊C4—1724no—
643C22⋊C4—1724no—
644C22⋊C4C2×D17218yes—
645C22⋊C4C2×D17218yes—
646C42—24no—
647C42—22no—
648C42—22no—
649C42—41no—
650C42—42no—
651C42—41no—
652C42—868no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—864no—
671C23—864no—
672C23—864no—
673C23—864no—
674C23—864no—
675C23—864no—
676C23—864no—
677C23C22×D17214yes—
678C23C22×D17212yes—
679C23C2×#1062189812yes—
680C23C2×#1062189812yes—
681C23C24×D4311yescharacteristic
682Q8—3444no—
683D4—3444no—
684D4—3444no—
685D4—3448no—
686D4—3448no—
687D4—17216no—
688D4—1728no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—48no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—864no—
724C2×C4—3448no—
725C2×C4C22×D17214yes—
726C2×C4C22×D17212yes—
727C2×C4C22×D17212yes—
728C2×C4C2×#1062189812yes—
729C2×C4C2×#1062189812yes—
730C2×C4C2×#1062189812yes—
731C2×C4C2×#1062189812yes—
732C2×C4#1306337012yes—
733C2×C4#1306337012yes—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—416no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—1724no—
749C22—1724no—
750C22—1724no—
751C22—1724no—
752C22—1724no—
753C22—1724no—
754C22—1724no—
755C22#1458344914yes—
756C22C23×D17211yescharacteristic
757C22C22×#1062189811yescharacteristic
758C22C22×#1062189811yescharacteristic
759C22C2×#1306337011yescharacteristic
760C22C2×#1306337011yescharacteristic
761C22#1458373511yescharacteristic
762C22#1458373511yescharacteristic
763C4—24no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—1724no—
772C4—1724no—
773C4—1724no—
774C4#1458348714yescomplemented
775C2—24no—
776C2—44no—
777C2—3444no—
778C2C2×#1458344911yescharacteristic
779C2C2×#1458348711yescharacteristic
780C2#1914798511yescharacteristic
781C2#1914835911yescharacteristic
782C2#1914835911yescharacteristic
783C2#1914843411yescharacteristic
784C2#1914844711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC2×C4×C22⋊C4×C43C2
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#35005
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583487C2semidirect
2. #19142947C2semidirect
3. #19142940C2semidirect
4. #19142877C2semidirect
5. #19140523C2semidirect
6. #19140329C2semidirect
7. #19139718C2semidirect
8. #19139688C2semidirect
9. #19139017C2semidirect
10. #19138958C2semidirect
11. #19138183C2semidirect
12. #19138109C2semidirect
13. #19137298C2semidirect
14. C4×#13063299C2semidirect
15. C2×C4×C22⋊C4×C43C2semidirect
17. C2×#13063325C22semidirect
18. C2×#13063322C22semidirect
30. C2×C4×D172C22semidirect
32. #14582839C22semidirect
33. #14582826C22semidirect
35. #14582817C22semidirect
38. #14582812C22semidirect
40. #14582805C22semidirect
41. #14582801C22semidirect
42. #14582801C22semidirect
43. #14582801C22semidirect
44. #14582801C22semidirect
45. #14582797C22semidirect
46. #14582797C22semidirect
47. #14582797C22semidirect
48. #14582791C22semidirect
49. #14582790C22semidirect
50. #14582784C22semidirect
55. #14582777C22semidirect
56. #14582773C22semidirect
57. #14582769C22semidirect
58. #14582769C22semidirect
63. C4×C4⋊Dic43C22semidirect
64. C4×(C2×D43)⋊C4C22semidirect
140. C2×C22⋊C4×C43D4semidirect
379. C4×C43#538semidirect
397. C2×C4×C22⋊C4D43semidirect
468. C43#35005semidirect
526. C2×C22⋊C4D172semidirect
774. C4#14583487semidirect

Maximal subgroups

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

subgroupindex
C2×#145834872
#191429472
#191429402
#191428772
#191405232
#191403292
#191397182
#191396882
#191390172
#191389582
#191381832
#191381092
#191372982
C4×#130632992
C2×C4×C22⋊C4×C432
#3500543