Finite Group Databasebeta

← #25138971

Subgroups — #25138971

Order 11008.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583150C211yesmaximal, characteristic, complemented
2C2×#14583150C211yesmaximal, characteristic, complemented
3C2×#14582977C211yesmaximal, characteristic, complemented
4C2×#14582942C211yesmaximal, characteristic, complemented
5#19138035C211yesmaximal, characteristic, complemented
6#19135983C211yesmaximal, characteristic, complemented
7#19135966C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135777C211yesmaximal, characteristic, complemented
10#19135460C211yesmaximal, characteristic, complemented
11#19135320C211yesmaximal, characteristic, complemented
12#19134917C211yesmaximal, characteristic, complemented
13#19134913C211yesmaximal, characteristic, complemented
14#19134626C211yesmaximal, characteristic, complemented
15C43×#2414C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063297—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14583150—24no—
24#14583150—24no—
25#14582977—24no—
26#14582942—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582821—21no—
43#14582815—21no—
44#14582801C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582776—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#394—21no—
57C43×#392—21no—
58C43×#390—21no—
59C43×#390C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#388—21no—
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C2×#10621877—22no—
75C2×#10621877D414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063299—41no—
84#13063297—44no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—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—
97#13063258—22no—
98#13063258—22no—
99#13063256—22no—
100#13063256—22no—
101#13063256D414yescomplemented
102C4⋊(C43⋊C8)—22no—
103#13063246—22no—
104#13063246—22no—
105#13063246—41no—
106#13063245—22no—
107#13063245—22no—
108#13063245—41no—
109C22⋊(C43⋊C8)—22no—
110C22⋊(C43⋊C8)—22no—
111C4×C43⋊C8—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×D4×C43—21no—
115C22×D4×C43—21no—
116C22×D4×C43D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—41no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126#117×C43—22no—
127#117×C43—41no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43C2311yescharacteristic
143#95×C43—21no—
144#95×C43—21no—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C24×C43C2×D411yescharacteristic
148C23×D43—21no—
149C2×D4×C43—22no—
150C2×D4×C43—22no—
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—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C22×C4×C43—21no—
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×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C2×D412yes—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43C2411yescharacteristic
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—81no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—81no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—81no—
209C4⋊C4×C43C2×D412yes—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—81no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—42no—
221C22⋊Dic43—42no—
222#10621882—44no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43C2×D412yes—
234Dic43⋊C4—42no—
235#10621877—28no—
236#10621877—44no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8C2×D412yes—
246C2×C43⋊C8C2×D412yes—
247C2×C43⋊C8C2×D412yes—
248C2×C43⋊C8#4112yes—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43#12112yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278D4×C43—44no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—84no—
284D4×C43—84no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
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#12112yes—
313C2×C4×C43AGL(1,ℤ/8)12yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C432−1+411yescharacteristic
320C22⋊D43—84no—
321C22⋊D43—84no—
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—84no—
332D172—41no—
333D172—41no—
334D172—41no—
335D172—41no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339C43⋊C8#12114yescomplemented
340#24792—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—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43C2×#12111yescharacteristic
363C22×C43D4211yescharacteristic
364C22×C43#54711yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43#57511yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57711yescharacteristic
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—42no—
380C4×C43—41no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43C2×#12111yescharacteristic
384C4×C43#53711yescharacteristic
385C4×C43#54811yescharacteristic
386C4×C43#55311yescharacteristic
387Dic43—42no—
388Dic43—81no—
389Dic43—81no—
390C2×#469—431no—
391C2×#469—431no—
392C2×#436—431no—
393C2×#428—431no—
394#2416—431no—
395#2414D4311yescharacteristic, complemented
396#2067—431no—
397#2065—431no—
398#2034—431no—
399#2033—431no—
400#1970—431no—
401#1941—431no—
402#1875—431no—
403#1874—431no—
404#1809—431no—
405C2×C43—42no—
406C2×C43—81no—
407C2×C43—161no—
408C2×C43#241611yescharacteristic
409C2×C43#305511yescharacteristic
410C2×C43#306211yescharacteristic
411C2×C43#327411yescharacteristic
412C2×C43#327511yescharacteristic
413C2×C43#335411yescharacteristic
414C2×C43#335511yescharacteristic
415D43—161no—
416C22×D8—431no—
417C22×M16—431no—
418C22×M16—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×#121C2×D4311yescharacteristic
423C2×#121C2×D4311yescharacteristic
424C2×C4×D4C2×D4311yescharacteristic
425C2×#117C2×D4311yescharacteristic
426C22×C4⋊C4—431no—
427#469—864no—
428#469—864no—
429#436—864no—
430#428—864no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#106—431no—
434C2×#106—431no—
435C2×#106—431no—
436C2×C4⋊C8—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C4×C8—431no—
446#396—861no—
447#394—21no—
448#394—861no—
449#392—21no—
450#390—21no—
451#390—431no—
452#390C2×D4311yescharacteristic
453#389—431no—
454#389C2×D4311yescharacteristic
455#388—21no—
456#386—861no—
457#380—431no—
458#380C2×D4311yescharacteristic
459#340—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463C43#2479211yescharacteristic, complemented, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4C22⋊D4311yescharacteristic
470C22×D4C22×D4311yescharacteristic
471C23×C4—861no—
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×D8—862no—
475C2×D8—862no—
476C2×D8—862no—
477C2×M16—434no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—862no—
481C2×M16—862no—
482C2×M16—862no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—431no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—41no—
491#121—862no—
492#121—862no—
493#121—862no—
494#121—1721no—
495#121—1724no—
496C4×D4—22no—
497C4×D4—22no—
498#117—22no—
499#117—41no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—1721no—
508C2×C4⋊C4C22⋊D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4C22⋊D4311yescharacteristic
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C42—21no—
526C2×C42C22×D4311yescharacteristic
527#107—862no—
528#107—862no—
529#106—434no—
530#106—862no—
531#106—862no—
532C4⋊C8—862no—
533#102—862no—
534#102—862no—
535#102—862no—
536#102—862no—
537#102—1721no—
538#102—1721no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C4×C8—862no—
542#95—21no—
543#95—21no—
544#95—861no—
545#95—861no—
546C24—21no—
547C24—861no—
548C24C2×C22⋊D4311yescharacteristic
549C24C2×C22⋊D4311yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—3441no—
572C2×D4—1722no—
573C2×D4—1722no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4—1722no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—3441no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4D4×D4312yes—
597C22×C4#1062190012yes—
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603D8—1724no—
604M16—868no—
605M16—1724no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—81no—
625C4⋊C4—432no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C4⋊C4D4×D4312yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—3441no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C42—21no—
648C42—21no—
649C42—42no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23#1306329712yes—
678C23C22×C22⋊D4311yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—3444no—
687D4—3444no—
688D4—1721no—
689D4—1721no—
690D4—1721no—
691D4—1721no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—862no—
720C2×C4—3444no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4#1306329712yes—
730C2×C4#1306335012yes—
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4C2×#1062190011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337211yescharacteristic
737C8—434no—
738C8—862no—
739C8—1721no—
740C8—1721no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—3441no—
763C22—3441no—
764C22—3441no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22C2×#1306329711yescharacteristic
770C22D4×C22⋊D4311yescharacteristic
771C22#1458354811yescharacteristic
772C22C2×#1306335011yescharacteristic
773C22#1458369711yescharacteristic
774C22#1458370211yescharacteristic
775C22#1458371011yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—3441no—
784C4—3441no—
785C4—1722no—
786C4#121×D4311yescharacteristic
787C4#1458347611yescharacteristic
788C4#1458355511yescharacteristic
789C4#1458359211yescharacteristic
790C2—42no—
791C2—81no—
792C2—161no—
793C2—6881no—
794C2#1913803211yescharacteristic
795C2#1914421611yescharacteristic
796C2#1914427111yescharacteristic
797C2#1914621511yescharacteristic
798C2#1914622211yescharacteristic
799C2#1914718411yescharacteristic
800C2#1914719511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2414C2
socleC23×C43C22×D4
hypercenter#2414D43
hypocenterC43#24792
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. C2×#14583150C2semidirect
2. C2×#14583150C2semidirect
3. C2×#14582977C2semidirect
4. C2×#14582942C2semidirect
5. #19138035C2semidirect
6. #19135983C2semidirect
7. #19135966C2semidirect
8. #19135781C2semidirect
9. #19135777C2semidirect
10. #19135460C2semidirect
11. #19135320C2semidirect
12. #19134917C2semidirect
13. #19134913C2semidirect
14. #19134626C2semidirect
15. C43×#2414C2semidirect
75. C2×#10621877D4semidirect
101. #13063256D4semidirect
339. C43⋊C8#121semidirect
395. #2414D43semidirect
463. C43#24792semidirect

Maximal subgroups

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

subgroupindex
C2×#145831502
C2×#145829772
C2×#145829422
#191380352
#191359832
#191359662
#191357812
#191357772
#191354602
#191353202
#191349172
#191349132
#191346262
C43×#24142
#2479243