Finite Group Databasebeta

← #25147532

Subgroups — #25147532

Order 11008.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583147C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583101C211yesmaximal, characteristic, complemented
4C2×#14582971C211yesmaximal, characteristic, complemented
5#19139496C211yesmaximal, characteristic
6#19135795C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19135416C211yesmaximal, characteristic, complemented
11#19135363C211yesmaximal, characteristic, complemented
12#19135029C211yesmaximal, characteristic, complemented
13#19135019C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic, complemented
15C43×#2542C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583147—24no—
24#14583130—24no—
25#14583101—24no—
26#14582971—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41#14582825—21no—
42#14582807—21no—
43#14582775—21no—
44#14582775—21no—
45#14582765C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#399—21no—
59C43×#399—21no—
60C43×#390—21no—
61C43×#384—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—41no—
72C2×#10621884—41no—
73C2×#10621877—22no—
74C2×#10621877—22no—
75C2×#10621877—41no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063299—22no—
84#13063299—22no—
85#13063299—41no—
86#13063299—41no—
87C4×D172—22no—
88C4×D172—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97#13063258—22no—
98#13063256—22no—
99C4⋊(C43⋊C8)D414yescomplemented
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—41no—
105#13063249—41no—
106#13063245—22no—
107#13063245D414yescomplemented
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—22no—
110#13063236—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43D411yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C4⋊Q8×C43—22no—
121C4⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123C22⋊Q8×C43—22no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128C22⋊Q8×C43—41no—
129C22⋊Q8×C43—41no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#95×C43—21no—
150C24×C43C2×D411yescharacteristic
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—41no—
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×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—81no—
194C2×C22⋊D43—81no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172C2×D412yes—
204C2×C4×D43—42no—
205C2×C4×D43—81no—
206C2×C4×D43—81no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—42no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43C2×D412yes—
217C4⋊C4×C43#4112yes—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C42×C43—42no—
225C42×C43C2×D412yes—
226C42×C43#4112yes—
227C22⋊Dic43—81no—
228C22⋊Dic43—81no—
229#10621884—44no—
230#10621884—44no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233(C2×D43)⋊C4—42no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240#10621877—44no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—44no—
251C2×C43⋊C8C2×D412yes—
252C2×C43⋊C8C2×D412yes—
253C2×C43⋊C8C2×D412yes—
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—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43#13712yes—
268C23×C43C22×D411yescharacteristic
269C22×D43—22no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280Q8×C43—41no—
281Q8×C43—41no—
282Q8×C43—41no—
283Q8×C43—41no—
284D4×C43—44no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
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—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43#12112yes—
316C2×C4×C43#12112yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—84no—
324C22⋊D43—84no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334D172—22no—
335D172—22no—
336D172—41no—
337D172—41no—
338C4×D43—84no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343#25400—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
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—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43C2×#12111yescharacteristic
359C22×C43D4211yescharacteristic
360C22×C43#54611yescharacteristic
361C22×C43C2×#13711yescharacteristic
362C22×C43#57511yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57711yescharacteristic
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—81no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43#53211yescharacteristic
381C4×C43#54011yescharacteristic
382C4×C43D4211yescharacteristic
383C4×C43#55011yescharacteristic
384Dic43—81no—
385Dic43—81no—
386Dic43—81no—
387C2×#468—431no—
388C2×#465—431no—
389C2×#461—431no—
390C2×#435—431no—
391#2542D4311yescharacteristic, complemented
392#2535—431no—
393#2036—431no—
394#2035—431no—
395#2000—431no—
396#2000—431no—
397#1960—431no—
398#1949—431no—
399#1894—431no—
400#1892—431no—
401#1762—431no—
402C2×C43—42no—
403C2×C43—81no—
404C2×C43#242811yescharacteristic
405C2×C43#305611yescharacteristic
406C2×C43#305711yescharacteristic
407C2×C43#326611yescharacteristic
408C2×C43#326711yescharacteristic
409C2×C43#330711yescharacteristic
410C2×C43#332011yescharacteristic
411D43—82no—
412C22×SD16—431no—
413C22×SD16—431no—
414C22×M16—431no—
415C23×C8—431no—
416C2×C4⋊Q8C2×D4311yescharacteristic
417C2×C22⋊Q8C2×D4311yescharacteristic
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×C22⋊Q8C2×D4311yescharacteristic
420C2×C22⋊Q8C2×D4311yescharacteristic
421C2×#121—431no—
422C2×#121—431no—
423C2×C4×D4—431no—
424C2×C4×D4C2×D4311yescharacteristic
425#468—864no—
426#465—864no—
427#461—864no—
428#435—864no—
429C2×#107—431no—
430C2×#106—431no—
431C2×C4⋊C8—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×#97—431no—
443#399—21no—
444#399—21no—
445#397—861no—
446#392—861no—
447#390—21no—
448#386—861no—
449#386—861no—
450#384—21no—
451#382—431no—
452#380—431no—
453#380—431no—
454C4×C4⋊C4C2×D4311yescharacteristic
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459C43#2540011yescharacteristic, complemented, Sylow
460C22×Q8C22×D4311yescharacteristic
461C22×Q8C22×D4311yescharacteristic
462C22×D4—431no—
463C22×D4—861no—
464C22×D4—861no—
465C22×D4C22⋊D4311yescharacteristic
466C23×C4—861no—
467C23×C4C22×D4311yescharacteristic
468C23×C4C22×D4311yescharacteristic
469C2×SD16—862no—
470C2×SD16—862no—
471C2×SD16—862no—
472C2×SD16—862no—
473C2×SD16—1721no—
474C2×SD16—1721no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—1721no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—862no—
483C22×C8—862no—
484C22×C8—1721no—
485C4⋊Q8—22no—
486C4⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—41no—
492C22⋊Q8—41no—
493C22⋊Q8—41no—
494C22⋊Q8—41no—
495#121—862no—
496#121—862no—
497#121—1721no—
498#121—1721no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—862no—
502C4×D4—862no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4C22⋊D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C42—21no—
527C2×C42C22×D4311yescharacteristic
528#107—862no—
529#106—862no—
530C4⋊C8—434no—
531#103—862no—
532#103—862no—
533#103—862no—
534#103—862no—
535#103—1721no—
536#103—1721no—
537#102—434no—
538#102—862no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541#97—862no—
542#95—21no—
543#95—861no—
544#95—861no—
545#95—861no—
546#95—861no—
547C24—861no—
548C24C2×C22⋊D4311yescharacteristic
549C24C2×C22⋊D4311yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—432no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—3441no—
572C2×D4—3441no—
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—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—3441no—
597C22×C4—3441no—
598C22×C4—1722no—
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604SD16—1724no—
605SD16—1724no—
606M16—1724no—
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—
618C2×C8—861no—
619C2×C8—1724no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4D4×D4312yes—
636C4⋊C4#1062190012yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—3441no—
644C22⋊C4—3441no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C42—42no—
649C42D4×D4312yes—
650C42#1062190012yes—
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—21no—
664C23—862no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23#1306335612yes—
672C23C22×C22⋊D4311yescharacteristic
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—44no—
682D4—862no—
683D4—862no—
684D4—3444no—
685D4—3444no—
686D4—1721no—
687D4—1721no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
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—3444no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4#1306329712yes—
729C2×C4#1306329712yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C2×#1062190011yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C8—862no—
737C8—862no—
738C8—862no—
739C8—1721no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—3441no—
755C22—3441no—
756C22—3441no—
757C22—3441no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22C2×#1306329711yescharacteristic
762C22D4×C22⋊D4311yescharacteristic
763C22#1458354311yescharacteristic
764C22C2×#1306335611yescharacteristic
765C22#1458369711yescharacteristic
766C22#1458370711yescharacteristic
767C22#1458370711yescharacteristic
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—3441no—
777C4—3441no—
778C4—3441no—
779C4#1458344711yescharacteristic
780C4#1458350311yescharacteristic
781C4#1458353411yescharacteristic
782C4#1458356911yescharacteristic
783C2—42no—
784C2—81no—
785C2—3442no—
786C2#1913818611yescharacteristic
787C2#1914422111yescharacteristic
788C2#1914423611yescharacteristic
789C2#1914610611yescharacteristic
790C2#1914612111yescharacteristic
791C2#1914657111yescharacteristic
792C2#1914676611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2542C2
socleC23×C43C22×D4
prime radical#19139496C2
hypercenter#2542D43
hypocenterC43#25400
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#14583147C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583101C2semidirect
4. C2×#14582971C2semidirect
6. #19135795C2semidirect
7. #19135788C2semidirect
8. #19135596C2semidirect
9. #19135596C2semidirect
10. #19135416C2semidirect
11. #19135363C2semidirect
12. #19135029C2semidirect
13. #19135019C2semidirect
14. #19134423C2semidirect
15. C43×#2542C2semidirect
99. C4⋊(C43⋊C8)D4semidirect
107. #13063245D4semidirect
391. #2542D43semidirect
459. C43#25400semidirect

Maximal subgroups

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

subgroupindex
C2×#145831472
C2×#145831302
C2×#145831012
C2×#145829712
#191394962
#191357952
#191357882
#191355962
#191354162
#191353632
#191350292
#191350192
#191344232
C43×#25422
#2540043