Finite Group Databasebeta

← #25147575

Subgroups — #25147575

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583155C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583121C211yesmaximal, characteristic, complemented
4C2×#14582971C211yesmaximal, characteristic, complemented
5#19139534C211yesmaximal, characteristic
6#19135791C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19135409C211yesmaximal, characteristic, complemented
11#19135356C211yesmaximal, characteristic, complemented
12#19135031C211yesmaximal, characteristic, complemented
13#19135016C211yesmaximal, characteristic, complemented
14#19134425C211yesmaximal, characteristic, complemented
15C43×#2538C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25#14583155—24no—
26#14583130—24no—
27#14583121—24no—
28#14582971—24no—
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063236C2211yescharacteristic
43#14582834—21no—
44#14582807—21no—
45#14582799—21no—
46#14582799—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#396—21no—
57C43×#396—21no—
58C43×#390—21no—
59C43×#389—21no—
60C43×#384C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621884—22no—
71C2×#10621884—22no—
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#13063313—22no—
84#13063313—22no—
85#13063304—22no—
86#13063304—22no—
87#13063304—41no—
88#13063304—41no—
89#13063299—22no—
90#13063299—22no—
91#13063299—41no—
92#13063299—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104#13063256—22no—
105#13063256—22no—
106C4⋊(C43⋊C8)D414yescomplemented
107#13063249—22no—
108#13063249D414yescomplemented
109#13063248—22no—
110#13063248—22no—
111#13063248—41no—
112#13063245—22no—
113#13063245—22no—
114#13063245—41no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117#13063236—22no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22⋊Q8×C43—22no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43—22no—
128C4×Q8×C43—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148#95×C43—21no—
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×C43C2×D412yes—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—41no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
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×C43—21no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—81no—
188C2×C22⋊D43—81no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—42no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43—81no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—81no—
221C22⋊C4×C43—81no—
222C42×C43—42no—
223C42×C43C2×D412yes—
224C42×C43#4112yes—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227#10621885—44no—
228#10621884—44no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43C2×D412yes—
236C4⋊Dic43#4112yes—
237Dic43⋊C4—42no—
238Dic43⋊C4—42no—
239C4×Dic43—81no—
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—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—44no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
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#12112yes—
312C2×C4×C43#12112yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C22⋊D43—84no—
320C22⋊D43—84no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330D172—41no—
331D172—41no—
332D172—41no—
333D172—41no—
334Dic86—41no—
335Dic86—41no—
336Dic86—41no—
337Dic86—41no—
338C43⋊C8—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342#25403—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
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—41no—
356C22×C43—41no—
357C22×C43C2×#12111yescharacteristic
358C22×C43D4211yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43C2×#13711yescharacteristic
361C22×C43#57511yescharacteristic
362C22×C43#57711yescharacteristic
363C22×C43#57711yescharacteristic
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43—81no—
370C2×D43—81no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—42no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43#53211yescharacteristic
380C4×C43#54011yescharacteristic
381C4×C43D4211yescharacteristic
382C4×C43#55011yescharacteristic
383Dic43—42no—
384Dic43—42no—
385Dic43—81no—
386C2×#470—431no—
387C2×#465—431no—
388C2×#464—431no—
389C2×#435—431no—
390#2540—431no—
391#2538D4311yescharacteristic, complemented
392#2035—431no—
393#2034—431no—
394#2001—431no—
395#2000—431no—
396#1959—431no—
397#1948—431no—
398#1895—431no—
399#1892—431no—
400#1763—431no—
401C2×C43—42no—
402C2×C43—81no—
403C2×C43#242811yescharacteristic
404C2×C43#305611yescharacteristic
405C2×C43#306011yescharacteristic
406C2×C43#326611yescharacteristic
407C2×C43#327111yescharacteristic
408C2×C43#331111yescharacteristic
409C2×C43#331611yescharacteristic
410D43—161no—
411C22×Q16—431no—
412C22×SD16—431no—
413C22×M16—431no—
414C23×C8—431no—
415C2×#124—431no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×C22⋊Q8C2×D4311yescharacteristic
420C2×#121—431no—
421C2×#121—431no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4C2×D4311yescharacteristic
424#470—864no—
425#465—864no—
426#464—864no—
427#435—864no—
428C2×#106—431no—
429C2×#106—431no—
430C2×C4⋊C8—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×#97—431no—
442#399—861no—
443#396—21no—
444#396—21no—
445#392—861no—
446#390—21no—
447#390—861no—
448#390—861no—
449#389—21no—
450#384C2×D4311yescharacteristic
451#380C2×D4311yescharacteristic
452#380C2×D4311yescharacteristic
453C4×C4⋊C4—431no—
454#340—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458C43#2540311yescharacteristic, complemented, Sylow
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—431no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4C22⋊D4311yescharacteristic
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C2×Q16—862no—
468C2×Q16—862no—
469C2×Q16—1721no—
470C2×SD16—862no—
471C2×SD16—862no—
472C2×SD16—1721no—
473C2×M16—862no—
474C2×M16—862no—
475C2×M16—1721no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8—1721no—
483#124—862no—
484#124—862no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—862no—
490C22⋊Q8—862no—
491C22⋊Q8—1721no—
492C22⋊Q8—1721no—
493#121—862no—
494#121—862no—
495#121—1721no—
496#121—1721no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×D4—22no—
500C4×D4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4C22⋊D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
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⋊C4—861no—
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C42—21no—
527C2×C42—861no—
528C2×C42C22×D4311yescharacteristic
529#106—862no—
530#106—862no—
531C4⋊C8—434no—
532#103—434no—
533#103—862no—
534#103—862no—
535#103—862no—
536#103—1721no—
537#102—862no—
538#102—862no—
539#102—1721no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542#97—862no—
543#95—21no—
544#95—21no—
545#95—861no—
546C24—861no—
547C24C2×C22⋊D4311yescharacteristic
548C24C2×C22⋊D4311yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×Q8D4×D4312yes—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—3441no—
571C2×D4—3441no—
572C2×D4—1722no—
573C2×D4—1722no—
574C2×D4—1722no—
575C2×D4—1722no—
576C22×C4—21no—
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—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600Q16—1724no—
601SD16—1724no—
602M16—1724no—
603C2×C8—432no—
604C2×C8—432no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—1724no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—81no—
628C4⋊C4—432no—
629C4⋊C4—432no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—1722no—
633C4⋊C4—1722no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C42—42no—
647C42—3441no—
648C42D4×D4312yes—
649C42#1062190012yes—
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—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23#1306335612yes—
671C23C22×C22⋊D4311yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—1721no—
677Q8—1721no—
678Q8—1721no—
679Q8—1721no—
680D4—44no—
681D4—3444no—
682D4—3444no—
683D4—1721no—
684D4—1721no—
685D4—1721no—
686D4—1721no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
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—862no—
718C2×C4—862no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4#1306329712yes—
727C2×C4#1306329712yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337111yescharacteristic
734C8—862no—
735C8—862no—
736C8—862no—
737C8—1721no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—3441no—
753C22—3441no—
754C22—3441no—
755C22—3441no—
756C22—3441no—
757C22—3441no—
758C22—3441no—
759C22C2×#1306329711yescharacteristic
760C22D4×C22⋊D4311yescharacteristic
761C22#1458353711yescharacteristic
762C22C2×#1306335611yescharacteristic
763C22#1458369711yescharacteristic
764C22#1458370711yescharacteristic
765C22#1458371011yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—3441no—
775C4—1722no—
776C4—1722no—
777C4#1458344411yescharacteristic
778C4#1458350211yescharacteristic
779C4#1458353311yescharacteristic
780C4#1458356711yescharacteristic
781C2—42no—
782C2—81no—
783C2—6881no—
784C2#1913818511yescharacteristic
785C2#1914422111yescharacteristic
786C2#1914425411yescharacteristic
787C2#1914610611yescharacteristic
788C2#1914617611yescharacteristic
789C2#1914662511yescharacteristic
790C2#1914670011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2538C2
socleC23×C43C22×D4
prime radical#19139534C2
hypercenter#2538D43
hypocenterC43#25403
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#14583155C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583121C2semidirect
4. C2×#14582971C2semidirect
6. #19135791C2semidirect
7. #19135784C2semidirect
8. #19135603C2semidirect
9. #19135596C2semidirect
10. #19135409C2semidirect
11. #19135356C2semidirect
12. #19135031C2semidirect
13. #19135016C2semidirect
14. #19134425C2semidirect
15. C43×#2538C2semidirect
106. C4⋊(C43⋊C8)D4semidirect
108. #13063249D4semidirect
391. #2538D43semidirect
458. C43#25403semidirect

Maximal subgroups

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

subgroupindex
C2×#145831552
C2×#145831302
C2×#145831212
C2×#145829712
#191395342
#191357912
#191357842
#191356032
#191355962
#191354092
#191353562
#191350312
#191350162
#191344252
C43×#25382
#2540343