Finite Group Databasebeta

← #25147381

Subgroups — #25147381

Order 11008.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583138C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583121C211yesmaximal, characteristic, complemented
4C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
5#19139534C211yesmaximal, characteristic
6#19135791C211yesmaximal, characteristic, complemented
7#19135777C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19135404C211yesmaximal, characteristic, complemented
11#19135361C211yesmaximal, characteristic, complemented
12#19135021C211yesmaximal, characteristic, complemented
13#19135016C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#2536C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25#14583138—24no—
26#14583130—24no—
27#14583121—24no—
28D4×C43⋊C8—24no—
29C2×#13063258C2211yescharacteristic
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×C4×C43⋊C8C2211yescharacteristic
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×#398—21no—
57C43×#394—21no—
58C43×#388—21no—
59C43×#388—21no—
60C43×#382C2211yescharacteristic
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—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
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#13063258—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—
117C4×C43⋊C8—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×C43D411yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
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—22no—
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—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C42×C43—42no—
221C42×C43C2×D412yes—
222C42×C43#4112yes—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225#10621885—44no—
226#10621884—44no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43#4112yes—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237C4×Dic43—81no—
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⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—44no—
248C2×C43⋊C8—44no—
249C2×C43⋊C8C2×D412yes—
250C2×C43⋊C8C2×D412yes—
251C2×C43⋊C8C2×D412yes—
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—21no—
263C23×C43—21no—
264C23×C43#13512yes—
265C23×C43#13512yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—28no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
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—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
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#12112yes—
310C2×C4×C43#12112yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C22⋊D43—84no—
318C22⋊D43—84no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328D172—41no—
329D172—41no—
330D172—41no—
331D172—41no—
332Dic86—41no—
333Dic86—41no—
334Dic86—41no—
335Dic86—41no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#25389—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
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×C43C2×#12111yescharacteristic
356C22×C43D4211yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43C2×#13511yescharacteristic
359C22×C43C2×#13511yescharacteristic
360C22×C43#57711yescharacteristic
361C22×C43#57811yescharacteristic
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43#53211yescharacteristic
378C4×C43#54011yescharacteristic
379C4×C43D4211yescharacteristic
380C4×C43#55011yescharacteristic
381Dic43—42no—
382Dic43—42no—
383Dic43—81no—
384C2×#467—431no—
385C2×#465—431no—
386C2×#464—431no—
387C2×C8×D4—431no—
388#2540—431no—
389#2536D4311yescharacteristic, complemented
390#2035—431no—
391#2033—431no—
392#2001—431no—
393#2000—431no—
394#1958—431no—
395#1949—431no—
396#1893—431no—
397#1892—431no—
398C4×#103—431no—
399C2×C43—42no—
400C2×C43—42no—
401C2×C43#242811yescharacteristic
402C2×C43#305011yescharacteristic
403C2×C43#306311yescharacteristic
404C2×C43#328211yescharacteristic
405C2×C43#328511yescharacteristic
406C2×C43#329611yescharacteristic
407C2×C43#330011yescharacteristic
408D43—161no—
409C22×Q16—431no—
410C22×SD16—431no—
411C23×C8—431no—
412C23×C8—431no—
413C2×#124—431no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8C2×D4311yescharacteristic
417C2×C22⋊Q8C2×D4311yescharacteristic
418C2×#121—431no—
419C2×#121—431no—
420C2×C4×Q8C2×D4311yescharacteristic
421C2×C4×D4C2×D4311yescharacteristic
422#467—864no—
423#465—864no—
424#464—864no—
425C8×D4—864no—
426C2×#107—431no—
427C2×#106—431no—
428C2×C4⋊C8—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C4×C8—431no—
440#399—861no—
441#398—21no—
442#394—21no—
443#392—861no—
444#390—861no—
445#390—861no—
446#388—21no—
447#388—21no—
448#382C2×D4311yescharacteristic
449#380C2×D4311yescharacteristic
450#380C2×D4311yescharacteristic
451C4×C4⋊C4—431no—
452#340—431no—
453#340—431no—
454#340—431no—
455#340—431no—
456C43#2538911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×Q8C22×D4311yescharacteristic
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4C22⋊D4311yescharacteristic
463C23×C4C22×D4311yescharacteristic
464C23×C4C22×D4311yescharacteristic
465C2×Q16—862no—
466C2×Q16—862no—
467C2×Q16—1721no—
468C2×SD16—862no—
469C2×SD16—862no—
470C2×SD16—1721no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—862no—
476C22×C8—862no—
477C22×C8—862no—
478C22×C8—862no—
479C22×C8—1721no—
480C22×C8—1721no—
481#124—862no—
482#124—862no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—41no—
486C22⋊Q8—41no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—1721no—
490C22⋊Q8—1721no—
491#121—862no—
492#121—862no—
493#121—1721no—
494#121—1721no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22⋊D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C22⋊C4C22⋊D4311yescharacteristic
522C2×C42—21no—
523C2×C42—861no—
524C2×C42C22×D4311yescharacteristic
525#107—862no—
526#106—862no—
527C4⋊C8—434no—
528#103—434no—
529#103—862no—
530#103—862no—
531#103—862no—
532#103—1721no—
533#102—862no—
534#102—862no—
535#102—1721no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C4×C8—862no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—861no—
544C24—861no—
545C24C2×C22⋊D4311yescharacteristic
546C24C2×C22⋊D4311yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8D4×D4312yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—3441no—
569C2×D4—3441no—
570C2×D4—1722no—
571C2×D4—1722no—
572C2×D4—1722no—
573C2×D4—1722no—
574C22×C4—21no—
575C22×C4—21no—
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—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598Q16—1724no—
599SD16—1724no—
600C2×C8—432no—
601C2×C8—432no—
602C2×C8—432no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—1724no—
613C2×C8—1724no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—1722no—
629C4⋊C4—1722no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—1722no—
637C22⋊C4—1722no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C42—42no—
643C42—3441no—
644C42D4×D4312yes—
645C42#1062190012yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—1721no—
659C23—1721no—
660C23—1721no—
661C23—1721no—
662C23—1721no—
663C23—1721no—
664C23—1721no—
665C23#1306334512yes—
666C23#1306334512yes—
667C23C22×C22⋊D4311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—1721no—
673Q8—1721no—
674Q8—1721no—
675Q8—1721no—
676D4—28no—
677D4—3444no—
678D4—3444no—
679D4—1721no—
680D4—1721no—
681D4—1721no—
682D4—1721no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
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—862no—
714C2×C4—862no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4#1306329712yes—
723C2×C4#1306329712yes—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4#1306337011yescharacteristic
729C2×C4#1306337111yescharacteristic
730C8—862no—
731C8—862no—
732C8—862no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22—3441no—
752C22—3441no—
753C22—3441no—
754C22—3441no—
755C22C2×#1306329711yescharacteristic
756C22D4×C22⋊D4311yescharacteristic
757C22#1458353711yescharacteristic
758C22C2×#1306334511yescharacteristic
759C22C2×#1306334511yescharacteristic
760C22#1458370711yescharacteristic
761C22#1458371411yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4—3441no—
771C4—1722no—
772C4—1722no—
773C4#1458344411yescharacteristic
774C4#1458350211yescharacteristic
775C4#1458353311yescharacteristic
776C4#1458356711yescharacteristic
777C2—42no—
778C2—42no—
779C2—6881no—
780C2#1913818511yescharacteristic
781C2#1914417311yescharacteristic
782C2#1914428211yescharacteristic
783C2#1914630311yescharacteristic
784C2#1914633211yescharacteristic
785C2#1914642411yescharacteristic
786C2#1914647611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2536C2
socleC23×C43C22×D4
prime radical#19139534C2
hypercenter#2536D43
hypocenterC43#25389
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#14583138C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583121C2semidirect
4. C2×D4×C43⋊C8C2semidirect
6. #19135791C2semidirect
7. #19135777C2semidirect
8. #19135603C2semidirect
9. #19135596C2semidirect
10. #19135404C2semidirect
11. #19135361C2semidirect
12. #19135021C2semidirect
13. #19135016C2semidirect
14. C4×#13063249C2semidirect
15. C43×#2536C2semidirect
106. C4⋊(C43⋊C8)D4semidirect
108. #13063249D4semidirect
389. #2536D43semidirect
456. C43#25389semidirect

Maximal subgroups

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

subgroupindex
C2×#145831382
C2×#145831302
C2×#145831212
C2×D4×C43⋊C82
#191395342
#191357912
#191357772
#191356032
#191355962
#191354042
#191353612
#191350212
#191350162
C4×#130632492
C43×#25362
#2538943