Finite Group Databasebeta

← #25130675

Subgroups — #25130675

Order 11008.

1336 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×#14583549C211yesmaximal, characteristic
2C2×#14583192C211yesmaximal, characteristic, complemented
3C2×#14583000C211yesmaximal, characteristic, complemented
4#19139502C211yesmaximal, characteristic, complemented
5#19135776C211yesmaximal, characteristic, complemented
6#19135774C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135566C211yesmaximal, characteristic, complemented
9#19135391C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134784C211yesmaximal, characteristic, complemented
14#19134603C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic, complemented
16C22×#10621900—21no—
17#14583549—24no—
18#14583549—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063307—21no—
21C2×#13063306—21no—
22C2×#13063302—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583192—24no—
31#14583000—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44#14582832—21no—
45#14582815—21no—
46#14582793—21no—
47#14582789—21no—
48#14582764C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C2×#10621900—28no—
64C2×#10621900—44no—
65C2×#10621900—44no—
66C22×Dic86—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C23×Dic43—21no—
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—22no—
76#13063324D414yes—
77#13063307—28no—
78#13063306—28no—
79#13063302—28no—
80#13063301—22no—
81#13063301—41no—
82#13063296—22no—
83#13063296—22no—
84Q8×Dic43—22no—
85Q8×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43D414yes—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C4⋊C4×D43—22no—
103C4⋊C4×D43—22no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43D411yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063259—22no—
114#13063259—22no—
115#13063258—22no—
116Dic43⋊C8—22no—
117#13063249—22no—
118#13063249—22no—
119#13063246—22no—
120#13063246—41no—
121C22⋊(C43⋊C8)—41no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—41no—
124#13063235—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C22×Q8×C43C2311yescharacteristic
130C22×D4×C43—21no—
131C22×D4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C2×SD16×C43—22no—
134C2×SD16×C43—22no—
135C2×SD16×C43—22no—
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43—41no—
140#121×C43—22no—
141#121×C43—22no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147#103×C43—22no—
148#102×C43—41no—
149C22⋊C8×C43—22no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C23×D43C2×D411yescharacteristic
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43#4112yescomplemented
159C2×D4×C43—24no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43C2×D412yes—
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×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43—22no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C22×Dic43—24no—
186C22×Dic43—24no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198#10621900—432no—
199C2×C4×D43—24no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×Dic86—24no—
209C2×Dic86—42no—
210C2×Dic86—42no—
211SD16×C43—28no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43#4112yescomplemented
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43C2×D412yes—
223C22⋊C4×C43—24no—
224C22⋊C4×C43—42no—
225C22⋊Dic43—24no—
226C22⋊Dic43—24no—
227C22⋊Dic43—22no—
228C22⋊Dic43—42no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43C2×D412yes—
241C4⋊Dic43C2×D412yes—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244Dic43⋊C4—22no—
245Dic43⋊C4—42no—
246C4×Dic43—42no—
247C4×Dic43C2×D412yes—
248C4×Dic43C2×D412yes—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43AGL(1,ℤ/8)12yes—
269C23×C43C22×D411yescharacteristic
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43AGL(1,ℤ/8)12yes—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—41no—
280Q8×C43—41no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—48no—
284D4×C43—41no—
285D4×C43—41no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C432−1+411yescharacteristic
308C22⋊D43—28no—
309C22⋊D43—48no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—48no—
320C2×Dic43—48no—
321C2×Dic43—41no—
322C2×Dic43—41no—
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#12012yes—
332C2×Dic43#12012yes—
333C4×D43—48no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338Dic86—48no—
339C8×C43—22no—
340C8×C43—41no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343#24132—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—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12011yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43#54711yescharacteristic
361C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C43#57811yescharacteristic
364C22×C43#57811yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—81no—
376C4×C43#52511yescharacteristic
377C4×C43#53711yescharacteristic
378C4×C43#54811yescharacteristic
379C4×C43#55011yescharacteristic
380Dic43—22no—
381Dic43—22no—
382Dic43—41no—
383Dic43—42no—
384Dic43—42no—
385Dic43—81no—
386Dic43—81no—
387C2×#547—431no—
388C2×#477—431no—
389C2×#440—431no—
390#2536—431no—
391#2033—431no—
392#2033—431no—
393#2000—431no—
394#2000D4311yescharacteristic, complemented
395#1993—431no—
396#1955—431no—
397#1872—431no—
398#1872—431no—
399#1852—431no—
400#1852—431no—
401#1804—431no—
402C2×C43—42no—
403C2×C43—82no—
404C2×C43#240711yescharacteristic
405C2×C43#300311yescharacteristic
406C2×C43#301111yescharacteristic
407C2×C43#330811yescharacteristic
408C2×C43#330811yescharacteristic
409C2×C43#334311yescharacteristic
410C2×C43#334311yescharacteristic
411D43—42no—
412C22×#41—861no—
413C22×SD16C2×D4311yescharacteristic
414#547—864no—
415#547—864no—
416C2×C4⋊Q8—431no—
417C2×#123—861no—
418C2×#123—861no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—861no—
421C2×C22⋊Q8C2×D4311yescharacteristic
422C2×#121—431no—
423C2×#121C2×D4311yescharacteristic
424C2×C4×Q8—431no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429#477—864no—
430#440—864no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×C4⋊C8—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103C2×D4311yescharacteristic
438C2×#102—431no—
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8C2×D4311yescharacteristic
445C2×#97—431no—
446#398—861no—
447#394—861no—
448#388—861no—
449#388—861no—
450#382—431no—
451#380—431no—
452#380—431no—
453#340—431no—
454#340—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340C2×D4311yescharacteristic
459C43#2413211yescharacteristic, complemented, Sylow
460C2×#41—868no—
461C2×#41—1724no—
462C2×#41—1724no—
463C22×Q8—861no—
464C22×Q8C22×D4311yescharacteristic
465C22×D4—21no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4C22×D4311yescharacteristic
469C23×C4—431no—
470C23×C4—861no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4C22×D4311yescharacteristic
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—22no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8C22×D4311yescharacteristic
480C22×C8C22×D4311yescharacteristic
481C4⋊Q8—434no—
482C4⋊Q8—862no—
483#123—868no—
484#123—868no—
485C22⋊Q8—22no—
486C22⋊Q8—41no—
487C22⋊Q8—868no—
488C22⋊Q8—862no—
489C22⋊Q8—1721no—
490#121—22no—
491#121—22no—
492#121—862no—
493#121—862no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×D4—434no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—862no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—862no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C42—431no—
527C2×C42—861no—
528#107—862no—
529#107—862no—
530#107—862no—
531C4⋊C8—862no—
532#103—22no—
533#103—862no—
534#103—862no—
535#102—41no—
536#102—862no—
537#102—1721no—
538C22⋊C8—22no—
539C22⋊C8—862no—
540C22⋊C8—1721no—
541C22⋊C8—1721no—
542#97—862no—
543#95—861no—
544#95—861no—
545#95—861no—
546#95—861no—
547C24—21no—
548C24—431no—
549C24D4×D4311yescharacteristic
550#41—17232no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—864no—
557C2×Q8—1722no—
558C2×Q8—1722no—
559C2×Q8#1062190012yescomplemented
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—864no—
572C2×D4—1722no—
573C2×D4—1722no—
574C2×D4D4×D4312yes—
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—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—1722no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608SD16—28no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8#1062190012yescomplemented
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—862no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—1722no—
638C4⋊C4—1722no—
639C4⋊C4D4×D4312yes—
640C22⋊C4—24no—
641C22⋊C4—42no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—432no—
650C42—432no—
651C42—1722no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—432no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23#1306335212yes—
673C23C2×D4×D4311yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—41no—
677Q8—41no—
678Q8—1728no—
679D4—22no—
680D4—22no—
681D4—48no—
682D4—41no—
683D4—41no—
684D4—868no—
685D4—1728no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
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—432no—
703C2×C4—432no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—1728no—
714C2×C4—1728no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1728no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C2×#1062190011yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337211yescharacteristic
736C8—22no—
737C8—41no—
738C8—1721no—
739C8—1721no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22#120×D4311yescharacteristic
762C22#1458353611yescharacteristic
763C22#1458354911yescharacteristic
764C22AGL(1,ℤ/8)×D4311yescharacteristic
765C22C2×#1306335211yescharacteristic
766C22#1458371311yescharacteristic
767C22#1458371511yescharacteristic
768C4—41no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—862no—
773C4—862no—
774C4—3441no—
775C4—3441no—
776C4—1721no—
777C4—1722no—
778C4—1722no—
779C4#1458340511yescharacteristic
780C4#1458347611yescharacteristic
781C4#1458355511yescharacteristic
782C4#1458356911yescharacteristic
783C2—42no—
784C2—82no—
785C2—1722no—
786C2#1913793311yescharacteristic
787C2#1914382311yescharacteristic
788C2#1914388711yescharacteristic
789C2#1914657911yescharacteristic
790C2#1914659011yescharacteristic
791C2#1914703011yescharacteristic
792C2#1914704111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radicalC2×#14583549C2
hypercenter#2000D43
hypocenterC43#24132
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#14583192C2semidirect
3. C2×#14583000C2semidirect
4. #19139502C2semidirect
5. #19135776C2semidirect
6. #19135774C2semidirect
7. #19135595C2semidirect
8. #19135566C2semidirect
9. #19135391C2semidirect
10. #19134903C2semidirect
11. #19134899C2semidirect
12. #19134785C2semidirect
13. #19134784C2semidirect
14. #19134603C2semidirect
15. C43×#2000C2semidirect
158. C2×Q8×C43#41semidirect
217. C2×C8×C43#41semidirect
394. #2000D43semidirect
459. C43#24132semidirect
559. C2×Q8#10621900semidirect
620. C2×C8#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835492
C2×#145831922
C2×#145830002
#191395022
#191357762
#191357742
#191355952
#191355662
#191353912
#191349032
#191348992
#191347852
#191347842
#191346032
C43×#20002
#2413243