Finite Group Databasebeta

← #25130741

Subgroups — #25130741

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583590C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic
4#19135796C211yesmaximal, characteristic, complemented
5#19135789C211yesmaximal, characteristic, complemented
6#19135595C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135564C211yesmaximal, characteristic, complemented
9#19135393C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134791C211yesmaximal, characteristic, complemented
13#19134781C211yesmaximal, characteristic, complemented
14#19134600C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16#14583590—24no—
17#14583590—24no—
18C2×#13063319—21no—
19C2×#13063317C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063310—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063301C2211yescharacteristic
24C2×#13063299—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063282—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31#14583199—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43#14582815—21no—
44#14582815—21no—
45#14582769C2211yescharacteristic
46#14582759—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#440—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C22×D172D411yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063319—28no—
72#13063317—22no—
73#13063317D414yescomplemented
74#13063315—28no—
75#13063310—28no—
76#13063301—22no—
77#13063301—22no—
78#13063301—22no—
79#13063301—22no—
80#13063299—44no—
81#13063296—22no—
82#13063296—22no—
83#13063296—41no—
84#13063296—41no—
85C4×D172—22no—
86C4×D172—22no—
87#13063283—22no—
88#13063283—22no—
89#13063282—28no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C4⋊C4×D43—22no—
103C4⋊C4×D43—22no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114#13063258—22no—
115#13063256—22no—
116C4⋊(C43⋊C8)—22no—
117#13063249—41no—
118#13063249—41no—
119#13063246—22no—
120#13063246—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—41no—
124(C2×D43)⋊C8—41no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43C2311yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43—21no—
130C2×SD16×C43—22no—
131C2×SD16×C43—22no—
132C2×SD16×C43—22no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4×Q8×C43—22no—
136C4×Q8×C43D414yescomplemented
137C4×D4×C43—22no—
138C4×D4×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C42×C43—21no—
144C2×C42×C43C2311yescharacteristic
145#107×C43—22no—
146#103×C43—22no—
147#102×C43—22no—
148#97×C43—22no—
149C24×C43—21no—
150C23×D43C2×D411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43C2×D412yes—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—81no—
178C2×C22⋊D43—81no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—41no—
188C2×C4×D43—24no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203SD16×C43—28no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43#4112yes—
210C4⋊C4×C43—24no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—42no—
216C42×C43—24no—
217C42×C43C2×D412yes—
218C42×C43C2×D412yes—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228C4⋊Dic43—22no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—42no—
236C4⋊Dic43—81no—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244C4×Dic43—24no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C23×C43—22no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43AGL(1,ℤ/8)12yes—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—41no—
276Q8×C43—41no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—41no—
280D4×C43—41no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—84no—
295C2×C4×C43#12012yes—
296C2×C4×C43#12012yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C432−1+411yescharacteristic
303C22⋊D43—84no—
304C22⋊D43—84no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323D172—44no—
324C4×D43—48no—
325C4×D43—41no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C8×C43—22no—
334C8×C43—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337#24137—431nomaximal, Sylow
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43C2×#12011yescharacteristic
346C22×C43#54611yescharacteristic
347C22×C43#54711yescharacteristic
348C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C43#57511yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57811yescharacteristic
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—81no—
371C4×C43#52511yescharacteristic
372C4×C43#53711yescharacteristic
373C4×C43#54811yescharacteristic
374C4×C43#55011yescharacteristic
375Dic43—41no—
376Dic43—41no—
377Dic43—42no—
378Dic43—42no—
379Dic43—81no—
380Dic43—81no—
381C2×#552—431no—
382C2×#478—431no—
383C2×#440D4311yescharacteristic, complemented
384#2537—431no—
385#2036—431no—
386#2035—431no—
387#2000—431no—
388#2000—431no—
389#1992—431no—
390#1955—431no—
391#1875—431no—
392#1874—431no—
393#1854—431no—
394#1852—431no—
395#1803—431no—
396C2×C43—82no—
397C2×C43#240711yescharacteristic
398C2×C43#300611yescharacteristic
399C2×C43#301311yescharacteristic
400C2×C43#331011yescharacteristic
401C2×C43#331511yescharacteristic
402C2×C43#334311yescharacteristic
403C2×C43#334811yescharacteristic
404D43—42no—
405D43—81no—
406C22×SD16C2×D4311yescharacteristic
407#552—864no—
408#552—864no—
409C2×#126—861no—
410C2×#125—431no—
411C2×#125—861no—
412C2×#123—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×#121—431no—
416C2×#121—431no—
417C2×#121—861no—
418C2×C4×Q8C2×D4311yescharacteristic
419C2×C4×D4—431no—
420C2×C4×D4C2×D4311yescharacteristic
421C2×#117—431no—
422C2×#117—861no—
423C22×C4⋊C4—431no—
424#478—864no—
425#440—24no—
426C2×#107—431no—
427C2×#107C2×D4311yescharacteristic
428C2×#106—431no—
429C2×C4⋊C8—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103C2×D4311yescharacteristic
433C2×#102—431no—
434C2×#102—431no—
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×#97C2×D4311yescharacteristic
441#394—861no—
442#394—861no—
443#384—431no—
444#380—431no—
445#380—431no—
446#380—861no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453C43#2413711yescharacteristic, complemented, Sylow
454C22×Q8C22×D4311yescharacteristic
455C22×D4—431no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4C22×D4311yescharacteristic
459C23×C4—21no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—861no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470#126—868no—
471#125—434no—
472#125—868no—
473#125—862no—
474#123—868no—
475C22⋊Q8—862no—
476C22⋊Q8—862no—
477C22⋊Q8—862no—
478C22⋊Q8—862no—
479#121—862no—
480#121—862no—
481#121—1721no—
482#121—1721no—
483#121—1724no—
484C4×Q8—22no—
485C4×Q8C22⋊D4314yescomplemented
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—862no—
489C4×D4—862no—
490#117—868no—
491#117—862no—
492#117—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—431no—
513C2×C22⋊C4—861no—
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×C42—21no—
521C2×C42—861no—
522C2×C42C22×D4311yescharacteristic
523#107—22no—
524#107—862no—
525#106—862no—
526C4⋊C8—862no—
527#103—22no—
528#103—1721no—
529#103—1721no—
530#102—22no—
531#102—862no—
532#102—862no—
533C22⋊C8—862no—
534C22⋊C8—862no—
535C22⋊C8—1721no—
536C22⋊C8—1721no—
537#97—22no—
538#95—861no—
539#95—861no—
540C24—21no—
541C24—431no—
542C24—431no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D4312yes—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—3441no—
557C2×D4—3441no—
558C2×D4—1721no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4#1062189812yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594SD16—28no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8#1062189812yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—862no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—3441no—
626C4⋊C4—1722no—
627C4⋊C4C2×C22⋊D4312yes—
628C22⋊C4—42no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—862no—
633C22⋊C4—862no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C22⋊C4—1722no—
638C42—24no—
639C42—864no—
640C42D4×D4312yes—
641C42C2×C22⋊D4312yes—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—432no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23C2×D4×D4311yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—3444no—
673D4—3444no—
674D4—1724no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—1728no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4#1306329312yes—
717C2×C4#1306329312yes—
718C2×C4C2×D4×D4311yescharacteristic
719C2×C4C22×C22⋊D4311yescharacteristic
720C2×C4C2×#1062189811yescharacteristic
721C2×C4C2×#1062189811yescharacteristic
722C2×C4#1306337111yescharacteristic
723C2×C4#1306337211yescharacteristic
724C8—22no—
725C8—41no—
726C8—1721no—
727C8—1721no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—862no—
736C22—862no—
737C22—862no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22—1721no—
746C22—1721no—
747C22—1721no—
748C22—1721no—
749C22C2×#1306329311yescharacteristic
750C22#1458354511yescharacteristic
751C22#1458355411yescharacteristic
752C22AGL(1,ℤ/8)×D4311yescharacteristic
753C22#1458369511yescharacteristic
754C22#1458370811yescharacteristic
755C22#1458371511yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—81no—
761C4—3441no—
762C4—3441no—
763C4—1721no—
764C4—1721no—
765C4—1722no—
766C4—1722no—
767C4#1458341011yescharacteristic
768C4#1458347711yescharacteristic
769C4#1458355811yescharacteristic
770C4#1458357011yescharacteristic
771C2—82no—
772C2—3441no—
773C2—1722no—
774C2#1913794011yescharacteristic
775C2#1914384311yescharacteristic
776C2#1914390911yescharacteristic
777C2#1914662111yescharacteristic
778C2#1914669611yescharacteristic
779C2#1914704011yescharacteristic
780C2#1914711511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radical#19139508C2
hypercenterC2×#440D43
hypocenterC43#24137
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583590C2semidirect
2. C2×#14583199C2semidirect
4. #19135796C2semidirect
5. #19135789C2semidirect
6. #19135595C2semidirect
7. #19135595C2semidirect
8. #19135564C2semidirect
9. #19135393C2semidirect
10. #19134914C2semidirect
11. #19134909C2semidirect
12. #19134791C2semidirect
13. #19134781C2semidirect
14. #19134600C2semidirect
15. C2×C43×#440C2semidirect
73. #13063317D4semidirect
136. C4×Q8×C43D4semidirect
383. C2×#440D43semidirect
453. C43#24137semidirect
485. C4×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835902
C2×#145831992
#191395082
#191357962
#191357892
#191355952
#191355642
#191353932
#191349142
#191349092
#191347912
#191347812
#191346002
C2×C43×#4402
#2413743