Finite Group Databasebeta

← #25149696

Subgroups — #25149696

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583588C211yesmaximal, characteristic, complemented
2C2×#14583143C211yesmaximal, characteristic, complemented
3#19138036C211yesmaximal, characteristic
4#19135935C211yesmaximal, characteristic, complemented
5#19135793C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic, complemented
7#19135599C211yesmaximal, characteristic, complemented
8#19134947C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134900C211yesmaximal, characteristic, complemented
11#19134890C211yesmaximal, characteristic, complemented
12#19134846C211yesmaximal, characteristic, complemented
13#19134781C211yesmaximal, characteristic, complemented
14#19134316C211yesmaximal, characteristic, complemented
15C2×C43×#482C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583588—24no—
19#14583588—24no—
20C2×#13063318—21no—
21C2×#13063317—21no—
22C2×#13063316C2211yescharacteristic
23C2×#13063307—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063297—21no—
27C2×#13063296C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063282—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14583143—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41#14582822—21no—
42#14582815—21no—
43#14582802C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582779—21no—
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C43×#482—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—41no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C2×#10621877—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063318—28no—
78#13063317—28no—
79#13063316—22no—
80#13063316—22no—
81#13063307—28no—
82#13063305—22no—
83#13063305—22no—
84#13063304—22no—
85#13063304D414yescomplemented
86#13063297—44no—
87#13063296—22no—
88#13063296—41no—
89#13063290—22no—
90#13063290—22no—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93#13063282—28no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43—41no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120#13063258—22no—
121#13063250—22no—
122#13063250—41no—
123#13063248—22no—
124#13063246—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—41no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C22×D4×C43—21no—
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#121×C43—22no—
135#121×C43—22no—
136#117×C43—22no—
137#117×C43D414yescomplemented
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C42×C43—21no—
144#107×C43—22no—
145#106×C43—22no—
146#102×C43—22no—
147#102×C43—22no—
148C22⋊C8×C43—22no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C22×C4×C43—21no—
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×C43C2×D412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—81no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43—81no—
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
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—42no—
196C2×C4×D43—42no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C2×D412yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—42no—
217C42×C43—24no—
218C22⋊Dic43—24no—
219C22⋊Dic43—22no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223#10621883—44no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—42no—
227C4⋊Dic43—24no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—42no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43#4112yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—22no—
241Dic43⋊C4—42no—
242C4×Dic43—24no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245#10621877—44no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8#4112yes—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43#12012yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43AGL(1,ℤ/8)12yes—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—84no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
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#12012yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C432−1+411yescharacteristic
301C22⋊D43—44no—
302C22⋊D43—84no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—84no—
325C4×D43—48no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330Dic86—22no—
331Dic86—22no—
332Dic86—41no—
333Dic86—41no—
334C8×C43—41no—
335C8×C43—41no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338#25560—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C2×#12011yescharacteristic
354C22×C43#54611yescharacteristic
355C22×C43#54711yescharacteristic
356C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C43#57511yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—81no—
371C4×C43#53211yescharacteristic
372C4×C43#53711yescharacteristic
373C4×C43#54611yescharacteristic
374C4×C43#54711yescharacteristic
375Dic43—42no—
376Dic43—41no—
377Dic43—42no—
378Dic43—41no—
379Dic43—41no—
380Dic43—42no—
381Dic43—81no—
382C2×#552—431no—
383C2×#482D4311yescharacteristic, complemented
384C2×#468—431no—
385#2416—431no—
386#2059—431no—
387#2035—431no—
388#2025—431no—
389#2000—431no—
390#1880—431no—
391#1874—431no—
392#1872—431no—
393#1870—431no—
394#1863—431no—
395#1852—431no—
396#1736—431no—
397C2×C43—42no—
398C2×C43—161no—
399C2×C43#243011yescharacteristic
400C2×C43#300611yescharacteristic
401C2×C43#301311yescharacteristic
402C2×C43#331011yescharacteristic
403C2×C43#332711yescharacteristic
404C2×C43#334311yescharacteristic
405C2×C43#335111yescharacteristic
406D43—42no—
407C22×SD16—431no—
408C22×M16—431no—
409#552—864no—
410#552—864no—
411C2×#126—861no—
412C2×#125—431no—
413C2×#125—861no—
414C2×#123—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×#121—431no—
418C2×#121—861no—
419C2×#121C2×D4311yescharacteristic
420C2×C4×Q8—431no—
421C2×C4×D4—431no—
422C2×#117—861no—
423C2×#117C2×D4311yescharacteristic
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426#482—24no—
427#468—864no—
428C2×#107—431no—
429C2×#107C2×D4311yescharacteristic
430C2×#106C2×D4311yescharacteristic
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#102—431no—
435C2×#102C2×D4311yescharacteristic
436C2×#102C2×D4311yescharacteristic
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8C2×D4311yescharacteristic
440#396—861no—
441#394—861no—
442#390—431no—
443#389—431no—
444#386—861no—
445#380—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#336—431no—
453#336—431no—
454C43#2556011yescharacteristic, complemented, Sylow
455C22×Q8—431no—
456C22×D4—21no—
457C22×D4—431no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C2×SD16—862no—
465C2×SD16—862no—
466C2×SD16—1721no—
467C2×M16—862no—
468C2×M16—862no—
469C2×M16—1721no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474#126—868no—
475#125—868no—
476#125—862no—
477#125—862no—
478#123—868no—
479C22⋊Q8—434no—
480C22⋊Q8—862no—
481C22⋊Q8—862no—
482C22⋊Q8—862no—
483#121—22no—
484#121—22no—
485#121—862no—
486#121—1721no—
487#121—1724no—
488C4×Q8—862no—
489C4×Q8—862no—
490C4×D4—862no—
491C4×D4—862no—
492#117—22no—
493#117—868no—
494#117C22⋊D4314yescomplemented
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—1721no—
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
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×C42—21no—
525C2×C42—431no—
526C2×C42—861no—
527#107—22no—
528#107—862no—
529#106—22no—
530#103—862no—
531#103—862no—
532#103—1721no—
533#102—22no—
534#102—22no—
535#102—862no—
536C22⋊C8—22no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—861no—
540#95—861no—
541C24—21no—
542C24—431no—
543C24D4×D4311yescharacteristic
544C2×Q8—432no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—3441no—
562C2×D4—1722no—
563C2×D4—1721no—
564C2×D4—1722no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—864no—
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—3441no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4312yes—
593C22×C4C2×C22⋊D4312yes—
594C22×C4C23×D4311yescharacteristic
595SD16—1724no—
596M16—1724no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—432no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—862no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—1722no—
627C4⋊C4—1722no—
628C4⋊C4C2×C22⋊D4312yes—
629C4⋊C4C2×C22⋊D4312yes—
630C22⋊C4—24no—
631C22⋊C4—42no—
632C22⋊C4—864no—
633C22⋊C4—862no—
634C22⋊C4—864no—
635C22⋊C4—862no—
636C22⋊C4—3441no—
637C22⋊C4—1722no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C42—24no—
641C42—864no—
642C42—861no—
643C42—861no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—432no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23#1306329312yes—
665C23C2×D4×D4311yescharacteristic
666Q8—862no—
667Q8—862no—
668Q8—1721no—
669Q8—1721no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—84no—
675D4—3444no—
676D4—1724no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—861no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—1728no—
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—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4#1306329312yes—
720C2×C4C2×D4×D4311yescharacteristic
721C2×C4C22×C22⋊D4311yescharacteristic
722C2×C4#41×D4311yescharacteristic
723C2×C4#41×D4311yescharacteristic
724C2×C4#1306337111yescharacteristic
725C2×C4#1306337211yescharacteristic
726C8—41no—
727C8—41no—
728C8—862no—
729C8—1721no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—1721no—
748C22—1721no—
749C22—1721no—
750C22—1721no—
751C22C2×#1306329311yescharacteristic
752C22#1458354111yescharacteristic
753C22#1458354711yescharacteristic
754C22AGL(1,ℤ/8)×D4311yescharacteristic
755C22#1458369511yescharacteristic
756C22#1458370611yescharacteristic
757C22#1458371311yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—81no—
762C4—3441no—
763C4—1722no—
764C4—1721no—
765C4—1722no—
766C4—1721no—
767C4—1722no—
768C4—1721no—
769C4#1458344511yescharacteristic
770C4#1458347711yescharacteristic
771C4#1458354111yescharacteristic
772C4#1458354711yescharacteristic
773C2—42no—
774C2—161no—
775C2—1722no—
776C2#1913820711yescharacteristic
777C2#1914384311yescharacteristic
778C2#1914390611yescharacteristic
779C2#1914661911yescharacteristic
780C2#1914686111yescharacteristic
781C2#1914702811yescharacteristic
782C2#1914714811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
prime radical#19138036C2
hypercenterC2×#482D43
hypocenterC43#25560
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14583588C2semidirect
2. C2×#14583143C2semidirect
4. #19135935C2semidirect
5. #19135793C2semidirect
6. #19135739C2semidirect
7. #19135599C2semidirect
8. #19134947C2semidirect
9. #19134909C2semidirect
10. #19134900C2semidirect
11. #19134890C2semidirect
12. #19134846C2semidirect
13. #19134781C2semidirect
14. #19134316C2semidirect
15. C2×C43×#482C2semidirect
85. #13063304D4semidirect
137. #117×C43D4semidirect
383. C2×#482D43semidirect
454. C43#25560semidirect
494. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145831432
#191380362
#191359352
#191357932
#191357392
#191355992
#191349472
#191349092
#191349002
#191348902
#191348462
#191347812
#191343162
C2×C43×#4822
#2556043