Finite Group Databasebeta

← #25134587

Subgroups — #25134587

Order 11008.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14583157C211yesmaximal, characteristic, complemented
3C2×#14583056C211yesmaximal, characteristic, complemented
4C2×#14583055C211yesmaximal, characteristic, complemented
5#19138018C211yesmaximal, characteristic
6#19135840C211yesmaximal, characteristic, complemented
7#19135790C211yesmaximal, characteristic, complemented
8#19135696C211yesmaximal, characteristic, complemented
9#19135604C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134907C211yesmaximal, characteristic, complemented
12#19134892C211yesmaximal, characteristic
13#19134865C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C2×C43×#419C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20Q8×C22⋊D43—24no—
21Q8×C22⋊D43—24no—
22C2×#13063323—21no—
23C2×#13063323C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063304—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063301—21no—
29C2×#13063301C2211yescharacteristic
30C2×Q8×Dic43C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×C4×C22⋊D43C2211yescharacteristic
33#14583157—24no—
34#14583056—24no—
35#14583055—24no—
36C2×#13063257C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46#14582824—21no—
47#14582815—21no—
48#14582804C2211yescharacteristic
49#14582798C2211yescharacteristic
50#14582797—21no—
51#14582790—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C22×M16×C43C2211yescharacteristic
59C2×#117×C43C2211yescharacteristic
60C43×#419—24no—
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#103×C43C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—41no—
73C2×Q8×D43—41no—
74C22×C22⋊D43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×Dic172—22no—
78C2×Dic172—22no—
79C2×Dic172—41no—
80C2×#10621885—22no—
81C2×#10621885—22no—
82C2×#10621885—22no—
83C2×#10621885—22no—
84C2×#10621885—41no—
85C2×#10621885—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063323—28no—
89#13063323—22no—
90#13063323—22no—
91#13063305—22no—
92#13063305—41no—
93#13063304—28no—
94#13063304—22no—
95#13063304—22no—
96#13063304—22no—
97#13063304D414yes—
98#13063301—28no—
99#13063301—22no—
100#13063301—22no—
101Q8×Dic43—22no—
102Q8×Dic43—22no—
103C4×C22⋊D43—28no—
104C4×C22⋊D43—22no—
105C4×C22⋊D43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4D411yescharacteristic
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43D411yescharacteristic
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×C4×Dic43—21no—
125C2×C4×Dic43C2311yescharacteristic
126#13063257—22no—
127#13063250—22no—
128#13063250—22no—
129#13063249—22no—
130#13063249—22no—
131#13063248—22no—
132#13063248—41no—
133C22⋊(C43⋊C8)—22no—
134(C2×D43)⋊C8—22no—
135(C2×D43)⋊C8—41no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C22×Q8×C43—22no—
141C22×Q8×C43—21no—
142C22×Q8×C43—22no—
143C22×Q8×C43—22no—
144C22×Q8×C43—41no—
145C22×Q8×C43—41no—
146C22×Q8×C43D414yes—
147C22×Q8×C43C2311yescharacteristic
148C22×Q8×C43C2311yescharacteristic
149C23×C4×C43—21no—
150C23×C4×C43C2311yescharacteristic
151C2×M16×C43—22no—
152C2×M16×C43—22no—
153C2×M16×C43—41no—
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#117×C43—22no—
157#117×C43—41no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C42×C43—21no—
162#103×C43—22no—
163#103×C43—22no—
164#103×C43—22no—
165#103×C43D414yescomplemented
166C24×C43C2×D411yescharacteristic
167C23×D43C2×D411yescharacteristic
168C2×Q8×C43—24no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—28no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—42no—
179C2×Q8×C43—42no—
180C2×Q8×C43—44no—
181C2×Q8×C43—44no—
182C2×Q8×C43—44no—
183C2×Q8×C43C2×D412yes—
184C2×Q8×C43C2×D412yes—
185C2×Q8×C43C2×D412yes—
186C2×Q8×C43#4112yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212Q8×D43—44no—
213Q8×D43—44no—
214Q8×D43—44no—
215Q8×D43—44no—
216C2×C4×D43—24no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—24no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—42no—
238C2×Dic86—42no—
239C2×Dic86C2×D412yes—
240M16×C43—44no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2×D412yes—
251C22⋊C4×C43—42no—
252C42×C43—42no—
253C22⋊Dic43—24no—
254C22⋊Dic43—22no—
255C22⋊Dic43—42no—
256#10621885—44no—
257#10621885—44no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—22no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—42no—
267C4⋊Dic43—42no—
268C4⋊Dic43C2×D412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—22no—
274Dic43⋊C4—42no—
275C4×Dic43—24no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284Dic172—44no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43#12012yes—
292C23×C43C22×D411yescharacteristic
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43#13712yes—
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—48no—
306Q8×C43—41no—
307Q8×C43—41no—
308Q8×C43#12114yes—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—48no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43#12012yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C22⋊D43—28no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—22no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43#13712yes—
357C4×D43—48no—
358C4×D43—41no—
359C4×D43—41no—
360C4×D43—41no—
361C4×D43—41no—
362Dic86—22no—
363Dic86—22no—
364Dic86—48no—
365Dic86—41no—
366Dic86—41no—
367Dic86—41no—
368Dic86—41no—
369Dic86—41no—
370Dic86—41no—
371C8×C43—22no—
372C8×C43—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#24453—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43C2×#12011yescharacteristic
384C22×C43D4211yescharacteristic
385C22×C43#54611yescharacteristic
386C22×C43C2×#13711yescharacteristic
387C22×C43C2×#13711yescharacteristic
388C22×C43#57811yescharacteristic
389C22×C43#57811yescharacteristic
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C4×C43—24no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43—81no—
402C4×C43C2×#12111yescharacteristic
403C4×C43#53411yescharacteristic
404C4×C43D4211yescharacteristic
405C4×C43#54611yescharacteristic
406Dic43—22no—
407Dic43—42no—
408Dic43—41no—
409Dic43—41no—
410Dic43—42no—
411Dic43—81no—
412Dic43—81no—
413C2×D4×Q8—431no—
414C2×#470—431no—
415C2×#451—431no—
416C2×#451—431no—
417C2×#419D4311yescharacteristic, complemented
418#2415—431no—
419#2043—431no—
420#2035—431no—
421#2016—431no—
422#2001—431no—
423#1878—431no—
424#1873—431no—
425#1870—431no—
426#1865—431no—
427#1787—431no—
428C2×C43—42no—
429C2×C43#241011yescharacteristic
430C2×C43#300411yescharacteristic
431C2×C43#301111yescharacteristic
432C2×C43#327011yescharacteristic
433C2×C43#327611yescharacteristic
434C2×C43#331211yescharacteristic
435C2×C43#332811yescharacteristic
436D43—42no—
437C23×Q8—431no—
438C23×Q8C2×D4311yescharacteristic
439C22×Q16—431no—
440C22×Q16—431no—
441C22×Q16—431no—
442C22×M16C2×D4311yescharacteristic
443D4×Q8—864no—
444D4×Q8—864no—
445C2×C4⋊Q8—431no—
446C2×C4⋊Q8—861no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—431no—
449C2×C22⋊Q8—431no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—861no—
452C2×C22⋊Q8—861no—
453C2×C4×Q8—431no—
454C2×C4×D4—431no—
455C2×C4×D4—861no—
456C2×#117C2×D4311yescharacteristic
457#470—864no—
458#451—864no—
459#451—864no—
460C2×#106—431no—
461#419—24no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103C2×D4311yescharacteristic
469C2×#103C2×D4311yescharacteristic
470C2×#103C2×D4311yescharacteristic
471C2×#103C2×D4311yescharacteristic
472C2×C22⋊C8—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475#397—861no—
476#394—861no—
477#391—431no—
478#389—431no—
479#389—861no—
480#388—861no—
481#380—431no—
482#340—431no—
483#340—431no—
484#336—431no—
485#336—431no—
486C43#2445311yescharacteristic, complemented, Sylow
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—431no—
494C22×Q8—431no—
495C22×Q8—861no—
496C22×Q8—862no—
497C22×Q8—862no—
498C22×Q8—862no—
499C22×Q8—862no—
500C22×Q8—1721no—
501C22×Q8—1721no—
502C22×Q8D17214yes—
503C22×Q8C22×D4311yescharacteristic
504C22×Q8C22×D4311yescharacteristic
505C22×D4—431no—
506C23×C4—21no—
507C23×C4—431no—
508C23×C4—861no—
509C23×C4C22×D4311yescharacteristic
510C2×Q16—862no—
511C2×Q16—862no—
512C2×Q16—862no—
513C2×Q16—862no—
514C2×Q16—862no—
515C2×Q16—862no—
516C2×Q16—1721no—
517C2×Q16—1721no—
518C2×Q16—1721no—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—41no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8C22×D4311yescharacteristic
525C22×C8C22×D4311yescharacteristic
526C4⋊Q8—862no—
527C4⋊Q8—868no—
528C4⋊Q8—862no—
529C22⋊Q8—434no—
530C22⋊Q8—862no—
531C22⋊Q8—868no—
532C22⋊Q8—868no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—1721no—
539C4×Q8—862no—
540C4×Q8—862no—
541C4×D4—868no—
542C4×D4—862no—
543C4×D4—862no—
544#117—22no—
545#117—41no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C42—21no—
568C2×C42—431no—
569C2×C42—861no—
570#106—862no—
571#103—22no—
572#103—22no—
573#103—22no—
574#103—862no—
575#103—862no—
576#103—862no—
577#103—862no—
578#103—862no—
579#103—1721no—
580#103C22⋊D4314yescomplemented
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—1721no—
584#95—861no—
585#95—861no—
586#95—861no—
587#95—861no—
588C24—431no—
589C24D4×D4311yescharacteristic
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—28no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—42no—
601C2×Q8—42no—
602C2×Q8—44no—
603C2×Q8—44no—
604C2×Q8—44no—
605C2×Q8—432no—
606C2×Q8—864no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8—1722no—
619C2×Q8—1722no—
620C2×Q8—1724no—
621C2×Q8—1724no—
622C2×Q8—1724no—
623C2×Q8—1724no—
624C2×Q8C2×D17212yes—
625C2×Q8C2×D17212yes—
626C2×Q8#1062189812yes—
627C2×Q8C2×C22⋊D4312yes—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—862no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—864no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4C2×D17212yes—
659C22×C4D4×D4311yescharacteristic
660C22×C4D4×D4312yes—
661C22×C4C23×D4311yescharacteristic
662Q16—1724no—
663Q16—1724no—
664Q16—1724no—
665M16—44no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8C2×C22⋊D4312yes—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—432no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—862no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C4⋊C4—1722no—
694C4⋊C4C2×C22⋊D4312yes—
695C22⋊C4—42no—
696C22⋊C4—864no—
697C22⋊C4—862no—
698C22⋊C4—864no—
699C22⋊C4—862no—
700C22⋊C4—1722no—
701C22⋊C4—1722no—
702C22⋊C4—1722no—
703C42—42no—
704C42—864no—
705C42—861no—
706C42—861no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—432no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23—861no—
718C23—861no—
719C23—861no—
720C23#1306329512yes—
721C23C2×D4×D4311yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—48no—
728Q8—41no—
729Q8—41no—
730Q8—862no—
731Q8—862no—
732Q8—1728no—
733Q8—1721no—
734Q8—1721no—
735Q8—1721no—
736Q8—1721no—
737Q8—1721no—
738Q8—1721no—
739Q8#1306329914yes—
740D4—868no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—432no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—862no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—862no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—1728no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306329512yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C22×C22⋊D4311yescharacteristic
789C2×C4C22×D17211yescharacteristic
790C2×C4C2×#1062189811yescharacteristic
791C2×C4#1306337011yescharacteristic
792C2×C4#1306337011yescharacteristic
793C8—22no—
794C8—41no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—1721no—
808C22—1721no—
809C22—1721no—
810C22—1721no—
811C22C2×#1306329511yescharacteristic
812C22D4×C22⋊D4311yescharacteristic
813C22#1458353911yescharacteristic
814C22#137×D4311yescharacteristic
815C22#137×D4311yescharacteristic
816C22#1458371511yescharacteristic
817C22#1458371511yescharacteristic
818C4—22no—
819C4—24no—
820C4—42no—
821C4—42no—
822C4—81no—
823C4—862no—
824C4—3441no—
825C4—3441no—
826C4—1721no—
827C4—1722no—
828C4—1721no—
829C4—1722no—
830C4C2×#1306329911yescharacteristic
831C4#1458346111yescharacteristic
832C4D4×C22⋊D4311yescharacteristic
833C4#1458353911yescharacteristic
834C2—42no—
835C2—1722no—
836C2#1913796311yescharacteristic
837C2#1914383111yescharacteristic
838C2#1914389111yescharacteristic
839C2#1914615911yescharacteristic
840C2#1914623511yescharacteristic
841C2#1914664711yescharacteristic
842C2#1914687411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#419D43
hypocenterC43#24453
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#14583157C2semidirect
3. C2×#14583056C2semidirect
4. C2×#14583055C2semidirect
6. #19135840C2semidirect
7. #19135790C2semidirect
8. #19135696C2semidirect
9. #19135604C2semidirect
10. #19134934C2semidirect
11. #19134907C2semidirect
13. #19134865C2semidirect
14. #19134528C2semidirect
15. C2×C43×#419C2semidirect
165. #103×C43D4semidirect
417. C2×#419D43semidirect
486. C43#24453semidirect
580. #103C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145831572
C2×#145830562
C2×#145830552
#191380182
#191358402
#191357902
#191356962
#191356042
#191349342
#191349072
#191348922
#191348652
#191345282
C2×C43×#4192
#2445343