Finite Group Databasebeta

← #25134593

Subgroups — #25134593

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×#14583155C211yesmaximal, characteristic, complemented
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583055C211yesmaximal, characteristic, complemented
4C2×#14582908C211yesmaximal, characteristic, complemented
5#19138024C211yesmaximal, characteristic
6#19135838C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135695C211yesmaximal, characteristic, complemented
9#19135603C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134893C211yesmaximal, characteristic
13#19134863C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C43C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14583155—24no—
24#14583055—24no—
25#14583055—24no—
26C2×#13063256C2211yescharacteristic
27#14582908—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41#14582827—21no—
42#14582813—21no—
43#14582805C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582794—21no—
46#14582793—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C23×Q8×C43C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54D4×Q8×C43—24no—
55D4×Q8×C43—24no—
56C2×C4⋊Q8×C43—21no—
57C2×C4⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43—21no—
59C2×C22⋊Q8×C43—21no—
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×C22⋊Q8×C43C2211yescharacteristic
62C2×C4×Q8×C43C2211yescharacteristic
63C2×C4×D4×C43—21no—
64C2×C4×D4×C43C2211yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—41no—
73C2×#10621885—41no—
74C2×#10621885—41no—
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—41no—
86#13063284—22no—
87#13063284—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99#13063256—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—41no—
108#13063249D414yescomplemented
109#13063248—22no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C22×Q8×C43—22no—
118C22×Q8×C43—22no—
119C22×Q8×C43—21no—
120C22×Q8×C43—21no—
121C22×Q8×C43—22no—
122C22×Q8×C43—22no—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—22no—
126C22×Q8×C43—41no—
127C22×Q8×C43—41no—
128C22×Q8×C43—41no—
129C22×Q8×C43—41no—
130C22×Q8×C43D414yes—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43D411yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C4⋊Q8×C43—28no—
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43—22no—
142C22⋊Q8×C43—28no—
143C22⋊Q8×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yes—
148C4×Q8×C43—22no—
149C4×Q8×C43—22no—
150C4×D4×C43—28no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C2×C4⋊C4×C43—21no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43D411yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43D411yescharacteristic
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C42×C43—21no—
165C2×C42×C43C2311yescharacteristic
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C2×Q8×C43—24no—
169C2×Q8×C43—24no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—28no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—42no—
185C2×Q8×C43—42no—
186C2×Q8×C43—42no—
187C2×Q8×C43—42no—
188C2×Q8×C43—44no—
189C2×Q8×C43—44no—
190C2×Q8×C43—44no—
191C2×Q8×C43—44no—
192C2×Q8×C43—44no—
193C2×Q8×C43—44no—
194C2×Q8×C43—44no—
195C2×Q8×C43C2×D412yes—
196C2×Q8×C43C2×D412yes—
197C2×Q8×C43C2×D412yes—
198C2×Q8×C43C2×D412yes—
199C2×Q8×C43#4112yes—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—24no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—24no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—22no—
252C42×C43—24no—
253C42×C43—21no—
254C42×C43—21no—
255C22⋊Dic43—42no—
256C22⋊Dic43—42no—
257C22⋊Dic43—42no—
258C22⋊Dic43—42no—
259#10621885—44no—
260#10621885—44no—
261#10621885—44no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—42no—
269Dic43⋊C4—42no—
270Dic43⋊C4—42no—
271C4×Dic43—42no—
272#10621877—44no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—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—
284C2×C43⋊C8C2×D412yes—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43#12012yes—
298C23×C43#13712yes—
299C23×C43C22×D411yescharacteristic
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—48no—
308Q8×C43—48no—
309Q8×C43—41no—
310Q8×C43—41no—
311Q8×C43—41no—
312Q8×C43—41no—
313Q8×C43#12114yes—
314D4×C43—28no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—48no—
336C2×C4×C43—48no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43#12012yes—
348C2×C4×C43#13712yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×Dic43—22no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367Dic86—41no—
368Dic86—41no—
369Dic86—41no—
370Dic86—41no—
371C43⋊C8—22no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#24453—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43C2×#12011yescharacteristic
391C22×C43D4211yescharacteristic
392C22×C43#54611yescharacteristic
393C22×C43C2×#13711yescharacteristic
394C22×C43C2×#13711yescharacteristic
395C22×C43#57811yescharacteristic
396C22×C43#57811yescharacteristic
397C4×C43—22no—
398C4×C43—24no—
399C4×C43—22no—
400C4×C43—41no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—41no—
404C4×C43—42no—
405C4×C43C2×#12111yescharacteristic
406C4×C43#53411yescharacteristic
407C4×C43D4211yescharacteristic
408C4×C43#54611yescharacteristic
409Dic43—42no—
410Dic43—81no—
411Dic43—81no—
412Dic43—81no—
413C2×D4×Q8D4311yescharacteristic
414C2×#470—431no—
415C2×#451—431no—
416C2×#451—431no—
417C2×#419—431no—
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—42no—
430C2×C43#241011yescharacteristic
431C2×C43#300411yescharacteristic
432C2×C43#301111yescharacteristic
433C2×C43#327011yescharacteristic
434C2×C43#327611yescharacteristic
435C2×C43#331211yescharacteristic
436C2×C43#332811yescharacteristic
437C23×Q8C2×D4311yescharacteristic
438C23×Q8C2×D4311yescharacteristic
439C22×Q16—431no—
440C22×Q16—431no—
441C22×Q16—431no—
442C22×M16—431no—
443D4×Q8—24no—
444D4×Q8—24no—
445C2×C4⋊Q8—21no—
446C2×C4⋊Q8C2×D4311yescharacteristic
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—431no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8C2×D4311yescharacteristic
452C2×C22⋊Q8C2×D4311yescharacteristic
453C2×C4×Q8C2×D4311yescharacteristic
454C2×C4×D4—21no—
455C2×C4×D4C2×D4311yescharacteristic
456C2×#117—431no—
457#470—864no—
458#451—864no—
459#451—864no—
460C2×#106—431no—
461#419—864no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
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—22no—
488C22×Q8—22no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—431no—
501C22×Q8C22⋊D4314yes—
502C22×Q8C22×D4311yescharacteristic
503C22×Q8C22×D4311yescharacteristic
504C22×Q8C22×D4311yescharacteristic
505C22×D4C22⋊D4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C22×D4311yescharacteristic
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—862no—
520C2×M16—862no—
521C2×M16—1721no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8—431no—
526C4⋊Q8—28no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537C22⋊Q8—1721no—
538C22⋊Q8C22⋊D4314yes—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×D4—28no—
542C4×D4—22no—
543C4×D4—22no—
544#117—862no—
545#117—1721no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
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—21no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4C22⋊D4311yescharacteristic
566C2×C22⋊C4C22⋊D4311yescharacteristic
567C2×C42—21no—
568C2×C42—861no—
569C2×C42C22×D4311yescharacteristic
570#106—862no—
571#103—434no—
572#103—862no—
573#103—862no—
574#103—862no—
575#103—862no—
576#103—862no—
577#103—862no—
578#103—862no—
579#103—862no—
580#103—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—1721no—
584#95—861no—
585#95—861no—
586#95—861no—
587#95—861no—
588C24C2×C22⋊D4311yescharacteristic
589C24C2×C22⋊D4311yescharacteristic
590C2×Q8—24no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—28no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8D4×D4312yes—
624C2×Q8#1062190012yes—
625C2×Q8C2×C22⋊D4312yes—
626C2×Q8C2×C22⋊D4312yes—
627C2×Q8C2×C22⋊D4312yes—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4C2×C22⋊D4311yescharacteristic
656C22×C4C2×C22⋊D4311yescharacteristic
657C22×C4C2×C22⋊D4311yescharacteristic
658C22×C4C2×C22⋊D4312yes—
659C22×C4C2×C22⋊D4312yes—
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C23×D4311yescharacteristic
662Q16—1724no—
663Q16—1724no—
664Q16—1724no—
665M16—1724no—
666C2×C8—432no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—432no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C4⋊C4—1722no—
694C4⋊C4C2×C22⋊D4312yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—1722no—
700C22⋊C4—1722no—
701C22⋊C4—1722no—
702C22⋊C4—1722no—
703C42—24no—
704C42—21no—
705C42—21no—
706C42—1722no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23#1306329412yes—
720C23#1306335612yes—
721C23C22×C22⋊D4311yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—48no—
730Q8—48no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—1721no—
736Q8—1721no—
737Q8—1721no—
738Q8—1721no—
739Q8#1306329714yes—
740D4—28no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—862no—
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#1306329412yes—
786C2×C4#1306335612yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C22×C22⋊D4311yescharacteristic
789C2×C4C22×C22⋊D4311yescharacteristic
790C2×C4C2×#1062190011yescharacteristic
791C2×C4#1306337011yescharacteristic
792C2×C4#1306337011yescharacteristic
793C8—862no—
794C8—1721no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22C2×#1306329411yescharacteristic
812C22D4×C22⋊D4311yescharacteristic
813C22#1458354311yescharacteristic
814C22C2×#1306335611yescharacteristic
815C22C2×#1306335611yescharacteristic
816C22#1458371411yescharacteristic
817C22#1458371411yescharacteristic
818C4—22no—
819C4—22no—
820C4—24no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—3441no—
827C4—3441no—
828C4—3441no—
829C4—1722no—
830C4C2×#1306329711yescharacteristic
831C4#1458345811yescharacteristic
832C4D4×C22⋊D4311yescharacteristic
833C4#1458354311yescharacteristic
834C2—42no—
835C2—42no—
836C2#1913796911yescharacteristic
837C2#1914382911yescharacteristic
838C2#1914389011yescharacteristic
839C2#1914616611yescharacteristic
840C2#1914624111yescharacteristic
841C2#1914664611yescharacteristic
842C2#1914687811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×D4×Q8D43
hypocenterC43#24453
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14583155C2semidirect
2. C2×#14583055C2semidirect
3. C2×#14583055C2semidirect
4. C2×#14582908C2semidirect
6. #19135838C2semidirect
7. #19135788C2semidirect
8. #19135695C2semidirect
9. #19135603C2semidirect
10. #19134936C2semidirect
11. #19134908C2semidirect
13. #19134863C2semidirect
14. #19134530C2semidirect
108. #13063249D4semidirect
486. C43#24453semidirect

Maximal subgroups

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

subgroupindex
C2×#145831552
C2×#145830552
C2×#145829082
#191380242
#191358382
#191357882
#191356952
#191356032
#191349362
#191349082
#191348932
#191348632
#191345302
C2×D4×Q8×C432
#2445343