Finite Group Databasebeta

← #25132198

Subgroups — #25132198

Order 11008.

1426 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583118C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583055C211yesmaximal, characteristic, complemented
4C2×#14583004C211yesmaximal, characteristic, complemented
5#19139517C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135394C211yesmaximal, characteristic, complemented
12#19134600C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×C43×#548C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22#14583118—24no—
23#14583061—24no—
24#14583055—24no—
25#14583004—24no—
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063236C2211yescharacteristic
43#14582822—21no—
44#14582822—21no—
45#14582802—21no—
46#14582795—21no—
47#14582769C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C43×#548—24no—
55C43×#548—24no—
56C2×#124×C43—21no—
57C2×#124×C43C2211yescharacteristic
58C2×C22⋊Q8×C43—21no—
59C2×C22⋊Q8×C43C2211yescharacteristic
60C2×#121×C43—21no—
61C2×#121×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—41no—
71C2×#10621885D414yescomplemented
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063304—22no—
80#13063304—22no—
81#13063304—41no—
82#13063304—41no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C4×Dic43—21no—
98#13063256—22no—
99C4⋊(C43⋊C8)—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—41no—
106#13063248—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C22⋊(C43⋊C8)—41no—
114#13063236—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—21no—
126C22×Q8×C43—22no—
127C22×Q8×C43—22no—
128C22×Q8×C43—41no—
129C22×Q8×C43—41no—
130C22×Q8×C43C2311yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C22×D4×C43—21no—
133C22×D4×C43—21no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140#124×C43—28no—
141#124×C43—22no—
142#124×C43D414yes—
143C22⋊Q8×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146#121×C43—28no—
147#121×C43—22no—
148#121×C43—22no—
149C4×Q8×C43—22no—
150C4×Q8×C43D414yes—
151C4×D4×C43—28no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43D411yescharacteristic
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
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×C43—21no—
167C24×C43C2×D411yescharacteristic
168C24×C43C2×D411yescharacteristic
169#41×C43—44no—
170#41×C43—44no—
171#41×C43—44no—
172#41×C43—44no—
173C2×Q8×C43—24no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
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—42no—
183C2×Q8×C43—42no—
184C2×Q8×C43—44no—
185C2×Q8×C43—44no—
186C2×Q8×C43—44no—
187C2×Q8×C43—44no—
188C2×Q8×C43C2×D412yes—
189C2×Q8×C43C2×D412yes—
190C2×Q8×C43C2×D412yes—
191C2×Q8×C43#4112yes—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—41no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43C2×D412yes—
207C22×C4×C43—24no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43—42no—
227C22×C4×C43—42no—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86C2×D412yes—
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—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C42×C43—24no—
255C42×C43C2×D412yes—
256C42×C43C2×D412yes—
257C22⋊Dic43—42no—
258C22⋊Dic43—42no—
259C22⋊Dic43—81no—
260C22⋊Dic43—81no—
261#10621885—28no—
262#10621885—44no—
263#10621883—44no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—42no—
271C4⋊Dic43—81no—
272Dic43⋊C4—42no—
273Dic43⋊C4—42no—
274Dic43⋊C4—42no—
275C4×Dic43—42no—
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⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8C2×D412yes—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43#13712yes—
309C23×C43C22×D411yescharacteristic
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—48no—
316Q8×C43—41no—
317Q8×C43—41no—
318Q8×C43#12114yes—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—44no—
322D4×C43—48no—
323D4×C43—48no—
324D4×C43—41no—
325D4×C43—41no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—48no—
342C2×C4×C43—48no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43#12012yes—
356C2×C4×C43#12012yes—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×Dic43—22no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C43⋊C8—22no—
380C43⋊C8—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383#24258—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C2×#12011yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43C2×#13711yescharacteristic
409C22×C43#57511yescharacteristic
410C22×C43#57711yescharacteristic
411C22×C43#57811yescharacteristic
412C4×C43—24no—
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43C2×#12111yescharacteristic
420C4×C43#53511yescharacteristic
421C4×C43D4211yescharacteristic
422C4×C43#54611yescharacteristic
423Dic43—42no—
424Dic43—81no—
425Dic43—81no—
426Dic43—81no—
427C2×#548D4311yescharacteristic
428C2×#464—431no—
429C2×#452—431no—
430C2×#451—431no—
431C2×#441—431no—
432#2538—431no—
433#2035—431no—
434#2034—431no—
435#2001—431no—
436#2000—431no—
437#1959—431no—
438#1955—431no—
439#1803—431no—
440#1788—431no—
441#1787—431no—
442C2×C43—42no—
443C2×C43—81no—
444C2×C43—82no—
445C2×C43#240811yescharacteristic
446C2×C43#300711yescharacteristic
447C2×C43#301311yescharacteristic
448C2×C43#327011yescharacteristic
449C2×C43#327111yescharacteristic
450C2×C43#331311yescharacteristic
451C2×C43#331611yescharacteristic
452C22×#41C2×D4311yescharacteristic
453C23×Q8C2×D4311yescharacteristic
454C22×Q16—431no—
455C22×Q16—431no—
456C22×SD16—431no—
457#548—24no—
458#548—24no—
459C2×#124—21no—
460C2×#124C2×D4311yescharacteristic
461C2×C22⋊Q8—21no—
462C2×C22⋊Q8—431no—
463C2×C22⋊Q8—431no—
464C2×C22⋊Q8C2×D4311yescharacteristic
465C2×#121—21no—
466C2×#121C2×D4311yescharacteristic
467C2×C4×Q8—431no—
468C2×C4×Q8C2×D4311yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D4311yescharacteristic
471#464—864no—
472#452—864no—
473#451—864no—
474#441—864no—
475C2×#106—431no—
476C2×C4⋊C8—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×#97—431no—
492#396—861no—
493#396—861no—
494#390—861no—
495#389—861no—
496#384—431no—
497#380—431no—
498#380—431no—
499#340—431no—
500#340—431no—
501C43#2425811yescharacteristic, complemented, Sylow
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—431no—
516C22×Q8C22×D4311yescharacteristic
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4C22⋊D4311yescharacteristic
521C22×D4C22×D4311yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C22×D4311yescharacteristic
525C23×C4C22×D4311yescharacteristic
526C2×Q16—434no—
527C2×Q16—862no—
528C2×Q16—862no—
529C2×Q16—862no—
530C2×Q16—862no—
531C2×Q16—1721no—
532C2×SD16—862no—
533C2×SD16—862no—
534C2×SD16—1721no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539#124—28no—
540#124—22no—
541#124C22⋊D4314yes—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—862no—
546C22⋊Q8—862no—
547C22⋊Q8—1721no—
548C22⋊Q8—1721no—
549#121—28no—
550#121—22no—
551#121—22no—
552C4×Q8—22no—
553C4×Q8—862no—
554C4×Q8—862no—
555C4×Q8C22⋊D4314yes—
556C4×D4—28no—
557C4×D4—22no—
558C4×D4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4C22⋊D4311yescharacteristic
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4C22⋊D4311yescharacteristic
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C42—21no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584#106—862no—
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—862no—
589#103—862no—
590#103—862no—
591#103—862no—
592#103—1721no—
593#102—862no—
594#102—862no—
595#102—1721no—
596C22⋊C8—862no—
597C22⋊C8—862no—
598C22⋊C8—1721no—
599C22⋊C8—1721no—
600#97—862no—
601#95—861no—
602#95—861no—
603C24—21no—
604C24C2×C22⋊D4311yescharacteristic
605C24C2×C22⋊D4311yescharacteristic
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610C2×Q8—24no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—432no—
626C2×Q8—861no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8D4×D4312yes—
632C2×Q8#1062190012yes—
633C2×Q8C2×C22⋊D4312yes—
634C2×Q8C2×C22⋊D4312yes—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—41no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4C2×C22⋊D4312yes—
650C22×C4—21no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4C2×C22⋊D4311yescharacteristic
676C22×C4C2×C22⋊D4311yescharacteristic
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C23×D4311yescharacteristic
680Q16—868no—
681Q16—1724no—
682SD16—1724no—
683C2×C8—432no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—3441no—
706C4⋊C4—1722no—
707C4⋊C4—1722no—
708C4⋊C4—1722no—
709C4⋊C4—1722no—
710C4⋊C4C2×C22⋊D4312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—3441no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C22⋊C4—1722no—
721C42—24no—
722C42—1722no—
723C42C2×C22⋊D4312yes—
724C42C2×C22⋊D4312yes—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23#1306335512yes—
746C23C22×C22⋊D4311yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—48no—
753Q8—41no—
754Q8—41no—
755Q8—862no—
756Q8—862no—
757Q8—1721no—
758Q8—1721no—
759Q8#1306329614yes—
760D4—22no—
761D4—22no—
762D4—44no—
763D4—48no—
764D4—48no—
765D4—41no—
766D4—41no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—862no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4#1306329412yes—
809C2×C4#1306329412yes—
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4C22×C22⋊D4311yescharacteristic
812C2×C4C22×C22⋊D4311yescharacteristic
813C2×C4C2×#1062190011yescharacteristic
814C2×C4#1306337011yescharacteristic
815C2×C4#1306337011yescharacteristic
816C8—862no—
817C8—1721no—
818C8—1721no—
819C8—1721no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#1306329411yescharacteristic
842C22D4×C22⋊D4311yescharacteristic
843C22#1458354311yescharacteristic
844C22C2×#1306335511yescharacteristic
845C22#1458369711yescharacteristic
846C22#1458370711yescharacteristic
847C22#1458371411yescharacteristic
848C4—24no—
849C4—22no—
850C4—22no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—3441no—
856C4—3441no—
857C4—3441no—
858C4—1722no—
859C4C2×#1306329611yescharacteristic
860C4#1458346611yescharacteristic
861C4D4×C22⋊D4311yescharacteristic
862C4#1458354311yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2#1913794511yescharacteristic
867C2#1914385511yescharacteristic
868C2#1914391011yescharacteristic
869C2#1914616111yescharacteristic
870C2#1914618111yescharacteristic
871C2#1914666111yescharacteristic
872C2#1914670611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#548C2
socleC23×C43C22×D4
hypercenterC2×#548D43
hypocenterC43#24258
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#14583118C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14583055C2semidirect
4. C2×#14583004C2semidirect
5. #19139517C2semidirect
6. #19135788C2semidirect
7. #19135781C2semidirect
8. #19135603C2semidirect
9. #19135598C2semidirect
10. #19135412C2semidirect
11. #19135394C2semidirect
12. #19134600C2semidirect
13. #19134535C2semidirect
14. #19134530C2semidirect
71. C2×#10621885D4semidirect
501. C43#24258semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×#145830612
C2×#145830552
C2×#145830042
#191395172
#191357882
#191357812
#191356032
#191355982
#191354122
#191353942
#191346002
#191345352
#191345302
C2×C43×#5482
#2425843