Finite Group Databasebeta

← #25134182

Subgroups — #25134182

Order 11008.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583543C211yesmaximal, characteristic
2C2×#14583140C211yesmaximal, characteristic, complemented
3C2×#14583062C211yesmaximal, characteristic, complemented
4C2×#14583050C211yesmaximal, characteristic, complemented
5#19138040C211yesmaximal, characteristic, complemented
6#19135835C211yesmaximal, characteristic, complemented
7#19135776C211yesmaximal, characteristic, complemented
8#19135691C211yesmaximal, characteristic, complemented
9#19135599C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134887C211yesmaximal, characteristic, complemented
13#19134844C211yesmaximal, characteristic, complemented
14#19134532C211yesmaximal, characteristic, complemented
15C22×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×Dic172C2211yescharacteristic, complemented
18C22×#10621883C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20#14583543—24no—
21#14583543—24no—
22C2×#13063312C2211yescharacteristic
23C2×#13063306—21no—
24C2×#13063305C2211yescharacteristic, complemented
25C2×#13063304C2211yescharacteristic
26C2×#13063304C2211yescharacteristic
27C2×#13063297—21no—
28C2×#13063296C2211yescharacteristic
29C2×#13063294—21no—
30C2×D4×Dic43C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C22×C22⋊Dic43—21no—
33#14583140—24no—
34#14583062—24no—
35#14583050—24no—
36C2×#13063259C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063250C2211yescharacteristic, complemented
39C2×#13063248C2211yescharacteristic, complemented
40C2×#13063248C2211yescharacteristic, complemented
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
46#14582829—21no—
47#14582821—21no—
48#14582804C2211yescharacteristic, complemented
49#14582798C2211yescharacteristic, complemented
50#14582778—21no—
51#14582759—21no—
52#14582756C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C23×C8×C43C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C2×#102×C43—24no—
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#102×C43C2211yescharacteristic
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—41no—
70C2×#10621900—41no—
71C22×Dic86C2311yescharacteristic
72C22×Dic86C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43D411yescharacteristic
76C23×Dic43—21no—
77C23×Dic43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×Dic172—22no—
80C2×Dic172—22no—
81C2×Dic172—41no—
82C2×#10621883—22no—
83C2×#10621883—22no—
84C2×#10621883—22no—
85C2×#10621883—22no—
86C2×#10621883—41no—
87C2×#10621883—41no—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063312—22no—
91#13063312—22no—
92#13063306—28no—
93#13063305—22no—
94#13063305—41no—
95#13063304—22no—
96#13063304—22no—
97#13063304—22no—
98#13063304D414yes—
99#13063297—28no—
100#13063296—22no—
101#13063296—22no—
102#13063294—28no—
103D4×Dic43—22no—
104D4×Dic43—22no—
105C4×C22⋊D43—22no—
106C4×C22⋊D43—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4D411yescharacteristic
114C2×C22⋊Dic43—28no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—21no—
120C2×C22⋊Dic43—21no—
121C2×C22⋊Dic43D411yescharacteristic
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×C4×Dic43C2311yescharacteristic
126#13063259—22no—
127#13063250—22no—
128#13063250—22no—
129#13063248—22no—
130#13063248—41no—
131#13063246—22no—
132#13063246—22no—
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—
140C25×C43—21no—
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43—21no—
144C22×D4×C43—22no—
145C22×D4×C43—41no—
146C22×D4×C43—41no—
147C22×D4×C43D414yes—
148C22×D4×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152C22×C8×C43—22no—
153C22×C8×C43—22no—
154C22×C8×C43—41no—
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—21no—
159C2×C4⋊C4×C43—41no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C4⋊C4×C43C2311yescharacteristic
162#102×C43—22no—
163#102×C43—22no—
164#102×C43—22no—
165#102×C43D414yescomplemented
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—24no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C23×D43C2×D411yescharacteristic
177C2×D4×C43—24no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—28no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—44no—
190C2×D4×C43—44no—
191C2×D4×C43—44no—
192C2×D4×C43C2×D412yes—
193C2×D4×C43C2×D412yes—
194C2×D4×C43C2×D412yes—
195C2×D4×C43#4112yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—42no—
203C22×C4×C43—42no—
204C22×C4×C43—81no—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D412yes—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—22no—
212C2×C22⋊D43—22no—
213C2×C22⋊D43—22no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—42no—
216C2×C22⋊D43—81no—
217C2×C22⋊D43—81no—
218C22×Dic43—24no—
219C22×Dic43—24no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—42no—
225C22×Dic43—42no—
226C22×Dic43—81no—
227C22×Dic43—81no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621900—44no—
232#10621900—44no—
233#10621900—44no—
234#10621900—44no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86C2×D412yes—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—44no—
259C2×C8×C43C2×D412yes—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—42no—
264C4⋊C4×C43C2×D412yes—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—22no—
270C22⋊Dic43—24no—
271C22⋊Dic43—42no—
272#10621883—44no—
273#10621883—44no—
274(C2×D43)⋊C4—22no—
275(C2×D43)⋊C4—42no—
276(C2×D43)⋊C4—81no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—42no—
281C4⋊Dic43—81no—
282C4⋊Dic43C2×D412yes—
283Dic43⋊C4—24no—
284Dic43⋊C4—22no—
285Dic43⋊C4—42no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294Dic172—44no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—48no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—48no—
315C23×C43—84no—
316C23×C43—84no—
317C23×C43—84no—
318C23×C43—84no—
319C23×C43—84no—
320C23×C43#12012yes—
321C23×C43#13512yes—
322C23×C43#13712yes—
323C23×C43C22×D411yescharacteristic
324C22×D43—21no—
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—48no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43#12114yes—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—84no—
353C2×C4×C43#12012yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C2×C4×C43H(5,𝔽2)11yescharacteristic
360C22⋊D43—48no—
361C22⋊D43—44no—
362C22⋊D43—84no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—48no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—84no—
386C4×D43—41no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—41no—
390Dic86—22no—
391Dic86—22no—
392Dic86—41no—
393Dic86—41no—
394Dic86—41no—
395Dic86—41no—
396Dic86—41no—
397Dic86—41no—
398C8×C43—22no—
399C8×C43—41no—
400C43⋊C8—41no—
401C43⋊C8—41no—
402#24426—431nomaximal, Sylow
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—24no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—816no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43—81no—
424C22×C43#45214yescomplemented
425C22×C43C2×#12011yescharacteristic
426C22×C43D4211yescharacteristic
427C22×C43#54611yescharacteristic
428C22×C43C2×#13511yescharacteristic
429C22×C43C2×#13711yescharacteristic
430C22×C43#57611yescharacteristic
431C22×C43#57711yescharacteristic
432C2×D43—41no—
433C2×D43—41no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C4×C43—22no—
440C4×C43—42no—
441C4×C43—81no—
442C4×C43C2×#12111yescharacteristic
443C4×C43#53411yescharacteristic
444C4×C43D4211yescharacteristic
445C4×C43#54611yescharacteristic
446Dic43—42no—
447Dic43—41no—
448Dic43—41no—
449Dic43—41no—
450Dic43—42no—
451Dic43—81no—
452Dic43—81no—
453C2×#546—431no—
454C2×#467—431no—
455C2×#452—431no—
456C2×#450—431no—
457C22×#102D4311yescharacteristic, complemented
458#2417—431no—
459#2042—431no—
460#2033—431no—
461#2015—431no—
462#2000—431no—
463#1877—431no—
464#1872—431no—
465#1869—431no—
466#1862—431no—
467#1788—431no—
468C2×C43—24no—
469C2×C43—44no—
470C2×C43—82no—
471C2×C43#241011yescharacteristic
472C2×C43C2×#45211yescharacteristic
473C2×C43#301211yescharacteristic
474C2×C43#326611yescharacteristic
475C2×C43#328011yescharacteristic
476C2×C43#329611yescharacteristic
477C2×C43#331411yescharacteristic
478D43—81no—
479C22×#41—431no—
480C23×D4C2×D4311yescharacteristic
481C22×Q16—431no—
482C22×SD16—431no—
483C22×SD16—431no—
484C23×C8C2×D4311yescharacteristic
485#546—864no—
486#546—864no—
487C2×#124—431no—
488C2×#123—861no—
489C2×C22⋊Q8—431no—
490C2×C22⋊Q8—431no—
491C2×C22⋊Q8—431no—
492C2×#121—431no—
493C2×#121—861no—
494C2×#120—861no—
495C2×C4×D4—431no—
496C2×C4×D4—431no—
497C22×C4⋊C4C2×D4311yescharacteristic
498C22×C22⋊C4—861no—
499#467—864no—
500#452—864no—
501#450—864no—
502C2×#107—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#102—24no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102C2×D4311yescharacteristic
511C2×#102C2×D4311yescharacteristic
512C2×#102C2×D4311yescharacteristic
513C2×#102C2×D4311yescharacteristic
514C2×C22⋊C8—431no—
515C2×C22⋊C8—431no—
516C2×C22⋊C8—431no—
517#398—861no—
518#396—861no—
519#391—431no—
520#389—431no—
521#386—861no—
522#380—431no—
523#380—861no—
524#340—431no—
525#340—431no—
526#336—431no—
527#336—431no—
528C43#2442611yescharacteristic, complemented, Sylow
529C25—21no—
530C2×#41—862no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—862no—
534C2×#41—1721no—
535C2×#41—1721no—
536C22×Q8—431no—
537C22×Q8—431no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4—431no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4D17214yes—
548C22×D4C22×D4311yescharacteristic
549C22×D4C22×D4311yescharacteristic
550C23×C4—21no—
551C23×C4—431no—
552C23×C4—861no—
553C23×C4—861no—
554C23×C4C22×D4311yescharacteristic
555C2×Q16—862no—
556C2×Q16—862no—
557C2×Q16—1721no—
558C2×SD16—862no—
559C2×SD16—862no—
560C2×SD16—862no—
561C2×SD16—862no—
562C2×SD16—1721no—
563C2×SD16—1721no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8—431no—
568C22×C8—431no—
569C22×C8C22×D4311yescharacteristic
570C22×C8C22×D4311yescharacteristic
571#124—862no—
572#124—862no—
573#123—868no—
574C22⋊Q8—434no—
575C22⋊Q8—862no—
576C22⋊Q8—862no—
577C22⋊Q8—862no—
578C22⋊Q8—862no—
579C22⋊Q8—1721no—
580#121—862no—
581#121—868no—
582#121—862no—
583#120—868no—
584C4×D4—862no—
585C4×D4—862no—
586C4×D4—862no—
587C4×D4—862no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4C22×D4311yescharacteristic
599C2×C4⋊C4C22×D4311yescharacteristic
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—868no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C42—431no—
612#107—862no—
613#103—862no—
614#103—862no—
615#103—862no—
616#103—1721no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—862no—
621#102—862no—
622#102C22⋊D4314yescomplemented
623C22⋊C8—862no—
624C22⋊C8—862no—
625C22⋊C8—1721no—
626#95—861no—
627#95—861no—
628#95—861no—
629#95—861no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24—431no—
640C24D4×D4311yescharacteristic
641#41—1724no—
642#41—1724no—
643#41—1724no—
644#41—1724no—
645C2×Q8—432no—
646C2×Q8—861no—
647C2×Q8—861no—
648C2×Q8—861no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—861no—
656C2×Q8—861no—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—3441no—
678C2×D4—3441no—
679C2×D4—1722no—
680C2×D4—1722no—
681C2×D4C2×D17212yes—
682C2×D4C2×D17212yes—
683C2×D4#1062189812yes—
684C2×D4C2×C22⋊D4312yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—3441no—
710C22×C4—3441no—
711C22×C4—1722no—
712C22×C4—1722no—
713C22×C4C2×D17212yes—
714C22×C4D4×D4311yescharacteristic
715C22×C4D4×D4312yes—
716C22×C4C23×D4311yescharacteristic
717Q16—1724no—
718SD16—1724no—
719SD16—1724no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—44no—
726C2×C8—861no—
727C2×C8—861no—
728C2×C8—861no—
729C2×C8—861no—
730C2×C8—861no—
731C2×C8—861no—
732C2×C8C2×C22⋊D4312yes—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—432no—
738C4⋊C4—862no—
739C4⋊C4—864no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—3441no—
744C4⋊C4—1722no—
745C4⋊C4—1722no—
746C4⋊C4C2×C22⋊D4312yes—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—862no—
752C22⋊C4—864no—
753C22⋊C4—862no—
754C22⋊C4—3441no—
755C22⋊C4—1722no—
756C22⋊C4—1722no—
757C42—861no—
758C42—861no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—48no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—48no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—861no—
785C23—861no—
786C23—861no—
787C23—861no—
788C23—861no—
789C23—861no—
790C23—861no—
791C23#1306329512yes—
792C23#1306334412yes—
793C23#1306335412yes—
794C23C2×D4×D4311yescharacteristic
795Q8—862no—
796Q8—862no—
797Q8—1721no—
798Q8—1721no—
799Q8—1721no—
800Q8—1721no—
801Q8—1721no—
802Q8—1721no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—3444no—
812D4—1728no—
813D4—1724no—
814D4#1306329914yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—861no—
829C2×C4—861no—
830C2×C4—862no—
831C2×C4—861no—
832C2×C4—862no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—861no—
839C2×C4—3444no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1728no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4—1721no—
851C2×C4—1721no—
852C2×C4—1721no—
853C2×C4—1721no—
854C2×C4—1721no—
855C2×C4#1306329512yes—
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4C22×C22⋊D4311yescharacteristic
858C2×C4C22×D17211yescharacteristic
859C2×C4C2×#1062189811yescharacteristic
860C2×C4#1306337011yescharacteristic
861C2×C4#1306337011yescharacteristic
862C8—22no—
863C8—41no—
864C8—1721no—
865C8—1721no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—1721no—
888C22—1721no—
889C22—1721no—
890C22—1721no—
891C22—1721no—
892C22—1721no—
893C22—1721no—
894C22#1458306214yescomplemented
895C22C2×#1306329511yescharacteristic
896C22D4×C22⋊D4311yescharacteristic
897C22#1458353911yescharacteristic
898C22C2×#1306334411yescharacteristic
899C22C2×#1306335411yescharacteristic
900C22#1458370011yescharacteristic
901C22#1458370511yescharacteristic
902C4—22no—
903C4—42no—
904C4—81no—
905C4—3441no—
906C4—3441no—
907C4—1721no—
908C4—1721no—
909C4—1722no—
910C4—1721no—
911C4—1722no—
912C4C2×#1306329911yescharacteristic
913C4#1458346111yescharacteristic
914C4D4×C22⋊D4311yescharacteristic
915C4#1458353911yescharacteristic
916C2—24no—
917C2—44no—
918C2—82no—
919C2—3441no—
920C2#1913796311yescharacteristic
921C2C2×#1458306211yescharacteristic
922C2#1914390411yescharacteristic
923C2#1914610511yescharacteristic
924C2#1914628011yescharacteristic
925C2#1914642611yescharacteristic
926C2#1914667211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
hypercenterC22×#102D43
hypocenterC43#24426
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14583140C2semidirect
3. C2×#14583062C2semidirect
4. C2×#14583050C2semidirect
5. #19138040C2semidirect
6. #19135835C2semidirect
7. #19135776C2semidirect
8. #19135691C2semidirect
9. #19135599C2semidirect
10. #19134927C2semidirect
11. #19134902C2semidirect
12. #19134887C2semidirect
13. #19134844C2semidirect
14. #19134532C2semidirect
15. C22×#102×C43C2semidirect
17. C22×Dic172C22semidirect
24. C2×#13063305C22semidirect
36. C2×#13063259C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063250C22semidirect
39. C2×#13063248C22semidirect
40. C2×#13063248C22semidirect
44. C2×(C2×D43)⋊C8C22semidirect
45. C2×(C2×D43)⋊C8C22semidirect
48. #14582804C22semidirect
49. #14582798C22semidirect
52. #14582756C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
165. #102×C43D4semidirect
424. C22×C43#452semidirect
457. C22×#102D43semidirect
528. C43#24426semidirect
622. #102C22⋊D43semidirect
894. C22#14583062semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×#145831402
C2×#145830622
C2×#145830502
#191380402
#191358352
#191357762
#191356912
#191355992
#191349272
#191349022
#191348872
#191348442
#191345322
C22×#102×C432
#2442643