Finite Group Databasebeta

← #25124073

Subgroups — #25124073

Order 11008.

1610 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C2×#14582936C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
6#19136977C211yesmaximal, characteristic, complemented
7#19135800C211yesmaximal, characteristic, complemented
8#19135799C211yesmaximal, characteristic, complemented
9#19135794C211yesmaximal, characteristic, complemented
10#19135791C211yesmaximal, characteristic, complemented
11#19135782C211yesmaximal, characteristic, complemented
12#19135781C211yesmaximal, characteristic, complemented
13#19135776C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#2033C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583409—24no—
21#14583409—24no—
22C2×#13063307—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×#13063293—21no—
27C2×D4×Dic43—21no—
28C2×(C22⋊D43)⋊C4—21no—
29C2×#13063283C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×#13063283C2211yescharacteristic
32#14582936—24no—
33C2×#13063259C2211yescharacteristic, complemented
34C2×#13063256C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36#14582892—24no—
37#14582892—24no—
38C2×#13063250C2211yescharacteristic, complemented
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063248C2211yescharacteristic, complemented
41C2×#13063248C2211yescharacteristic, complemented
42C2×#13063246C2211yescharacteristic, complemented
43C2×#13063246C2211yescharacteristic, complemented
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C22⋊C8×D43—24no—
48#14582761—21no—
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582754—21no—
53C22⋊C4×Dic43—21no—
54#14582746—21no—
55#14582662C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57#14582661C2211yescharacteristic, complemented
58C2×#121×C43C2211yescharacteristic
59C2×#107×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C24×D43D411yescharacteristic
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900—22no—
71C2×#10621900D414yes—
72C22×Dic86C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C23×Dic43—21no—
76C23×Dic43D411yescharacteristic
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—22no—
90C2×C8×D43—22no—
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—22no—
94C2×C8×D43D414yescomplemented
95#13063307—28no—
96#13063305—22no—
97#13063305—22no—
98#13063304—22no—
99#13063304—22no—
100#13063296—22no—
101#13063296—22no—
102#13063293—28no—
103D4×Dic43—28no—
104(C22⋊D43)⋊C4—28no—
105#13063283—22no—
106#13063283—22no—
107#13063283—22no—
108#13063283—22no—
109#13063283—22no—
110#13063283D414yes—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43C2311yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×C4×Dic43—21no—
126C2×C4×Dic43—21no—
127C2×C4×Dic43—21no—
128#13063259—22no—
129#13063256—22no—
130#13063256—22no—
131#13063250—22no—
132#13063250—22no—
133#13063248—22no—
134#13063248—22no—
135#13063246—22no—
136#13063246—22no—
137C22⋊(C43⋊C8)—22no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C22×D4×C43—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148#121×C43—22no—
149#121×C43—22no—
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155#107×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158C22⋊C8×C43—22no—
159#95×C43—21no—
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—41no—
168C23×D43—41no—
169C23×D43C2×D411yescharacteristic
170C23×D43C2×D411yescharacteristic
171C2×D4×C43—24no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43C2×D412yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C22×Dic43—24no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209#10621900—28no—
210#10621900—28no—
211#10621900—44no—
212#10621900—44no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43—44no—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43#4112yes—
233C2×C4×D43#4112yes—
234C2×C4×D43#4112yes—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86C2×D412yes—
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×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2×D412yes—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—42no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—42no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4—42no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C2×D412yes—
271Dic43⋊C4—24no—
272C4×Dic43—24no—
273C4×Dic43—42no—
274C4×Dic43—42no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8C2×D412yes—
281C8×D43—28no—
282C8×D43—44no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43#13512yes—
297C23×C43C22×D411yescharacteristic
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—28no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43—44no—
313C22×D43—44no—
314C22×D43—44no—
315C22×D43#12012yes—
316C22×D43#12112yes—
317C22×D43#12312yes—
318C22×D43#13512yes—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—48no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C22⋊D43—48no—
347C22⋊D43—48no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—44no—
358C2×Dic43—48no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43#12012yes—
366C2×Dic43#12112yes—
367C2×Dic43#12312yes—
368C4×D43—44no—
369C4×D43—41no—
370C4×D43—41no—
371C4×D43—41no—
372C4×D43—41no—
373C4×D43—44no—
374C4×D43#12114yes—
375C4×D43#12114yes—
376C4×D43#12314yes—
377C4×D43#12414yes—
378Dic86—22no—
379Dic86—22no—
380Dic86—41no—
381Dic86—41no—
382C8×C43—22no—
383C8×C43—41no—
384C43⋊C8—22no—
385C43⋊C8—41no—
386#23479—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43C2×#12011yescharacteristic
402C22×C43C2×#12111yescharacteristic
403C22×C43C2×#12311yescharacteristic
404C22×C43C2×#13511yescharacteristic
405C22×C43C2×#13511yescharacteristic
406C22×C43#57511yescharacteristic
407C22×C43#57511yescharacteristic
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—416no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43#39414yes—
423C4×C43—41no—
424C4×C43—42no—
425C4×C43—81no—
426C4×C43—81no—
427C4×C43C2×#12111yescharacteristic
428C4×C43C2×#12111yescharacteristic
429C4×C43C2×#12311yescharacteristic
430C4×C43C2×#12411yescharacteristic
431Dic43—42no—
432Dic43—41no—
433Dic43—42no—
434Dic43—81no—
435Dic43—81no—
436Dic43#39414yes—
437C2×#525—431no—
438C2×#427—431no—
439C2×#416—431no—
440C2×#416—431no—
441C22×C22⋊C8—431no—
442#2280—431no—
443#2036—431no—
444#2036—431no—
445#2035—431no—
446#2035—431no—
447#2034—431no—
448#2034—431no—
449#2033—431no—
450#2033D4311yescharacteristic, complemented
451#1735—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43C2×#39411yescharacteristic
455C2×C43#300211yescharacteristic
456C2×C43#300211yescharacteristic
457C2×C43#305011yescharacteristic
458C2×C43#305411yescharacteristic
459C2×C43#309111yescharacteristic
460C2×C43#309111yescharacteristic
461D43—24no—
462D43—42no—
463C22×#41—431no—
464C24×C4—431no—
465C23×C8—431no—
466C23×C8—431no—
467#525—864no—
468#525—864no—
469C2×#123—861no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×#121—431no—
473C2×#121C2×D4311yescharacteristic
474C2×#120—861no—
475C2×C4×D4—861no—
476C2×C4×D4—861no—
477C2×#117—431no—
478C2×#117—431no—
479C2×#117—431no—
480#427—864no—
481C2×#107—431no—
482C2×#107C2×D4311yescharacteristic, complemented
483C2×#106—431no—
484C2×#106—431no—
485#416—864no—
486#416—864no—
487C2×#103—431no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102C2×D4311yescharacteristic, complemented
494C2×#102C2×D4311yescharacteristic, complemented
495C2×C22⋊C8—431no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8—864no—
499C2×C22⋊C8C2×D4311yescharacteristic
500#381—861no—
501#380—431no—
502#380—431no—
503#380—431no—
504#380C2×D4311yescharacteristic
505#379—861no—
506C4×C22⋊C4—861no—
507C4×C22⋊C4—861no—
508#340—431no—
509#340—431no—
510#340—431no—
511#340C2×D4311yescharacteristic, complemented
512C43#2347911yescharacteristic, complemented, Sylow
513C25—431no—
514C2×#41—434no—
515C2×#41—862no—
516C2×#41—862no—
517C2×#41—862no—
518C2×#41—862no—
519C2×#41—862no—
520C22×Q8—431no—
521C22×D4—21no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—431no—
526C23×C4—431no—
527C23×C4—431no—
528C23×C4—431no—
529C23×C4—431no—
530C23×C4—862no—
531C23×C4—862no—
532C23×C4—862no—
533C23×C4—862no—
534C23×C4—862no—
535C23×C4—862no—
536C23×C4—861no—
537C23×C4C22×D4311yescharacteristic
538C22×C8—431no—
539C22×C8—434no—
540C22×C8—431no—
541C22×C8—862no—
542C22×C8—862no—
543C22×C8—862no—
544C22×C8—862no—
545C22×C8—862no—
546C22×C8C22×D4311yescharacteristic
547C22×C8C22×D4311yescharacteristic
548#123—868no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8—862no—
552C22⋊Q8—862no—
553#121—22no—
554#121—22no—
555#121—862no—
556#121—862no—
557#120—868no—
558C4×D4—868no—
559C4×D4—868no—
560#117—434no—
561#117—862no—
562#117—862no—
563#117—862no—
564#117—862no—
565#117—862no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4C22×D4311yescharacteristic
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C42—861no—
586C2×C42—861no—
587C2×C42—861no—
588#107—22no—
589#107—862no—
590#106—862no—
591#106—862no—
592#103—862no—
593#103—862no—
594#103—862no—
595#103—862no—
596#102—22no—
597#102—22no—
598#102—862no—
599#102—862no—
600C22⋊C8—22no—
601C22⋊C8—862no—
602C22⋊C8—862no—
603C22⋊C8—862no—
604#95—21no—
605#95—861no—
606#95—861no—
607#95—861no—
608C24—21no—
609C24—431no—
610C24—431no—
611C24—862no—
612C24—862no—
613C24—862no—
614C24—862no—
615C24—862no—
616C24—1721no—
617C24—1721no—
618C24D4×D4311yescharacteristic
619#41—868no—
620#41—868no—
621#41—1724no—
622#41—1724no—
623C2×Q8—432no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—861no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—1722no—
640C2×D4—1722no—
641C2×D4—1722no—
642C2×D4—1722no—
643C2×D4D4×D4312yes—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—431no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—432no—
657C22×C4—432no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—431no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—862no—
667C22×C4—862no—
668C22×C4—864no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—1724no—
682C22×C4—1724no—
683C22×C4—1724no—
684C22×C4—1724no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4D4×D4311yescharacteristic
688C22×C4C23×D4311yescharacteristic
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—432no—
695C2×C8—868no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—1724no—
702C2×C8D4×D4312yes—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—432no—
709C4⋊C4—864no—
710C4⋊C4—864no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4D4×D4312yes—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—864no—
722C22⋊C4—864no—
723C22⋊C4—1722no—
724C22⋊C4—1722no—
725C22⋊C4—1722no—
726C22⋊C4—1722no—
727C22⋊C4—1722no—
728C42—864no—
729C42—1722no—
730C42—1722no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—432no—
745C23—432no—
746C23—432no—
747C23—432no—
748C23—868no—
749C23—861no—
750C23—861no—
751C23—861no—
752C23—861no—
753C23—861no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23—1724no—
760C23—1724no—
761C23—1724no—
762C23—1724no—
763C23—1724no—
764C23—1724no—
765C23#1306334412yes—
766C23C2×D4×D4311yescharacteristic
767Q8—862no—
768Q8—862no—
769Q8—1721no—
770Q8—1721no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—1728no—
777D4—1728no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
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—432no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—434no—
798C2×C4—434no—
799C2×C4—434no—
800C2×C4—434no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—862no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—1724no—
807C2×C4—1724no—
808C2×C4—1724no—
809C2×C4—1728no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4#41×D4311yescharacteristic
828C2×C4#41×D4311yescharacteristic
829C2×C4#41×D4311yescharacteristic
830C8—22no—
831C8—41no—
832C8—862no—
833C8—1721no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—434no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—17216no—
859C22—1721no—
860C22—1721no—
861C22—1721no—
862C22—1721no—
863C22#120×D4311yescharacteristic
864C22#121×D4311yescharacteristic
865C22#123×D4311yescharacteristic
866C22#135×D4311yescharacteristic
867C22C2×#1306334411yescharacteristic
868C22#1458369511yescharacteristic
869C22#1458369811yescharacteristic
870C4—41no—
871C4—42no—
872C4—81no—
873C4—81no—
874C4—434no—
875C4—3441no—
876C4—3441no—
877C4—1721no—
878C4—1722no—
879C4—1722no—
880C4#121×D4311yescharacteristic
881C4#121×D4311yescharacteristic
882C4#123×D4311yescharacteristic
883C4#124×D4311yescharacteristic
884C2—42no—
885C2—82no—
886C2—864no—
887C2—1722no—
888C2#394×D4311yescharacteristic
889C2#1914380811yescharacteristic
890C2#1914381611yescharacteristic
891C2#1914417411yescharacteristic
892C2#1914419911yescharacteristic
893C2#1914450311yescharacteristic
894C2#1914450711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2033C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
hypercenter#2033D43
hypocenterC43#23479
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#14582936C2semidirect
3. C2×#14582892C2semidirect
4. C2×#14582892C2semidirect
5. C2×C22⋊C8×D43C2semidirect
6. #19136977C2semidirect
7. #19135800C2semidirect
8. #19135799C2semidirect
9. #19135794C2semidirect
10. #19135791C2semidirect
11. #19135782C2semidirect
12. #19135781C2semidirect
13. #19135776C2semidirect
14. #19134310C2semidirect
15. C43×#2033C2semidirect
33. C2×#13063259C22semidirect
34. C2×#13063256C22semidirect
35. C2×#13063256C22semidirect
38. C2×#13063250C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063248C22semidirect
41. C2×#13063248C22semidirect
42. C2×#13063246C22semidirect
43. C2×#13063246C22semidirect
55. #14582662C22semidirect
56. #14582661C22semidirect
57. #14582661C22semidirect
59. C2×#107×C43C22semidirect
60. C2×#102×C43C22semidirect
61. C2×#102×C43C22semidirect
64. C43×#340C22semidirect
94. C2×C8×D43D4semidirect
450. #2033D43semidirect
482. C2×#107C2×D43semidirect
493. C2×#102C2×D43semidirect
494. C2×#102C2×D43semidirect
511. #340C2×D43semidirect
512. C43#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
C2×#145829362
C2×#145828922
C2×C22⋊C8×D432
#191369772
#191358002
#191357992
#191357942
#191357912
#191357822
#191357812
#191357762
#191343102
C43×#20332
#2347943