Finite Group Databasebeta

← #25124093

Subgroups — #25124093

Order 11008.

1558 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14582938C211yesmaximal, characteristic, complemented
3C2×#14582906C211yesmaximal, characteristic, complemented
4C2×#14582906C211yesmaximal, characteristic, complemented
5C2×#14582861C211yesmaximal, characteristic
6#19136977C211yesmaximal, characteristic
7#19135801C211yesmaximal, characteristic, complemented
8#19135799C211yesmaximal, characteristic, complemented
9#19135797C211yesmaximal, characteristic, complemented
10#19135795C211yesmaximal, characteristic, complemented
11#19135793C211yesmaximal, characteristic, complemented
12#19135791C211yesmaximal, characteristic, complemented
13#19135789C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2035C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063302—21no—
24C2×#13063301C2211yescharacteristic
25C22⋊Q8×D43—24no—
26C22⋊Q8×D43—24no—
27C2×#13063283C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C22⋊C4×D43—21no—
32#14582938—24no—
33C2×#13063259C2211yescharacteristic, complemented
34C2×#13063258C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36#14582906—24no—
37#14582906—24no—
38C2×#13063250C2211yescharacteristic, complemented
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063249C2211yescharacteristic, complemented
41C2×#13063249C2211yescharacteristic, complemented
42C2×#13063248C2211yescharacteristic, complemented
43C2×#13063248C2211yescharacteristic, complemented
44#14582861—24no—
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
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×C22⋊Q8×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C24×D43D411yescharacteristic
66C22×Dic86—21no—
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—22no—
73C2×Q8×D43D414yes—
74C23×Dic43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43—21no—
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
87C2×#10621872—22no—
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—22no—
91C2×#10621872—22no—
92C2×#10621872D414yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063305—22no—
96#13063305—22no—
97#13063304—22no—
98#13063304—22no—
99#13063303—28no—
100#13063302—28no—
101#13063301—22no—
102#13063301—22no—
103#13063283—22no—
104#13063283—22no—
105#13063283—22no—
106#13063283—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C4⋊C4×D43—28no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43D414yes—
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—
125C22⋊C4×D43—28no—
126C2×C4×Dic43—21no—
127C2×C4×Dic43—21no—
128#13063259—22no—
129#13063258—22no—
130#13063256—22no—
131#13063250—22no—
132#13063250—22no—
133#13063249—22no—
134#13063249—22no—
135#13063248—22no—
136#13063248—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×Q8×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22⋊Q8×C43—22no—
148C22⋊Q8×C43—22no—
149C2×C4⋊C4×C43—21no—
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155#106×C43—22no—
156#103×C43—22no—
157#103×C43—22no—
158C22⋊C8×C43—22no—
159#95×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—41no—
167C23×D43—41no—
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C2×D412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197Q8×D43—28no—
198Q8×D43—28no—
199Q8×D43—44no—
200Q8×D43—44no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43—44no—
221C2×C4×D43—42no—
222C2×C4×D43—42no—
223C2×C4×D43C2×D412yes—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D412yes—
226C2×C4×D43#4112yes—
227C2×C4×D43#4112yes—
228C2×C4×D43#4112yes—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—24no—
235C2×Dic86—42no—
236C2×Dic86—42no—
237C2×Dic86C2×D412yes—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43C2×D412yes—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2×D412yes—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—42no—
253C22⋊Dic43—24no—
254C22⋊Dic43—42no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261C4⋊Dic43—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271C4×Dic43—42no—
272C4×Dic43—42no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8C2×D412yes—
279#10621872—28no—
280#10621872—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43#13712yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—28no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—44no—
301C22×D43—44no—
302C22×D43—44no—
303C22×D43—44no—
304C22×D43—44no—
305C22×D43—44no—
306C22×D43#12012yes—
307C22×D43#12112yes—
308C22×D43#12312yes—
309C22×D43#13712yes—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—41no—
313Q8×C43—41no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
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—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×Dic43—22no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—44no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43#12012yes—
356C2×Dic43#12112yes—
357C2×Dic43#12312yes—
358C4×D43—48no—
359C4×D43—44no—
360C4×D43—48no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—44no—
366C4×D43#12114yes—
367C4×D43#12114yes—
368C4×D43#12314yes—
369C4×D43#12414yes—
370Dic86—22no—
371Dic86—22no—
372Dic86—41no—
373Dic86—41no—
374Dic86—48no—
375C8×C43—22no—
376C8×C43—41no—
377C43⋊C8—22no—
378C43⋊C8—41no—
379#23481—431nomaximal, Sylow
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43C2×#12011yescharacteristic
388C22×C43C2×#12111yescharacteristic
389C22×C43C2×#12311yescharacteristic
390C22×C43C2×#13711yescharacteristic
391C22×C43C2×#13711yescharacteristic
392C22×C43#57511yescharacteristic
393C22×C43#57511yescharacteristic
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—416no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43#39414yes—
409C4×C43—42no—
410C4×C43—41no—
411C4×C43—42no—
412C4×C43—81no—
413C4×C43—81no—
414C4×C43C2×#12111yescharacteristic
415C4×C43C2×#12111yescharacteristic
416C4×C43C2×#12311yescharacteristic
417C4×C43C2×#12411yescharacteristic
418Dic43—42no—
419Dic43—41no—
420Dic43—42no—
421Dic43—81no—
422Dic43—81no—
423Dic43#39414yes—
424C22×C22⋊Q8—431no—
425C2×#428—431no—
426C2×#419—431no—
427C2×#419—431no—
428C2×#407—431no—
429#2280—431no—
430#2036—431no—
431#2036—431no—
432#2036—431no—
433#2036—431no—
434#2035—431no—
435#2035—431no—
436#2035—431no—
437#2035D4311yescharacteristic, complemented
438#1736—431no—
439C2×C43—42no—
440C2×C43C2×#39411yescharacteristic
441C2×C43#300411yescharacteristic
442C2×C43#300511yescharacteristic
443C2×C43#305611yescharacteristic
444C2×C43#305611yescharacteristic
445C2×C43#309511yescharacteristic
446C2×C43#309511yescharacteristic
447D43—24no—
448D43—42no—
449C23×Q8—431no—
450C24×C4—431no—
451C22×M16—431no—
452C22×M16—431no—
453C2×C22⋊Q8—431no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C2×C22⋊Q8—861no—
457C2×C22⋊Q8—861no—
458C2×C22⋊Q8—864no—
459C2×C22⋊Q8—864no—
460C2×C22⋊Q8C2×D4311yescharacteristic
461C2×#117—431no—
462C2×#117—431no—
463C22×C4⋊C4—431no—
464C22×C4⋊C4—861no—
465C22×C22⋊C4—861no—
466#428—864no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#106—431no—
470C2×#106C2×D4311yescharacteristic, complemented
471#419—864no—
472#419—864no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103C2×D4311yescharacteristic, complemented
480C2×#103C2×D4311yescharacteristic, complemented
481#407—864no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485C2×C22⋊C8C2×D4311yescharacteristic
486#381—861no—
487#380—431no—
488#380—431no—
489#380—431no—
490#380C2×D4311yescharacteristic
491#379—861no—
492C4×C22⋊C4—861no—
493C4×C22⋊C4—861no—
494#340—431no—
495#340—431no—
496#340—431no—
497#340C2×D4311yescharacteristic, complemented
498C43#2348111yescharacteristic, complemented, Sylow
499C25—431no—
500C22×Q8—434no—
501C22×Q8—431no—
502C22×Q8—861no—
503C22×Q8—862no—
504C22×Q8—862no—
505C22×Q8—862no—
506C22×Q8—862no—
507C22×Q8—862no—
508C22×Q8C22×D4311yescharacteristic
509C23×C4—431no—
510C23×C4—431no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—431no—
514C23×C4—862no—
515C23×C4—862no—
516C23×C4—862no—
517C23×C4—862no—
518C23×C4—862no—
519C23×C4—862no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C2×M16—434no—
524C2×M16—862no—
525C2×M16—862no—
526C2×M16—862no—
527C2×M16—862no—
528C2×M16—862no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8C22×D4311yescharacteristic
532C22×C8C22×D4311yescharacteristic
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—868no—
536C22⋊Q8—862no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—862no—
543#117—862no—
544#117—862no—
545#117—862no—
546#117—862no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—862no—
553C2×C4⋊C4—868no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—868no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—861no—
573C2×C42—861no—
574#107—862no—
575#107—862no—
576#106—22no—
577#106—862no—
578#103—22no—
579#103—22no—
580#103—862no—
581#103—862no—
582#103—862no—
583#103—862no—
584#103—862no—
585#103—862no—
586C22⋊C8—22no—
587C22⋊C8—862no—
588C22⋊C8—862no—
589C22⋊C8—862no—
590#95—21no—
591#95—861no—
592#95—861no—
593#95—861no—
594C24—431no—
595C24—431no—
596C24—862no—
597C24—862no—
598C24—862no—
599C24—862no—
600C24—862no—
601C24—1721no—
602C24—1721no—
603C24D4×D4311yescharacteristic
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—432no—
610C2×Q8—864no—
611C2×Q8—868no—
612C2×Q8—868no—
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×Q8D4×D4312yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—431no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—864no—
645C22×C4—864no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4—1724no—
665C22×C4—1724no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4D4×D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672M16—868no—
673M16—1724no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—432no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8D4×D4312yes—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—432no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4D4×D4312yes—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C42—1722no—
714C42—1722no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—432no—
722C23—432no—
723C23—432no—
724C23—432no—
725C23—868no—
726C23—861no—
727C23—861no—
728C23—861no—
729C23—861no—
730C23—861no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—1724no—
737C23—1724no—
738C23—1724no—
739C23—1724no—
740C23—1724no—
741C23—1724no—
742C23#1306335412yes—
743C23C2×D4×D4311yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748Q8—862no—
749Q8—862no—
750Q8—1728no—
751Q8—1721no—
752Q8—1721no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
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—432no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—434no—
776C2×C4—434no—
777C2×C4—434no—
778C2×C4—434no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—1724no—
785C2×C4—1724no—
786C2×C4—1728no—
787C2×C4—1728no—
788C2×C4—1724no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#41×D4311yescharacteristic
808C2×C4#41×D4311yescharacteristic
809C8—22no—
810C8—41no—
811C8—862no—
812C8—1721no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—434no—
821C22—862no—
822C22—862no—
823C22—862no—
824C22—862no—
825C22—862no—
826C22—862no—
827C22—862no—
828C22—862no—
829C22—862no—
830C22—17216no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22#120×D4311yescharacteristic
836C22#121×D4311yescharacteristic
837C22#123×D4311yescharacteristic
838C22#137×D4311yescharacteristic
839C22C2×#1306335411yescharacteristic
840C22#1458369611yescharacteristic
841C22#1458369811yescharacteristic
842C4—41no—
843C4—42no—
844C4—42no—
845C4—81no—
846C4—81no—
847C4—434no—
848C4—3441no—
849C4—3441no—
850C4—1721no—
851C4—1722no—
852C4—1722no—
853C4#121×D4311yescharacteristic
854C4#121×D4311yescharacteristic
855C4#123×D4311yescharacteristic
856C4#124×D4311yescharacteristic
857C2—42no—
858C2—864no—
859C2—1722no—
860C2#394×D4311yescharacteristic
861C2#1914382611yescharacteristic
862C2#1914383811yescharacteristic
863C2#1914421811yescharacteristic
864C2#1914422411yescharacteristic
865C2#1914453811yescharacteristic
866C2#1914454211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2035C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2035D43
hypocenterC43#23481
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#14582938C2semidirect
3. C2×#14582906C2semidirect
4. C2×#14582906C2semidirect
7. #19135801C2semidirect
8. #19135799C2semidirect
9. #19135797C2semidirect
10. #19135795C2semidirect
11. #19135793C2semidirect
12. #19135791C2semidirect
13. #19135789C2semidirect
14. #19134313C2semidirect
15. C43×#2035C2semidirect
33. C2×#13063259C22semidirect
34. C2×#13063258C22semidirect
35. C2×#13063256C22semidirect
38. C2×#13063250C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063249C22semidirect
41. C2×#13063249C22semidirect
42. C2×#13063248C22semidirect
43. C2×#13063248C22semidirect
55. #14582662C22semidirect
56. #14582661C22semidirect
57. #14582661C22semidirect
59. C2×#106×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
64. C43×#340C22semidirect
437. #2035D43semidirect
470. C2×#106C2×D43semidirect
479. C2×#103C2×D43semidirect
480. C2×#103C2×D43semidirect
497. #340C2×D43semidirect
498. C43#23481semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145829382
C2×#145829062
C2×#145828612
#191369772
#191358012
#191357992
#191357972
#191357952
#191357932
#191357912
#191357892
#191343132
C43×#20352
#2348143