Finite Group Databasebeta

← #25124102

Subgroups — #25124102

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C2×#14582940C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582897C211yesmaximal, characteristic, complemented
5C2×#14582861C211yesmaximal, characteristic, complemented
6#380×D43C211yesmaximal, characteristic, complemented
7#19135801C211yesmaximal, characteristic, complemented
8#19135800C211yesmaximal, characteristic, complemented
9#19135792C211yesmaximal, characteristic, complemented
10#19135791C211yesmaximal, characteristic, complemented
11#19135783C211yesmaximal, characteristic, complemented
12#19135782C211yesmaximal, characteristic, complemented
13#19135774C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2033C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
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×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C22⋊C4×D43—21no—
33#14582940—24no—
34C2×#13063258C2211yescharacteristic, complemented
35C2×#13063257C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37#14582897—24no—
38#14582897—24no—
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063250C2211yescharacteristic, complemented
41C2×#13063248C2211yescharacteristic, complemented
42C2×#13063248C2211yescharacteristic, complemented
43C2×#13063246C2211yescharacteristic, complemented
44C2×#13063246C2211yescharacteristic, complemented
45#14582861—24no—
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582758—21no—
51#14582757—21no—
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic
54#95×D43—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×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43D411yescharacteristic
86C22×C4×D43D411yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C2×#10621872—22no—
90C2×#10621872—22no—
91C2×#10621872—22no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872D414yescomplemented
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063307—28no—
98#13063305—22no—
99#13063305—22no—
100#13063304—22no—
101#13063304—22no—
102#13063296—22no—
103#13063296—22no—
104#13063293—28no—
105D4×Dic43—28no—
106(C22⋊D43)⋊C4—28no—
107#13063283—22no—
108#13063283D414yes—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×C4⋊Dic43C2311yescharacteristic
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C4⋊C4×D43—22no—
117C4⋊C4×D43—22no—
118C4⋊C4×D43—22no—
119C4⋊C4×D43—22no—
120C2×C22⋊Dic43—21no—
121C2×C22⋊Dic43—21no—
122C2×C22⋊Dic43—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4—21no—
127C22⋊C4×D43—44no—
128C2×C4×Dic43—21no—
129#13063258—22no—
130#13063257—22no—
131#13063256—22no—
132#13063250—22no—
133#13063250—22no—
134#13063248—22no—
135#13063248—22no—
136#13063246—22no—
137#13063246—22no—
138C22⋊(C43⋊C8)—22no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C22×D4×C43—21no—
145C22×D4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#121×C43—22no—
150#121×C43—22no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#107×C43—22no—
157#102×C43—22no—
158#102×C43—22no—
159C22⋊C8×C43—22no—
160#95×C43—21no—
161C24×C43—21no—
162C24×C43C2×D411yescharacteristic
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—41no—
169C23×D43—41no—
170C23×D43C2×D411yescharacteristic
171C23×D43C2×D411yescharacteristic
172C2×D4×C43—24no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43C2×D412yes—
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×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C2×C22⋊D43—24no—
193C2×C22⋊D43—24no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C22×Dic43—24no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—42no—
207C22×Dic43—42no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210#10621900—28no—
211#10621900—28no—
212#10621900—44no—
213#10621900—44no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2×D412yes—
238C2×C4×D43C2×D412yes—
239C2×C4×D43#4112yes—
240C2×C4×D43#4112yes—
241C2×C4×D43#4112yes—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86C2×D412yes—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43C2×D412yes—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2×D412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—42no—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264C22⋊Dic43—42no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—42no—
268(C2×D43)⋊C4—42no—
269C4⋊Dic43—24no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43C2×D412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—42no—
278Dic43⋊C4—42no—
279C4×Dic43—24no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8C2×D412yes—
286#10621872—28no—
287#10621872—44no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—22no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43AGL(1,ℤ/8)12yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—28no—
308C22×D43—21no—
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—44no—
315C22×D43—44no—
316C22×D43—44no—
317C22×D43—44no—
318C22×D43—44no—
319C22×D43—44no—
320C22×D43#12012yes—
321C22×D43#12112yes—
322C22×D43#12312yes—
323C22×D43#13712yes—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—48no—
327D4×C43—41no—
328D4×C43—41no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
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×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C22⋊D43—48no—
352C22⋊D43—48no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—44no—
363C2×Dic43—48no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43#12012yes—
371C2×Dic43#12112yes—
372C2×Dic43#12312yes—
373C4×D43—44no—
374C4×D43—41no—
375C4×D43—41no—
376C4×D43—41no—
377C4×D43—41no—
378C4×D43—44no—
379C4×D43—84no—
380C4×D43—84no—
381C4×D43#12114yes—
382C4×D43#12114yes—
383C4×D43#12314yes—
384C4×D43#12414yes—
385Dic86—22no—
386Dic86—22no—
387Dic86—41no—
388Dic86—41no—
389C8×C43—22no—
390C8×C43—41no—
391C43⋊C8—22no—
392C43⋊C8—41no—
393#23482—431nomaximal, Sylow
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43C2×#12011yescharacteristic
409C22×C43C2×#12111yescharacteristic
410C22×C43C2×#12311yescharacteristic
411C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C43C2×#13711yescharacteristic
413C22×C43#57511yescharacteristic
414C22×C43#57511yescharacteristic
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—416no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43—41no—
428C2×D43—41no—
429C2×D43#39414yes—
430C4×C43—41no—
431C4×C43—42no—
432C4×C43—81no—
433C4×C43—81no—
434C4×C43C2×#12111yescharacteristic
435C4×C43C2×#12111yescharacteristic
436C4×C43C2×#12311yescharacteristic
437C4×C43C2×#12411yescharacteristic
438Dic43—42no—
439Dic43—41no—
440Dic43—42no—
441Dic43—81no—
442Dic43—81no—
443Dic43#39414yes—
444C2×#525—431no—
445C2×#428—431no—
446C2×#417—431no—
447C2×#417—431no—
448C2×#407—431no—
449C2×#380—431no—
450#2036—431no—
451#2036—431no—
452#2035—431no—
453#2035—431no—
454#2034—431no—
455#2034—431no—
456#2033—431no—
457#2033D4311yescharacteristic, complemented
458#1736—431no—
459C2×C43—42no—
460C2×C43—82no—
461C2×C43C2×#39411yescharacteristic
462C2×C43#300611yescharacteristic
463C2×C43#300711yescharacteristic
464C2×C43#305511yescharacteristic
465C2×C43#305611yescharacteristic
466C2×C43#309211yescharacteristic
467C2×C43#309311yescharacteristic
468D43—24no—
469D43—42no—
470C22×#41—431no—
471C24×C4—431no—
472C22×M16—431no—
473C22×M16—431no—
474#525—864no—
475#525—864no—
476C2×#123—861no—
477C2×C22⋊Q8—431no—
478C2×C22⋊Q8—431no—
479C2×#121—431no—
480C2×#121C2×D4311yescharacteristic
481C2×#120—861no—
482C2×C4×D4—861no—
483C2×C4×D4—861no—
484C2×#117—431no—
485C22×C4⋊C4—431no—
486C22×C4⋊C4—431no—
487C22×C22⋊C4—861no—
488#428—864no—
489C2×#107—431no—
490C2×#107C2×D4311yescharacteristic, complemented
491C2×#106—431no—
492C2×#106—431no—
493#417—864no—
494#417—864no—
495C2×#103—431no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#102—431no—
500C2×#102—431no—
501C2×#102C2×D4311yescharacteristic, complemented
502C2×#102C2×D4311yescharacteristic, complemented
503#407—864no—
504C2×C22⋊C8—431no—
505C2×C22⋊C8—431no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8C2×D4311yescharacteristic
508#380—431no—
509#380—431no—
510#380—431no—
511#380—861no—
512#380—861no—
513#380C2×D4311yescharacteristic
514C2×#95—861no—
515#340—431no—
516#340—431no—
517#340—431no—
518#340C2×D4311yescharacteristic, complemented
519C43#2348211yescharacteristic, complemented, Sylow
520C25—431no—
521C2×#41—434no—
522C2×#41—862no—
523C2×#41—862no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C22×Q8—431no—
528C22×D4—21no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4C22×D4311yescharacteristic
532C23×C4—431no—
533C23×C4—431no—
534C23×C4—431no—
535C23×C4—431no—
536C23×C4—431no—
537C23×C4—862no—
538C23×C4—862no—
539C23×C4—862no—
540C23×C4—862no—
541C23×C4—862no—
542C23×C4—862no—
543C23×C4—861no—
544C23×C4—861no—
545C23×C4—861no—
546C23×C4C22×D4311yescharacteristic
547C2×M16—434no—
548C2×M16—862no—
549C2×M16—862no—
550C2×M16—862no—
551C2×M16—862no—
552C2×M16—862no—
553C22×C8—431no—
554C22×C8—431no—
555C22×C8C22×D4311yescharacteristic
556C22×C8C22×D4311yescharacteristic
557#123—868no—
558C22⋊Q8—862no—
559C22⋊Q8—862no—
560C22⋊Q8—862no—
561C22⋊Q8—862no—
562#121—22no—
563#121—22no—
564#121—862no—
565#121—862no—
566#120—868no—
567C4×D4—868no—
568C4×D4—868no—
569#117—434no—
570#117—862no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—431no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—862no—
576C2×C4⋊C4—862no—
577C2×C4⋊C4—862no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C4⋊C4C22×D4311yescharacteristic
584C2×C4⋊C4C22×D4311yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C22⋊C4—1724no—
595C2×C42—861no—
596#107—22no—
597#107—862no—
598#106—862no—
599#106—862no—
600#103—862no—
601#103—862no—
602#103—862no—
603#103—862no—
604#102—22no—
605#102—22no—
606#102—862no—
607#102—862no—
608C22⋊C8—22no—
609C22⋊C8—862no—
610C22⋊C8—862no—
611C22⋊C8—862no—
612#95—21no—
613#95—861no—
614#95—861no—
615#95—861no—
616C24—21no—
617C24—431no—
618C24—431no—
619C24—862no—
620C24—862no—
621C24—862no—
622C24—862no—
623C24—862no—
624C24—1721no—
625C24—1721no—
626C24D4×D4311yescharacteristic
627#41—868no—
628#41—868no—
629#41—1724no—
630#41—1724no—
631C2×Q8—432no—
632C2×Q8—861no—
633C2×Q8—861no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—864no—
646C2×D4—864no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4D4×D4312yes—
652C22×C4—21no—
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—431no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—431no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—864no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—1724no—
690C22×C4—1724no—
691C22×C4—1724no—
692C22×C4—1724no—
693C22×C4—1722no—
694C22×C4—1722no—
695C22×C4—1722no—
696C22×C4—1722no—
697C22×C4—1722no—
698C22×C4—1722no—
699C22×C4—1722no—
700C22×C4—1722no—
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4311yescharacteristic
703M16—868no—
704M16—1724no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—432no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8D4×D4312yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—432no—
723C4⋊C4—864no—
724C4⋊C4—864no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—1722no—
731C4⋊C4—1722no—
732C4⋊C4D4×D4312yes—
733C22⋊C4—24no—
734C22⋊C4—42no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C22⋊C4—1722no—
740C22⋊C4—1722no—
741C22⋊C4—1722no—
742C42—864no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—432no—
757C23—432no—
758C23—432no—
759C23—432no—
760C23—868no—
761C23—861no—
762C23—861no—
763C23—861no—
764C23—861no—
765C23—861no—
766C23—861no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—861no—
771C23—1724no—
772C23—1724no—
773C23—1724no—
774C23—1724no—
775C23—1724no—
776C23—1724no—
777C23#1306334912yes—
778C23C2×D4×D4311yescharacteristic
779Q8—862no—
780Q8—862no—
781Q8—1721no—
782Q8—1721no—
783D4—22no—
784D4—22no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—1728no—
789D4—1728no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—434no—
810C2×C4—434no—
811C2×C4—434no—
812C2×C4—434no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—3444no—
819C2×C4—3444no—
820C2×C4—1724no—
821C2×C4—1724no—
822C2×C4—1724no—
823C2×C4—1728no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4C2×D4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C2×C4C2×D4×D4311yescharacteristic
841C2×C4#41×D4311yescharacteristic
842C2×C4#41×D4311yescharacteristic
843C2×C4#41×D4311yescharacteristic
844C8—22no—
845C8—41no—
846C8—862no—
847C8—1721no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—434no—
863C22—862no—
864C22—862no—
865C22—862no—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—862no—
870C22—862no—
871C22—862no—
872C22—17216no—
873C22—1721no—
874C22—1721no—
875C22—1721no—
876C22—1721no—
877C22#120×D4311yescharacteristic
878C22#121×D4311yescharacteristic
879C22#123×D4311yescharacteristic
880C22C2×#1306334911yescharacteristic
881C22#137×D4311yescharacteristic
882C22#1458369511yescharacteristic
883C22#1458369611yescharacteristic
884C4—41no—
885C4—42no—
886C4—81no—
887C4—81no—
888C4—434no—
889C4—3441no—
890C4—3441no—
891C4—1721no—
892C4—1722no—
893C4—1722no—
894C4#121×D4311yescharacteristic
895C4#121×D4311yescharacteristic
896C4#123×D4311yescharacteristic
897C4#124×D4311yescharacteristic
898C2—42no—
899C2—82no—
900C2—864no—
901C2—1722no—
902C2#394×D4311yescharacteristic
903C2#1914384211yescharacteristic
904C2#1914385211yescharacteristic
905C2#1914421111yescharacteristic
906C2#1914422011yescharacteristic
907C2#1914451411yescharacteristic
908C2#1914452311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2033C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
hypercenter#2033D43
hypocenterC43#23482
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×#14582940C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582897C2semidirect
5. C2×#14582861C2semidirect
6. #380×D43C2semidirect
7. #19135801C2semidirect
8. #19135800C2semidirect
9. #19135792C2semidirect
10. #19135791C2semidirect
11. #19135783C2semidirect
12. #19135782C2semidirect
13. #19135774C2semidirect
14. #19134313C2semidirect
15. C43×#2033C2semidirect
34. C2×#13063258C22semidirect
35. C2×#13063257C22semidirect
36. C2×#13063256C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063250C22semidirect
41. C2×#13063248C22semidirect
42. C2×#13063248C22semidirect
43. C2×#13063246C22semidirect
44. 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×#10621872D4semidirect
457. #2033D43semidirect
490. C2×#107C2×D43semidirect
501. C2×#102C2×D43semidirect
502. C2×#102C2×D43semidirect
518. #340C2×D43semidirect
519. C43#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
C2×#145829402
C2×#145828972
C2×#145828612
#380×D432
#191358012
#191358002
#191357922
#191357912
#191357832
#191357822
#191357742
#191343132
C43×#20332
#2348243