Finite Group Databasebeta

← #25105730

Subgroups — #25105730

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2#19136978C211yesmaximal, characteristic, complemented
3#19135041C214yesmaximal, complemented
4#19134897C214yesmaximal, complemented
5#19134692C212yesmaximal, complemented
6#19134538C212yesmaximal, complemented
7C2×C43×#407C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583410—21no—
10#14583410—21no—
11#14583410—21no—
12#14583410—21no—
13#14583410C412yescomplemented
14#14583410C412yescomplemented
15#14583410C2212yes—
16#14583410C2212yes—
17C2×#13063308—21no—
18C2×#13063304C411yescharacteristic, complemented
19C2×#13063304C411yescharacteristic, complemented
20C2×#13063299C411yescharacteristic, complemented
21C2×#13063299C411yescharacteristic, complemented
22C2×#13063294—21no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284C2211yescharacteristic
26C2×#13063284C2212yescomplemented
27C2×#13063251C2218yescomplemented
28#14582762—21no—
29#14582759—21no—
30#14582759—21no—
31#14582755—21no—
32C4×C22⋊Dic43C2212yes—
33C4×C22⋊Dic43C2212yescomplemented
34#14582660C2218yescomplemented
35C24×C4×C43C2211yescharacteristic
36C22×M16×C43C2212yescomplemented
37C43×#407—21no—
38C43×#407—21no—
39C43×#407C2212yes—
40C43×#407C2212yescomplemented
41C2×C22⋊C8×C43—21no—
42C2×C22⋊C8×C43—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—44no—
46C2×#10621898C2×C412yes—
47C2×#10621898C2312yes—
48C22×Dic86C2×C411yescharacteristic
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C4×D43—21no—
54#13063308—22no—
55#13063308—22no—
56#13063308—22no—
57#13063308—22no—
58#13063304—21no—
59#13063304—21no—
60#13063304—21no—
61#13063304—21no—
62#13063304C2×C412yes—
63#13063304C2×C412yes—
64#13063304C2×C412yes—
65#13063304C2×C412yes—
66#13063299—21no—
67#13063299—21no—
68#13063299—21no—
69#13063299—21no—
70#13063299C2×C412yes—
71#13063299C2×C412yes—
72#13063299C2×C412yes—
73#13063299C2×C412yes—
74#13063294—22no—
75#13063294—22no—
76#13063294—22no—
77#13063294—22no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86#13063284—21no—
87#13063284—21no—
88#13063284—44no—
89#13063284C2×C412yes—
90#13063284C2312yes—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2314yes—
106#13063251—48no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C25×C43D411yescharacteristic
110C23×C4×C43—44no—
111C23×C4×C43C2×C411yescharacteristic
112C23×C4×C43C2×C411yescharacteristic
113C23×C4×C43C2×C411yescharacteristic
114C23×C4×C43C2×C411yescharacteristic
115C23×C4×C43D411yescharacteristic
116C23×C4×C43D411yescharacteristic
117C23×C4×C43D411yescharacteristic
118C23×C4×C43D411yescharacteristic
119C23×C4×C43D411yescharacteristic
120C23×C4×C43D411yescharacteristic
121C23×C4×C43D411yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—22no—
126C2×M16×C43—44no—
127C2×M16×C43C2314yes—
128C22×C8×C43—22no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C22⋊C8×C43—22no—
132C22⋊C8×C43—22no—
133C24×C43—42no—
134C24×C43—42no—
135C24×C43—42no—
136C24×C43C22⋊C411yescharacteristic
137C24×C43C22⋊C411yescharacteristic
138C24×C43C22⋊C411yescharacteristic
139C24×C43C22⋊C411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—24no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C22⋊C411yescharacteristic
159C22×C4×C43C22⋊C411yescharacteristic
160C22×C4×C43C22⋊C411yescharacteristic
161C22×C4×C43C22⋊C411yescharacteristic
162C22×C4×C43C22⋊C411yescharacteristic
163C22×C4×C43C22⋊C411yescharacteristic
164C22×C4×C43C22⋊C411yescharacteristic
165C22×C4×C43C22⋊C411yescharacteristic
166C22×C4×C43C22⋊C411yescharacteristic
167C22×C4×C43C22⋊C411yescharacteristic
168C22×C4×C43C22⋊C411yescharacteristic
169C22×C4×C43C22⋊C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C2×C22⋊D43—44no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—24no—
199#10621898—28no—
200#10621898—44no—
201#10621898—44no—
202#10621898—44no—
203C2×D172—21no—
204C2×D172—42no—
205C2×D172C22×C412yes—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—44no—
209C2×Dic86—21no—
210C2×Dic86—42no—
211C2×Dic86C22×C412yes—
212M16×C43—28no—
213M16×C43—44no—
214C2×C8×C43—24no—
215C2×C8×C43—44no—
216C22⋊Dic43—22no—
217C22⋊Dic43—22no—
218C22⋊Dic43—22no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—44no—
223C22⋊Dic43—44no—
224C22⋊Dic43—44no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—44no—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C22×C412yes—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238C4×Dic43—22no—
239C4×Dic43—22no—
240C4×Dic43—28no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—416no—
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C2×C22⋊C411yescharacteristic
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—42no—
272C22×D43—42no—
273C22×D43—42no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43H(5,𝔽2)14yes—
310C22⋊D43—44no—
311C22⋊D43—44no—
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C22⋊D43—44no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—44no—
323C2×Dic43—44no—
324C2×Dic43—44no—
325D172—24no—
326D172—42no—
327C4×D43—44no—
328C4×D43—44no—
329Dic86—24no—
330Dic86—42no—
331C8×C43—44no—
332#21774—431nomaximal, Sylow
333C22×C43—21no—
334C22×C43—21no—
335C22×C43—21no—
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—44no—
352C22×C43—44no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43—44no—
357C22×C43—44no—
358C22×C43#42112yes—
359C22×C43#42112yes—
360C22×C43C22×C22⋊C411yescharacteristic
361C22×C43#53412yes—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—84no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43#51812yes—
373C4×C43#53412yes—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—84no—
378C2×#525—431no—
379C2×#407D4311yescharacteristic, complemented
380#2280—431no—
381#1897—434no—
382#1871—434no—
383#1826—432no—
384#1789—432no—
385C2×C43—22no—
386C2×C43—22no—
387C2×C43—22no—
388C2×C43—41no—
389C2×C43—41no—
390C2×C43—41no—
391C2×C43—41no—
392C2×C43#230811yescharacteristic
393C2×C43C2×#42111yescharacteristic
394C2×C43C2×#42111yescharacteristic
395D43—82no—
396C22×#41—431no—
397C24×C4C2×D4311yescharacteristic
398C22×M16C2×D4312yescomplemented
399#525—432no—
400#525—432no—
401#525—432no—
402#525—432no—
403#525—861no—
404#525—861no—
405#525—861no—
406#525—861no—
407C2×#123—861no—
408C2×C22⋊Q8—431no—
409C2×C22⋊Q8—431no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#120—861no—
413C2×C4×D4—861no—
414C2×C4×D4—861no—
415C2×#117—432no—
416C2×#117—431no—
417C2×#104—438no—
418#407—21no—
419#407—21no—
420#407C2×D4312yes—
421#407C2×D4312yescomplemented
422C2×C22⋊C8—21no—
423C2×C22⋊C8—21no—
424#381—861no—
425#380—861no—
426#380—861no—
427#379—861no—
428C4×C22⋊C4—432no—
429C4×C22⋊C4—432no—
430#339—438no—
431C43#2177411yescharacteristic, complemented, Sylow
432C25D17211yescharacteristic
433C2×#41—432no—
434C2×#41—432no—
435C2×#41—861no—
436C2×#41—861no—
437C2×#41—1724no—
438C22×Q8—431no—
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4—861no—
443C23×C4—44no—
444C23×C4—861no—
445C23×C4C4×D4311yescharacteristic
446C23×C4C4×D4311yescharacteristic
447C23×C4C4×D4311yescharacteristic
448C23×C4C4×D4311yescharacteristic
449C23×C4D17211yescharacteristic
450C23×C4D17211yescharacteristic
451C23×C4D17211yescharacteristic
452C23×C4C22⋊D4311yescharacteristic
453C23×C4C22⋊D4311yescharacteristic
454C23×C4C22⋊D4311yescharacteristic
455C23×C4C22⋊D4311yescharacteristic
456C23×C4C22×D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459C2×M16—22no—
460C2×M16—44no—
461C2×M16C22×D4314yes—
462C22×C8—22no—
463#123—862no—
464#123—862no—
465#123—862no—
466#123—862no—
467C22⋊Q8—432no—
468C22⋊Q8—432no—
469C22⋊Q8—432no—
470C22⋊Q8—432no—
471C22⋊Q8—861no—
472C22⋊Q8—861no—
473C22⋊Q8—861no—
474C22⋊Q8—861no—
475#121—432no—
476#121—432no—
477#121—432no—
478#121—432no—
479#121—861no—
480#121—861no—
481#121—861no—
482#121—861no—
483#120—862no—
484#120—862no—
485#120—862no—
486#120—862no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—862no—
495#117—432no—
496#117—432no—
497#117—861no—
498#117—861no—
499#117—1724no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—862no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—862no—
513C2×C42—434no—
514C2×C42—861no—
515#104—1728no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#95—862no—
521#95—862no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—861no—
526C24(C2×D43)⋊C411yescharacteristic
527C24(C2×D43)⋊C411yescharacteristic
528C24(C2×D43)⋊C411yescharacteristic
529C24(C2×D43)⋊C411yescharacteristic
530C24C2×D17211yescharacteristic
531C24C2×D17211yescharacteristic
532C24C2×D17211yescharacteristic
533#41—868no—
534#41—1724no—
535#41—1724no—
536#41—1724no—
537C2×Q8—432no—
538C2×Q8—861no—
539C2×Q8—1722no—
540C2×D4—432no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—861no—
548C2×D4—1722no—
549C2×D4—1724no—
550C2×D4—1724no—
551C2×D4—1724no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—864no—
572C22×C4—1724no—
573C22×C4(C2×D43)⋊C411yescharacteristic
574C22×C4(C2×D43)⋊C411yescharacteristic
575C22×C4(C2×D43)⋊C411yescharacteristic
576C22×C4(C2×D43)⋊C411yescharacteristic
577C22×C4(C2×D43)⋊C411yescharacteristic
578C22×C4(C2×D43)⋊C411yescharacteristic
579C22×C4(C2×D43)⋊C411yescharacteristic
580C22×C4(C2×D43)⋊C411yescharacteristic
581C22×C4(C2×D43)⋊C411yescharacteristic
582C22×C4(C2×D43)⋊C411yescharacteristic
583C22×C4(C2×D43)⋊C411yescharacteristic
584C22×C4(C2×D43)⋊C411yescharacteristic
585C22×C4C2×C4×D4311yescharacteristic
586C22×C4C2×C4×D4311yescharacteristic
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4C2×C4×D4311yescharacteristic
591C22×C4C2×D17211yescharacteristic
592C22×C4C2×D17211yescharacteristic
593C22×C4C2×D17211yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C23×D4311yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—24no—
604C2×C8—44no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—862no—
610C4⋊C4—862no—
611C4⋊C4—862no—
612C4⋊C4—862no—
613C4⋊C4—1724no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—1724no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C42—862no—
628C42—862no—
629C42—868no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—862no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23C2×(C2×D43)⋊C411yescharacteristic
657C23C2×(C2×D43)⋊C411yescharacteristic
658C23C2×(C2×D43)⋊C411yescharacteristic
659C23C2×(C2×D43)⋊C411yescharacteristic
660C23C2×(C2×D43)⋊C411yescharacteristic
661C23C2×(C2×D43)⋊C411yescharacteristic
662C23C22×D17211yescharacteristic
663Q8—864no—
664Q8—1722no—
665D4—864no—
666D4—1722no—
667D4—1724no—
668D4—1724no—
669D4—1724no—
670D4—1724no—
671D4—1724no—
672D4—1724no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—1724no—
704C2×C4—1724no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1724no—
711C2×C4C2×(C2×D43)⋊C411yescharacteristic
712C2×C4C2×(C2×D43)⋊C411yescharacteristic
713C2×C4C2×(C2×D43)⋊C411yescharacteristic
714C2×C4C2×(C2×D43)⋊C411yescharacteristic
715C2×C4C2×(C2×D43)⋊C411yescharacteristic
716C2×C4C2×(C2×D43)⋊C411yescharacteristic
717C2×C4C22×C4×D4311yescharacteristic
718C2×C4C22×C22⋊D4311yescharacteristic
719C2×C4#1306337014yes—
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—3444no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22#1458291512yes—
751C22#1458291512yes—
752C22C22×(C2×D43)⋊C411yescharacteristic
753C22#1458346112yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—3444no—
761C4—1722no—
762C4—1722no—
763C4—1722no—
764C4#1458337212yes—
765C4#1458345812yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—3442no—
774C2#1913717011yescharacteristic
775C2C2×#1458291511yescharacteristic
776C2C2×#1458291511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43#21774
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #19136978C2semidirect
3. #19135041C2semidirect
4. #19134897C2semidirect
5. #19134692C2semidirect
6. #19134538C2semidirect
7. C2×C43×#407C2semidirect
13. #14583410C4semidirect
14. #14583410C4semidirect
18. C2×#13063304C4semidirect
19. C2×#13063304C4semidirect
20. C2×#13063299C4semidirect
21. C2×#13063299C4semidirect
26. C2×#13063284C22semidirect
27. C2×#13063251C22semidirect
33. C4×C22⋊Dic43C22semidirect
34. #14582660C22semidirect
36. C22×M16×C43C22semidirect
40. C43×#407C22semidirect
379. C2×#407D43semidirect
398. C22×M16C2×D43semidirect
421. #407C2×D43semidirect
431. C43#21774semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
#191369782
#191350412
#191348972
#191346922
#191345382
C2×C43×#4072
#2177443