Finite Group Databasebeta

← #25106597

Subgroups — #25106597

Order 11008.

1242 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19135039C211yesmaximal, characteristic, complemented
7#19135038C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19134614C212yesmaximal, complemented
10#19134613C212yesmaximal, complemented
11C43×#1896C211yesmaximal, characteristic, complemented
12#14583452C2211yescharacteristic
13#14583451C411yescharacteristic, complemented
14#14583451C411yescharacteristic, complemented
15#14583445C2211yescharacteristic
16#14583444C411yescharacteristic, complemented
17#14583444C411yescharacteristic, complemented
18#14583435C411yescharacteristic, complemented
19#14583435C411yescharacteristic, complemented
20#14583430C411yescharacteristic, complemented
21#14583430C411yescharacteristic, complemented
22#14583429—21no—
23#14583429—21no—
24#14583426—21no—
25#14583426—21no—
26#14583410C2211yescharacteristic
27#14583405—21no—
28#14583405—21no—
29#41×Dic43C2211yescharacteristic
30#14583367C2211yescharacteristic
31C4×#10621900—21no—
32C4×#10621900—21no—
33C22×Dic43⋊C4—21no—
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582953—21no—
37#14582953—21no—
38#14582949—21no—
39#14582949—21no—
40#14582922C2212yes—
41C2×#13063253C2212yes—
42C2×#13063252C2212yes—
43C2×#13063251C2212yes—
44#14582863C2211yescharacteristic
45M16×Dic43C2212yes—
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4—21no—
48C4×Dic43⋊C4C2212yes—
49C4×Dic43⋊C4C2212yes—
50C2×C43⋊#95—21no—
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C43×#525C2211yescharacteristic
55C22×C42×C43C2211yescharacteristic
56C2×#104×C43C2212yes—
57C43×#407C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898C2311yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43—21no—
63C23×Dic43D411yescharacteristic
64C23×Dic43D411yescharacteristic
65C2×#10621877C2312yes—
66#13063324C2×C411yescharacteristic, complemented
67#13063324C2×C411yescharacteristic, complemented
68#13063323C2×C411yescharacteristic, complemented
69#13063321C2×C411yescharacteristic, complemented
70#13063320—21no—
71#13063320—21no—
72#13063318—21no—
73#13063318—21no—
74#13063316C2×C411yescharacteristic, complemented
75#13063316C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063314C2×C411yescharacteristic, complemented
79#13063312C2×C411yescharacteristic, complemented
80#13063311—21no—
81#13063311—21no—
82#13063309—21no—
83#13063309—21no—
84#13063308—21no—
85#13063306—21no—
86#13063306—21no—
87#13063304C2×C411yescharacteristic
88#13063304C2×C411yescharacteristic
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063302—21no—
93#13063299C2×C411yescharacteristic
94#13063299C2×C411yescharacteristic
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063297—21no—
99#13063294—21no—
100Q8×Dic43C2×C411yescharacteristic, complemented
101Q8×Dic43C2×C411yescharacteristic, complemented
102C4×Dic86—21no—
103C4×Dic86—21no—
104#13063290—21no—
105#13063290—21no—
106#13063290C2×C411yescharacteristic, complemented
107#13063290C2×C411yescharacteristic, complemented
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113D4×Dic43C2×C411yescharacteristic, complemented
114#13063287C2×C411yescharacteristic, complemented
115#13063287C2×C411yescharacteristic, complemented
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126#13063284—21no—
127#13063284C2311yescharacteristic
128#13063283—21no—
129#13063283—21no—
130#13063282—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134#13063281—21no—
135C2×Dic43⋊C4—28no—
136C2×Dic43⋊C4—22no—
137C2×Dic43⋊C4—22no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—42no—
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2311yescharacteristic
154C42×D43—21no—
155Dic43⋊C8—22no—
156Dic43⋊C8—22no—
157#13063253—42no—
158#13063252—42no—
159#13063251—42no—
160C22⋊(C43⋊C8)—21no—
161C22⋊(C43⋊C8)—21no—
162#13063235—22no—
163C8×Dic43—22no—
164C43⋊#95—22no—
165C43⋊#95—22no—
166C2×#41×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C23×C4×C43C2311yescharacteristic
169C2×M16×C43C2312yes—
170#123×C43—21no—
171C22⋊Q8×C43C2×C411yescharacteristic
172C22⋊Q8×C43C2×C411yescharacteristic
173#121×C43C2×C411yescharacteristic
174#121×C43C2×C411yescharacteristic
175#120×C43—21no—
176C4×D4×C43—21no—
177C4×D4×C43—21no—
178#117×C43C2311yescharacteristic
179C2×C42×C43—21no—
180C2×C42×C43—42no—
181C2×C42×C43C2312yes—
182#104×C43—42no—
183C22⋊C8×C43—21no—
184C22⋊C8×C43—21no—
185C24×C43C2×D411yescharacteristic
186#41×C43—22no—
187#41×C43—22no—
188C2×Q8×C43C22×C411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43C22×C411yescharacteristic
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—24no—
196C22×C4×C43—21no—
197C22×C4×C43—22no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43C22×C411yescharacteristic
201C22×C4×C43C22×C411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—21no—
207C2×C22⋊D43—21no—
208C2×C22⋊D43—21no—
209C2×C22⋊D43—21no—
210C2×C22⋊D43—21no—
211C22×Dic43—24no—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—22no—
216C22×Dic43—42no—
217C22×Dic43—42no—
218C22×Dic43—42no—
219C22×Dic43C22⋊C411yescharacteristic
220C22×Dic43C22⋊C411yescharacteristic
221C22×Dic43C22⋊C411yescharacteristic
222C22×Dic43C22⋊C411yescharacteristic
223C22×Dic43C22⋊C411yescharacteristic
224C22×Dic43C22⋊C411yescharacteristic
225C22×Dic43C22⋊C411yescharacteristic
226C22×Dic43C22⋊C411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621900—44no—
232#10621900—44no—
233#10621898—22no—
234#10621898—22no—
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86C22×C411yescharacteristic
242M16×C43—22no—
243M16×C43—22no—
244C2×C8×C43—22no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C22×C411yescharacteristic
248C4⋊C4×C43C22×C411yescharacteristic
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C42×C43—21no—
255C42×C43—22no—
256C42×C43—22no—
257C42×C43—42no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43C22×C411yescharacteristic
276C4⋊Dic43C22×C411yescharacteristic
277Dic43⋊C4—28no—
278Dic43⋊C4—28no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289C4×Dic43—21no—
290C4×Dic43—21no—
291C4×Dic43—21no—
292C4×Dic43—21no—
293C4×Dic43—21no—
294C4×Dic43—22no—
295C4×Dic43—22no—
296C4×Dic43—42no—
297C4×Dic43C22⋊C411yescharacteristic
298C4×Dic43C22⋊C411yescharacteristic
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22⋊C411yescharacteristic
301C4×Dic43C22⋊C411yescharacteristic
302C4×Dic43C22⋊C411yescharacteristic
303C4×Dic43C22⋊C411yescharacteristic
304C4×Dic43C22⋊C411yescharacteristic
305C4×Dic43C22×C411yescharacteristic
306C4×Dic43C22×C411yescharacteristic
307C4×Dic43C22×C411yescharacteristic
308C4×Dic43C22×C411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313#10621877—22no—
314#10621877—22no—
315C2×C43⋊C8—22no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—21no—
321C23×C43C2×C22⋊C411yescharacteristic
322C23×C43C2×C22⋊C411yescharacteristic
323C23×C43C22×D411yescharacteristic
324C22×D43—21no—
325Q8×C43—22no—
326D4×C43—22no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—42no—
330D4×C43—42no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—24no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—48no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C432−1+412yes—
351C22⋊D43—42no—
352C22⋊D43—41no—
353C22⋊D43—41no—
354C22⋊D43—42no—
355C22⋊D43—42no—
356C22⋊D43—42no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—24no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—42no—
373C2×Dic43—48no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—42no—
377C2×Dic43#10414yescomplemented
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C411yescharacteristic
383C2×Dic43C2×C22⋊C411yescharacteristic
384C2×Dic43C2×C22⋊C411yescharacteristic
385C2×Dic43C2×C22⋊C411yescharacteristic
386D172—22no—
387C4×D43—42no—
388C4×D43—42no—
389C4×D43—42no—
390Dic86—22no—
391Dic86—42no—
392Dic86—42no—
393C8×C43—42no—
394C43⋊C8—42no—
395#21899—431nomaximal, Sylow
396C22×C43—24no—
397C22×C43—24no—
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43C2×#10412yes—
408C22×C43#42112yes—
409C22×C43C22×C22⋊C411yescharacteristic
410C22×C43#53511yescharacteristic
411C22×C43#53611yescharacteristic
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—41no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—44no—
418C4×C43—41no—
419C4×C43—41no—
420C4×C43—41no—
421C4×C43#52012yes—
422C4×C43#53712yes—
423Dic43—21no—
424Dic43—21no—
425Dic43—21no—
426Dic43—21no—
427Dic43—21no—
428Dic43—21no—
429Dic43—44no—
430Dic43—41no—
431Dic43—41no—
432Dic43—41no—
433Dic43C2×#10412yes—
434Dic43C2×#10412yes—
435#3444—431no—
436#2920—431no—
437C2×C4×C4⋊C4—431no—
438#1986—432no—
439#1980—432no—
440#1896—431no—
441#1896—431no—
442#1896—431no—
443#1896D4311yescharacteristic, complemented
444#1806—432no—
445#1806—432no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—22no—
449C2×C43—22no—
450C2×C43—81no—
451C2×C43#231111yescharacteristic
452C2×C43C22×#10411yescharacteristic
453C2×C43C2×#42111yescharacteristic
454D43—81no—
455#533—431no—
456#533—431no—
457#533—431no—
458#532—431no—
459#532—431no—
460#532—431no—
461#529—431no—
462#529—431no—
463#529—431no—
464#529—431no—
465#529—861no—
466#529—861no—
467#529—861no—
468#529—861no—
469#525—431no—
470#525—861no—
471#525—861no—
472#525C2×D4311yescharacteristic
473C4×#41—431no—
474C4×#41—431no—
475C4×#41—861no—
476C4×#41—861no—
477C22×C4⋊C4—861no—
478C22×C42—431no—
479C22×C42—431no—
480C22×C42C2×D4311yescharacteristic
481#432—861no—
482#432—861no—
483#431—861no—
484#431—861no—
485#423—432no—
486C2×#104—432no—
487C2×#104—432no—
488C2×#104—432no—
489C2×#104C2×D4312yes—
490#407—431no—
491#407C2×D4311yescharacteristic
492C4×M16—432no—
493C4×C4⋊C4—432no—
494C4×C4⋊C4—432no—
495C4×C4⋊C4—861no—
496C4×C4⋊C4—861no—
497C2×#95—861no—
498#339—432no—
499#339—432no—
500#339—432no—
501#339C2×D4312yes—
502C43#2189911yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41C22×D4311yescharacteristic
507C23×C4—21no—
508C23×C4—431no—
509C23×C4—431no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×M16—432no—
513C2×M16C22×D4312yes—
514C4⋊Q8—431no—
515C4⋊Q8—431no—
516C4⋊Q8—431no—
517#127—431no—
518#126—861no—
519#126—861no—
520#126—861no—
521#126—861no—
522#125—431no—
523#125—431no—
524#125—861no—
525#125—861no—
526#124—431no—
527#124—431no—
528#124—861no—
529#124—861no—
530#123—21no—
531#123—861no—
532#123—861no—
533#123—861no—
534#123—861no—
535#123—861no—
536C22⋊Q8—431no—
537C22⋊Q8—431no—
538C22⋊Q8—861no—
539C22⋊Q8—861no—
540C22⋊Q8—861no—
541C22⋊Q8—861no—
542C22⋊Q8C4×D4311yescharacteristic
543C22⋊Q8C4×D4311yescharacteristic
544#121—431no—
545#121—431no—
546#121—861no—
547#121—861no—
548#121—861no—
549#121—861no—
550#121C4×D4311yescharacteristic
551#121C4×D4311yescharacteristic
552#120—21no—
553#120—861no—
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—431no—
557C4×Q8—431no—
558C4×Q8—861no—
559C4×Q8—861no—
560C4×Q8—861no—
561C4×Q8—861no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—431no—
565C4×D4—431no—
566C4×D4—431no—
567C4×D4—431no—
568C4×D4—861no—
569C4×D4—861no—
570C4×D4—861no—
571C4×D4—861no—
572C4×D4—861no—
573C4×D4—861no—
574C4×D4—861no—
575C4×D4—861no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582#117—431no—
583#117—861no—
584#117—861no—
585#117—861no—
586#117—861no—
587#117—861no—
588#117—861no—
589#117—861no—
590#117—861no—
591#117C22×D4311yescharacteristic
592C2×C4⋊C4—862no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—868no—
595C2×C42—21no—
596C2×C42—42no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—431no—
600C2×C42—431no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—431no—
604C2×C42—431no—
605C2×C42—431no—
606C2×C42—431no—
607C2×C42—431no—
608C2×C42—431no—
609C2×C42—432no—
610C2×C42—861no—
611C2×C42—861no—
612C2×C42—861no—
613C2×C42—1722no—
614C2×C42C22×D4312yes—
615C4⋊C8—862no—
616C4⋊C8—862no—
617#104—42no—
618#104—1722no—
619#104—1722no—
620#104—1722no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623C22⋊C8—861no—
624C22⋊C8—861no—
625#97—862no—
626C4×C8—862no—
627#95—862no—
628#95—862no—
629C24D4×D4311yescharacteristic
630#41—22no—
631#41—22no—
632#41—862no—
633#41—862no—
634#41—1724no—
635#41—1724no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8C2×C4×D4311yescharacteristic
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—431no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4C2×C4×D4311yescharacteristic
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—864no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—864no—
675C22×C4—862no—
676C22×C4—861no—
677C22×C4—1722no—
678C22×C4—1722no—
679C22×C4—1722no—
680C22×C4C2×C4×D4311yescharacteristic
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4D4×D4311yescharacteristic
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686M16—22no—
687M16—22no—
688M16—862no—
689M16—862no—
690C2×C8—22no—
691C2×C8—862no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—868no—
709C4⋊C4—868no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4C2×C4×D4311yescharacteristic
713C4⋊C4C2×C4×D4311yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C42—21no—
733C42—22no—
734C42—22no—
735C42—42no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—431no—
744C42—431no—
745C42—431no—
746C42—431no—
747C42—431no—
748C42—431no—
749C42—431no—
750C42—431no—
751C42—431no—
752C42—861no—
753C42—861no—
754C42—861no—
755C42—861no—
756C42—861no—
757C42—862no—
758C42—862no—
759C42—1722no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—861no—
766C23C22⋊C4×D4311yescharacteristic
767C23C22⋊C4×D4311yescharacteristic
768C23C2×D4×D4311yescharacteristic
769Q8—22no—
770Q8—862no—
771Q8—1722no—
772Q8—1722no—
773D4—22no—
774D4—42no—
775D4—42no—
776D4—41no—
777D4—41no—
778D4—862no—
779D4—1722no—
780D4—1722no—
781D4—1722no—
782D4—1722no—
783D4—1721no—
784D4—1721no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—431no—
800C2×C4—431no—
801C2×C4—434no—
802C2×C4—431no—
803C2×C4—431no—
804C2×C4—431no—
805C2×C4—431no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—864no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1722no—
827C2×C4—1728no—
828C2×C4—1722no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4C22⋊C4×D4311yescharacteristic
832C2×C4C22⋊C4×D4311yescharacteristic
833C2×C4C22×C4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#1306337012yes—
836C2×C4#1306337212yes—
837C8—42no—
838C8—1722no—
839C22—24no—
840C22—24no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—1721no—
851C22—1721no—
852C22—1721no—
853C22#104×D4312yes—
854C22#1458291412yes—
855C22C2×C22⋊C4×D4311yescharacteristic
856C22#1458346411yescharacteristic
857C22#1458347111yescharacteristic
858C4—21no—
859C4—21no—
860C4—44no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—432no—
865C4—432no—
866C4—861no—
867C4—861no—
868C4—861no—
869C4—861no—
870C4—861no—
871C4—861no—
872C4—1724no—
873C4—1721no—
874C4—1721no—
875C4—1721no—
876C4#1458337812yes—
877C4#1458347612yes—
878C2—21no—
879C2—22no—
880C2—22no—
881C2—21no—
882C2—81no—
883C2—3441no—
884C2#1913718211yescharacteristic
885C2C2×#104×D4311yescharacteristic
886C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1896C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1896D43
hypocenterC43#21899
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×C4×Dic43⋊C4C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19135039C2semidirect
7. #19135038C2semidirect
8. #19135036C2semidirect
9. #19134614C2semidirect
10. #19134613C2semidirect
11. C43×#1896C2semidirect
13. #14583451C4semidirect
14. #14583451C4semidirect
16. #14583444C4semidirect
17. #14583444C4semidirect
18. #14583435C4semidirect
19. #14583435C4semidirect
20. #14583430C4semidirect
21. #14583430C4semidirect
66. #13063324C2×C4semidirect
67. #13063324C2×C4semidirect
68. #13063323C2×C4semidirect
69. #13063321C2×C4semidirect
74. #13063316C2×C4semidirect
75. #13063316C2×C4semidirect
78. #13063314C2×C4semidirect
79. #13063312C2×C4semidirect
100. Q8×Dic43C2×C4semidirect
101. Q8×Dic43C2×C4semidirect
106. #13063290C2×C4semidirect
107. #13063290C2×C4semidirect
112. D4×Dic43C2×C4semidirect
113. D4×Dic43C2×C4semidirect
114. #13063287C2×C4semidirect
115. #13063287C2×C4semidirect
377. C2×Dic43#104semidirect
443. #1896D43semidirect
502. C43#21899semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
C2×C4×Dic43⋊C42
#191355372
#191355122
#191350392
#191350382
#191350362
#191346142
#191346132
C43×#18962
#2189943