Finite Group Databasebeta

← #25106184

Subgroups — #25106184

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583427C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
4#19135529C212yesmaximal, complemented
5#19135387C212yesmaximal, complemented
6#19134886C212yesmaximal, complemented
7#19134884C212yesmaximal, complemented
8#19134579C211yesmaximal, characteristic, complemented
9#19134576C211yesmaximal, characteristic, complemented
10#19134576C211yesmaximal, characteristic, complemented
11C43×#1798C211yesmaximal, characteristic, complemented
12C22×C8×D43C2212yes—
13#14583427—24no—
14#14583427—24no—
15C2×#13063320C411yescharacteristic
16C2×#13063318C411yescharacteristic
17C2×#13063315C411yescharacteristic
18C2×#13063311C411yescharacteristic
19C2×#13063310C411yescharacteristic
20C2×#13063307C411yescharacteristic
21C2×#13063303C411yescharacteristic
22C2×#13063298C411yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×#13063282C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14582951—24no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×Dic43⋊C8C2212yes—
33C4⋊C8×D43—24no—
34C2×C22⋊(C43⋊C8)C2212yes—
35C2×(C2×D43)⋊C8C2212yes—
36C2×(C2×D43)⋊C8C2212yes—
37C2×(C2×D43)⋊C8C2212yes—
38C2×C8×Dic43C2212yes—
39#14582654C2212yes—
40#14582653C2212yes—
41#14582653C2212yes—
42C2×#117×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×C4⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2212yes—
46C43×#336C2212yes—
47C22×Dic86C2×C411yescharacteristic
48C22×D172C2×C411yescharacteristic
49C22×C22⋊D43C2×C411yescharacteristic
50C22×C22⋊D43C2×C411yescharacteristic
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C22×C43⋊C8C2312yes—
56C22×C43⋊C8C2312yes—
57C2×C8×D43—24no—
58C2×C8×D43—42no—
59C2×C8×D43—42no—
60#13063320—24no—
61#13063318—24no—
62#13063315—24no—
63#13063311—24no—
64#13063310—24no—
65#13063307—24no—
66#13063303—24no—
67#13063298—24no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70C4×D172—22no—
71C4×D172—22no—
72C4×C22⋊D43—22no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—22no—
75C4×C22⋊D43—22no—
76#13063282—22no—
77#13063282—22no—
78C2×C4⋊Dic43C2×C411yescharacteristic
79C2×C4⋊Dic43C2×C411yescharacteristic
80C2×Dic43⋊C4C2×C411yescharacteristic
81C2×Dic43⋊C4C2×C411yescharacteristic
82C2×Dic43⋊C4C2×C411yescharacteristic
83C2×Dic43⋊C4C2×C411yescharacteristic
84C2×Dic43⋊C4C2×C411yescharacteristic
85C2×Dic43⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic43C2×C411yescharacteristic
87C2×C22⋊Dic43C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C411yescharacteristic
89C2×(C2×D43)⋊C4C2×C411yescharacteristic
90C2×(C2×D43)⋊C4C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C411yescharacteristic
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×(C2×D43)⋊C4C2×C411yescharacteristic
94C2×C4×Dic43C2×C411yescharacteristic
95C2×C4×Dic43C2×C411yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98C42×D43D414yes—
99C42×D43D414yes—
100C4⋊(C43⋊C8)—22no—
101C4⋊(C43⋊C8)—22no—
102Dic43⋊C8—24no—
103C22⋊(C43⋊C8)—42no—
104(C2×D43)⋊C8—24no—
105(C2×D43)⋊C8—42no—
106(C2×D43)⋊C8—42no—
107C8×Dic43—24no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2312yes—
110C22×C8×C43C2312yes—
111#117×C43—22no—
112#117×C43—22no—
113C2×C4⋊C4×C43C2×C411yescharacteristic
114C2×C4⋊C4×C43C2×C411yescharacteristic
115C2×C22⋊C4×C43C2×C411yescharacteristic
116C2×C22⋊C4×C43C2×C411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—22no—
120C4⋊C8×C43—22no—
121C22⋊C8×C43—42no—
122C24×C43C22×C411yescharacteristic
123C23×D43C22×C411yescharacteristic
124C23×D43C22×C411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C22×C411yescharacteristic
132C22×C4×C43C22×C411yescharacteristic
133C22×C4×C43C22×C411yescharacteristic
134C22×C4×C43C22×C411yescharacteristic
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C2×C22⋊D43—22no—
138C2×C22⋊D43—24no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—24no—
141C22×Dic43C22×C411yescharacteristic
142C22×Dic43C22×C411yescharacteristic
143C22×Dic43C22×C411yescharacteristic
144C22×Dic43C22×C411yescharacteristic
145C22×Dic43C22×C411yescharacteristic
146C22×Dic43C22×C411yescharacteristic
147C2×D172—22no—
148C2×D172—24no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—24no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—24no—
161C2×C4×D43C22⋊C414yes—
162C2×C4×D43C22⋊C414yes—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×Dic86—22no—
166C2×Dic86—24no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43C2×D412yes—
180C42×C43C2×D412yes—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43C22⋊C414yes—
200C4×Dic43C22⋊C414yes—
201C4×Dic43C2×D412yes—
202C4×Dic43C2×D412yes—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C8×D43—48no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43C23×C411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—22no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43C2×C22⋊C412yes—
225C22×D43#13114yes—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C2×C22⋊C412yes—
240C2×C4×C43C2×C22⋊C412yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C22⋊D43—44no—
248C22⋊D43—44no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43#13114yes—
263D172—44no—
264C4×D43—28no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—28no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274Dic86—44no—
275C8×C43—42no—
276C8×C43—42no—
277C43⋊C8—42no—
278C43⋊C8—42no—
279#21848—431nomaximal, Sylow
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43C22×C22⋊C411yescharacteristic
286C22×C43#52011yescharacteristic
287C22×C43#52011yescharacteristic
288C22×C43C2×#13112yes—
289C22×C43C2×#13112yes—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43#40814yes—
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43#53511yescharacteristic
306C4×C43#53611yescharacteristic
307C4×C43#53711yescharacteristic
308C4×C43#53711yescharacteristic
309Dic43—22no—
310Dic43—22no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43#40814yes—
315C2×#529—431no—
316C2×#431—431no—
317C22×C4⋊C8—431no—
318#1984—432no—
319#1954—432no—
320#1869—432no—
321#1869—432no—
322#1798—431no—
323#1798—431no—
324#1798—431no—
325#1798D4311yescharacteristic, complemented
326C2×C43—81no—
327C2×C43#231111yescharacteristic
328C2×C43C2×#40811yescharacteristic
329C2×C43C2×#40811yescharacteristic
330C2×C43#299412yes—
331C2×C43#299412yes—
332D43—24no—
333D43—81no—
334C23×C8—432no—
335#529—864no—
336#529—864no—
337C2×#126—431no—
338C2×#126—431no—
339C2×#125—431no—
340C2×#124—431no—
341C2×#123—431no—
342C2×#123—431no—
343C2×C22⋊Q8—431no—
344C2×#121—431no—
345C2×C4×Q8—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×#117—431no—
350C2×#117C2×D4311yescharacteristic
351C22×C42—431no—
352#431—864no—
353C2×C4⋊C8—432no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8—864no—
357C2×C4⋊C8C2×D4311yescharacteristic
358C2×C4⋊C8C2×D4311yescharacteristic
359C2×C22⋊C8—432no—
360C2×C22⋊C8—432no—
361C2×C22⋊C8—432no—
362C2×C22⋊C8—432no—
363C2×C22⋊C8C2×D4312yes—
364C2×C4×C8—432no—
365#336—432no—
366#336—432no—
367#336—432no—
368#336C2×D4312yes—
369C43#2184811yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4—431no—
372C22×D4—431no—
373C22×D4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4C22×D4311yescharacteristic
379C22×C8—432no—
380C22×C8—432no—
381C22×C8—864no—
382C22×C8—1722no—
383C22×C8—1722no—
384C22×C8C22×D4312yes—
385C22×C8C22×D4312yes—
386#126—864no—
387#126—864no—
388#125—864no—
389#124—864no—
390#123—864no—
391#123—864no—
392C22⋊Q8—864no—
393#121—864no—
394C4×Q8—862no—
395C4×Q8—862no—
396C4×D4—862no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—862no—
402#117—22no—
403#117—22no—
404#117—862no—
405#117—862no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4C4×D4311yescharacteristic
415C2×C4⋊C4C4×D4311yescharacteristic
416C2×C22⋊C4—431no—
417C2×C22⋊C4—431no—
418C2×C22⋊C4—431no—
419C2×C22⋊C4—431no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—431no—
422C2×C22⋊C4—431no—
423C2×C22⋊C4—431no—
424C2×C22⋊C4C4×D4311yescharacteristic
425C2×C22⋊C4C4×D4311yescharacteristic
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—434no—
430C2×C42—434no—
431C2×C42—431no—
432C2×C42C22×D4311yescharacteristic
433C2×C42C22×D4311yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—864no—
437C4⋊C8—862no—
438C4⋊C8—862no—
439C22⋊C8—42no—
440C22⋊C8—864no—
441C22⋊C8—1722no—
442C22⋊C8—1722no—
443C22⋊C8—1722no—
444C4×C8—864no—
445C24—431no—
446C24—431no—
447C24C2×C4×D4311yescharacteristic
448C2×Q8—862no—
449C2×Q8—864no—
450C2×D4—862no—
451C2×D4—864no—
452C2×D4—862no—
453C2×D4—864no—
454C2×D4—862no—
455C2×D4—864no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—434no—
466C22×C4—434no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4C2×C4×D4311yescharacteristic
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4311yescharacteristic
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—862no—
499C2×C8—862no—
500C2×C8—862no—
501C2×C8—862no—
502C2×C8—1728no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C42—21no—
524C42—21no—
525C42—434no—
526C42—434no—
527C42—432no—
528C42—432no—
529C42—861no—
530C42—861no—
531C42D4×D4312yes—
532C42D4×D4312yes—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—22no—
538C23—432no—
539C23—434no—
540C23—861no—
541C23—861no—
542C23—862no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—862no—
547C23—862no—
548C23C22×C4×D4311yescharacteristic
549Q8—1724no—
550D4—1724no—
551D4—1724no—
552D4—1724no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—432no—
567C2×C4—434no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—868no—
571C2×C4—868no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4C22⋊C4×D4312yes—
591C2×C4C22⋊C4×D4312yes—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C2×D4×D4311yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337111yescharacteristic
596C2×C4#1306337211yescharacteristic
597C2×C4#1306337311yescharacteristic
598C8—42no—
599C8—42no—
600C8—1722no—
601C8—1722no—
602C22—42no—
603C22—42no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—434no—
608C22—864no—
609C22—864no—
610C22—862no—
611C22—862no—
612C22—1722no—
613C22—1722no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22C2×C22⋊C4×D4311yescharacteristic
618C22#1458337911yescharacteristic
619C22#1458338011yescharacteristic
620C22#131×D4312yes—
621C22#131×D4312yes—
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—434no—
628C4—862no—
629C4—862no—
630C4—1721no—
631C4—1721no—
632C4—1721no—
633C4#1458346511yescharacteristic
634C4#1458347211yescharacteristic
635C4#1458347811yescharacteristic
636C4#1458347911yescharacteristic
637C2—81no—
638C2—864no—
639C2—3441no—
640C2#1913718411yescharacteristic
641C2#408×D4311yescharacteristic
642C2#408×D4311yescharacteristic
643C2#1914374912yes—
644C2#1914375312yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1798C2
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1798D43
hypocenterC43#21848
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. C2×C4⋊C8×D43C2semidirect
4. #19135529C2semidirect
5. #19135387C2semidirect
6. #19134886C2semidirect
7. #19134884C2semidirect
8. #19134579C2semidirect
9. #19134576C2semidirect
10. #19134576C2semidirect
11. C43×#1798C2semidirect
325. #1798D43semidirect
369. C43#21848semidirect

Maximal subgroups

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

subgroupindex
C2×#145834272
C2×#145829512
C2×C4⋊C8×D432
#191355292
#191353872
#191348862
#191348842
#191345792
#191345762
C43×#17982
#2184843