Finite Group Databasebeta

← #25106297

Subgroups — #25106297

Order 11008.

1138 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583436C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19135558C212yesmaximal, complemented
5#19135403C212yesmaximal, complemented
6#19134916C212yesmaximal
7#19134904C212yesmaximal, complemented
8#19134600C211yesmaximal, characteristic, complemented
9#19134596C211yesmaximal, characteristic, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12#14583436—24no—
13#14583436C418yescomplemented
14C2×#13063320—21no—
15C2×#13063316C2211yescharacteristic
16C2×#13063314C2211yescharacteristic
17C2×#13063310—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×C4×D172—21no—
21C2×C4×D172C2211yescharacteristic
22C2×#13063283C2212yes—
23C2×#13063282—21no—
24C2×C42×D43C2211yescharacteristic
25#14582951—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2212yes—
28C2×#13063247C2212yes—
29C2×#13063245C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C8×Dic43C2212yes—
32#14582769C2211yescharacteristic
33#14582764C2212yes—
34#14582756—21no—
35#14582756—21no—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×Q8×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#103×C43C2212yes—
44C43×#384C2211yescharacteristic
45C43×#340C2212yes—
46C22×D172—21no—
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D411yescharacteristic
51C22×C4×D43C2311yescharacteristic
52C22×C43⋊C8C2312yes—
53#13063320—28no—
54#13063316—22no—
55#13063316C2×C414yes—
56#13063314—22no—
57#13063314C2×C414yes—
58#13063310—28no—
59#13063301—22no—
60#13063301C2×C414yes—
61#13063300—22no—
62#13063300C2×C414yes—
63C4×D172—28no—
64C4×D172—22no—
65C4×D172C2×C414yes—
66#13063283—42no—
67#13063283—42no—
68#13063282—28no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88C4⋊(C43⋊C8)—22no—
89#13063249—42no—
90#13063247—42no—
91#13063245—42no—
92(C2×D43)⋊C8—24no—
93C8×Dic43—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C22×Q8×C43C2311yescharacteristic
97C22×C8×C43C2312yes—
98C4×Q8×C43—22no—
99C4×Q8×C43C2×C414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—22no—
108#103×C43—42no—
109C23×D43—21no—
110C23×D43C2×D411yescharacteristic
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43C22×C412yes—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2411yescharacteristic
123C22×Dic43—21no—
124C22×Dic43—22no—
125C22×Dic43C2×D411yescharacteristic
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C2×D172—21no—
129C2×D172—24no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—42no—
135C2×D172—42no—
136C2×D172C22×C412yes—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—24no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43C22⋊C414yes—
149C2×C4×D43C22⋊C414yes—
150C2×C4×D43C22×C412yes—
151C2×C4×D43C2×D412yes—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43C22×C412yes—
162C42×C43—24no—
163C42×C43C22×C412yes—
164C42×C43C2×D412yes—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—44no—
171C4⋊Dic43—21no—
172C4⋊Dic43—24no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—42no—
176C4⋊Dic43—42no—
177C4⋊Dic43C22×C412yes—
178Dic43⋊C4—24no—
179Dic43⋊C4—24no—
180C4×Dic43—44no—
181C4×Dic43C22⋊C414yes—
182C4×Dic43C22⋊C414yes—
183C4×Dic43C22×C412yes—
184C4×Dic43C2×D412yes—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43C22×D411yescharacteristic
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—22no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43C2×C22⋊C412yes—
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—41no—
206Q8×C43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43C2×C22⋊C412yes—
219C2×C4×C43C2×C22⋊C412yes—
220C2×C4×C43#13512yes—
221C2×C4×C43#13512yes—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43C2×C22⋊C412yes—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C412yes—
243D172—22no—
244D172—22no—
245D172—48no—
246D172—41no—
247D172—41no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—28no—
253C4×D43—44no—
254C4×D43—48no—
255C8×C43—42no—
256C43⋊C8—42no—
257#21862—431nomaximal, Sylow
258C22×C43C22×C22⋊C411yescharacteristic
259C22×C43#53511yescharacteristic
260C22×C43#53611yescharacteristic
261C22×C43C2×#13511yescharacteristic
262C22×C43C2×#13511yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57511yescharacteristic
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—82no—
283C4×C43#41614yes—
284C4×C43#52011yescharacteristic
285C4×C43#52011yescharacteristic
286C4×C43#53711yescharacteristic
287C4×C43#53711yescharacteristic
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—42no—
292Dic43—82no—
293C2×#529—431no—
294C2×#431—431no—
295#2285—431no—
296#1991—432no—
297#1958—432no—
298#1875—432no—
299#1873—432no—
300#1803—431no—
301#1803D4311yescharacteristic, complemented
302#1802—431no—
303#1802—431no—
304C2×C43#231111yescharacteristic
305C2×C43C2×#41611yescharacteristic
306C2×C43#289611yescharacteristic
307C2×C43#321211yescharacteristic
308C2×C43#321211yescharacteristic
309C2×C43#323311yescharacteristic
310C2×C43#323311yescharacteristic
311D43—42no—
312D43—82no—
313#529—438no—
314#529—864no—
315C2×#126—861no—
316C2×#125—431no—
317C2×#124—431no—
318C2×#123—861no—
319C2×C22⋊Q8—431no—
320C2×#121—431no—
321C2×C4×Q8C2×D4311yescharacteristic
322C2×C4×D4—431no—
323C2×C4×D4—861no—
324C2×#117—432no—
325C2×#117—861no—
326C22×C42—431no—
327#431—864no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330C2×#103—432no—
331C2×#103C2×D4312yes—
332C2×#102—432no—
333C2×#102—432no—
334C2×C22⋊C8—432no—
335C2×C4×C8—432no—
336#384—431no—
337#384C2×D4311yescharacteristic
338#382—432no—
339#380—861no—
340#380—861no—
341C4×C4⋊C4—861no—
342C4×C4⋊C4—861no—
343#340—432no—
344#340—432no—
345#340—432no—
346#340C2×D4312yes—
347C43#2186211yescharacteristic, complemented, Sylow
348C22×Q8C22×D4311yescharacteristic
349C22×D4—431no—
350C22×D4—861no—
351C23×C4—431no—
352C23×C4—431no—
353C23×C4—431no—
354C23×C4—861no—
355C22×C8—432no—
356C22×C8C22×D4312yes—
357#126—868no—
358#125—434no—
359#125—862no—
360#124—434no—
361#124—862no—
362#123—868no—
363C22⋊Q8—434no—
364C22⋊Q8—862no—
365#121—434no—
366#121—862no—
367C4×Q8—22no—
368C4×Q8C4×D4314yes—
369C4×D4—434no—
370C4×D4—868no—
371C4×D4—862no—
372#117—868no—
373#117—1722no—
374#117—1722no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4C22×D4312yes—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—862no—
393C2×C42—21no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—434no—
398C2×C42—434no—
399C2×C42—862no—
400C2×C42C22×D4311yescharacteristic
401C4⋊C8—22no—
402C4⋊C8—862no—
403#103—42no—
404#103—1722no—
405#102—1722no—
406#102—1722no—
407C22⋊C8—864no—
408C4×C8—864no—
409#95—862no—
410#95—862no—
411C24—431no—
412C24—861no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C2×C4×D4312yes—
419C2×D4—432no—
420C2×D4—864no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—1722no—
427C2×D4—1722no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—434no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—434no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—864no—
446C22×C4—862no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—862no—
458C2×C8—862no—
459C2×C8—862no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—432no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C4⋊C4C2×C4×D4312yes—
476C22⋊C4—864no—
477C22⋊C4—864no—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—1724no—
482C42—24no—
483C42—434no—
484C42—434no—
485C42—432no—
486C42—432no—
487C42—1724no—
488C42C2×C4×D4312yes—
489C42D4×D4312yes—
490C23—432no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23—861no—
496C23—861no—
497C23—862no—
498C23—1721no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23—1721no—
503C23—1721no—
504C23C2×D4×D4311yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—862no—
510D4—862no—
511D4—1728no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—432no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—868no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—1724no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1728no—
547C2×C4C22⋊C4×D4312yes—
548C2×C4C22⋊C4×D4312yes—
549C2×C4#1306334612yes—
550C2×C4#1306334812yes—
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4#1306337011yescharacteristic
554C2×C4#1306337111yescharacteristic
555C2×C4#1306337211yescharacteristic
556C2×C4#1306337311yescharacteristic
557C8—42no—
558C8—1722no—
559C22—862no—
560C22—862no—
561C22—862no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—1722no—
567C22—1722no—
568C22—1722no—
569C22—1721no—
570C22—1721no—
571C22—1721no—
572C22—1721no—
573C22C2×C22⋊C4×D4311yescharacteristic
574C22#1458346511yescharacteristic
575C22#1458347211yescharacteristic
576C22C2×#1306334611yescharacteristic
577C22C2×#1306334811yescharacteristic
578C22#1458369511yescharacteristic
579C22#1458369811yescharacteristic
580C4—22no—
581C4—42no—
582C4—42no—
583C4—82no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—3442no—
588C4—1722no—
589C4#1458289414yes—
590C4#1458337911yescharacteristic
591C4#1458338011yescharacteristic
592C4#1458347811yescharacteristic
593C4#1458347911yescharacteristic
594C2—3442no—
595C2—1722no—
596C2#1913718411yescharacteristic
597C2C2×#1458289411yescharacteristic
598C2#1914311111yescharacteristic
599C2#1914557511yescharacteristic
600C2#1914557611yescharacteristic
601C2#1914577811yescharacteristic
602C2#1914577911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
cosocleC22×C4×C43C24
hypercenter#1803D43
hypocenterC43#21862
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. #19137000C2semidirect
4. #19135558C2semidirect
5. #19135403C2semidirect
7. #19134904C2semidirect
8. #19134600C2semidirect
9. #19134596C2semidirect
10. #19134592C2semidirect
11. C43×#1803C2semidirect
13. #14583436C4semidirect
301. #1803D43semidirect
347. C43#21862semidirect

Maximal subgroups

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

subgroupindex
C2×#145834362
C2×#145829512
#191370002
#191355582
#191354032
#191349162
#191349042
#191346002
#191345962
#191345922
C43×#18032
#2186243