Finite Group Databasebeta

← #25196764

Subgroups — #25196764

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140417C211yesmaximal, characteristic
2#19137275C211yesmaximal, characteristic
3#19136163C211yesmaximal, characteristic, complemented
4#19136142C211yesmaximal, characteristic, complemented
5#19135733C211yesmaximal, characteristic, complemented
6#19135172C211yesmaximal, characteristic, complemented
7#19135165C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic
9#19135017C211yesmaximal, characteristic
10#19134846C211yesmaximal, characteristic, complemented
11#19134846C211yesmaximal, characteristic, complemented
12#19134629C211yesmaximal, characteristic
13#19134621C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#2057C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27#14582837—21no—
28#14582834—21no—
29#14582818—21no—
30#14582810—21no—
31#14582805C2211yescharacteristic
32#14582795—21no—
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582789—21no—
36#14582788—21no—
37#14582782—21no—
38#14582765C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69#13063305—22no—
70#13063305Q814yescomplemented
71#13063290—41no—
72#13063290—41no—
73#13063282—41no—
74#13063282—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063257—22no—
95#13063250—22no—
96#13063250—22no—
97#13063248—41no—
98#13063248—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4⋊Q8×C43—41no—
113C4⋊Q8×C43—41no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—41no—
122#107×C43—41no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C2×Q8×C43—42no—
126C2×Q8×C43—81no—
127C2×Q8×C43—81no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43C2×Q812yes—
147C2×C4×D43#4112yes—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C2×Q812yes—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43#4112yes—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43C2×Q812yes—
170C42×C43—21no—
171C42×C43—21no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200#10621872—44no—
201C8×D43—44no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43C22⋊Q812yes—
210Q8×C43—84no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43C22⋊Q812yes—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264C8×C43—22no—
265C8×C43—22no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#29171—431nomaximal, Sylow
269C22×C43C2×C22⋊Q811yescharacteristic
270C22×C43#53211yescharacteristic
271C22×C43#53411yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#55111yescharacteristic
290C4×C43#55111yescharacteristic
291C4×C43#55411yescharacteristic
292C4×C43#55411yescharacteristic
293Dic43—22no—
294Dic43—42no—
295Dic43—41no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300#2628—431no—
301#2323—431no—
302#2101—431no—
303#2097—431no—
304#2057D4311yescharacteristic, complemented
305#2024—431no—
306#1919—431no—
307#1918—431no—
308#1894—431no—
309#1892—431no—
310#1863—431no—
311#1863—431no—
312#1809—431no—
313#1808—431no—
314#1729—431no—
315C2×C43#256411yescharacteristic
316C2×C43#308211yescharacteristic
317C2×C43#308311yescharacteristic
318C2×C43#317511yescharacteristic
319C2×C43#317811yescharacteristic
320C2×C43#319811yescharacteristic
321C2×C43#320211yescharacteristic
322D43—42no—
323C22×M16—431no—
324C23×C8—431no—
325C2×C4⋊Q8C2×D4311yescharacteristic
326C2×C22⋊Q8—431no—
327C2×C4×Q8—431no—
328C2×#117—431no—
329C2×#107—431no—
330C2×#107C2×D4311yescharacteristic
331C2×#107C2×D4311yescharacteristic
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103—431no—
337#400—861no—
338#399—861no—
339#395—861no—
340#393—861no—
341#391—431no—
342#389—431no—
343#389—431no—
344#389—861no—
345#389C2×D4311yescharacteristic
346#388—861no—
347#388—861no—
348#387—861no—
349#382—431no—
350#380—431no—
351#380—431no—
352#380—431no—
353C4×C4⋊C4—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340C2×D4311yescharacteristic
361#340C2×D4311yescharacteristic
362#336—431no—
363#336—431no—
364#336—431no—
365#336C2×D4311yescharacteristic
366C43#2917111yescharacteristic, complemented, Sylow
367C22×Q8—21no—
368C22×Q8—431no—
369C23×C4—431no—
370C2×M16—862no—
371C2×M16—862no—
372C2×M16—1721no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—862no—
376C22×C8—862no—
377C22×C8—1721no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C4⋊Q8—41no—
381C4⋊Q8—41no—
382C22⋊Q8—434no—
383C22⋊Q8—862no—
384C4×Q8—1721no—
385C4×Q8—1721no—
386#117—1721no—
387#117—1721no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—41no—
414#107—41no—
415#107—862no—
416#106—862no—
417#103—862no—
418#103—862no—
419#103—1721no—
420#103—1721no—
421#95—21no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432C24—431no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—81no—
436C2×Q8—432no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462M16—1724no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—1724no—
474C2×C8#1062190212yes—
475C2×C8#1062190212yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—864no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4—1722no—
497C4⋊C4Q8×D4312yes—
498C22⋊C4—864no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—21no—
506C42—861no—
507C42—861no—
508C42—3441no—
509C42—1722no—
510C23—432no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23C2×D4×D4311yescharacteristic
518Q8—84no—
519Q8—862no—
520Q8—862no—
521Q8—1721no—
522Q8—1721no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—432no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C2×Q8×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4C2×#1062190211yescharacteristic
569C2×C4C2×#1062190211yescharacteristic
570C2×C4#1306337011yescharacteristic
571C2×C4#1306337011yescharacteristic
572C8—22no—
573C8—22no—
574C8—1721no—
575C8—1721no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22C22⋊Q8×D4311yescharacteristic
584C22#1458345011yescharacteristic
585C22#1458345911yescharacteristic
586C22#1458370011yescharacteristic
587C22#1458370911yescharacteristic
588C22#1458371211yescharacteristic
589C22#1458371511yescharacteristic
590C4—41no—
591C4—41no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4—1722no—
602C4—1721no—
603C4#1458357611yescharacteristic
604C4#1458357611yescharacteristic
605C4#1458361011yescharacteristic
606C4#1458361011yescharacteristic
607C2—1722no—
608C2#1913977611yescharacteristic
609C2#1914443211yescharacteristic
610C2#1914444111yescharacteristic
611C2#1914523711yescharacteristic
612C2#1914526811yescharacteristic
613C2#1914544311yescharacteristic
614C2#1914548811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2057C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2057D43
hypocenterC43#29171
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
3. #19136163C2semidirect
4. #19136142C2semidirect
5. #19135733C2semidirect
6. #19135172C2semidirect
7. #19135165C2semidirect
10. #19134846C2semidirect
11. #19134846C2semidirect
15. C43×#2057C2semidirect
70. #13063305Q8semidirect
304. #2057D43semidirect
366. C43#29171semidirect

Maximal subgroups

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

subgroupindex
#191404172
#191372752
#191361632
#191361422
#191357332
#191351722
#191351652
#191350272
#191350172
#191348462
#191346292
#191346212
#191342902
C43×#20572
#2917143