Finite Group Databasebeta

← #25155416

Subgroups — #25155416

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583299C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic
3#19138320C211yesmaximal, characteristic
4#19138302C211yesmaximal, characteristic
5#19136080C211yesmaximal, characteristic, complemented
6#19136075C211yesmaximal, characteristic, complemented
7#19135932C211yesmaximal, characteristic, complemented
8#19135931C211yesmaximal, characteristic, complemented
9#19135332C211yesmaximal, characteristic, complemented
10#19135322C211yesmaximal, characteristic, complemented
11#19134790C211yesmaximal, characteristic
12#19134762C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic
14#19134381C211yesmaximal, characteristic
15C43×#1854C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14583299—24no—
21#14582942—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582841—21no—
33#14582835—21no—
34#14582831—21no—
35#14582822—21no—
36#14582798C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797—21no—
39#14582795C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582783—21no—
42#14582774—21no—
43#14582768C2211yescharacteristic
44#14582764C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582757—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C23×Dic43—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877Q814yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—22no—
69#13063316—41no—
70#13063316—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×C22⋊Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94#13063258—22no—
95#13063258D414yes—
96#13063257—22no—
97#13063257—41no—
98#13063256—22no—
99#13063256—22no—
100#13063256—22no—
101#13063235—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#117×C43—22no—
116#117×C43—41no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124#107×C43—41no—
125#106×C43—22no—
126C22⋊C8×C43Q814yes—
127#95×C43—21no—
128C24×C43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×Q812yes—
139C22×C4×C43C2×Q812yes—
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—81no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C2×Q812yes—
157C2×C8×C43C2×Q812yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C2×D412yes—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C42×C43—42no—
169C22⋊Dic43—41no—
170C22⋊Dic43—41no—
171C22⋊Dic43—81no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—42no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184C4⋊Dic43C2×D412yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195#10621877—28no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D412yes—
199C2×C43⋊C8C2×Q812yes—
200C2×C43⋊C8C2×Q812yes—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C4⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
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×C43C4⋊Q812yes—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×Q811yescharacteristic
231C2×C4×C43C22×Q811yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×C4×C432−1+411yescharacteristic
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—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—84no—
260C8×C43—22no—
261C8×C43—22no—
262C43⋊C8—22no—
263C43⋊C8C22⋊Q814yes—
264#26075—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×C4⋊Q811yescharacteristic
273C22×C43D4211yescharacteristic
274C22×C43#54711yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×C22⋊Q811yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43D4×Q811yescharacteristic
287C4×C43#55411yescharacteristic
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—42no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296C2×#499—431no—
297C2×#428—431no—
298#2442—431no—
299#2441—431no—
300#2085—431no—
301#2084—431no—
302#2059—431no—
303#2059—431no—
304#1943—431no—
305#1941—431no—
306#1854D4311yescharacteristic
307#1853—431no—
308#1847—431no—
309#1809—431no—
310#1753—431no—
311C2×C43—42no—
312C2×C43#244011yescharacteristic
313C2×C43#316311yescharacteristic
314C2×C43#316611yescharacteristic
315C2×C43#326711yescharacteristic
316C2×C43#327111yescharacteristic
317C2×C43#335111yescharacteristic
318C2×C43#335111yescharacteristic
319C22×M16—431no—
320C2×#125—431no—
321C2×#125—431no—
322C2×#117C2×D4311yescharacteristic
323C22×C4⋊C4—431no—
324#499—864no—
325#428—864no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107C2×D4311yescharacteristic
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×#106C2×D4311yescharacteristic
336C2×C22⋊C8C2×D4311yescharacteristic
337C2×#97—431no—
338C2×C4×C8—431no—
339#400—861no—
340#399—861no—
341#398—861no—
342#396—861no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—861no—
348#387—861no—
349#385—861no—
350#384—431no—
351#382—431no—
352#380—431no—
353#380—861no—
354#380C2×D4311yescharacteristic
355C4×C22⋊C4—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—
364C43#2607511yescharacteristic, complemented, Sylow
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—434no—
368C2×M16—862no—
369C2×M16—862no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376#125—1721no—
377#125—1721no—
378#117—22no—
379#117—41no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—1721no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42—431no—
408C2×C42—431no—
409#107—41no—
410#107—434no—
411#107—862no—
412#107—862no—
413#106—22no—
414#106—862no—
415#106—862no—
416#106—862no—
417#106—862no—
418#106—1721no—
419C22⋊C8Dic8614yes—
420#97—862no—
421C4×C8—862no—
422#95—21no—
423#95—431no—
424#95—431no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432C24D4×D4311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—3441no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4C2×Dic8612yes—
453C22×C4D4×D4311yescharacteristic
454C22×C4Q8×D4312yes—
455C22×C4C23×D4311yescharacteristic
456M16—868no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—432no—
462C2×C8—432no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8C2×Dic8612yes—
468C2×C8C2×Dic8612yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—432no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—3441no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—1722no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4D4×D4312yes—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—3441no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C42—42no—
502C42—861no—
503C42—861no—
504C42—861no—
505C42—861no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23#1306332412yes—
513C23C2×D4×D4311yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—3444no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4#1306332412yes—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337011yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—22no—
565C8—22no—
566C8—434no—
567C8—862no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#1306332411yescharacteristic
576C22#1458353111yescharacteristic
577C22#1458354711yescharacteristic
578C22#1458369511yescharacteristic
579C22#1458369811yescharacteristic
580C22#1458370611yescharacteristic
581C22#1458370611yescharacteristic
582C4—22no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4—1722no—
592C4—1721no—
593C4—1721no—
594C4—1721no—
595C4C22⋊Q8×D4311yescharacteristic
596C4#1458352811yescharacteristic
597C4D4×Dic8611yescharacteristic
598C4#1458360811yescharacteristic
599C2—42no—
600C2#1913829611yescharacteristic
601C2#1914512711yescharacteristic
602C2#1914514511yescharacteristic
603C2#1914612311yescharacteristic
604C2#1914617811yescharacteristic
605C2#1914714811yescharacteristic
606C2#1914715311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1854D43
hypocenterC43#26075
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#14583299C2semidirect
5. #19136080C2semidirect
6. #19136075C2semidirect
7. #19135932C2semidirect
8. #19135931C2semidirect
9. #19135332C2semidirect
10. #19135322C2semidirect
12. #19134762C2semidirect
364. C43#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#145832992
C2×#145829422
#191383202
#191383022
#191360802
#191360752
#191359322
#191359312
#191353322
#191353222
#191347902
#191347622
#191346262
#191343812
C43×#18542
#2607543