Finite Group Databasebeta

← #25155409

Subgroups — #25155409

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×#14583301C211yesmaximal, characteristic, complemented
2C2×#14582941C211yesmaximal, characteristic
3#19138319C211yesmaximal, characteristic
4#19138308C211yesmaximal, characteristic
5#19136078C211yesmaximal, characteristic, complemented
6#19136073C211yesmaximal, characteristic, complemented
7#19135934C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135333C211yesmaximal, characteristic, complemented
10#19135323C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic
12#19134790C211yesmaximal, characteristic
13#19134763C211yesmaximal, characteristic, complemented
14#19134628C211yesmaximal, characteristic
15C43×#1753C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14583301—24no—
21#14582941—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063257C2211yescharacteristic
31C2×#13063257C2211yescharacteristic
32#14582841—21no—
33#14582835—21no—
34#14582833—21no—
35#14582822—21no—
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582782—21no—
42#14582771—21no—
43#14582769C2211yescharacteristic
44#14582765C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582757—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C23×Dic43—21no—
62#13063317—22no—
63#13063317—22no—
64#13063317—41no—
65#13063317—41no—
66#13063284—22no—
67#13063284—41no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
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×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C4×Dic43—21no—
93#13063259—22no—
94#13063259—22no—
95#13063259—41no—
96#13063259D414yes—
97#13063257—22no—
98#13063257—22no—
99#13063257—22no—
100#13063257—22no—
101#13063257—22no—
102#13063257—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C23×C4×C43C2311yescharacteristic
112C2×M16×C43—22no—
113C2×M16×C43—22no—
114C2×M16×C43Q814yes—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C22⋊C4×C43D411yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C22⋊C8×C43Q814yes—
124#97×C43—22no—
125C4×C8×C43—22no—
126#95×C43D411yescharacteristic
127#95×C43D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
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—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—81no—
152M16×C43—28no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D412yes—
160C2×C8×C43C2×Q812yes—
161C2×C8×C43C2×Q812yes—
162C2×C8×C43C2×Q812yes—
163C2×C8×C43C2×Q812yes—
164C2×C8×C43#4112yes—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C22⋊Dic43—42no—
172C22⋊Dic43—42no—
173C22⋊Dic43—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4⋊Dic43—42no—
190C4⋊Dic43—81no—
191C4⋊Dic43C2×D412yes—
192C4⋊Dic43C2×D412yes—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200Dic43⋊C4—81no—
201C4×Dic43—42no—
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—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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—22no—
236C2×Dic43—22no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
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×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—84no—
260C8×C43—22no—
261C8×C43—22no—
262C8×C43—22no—
263C8×C43C22⋊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—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43C2×C22⋊Q811yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43D4×Q811yescharacteristic
287C4×C43#55411yescharacteristic
288Dic43—42no—
289Dic43—42no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
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#1854—431no—
307#1853—431no—
308#1847—431no—
309#1809—431no—
310#1753D4311yescharacteristic
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×M16C2×D4311yescharacteristic
320C2×#125—431no—
321C2×#125—431no—
322C2×#117—431no—
323C22×C4⋊C4—431no—
324#499—864no—
325#428—864no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×C22⋊C8C2×D4311yescharacteristic
337C2×#97C2×D4311yescharacteristic
338C2×C4×C8C2×D4311yescharacteristic
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—431no—
354#380—861no—
355C4×C22⋊C4C2×D4311yescharacteristic
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#336C2×D4311yescharacteristic
363#336C2×D4311yescharacteristic
364C43#2607511yescharacteristic, complemented, Sylow
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—22no—
368C2×M16—22no—
369C2×M16Dic8614yes—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376#125—1721no—
377#125—1721no—
378#117—862no—
379#117—1721no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—862no—
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—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—1721no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4D17211yescharacteristic
405C2×C22⋊C4D17211yescharacteristic
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409#107—434no—
410#107—862no—
411#107—862no—
412#107—1721no—
413#106—862no—
414#106—862no—
415#106—862no—
416#106—862no—
417#106—862no—
418#106—1721no—
419C22⋊C8Dic8614yes—
420#97—22no—
421C4×C8—22no—
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#95D17211yescharacteristic
431#95D17211yescharacteristic
432C24C2×D17211yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4C2×Dic8612yes—
449C22×C4C2×Dic8612yes—
450C22×C4C2×D17211yescharacteristic
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4C2×D17211yescharacteristic
455C22×C4C23×D4311yescharacteristic
456M16—28no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8C2×Dic8612yes—
464C2×C8C2×Dic8612yes—
465C2×C8C2×Dic8612yes—
466C2×C8C2×Dic8612yes—
467C2×C8D4×D4312yes—
468C2×C8#1062190012yes—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—3441no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—1722no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23#1306332512yes—
513C23C22×D17211yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—3444no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
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#1306332512yes—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×Dic8611yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C2×C4#1306337111yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—22no—
565C8—22no—
566C8—22no—
567C8#1306330214yes—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#1306332511yescharacteristic
576C22D4×D17211yescharacteristic
577C22#1458355311yescharacteristic
578C22#1458369911yescharacteristic
579C22#1458369911yescharacteristic
580C22#1458371111yescharacteristic
581C22#1458371111yescharacteristic
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—3441no—
593C4—1722no—
594C4—1722no—
595C4C2×#1306330211yescharacteristic
596C4#1458352711yescharacteristic
597C4D4×Dic8611yescharacteristic
598C4#1458360611yescharacteristic
599C2—42no—
600C2#1913829711yescharacteristic
601C2#1914512611yescharacteristic
602C2#1914514711yescharacteristic
603C2#1914612511yescharacteristic
604C2#1914618511yescharacteristic
605C2#1914715711yescharacteristic
606C2#1914715711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1753D43
hypocenterC43#26075
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#14583301C2semidirect
5. #19136078C2semidirect
6. #19136073C2semidirect
7. #19135934C2semidirect
8. #19135934C2semidirect
9. #19135333C2semidirect
10. #19135323C2semidirect
13. #19134763C2semidirect
364. C43#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#145833012
C2×#145829412
#191383192
#191383082
#191360782
#191360732
#191359342
#191353332
#191353232
#191347962
#191347902
#191347632
#191346282
C43×#17532
#2607543