Finite Group Databasebeta

← #25107208

Subgroups — #25107208

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137218C211yesmaximal, characteristic
2#19137204C211yesmaximal, characteristic
3#19135365C211yesmaximal, characteristic, complemented
4#19135365C211yesmaximal, characteristic, complemented
5#19135359C211yesmaximal, characteristic, complemented
6#19135354C211yesmaximal, characteristic, complemented
7#19134796C211yesmaximal, characteristic
8#19134796C211yesmaximal, characteristic
9#19134790C211yesmaximal, characteristic
10#19134785C211yesmaximal, characteristic
11#19134763C211yesmaximal, characteristic, complemented
12#19134759C211yesmaximal, characteristic, complemented
13#19134729C211yesmaximal, characteristic, complemented
14#19134723C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26#14582798—21no—
27#14582798—21no—
28#14582792—21no—
29#14582792—21no—
30#14582785—21no—
31#14582785—21no—
32#14582774—21no—
33#14582774—21no—
34#14582769C2211yescharacteristic
35#14582769C2211yescharacteristic
36#14582769C2211yescharacteristic
37#14582765C2211yescharacteristic
38#14582765C2211yescharacteristic
39#14582765C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C43×#433C418yescomplemented
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C23×Dic43—21no—
61#13063284—41no—
62#13063284—41no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—41no—
71C2×C4⋊Dic43—41no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—41no—
87#13063259—41no—
88#13063259—41no—
89#13063259—41no—
90#13063257—41no—
91#13063257—41no—
92#13063257—41no—
93#13063257—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#117×C43C2×C414yes—
110#117×C43Q814yes—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C4⋊C8×C43C2×C414yescomplemented
118C4⋊C8×C43C2×C414yescomplemented
119C22⋊C8×C43C2×C414yes—
120C22⋊C8×C43C2×C414yes—
121#97×C43C2×C414yescomplemented
122C4×C8×C43C2×C414yescomplemented
123C24×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yes—
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—81no—
146C22×Dic43—81no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C22×C412yes—
156C2×C8×C43C22×C412yes—
157C2×C8×C43C22×C412yes—
158C2×C8×C43C22×C412yes—
159C4⋊C4×C43C4⋊C414yes—
160C4⋊C4×C43C4⋊C414yes—
161C22⋊C4×C43C4⋊C414yes—
162C22⋊C4×C43C4⋊C414yes—
163C42×C43C22×C412yes—
164C42×C43C22×C412yes—
165C42×C43C2×Q812yes—
166C42×C43C2×Q812yes—
167C22⋊Dic43—42no—
168C22⋊Dic43—81no—
169C22⋊Dic43—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
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—42no—
187C4⋊Dic43—81no—
188C4⋊Dic43—81no—
189C4⋊Dic43—81no—
190C4⋊Dic43—81no—
191C4⋊Dic43—81no—
192C4⋊Dic43—81no—
193C4×Dic43—42no—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43C2×C4⋊C412yes—
203C23×C43C22×D411yescharacteristic
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43C2×C4⋊C412yes—
219C2×C4×C43C2×C4⋊C412yes—
220C2×C4×C43C2×C4⋊C412yes—
221C2×C4×C43C2×C4⋊C412yes—
222C2×C4×C43C2×C4⋊C412yes—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×Q811yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
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—84no—
254C8×C43—22no—
255C8×C43—22no—
256C8×C43—22no—
257C8×C43—22no—
258#21992—431nomaximal, Sylow
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C22×C4⋊C411yescharacteristic
267C22×C43#53511yescharacteristic
268C22×C43#53611yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57811yescharacteristic
273C4×C43—22no—
274C4×C43—22no—
275C4×C43—22no—
276C4×C43—22no—
277C4×C43—22no—
278C4×C43#52011yescharacteristic
279C4×C43#52011yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#54411yescharacteristic
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290C2×#433D4311yescharacteristic
291#2317—431no—
292#2314—431no—
293#1949—431no—
294#1949—431no—
295#1948—431no—
296#1947—431no—
297#1854—431no—
298#1854—431no—
299#1853—431no—
300#1852—431no—
301#1847—431no—
302#1846—431no—
303#1836—431no—
304#1834—431no—
305C2×C43—42no—
306C2×C43#231711yescharacteristic
307C2×C43#291211yescharacteristic
308C2×C43#291311yescharacteristic
309C2×C43#322411yescharacteristic
310C2×C43#322511yescharacteristic
311C2×C43#324111yescharacteristic
312C2×C43#324211yescharacteristic
313C2×#117—431no—
314C2×#117C2×D4311yescharacteristic
315C22×C4⋊C4—431no—
316#433Dic4318yescomplemented
317C2×#107—431no—
318C2×#107—431no—
319C2×#107—431no—
320C2×#107—431no—
321C2×#106—431no—
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×C4⋊C8C2×D4311yescharacteristic
326C2×C4⋊C8C2×D4311yescharacteristic
327C2×C22⋊C8C2×D4311yescharacteristic
328C2×C22⋊C8C2×D4311yescharacteristic
329C2×#97C2×D4311yescharacteristic
330C2×C4×C8C2×D4311yescharacteristic
331#389—861no—
332#389—861no—
333#388—861no—
334#388—861no—
335#387—861no—
336#387—861no—
337#385—861no—
338#385—861no—
339#384—431no—
340#384—431no—
341#384—431no—
342#382—431no—
343#382—431no—
344#382—431no—
345#380—431no—
346#380—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357C43#2199211yescharacteristic, complemented, Sylow
358C23×C4—861no—
359C23×C4C22×D4311yescharacteristic
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364#117—1721no—
365#117—1721no—
366#117Dic8614yes—
367#117C2×Dic4314yes—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—1721no—
384C2×C4⋊C4—1721no—
385C2×C4⋊C4D17211yescharacteristic
386C2×C4⋊C4D17211yescharacteristic
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4D17211yescharacteristic
391C2×C22⋊C4D17211yescharacteristic
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397#107—1721no—
398#107—1721no—
399#107—1721no—
400#107—1721no—
401#106—1721no—
402#106—1721no—
403#106—1721no—
404#106—1721no—
405C4⋊C8C2×Dic4314yescomplemented
406C4⋊C8C2×Dic4314yescomplemented
407C22⋊C8C2×Dic4314yes—
408C22⋊C8C2×Dic4314yes—
409#97C2×Dic4314yescomplemented
410C4×C8C2×Dic4314yescomplemented
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24C2×D17211yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—3441no—
435C22×C4—3441no—
436C22×C4—1722no—
437C22×C4C2×Dic8612yes—
438C22×C4C2×D17211yescharacteristic
439C22×C4C2×D17211yescharacteristic
440C22×C4C2×D17211yescharacteristic
441C22×C4C2×D17211yescharacteristic
442C22×C4C2×D17211yescharacteristic
443C22×C4C22×Dic4312yes—
444C22×C4C23×D4311yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C22×Dic4312yes—
454C2×C8C22×Dic4312yes—
455C2×C8C22×Dic4312yes—
456C2×C8C22×Dic4312yes—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—3441no—
474C4⋊C4—3441no—
475C4⋊C4—3441no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—1722no—
480C4⋊C4C4⋊Dic4314yes—
481C4⋊C4C4⋊Dic4314yes—
482C22⋊C4—3441no—
483C22⋊C4—3441no—
484C22⋊C4—1722no—
485C22⋊C4C4⋊Dic4314yes—
486C22⋊C4C4⋊Dic4314yes—
487C42—3441no—
488C42—3441no—
489C42—1722no—
490C42C2×Dic8612yes—
491C42C2×Dic8612yes—
492C42C22×Dic4312yes—
493C42C22×Dic4312yes—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×C4⋊Dic4312yes—
501C23C22×D17211yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—3444no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4C2×C4⋊Dic4312yes—
542C2×C4C2×C4⋊Dic4312yes—
543C2×C4C2×C4⋊Dic4312yes—
544C2×C4C2×C4⋊Dic4312yes—
545C2×C4C2×C4⋊Dic4312yes—
546C2×C4C23×Dic4311yescharacteristic
547C2×C4C22×Dic8611yescharacteristic
548C2×C4#1306337111yescharacteristic
549C2×C4#1306337111yescharacteristic
550C2×C4#1306337211yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×C4⋊Dic4311yescharacteristic
564C22#1458346811yescharacteristic
565C22#1458347511yescharacteristic
566C22#1458370411yescharacteristic
567C22#1458371111yescharacteristic
568C22#1458371111yescharacteristic
569C22#1458371611yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—3441no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4—3441no—
581C4—3441no—
582C4—3441no—
583C4#1458338211yescharacteristic
584C4#1458338211yescharacteristic
585C4#1458352711yescharacteristic
586C4#1458352711yescharacteristic
587C2—42no—
588C2#1913721811yescharacteristic
589C2#1914319011yescharacteristic
590C2#1914319511yescharacteristic
591C2#1914569111yescharacteristic
592C2#1914570611yescharacteristic
593C2#1914585011yescharacteristic
594C2#1914586511yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#21992
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #19135365C2semidirect
4. #19135365C2semidirect
5. #19135359C2semidirect
6. #19135354C2semidirect
11. #19134763C2semidirect
12. #19134759C2semidirect
13. #19134729C2semidirect
14. #19134723C2semidirect
53. C43×#433C4semidirect
117. C4⋊C8×C43C2×C4semidirect
118. C4⋊C8×C43C2×C4semidirect
121. #97×C43C2×C4semidirect
122. C4×C8×C43C2×C4semidirect
316. #433Dic43semidirect
357. C43#21992semidirect
405. C4⋊C8C2×Dic43semidirect
406. C4⋊C8C2×Dic43semidirect
409. #97C2×Dic43semidirect
410. C4×C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372182
#191372042
#191353652
#191353592
#191353542
#191347962
#191347902
#191347852
#191347632
#191347592
#191347292
#191347232
C2×C43×#4332
#2199243