Finite Group Databasebeta

← #25097175

Subgroups — #25097175

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582856C211yesmaximal, characteristic
2#19137205C211yesmaximal, characteristic
3#19137203C211yesmaximal, characteristic
4#19134763C211yesmaximal, characteristic, complemented
5#19134725C211yesmaximal, characteristic, complemented
6#19134722C211yesmaximal, characteristic, complemented
7#19134629C211yesmaximal, characteristic
8#19134625C211yesmaximal, characteristic
9#19134621C211yesmaximal, characteristic
10#19134617C211yesmaximal, characteristic
11#19134495C211yesmaximal, characteristic, complemented
12#19134494C211yesmaximal, characteristic, complemented
13#107×Dic43C211yesmaximal, characteristic, complemented
14#106×Dic43C211yesmaximal, characteristic, complemented
15C43×#1847C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23#14582856C418yescomplemented
24C2×#13063235C2211yescharacteristic
25C2×C4×C43⋊C8C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582791—21no—
28#14582791—21no—
29#14582789—21no—
30#14582789—21no—
31#14582786—21no—
32#14582786—21no—
33#14582780—21no—
34#14582780—21no—
35#14582769C2211yescharacteristic
36#14582765C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C43×#384C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872C2×C414yes—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43C2×C414yes—
69#13063282C2×C414yes—
70#13063282Q814yes—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063259—22no—
92#13063257—22no—
93#13063257—22no—
94#13063235C2×C414yes—
95C4×C43⋊C8C2×C414yes—
96C8×Dic43C2×C414yes—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—22no—
117#107×C43—22no—
118#106×C43—22no—
119#106×C43—22no—
120#97×C43C2×C414yes—
121#95×C43—21no—
122#95×C43—21no—
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43C22×C412yes—
143C2×C4×D43C2×Q812yes—
144C2×C8×C43C22×C412yes—
145C2×C8×C43C22×C412yes—
146C2×C8×C43#4112yes—
147C2×C8×C43#4112yes—
148C2×C8×C43#4112yes—
149C2×C8×C43#4112yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—81no—
159C4⋊C4×C43—81no—
160C42×C43C22×C412yes—
161C42×C43C2×Q812yes—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164(C2×D43)⋊C4—81no—
165(C2×D43)⋊C4—81no—
166(C2×D43)⋊C4C4⋊C414yes—
167(C2×D43)⋊C4C4⋊C414yes—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—81no—
177C4⋊Dic43—81no—
178Dic43⋊C4C4⋊C414yes—
179Dic43⋊C4C4⋊C414yes—
180C4×Dic43—81no—
181C4×Dic43—81no—
182C4×Dic43—81no—
183C4×Dic43—81no—
184C4×Dic43C22×C412yes—
185C4×Dic43C2×Q812yes—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8C22×C412yes—
191C2×C43⋊C8C22×C412yes—
192#10621872—28no—
193C8×D43—28no—
194C23×C43C22×D411yescharacteristic
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43C2×C4⋊C412yes—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C2×C4⋊C412yes—
219C2×C4×C43C2×C4⋊C412yes—
220C2×C4×C43C23×C411yescharacteristic
221C2×C4×C43C22×Q811yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
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×Dic43C2×C4⋊C412yes—
245C2×Dic43C2×C4⋊C412yes—
246C2×Dic43C2×C4⋊C412yes—
247C4×D43—22no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—22no—
251C8×C43#11714yes—
252C8×C43#11714yes—
253C43⋊C8—22no—
254C43⋊C8—22no—
255#20822—431nomaximal, Sylow
256C22×C43C22×C4⋊C411yescharacteristic
257C22×C43#53211yescharacteristic
258C22×C43#53211yescharacteristic
259C22×C43#57611yescharacteristic
260C22×C43#57711yescharacteristic
261C22×C43#57711yescharacteristic
262C22×C43#57811yescharacteristic
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#11711yescharacteristic
277C4×C43C2×#11711yescharacteristic
278C4×C43#53311yescharacteristic
279C4×C43#53311yescharacteristic
280Dic43—22no—
281Dic43—22no—
282Dic43—22no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287C2×#405—431no—
288#2314—431no—
289#2314—431no—
290#1847—431no—
291#1847D4311yescharacteristic, complemented
292#1835—431no—
293#1834—431no—
294#1809—431no—
295#1809—431no—
296#1808—431no—
297#1807—431no—
298#1776—431no—
299#1776—431no—
300C4×#107—431no—
301C4×#106—431no—
302C2×C43#228511yescharacteristic
303C2×C43#291211yescharacteristic
304C2×C43#291311yescharacteristic
305C2×C43#317811yescharacteristic
306C2×C43#317811yescharacteristic
307C2×C43#317911yescharacteristic
308C2×C43#317911yescharacteristic
309D43—42no—
310C22×M16—431no—
311C23×C8—431no—
312C2×#117—431no—
313C2×#107—431no—
314C2×#107—431no—
315C2×#107C2×D4311yescharacteristic
316C2×#107C2×D4311yescharacteristic
317C2×#106—431no—
318C2×#106—431no—
319C2×#106C2×D4311yescharacteristic
320C2×#106C2×D4311yescharacteristic
321#405—438no—
322C2×#97—431no—
323C2×#97C2×D4311yescharacteristic
324C2×C4×C8—431no—
325C2×C4×C8—431no—
326#388—861no—
327#388—861no—
328#388—861no—
329#388—861no—
330#387—861no—
331#387—861no—
332#387—861no—
333#387—861no—
334#384—431no—
335#384C2×D4311yescharacteristic
336#382—431no—
337#382C2×D4311yescharacteristic
338#380—431no—
339#380—431no—
340#380—431no—
341#380—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354C43#2082211yescharacteristic, complemented, Sylow
355C23×C4—431no—
356C2×M16—434no—
357C2×M16—862no—
358C2×M16—862no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—434no—
362C22×C8—862no—
363C22×C8—862no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366#117—434no—
367#117—434no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—431no—
383C2×C22⋊C4—431no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42C22×D4311yescharacteristic
394#107—22no—
395#107—22no—
396#107—862no—
397#107—862no—
398#106—22no—
399#106—22no—
400#106—862no—
401#106—862no—
402#97—434no—
403#97C4×D4314yes—
404C4×C8—434no—
405C4×C8—434no—
406#95—21no—
407#95—21no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418C24—431no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—432no—
427C22×C4—432no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4D4×D4311yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439M16—868no—
440C2×C8—432no—
441C2×C8—432no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—868no—
447C2×C8C2×C4×D4312yes—
448C2×C8C2×C4×D4312yes—
449C2×C8#1062190012yes—
450C2×C8#1062190012yes—
451C2×C8#1062190212yes—
452C2×C8#1062190212yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—434no—
464C4⋊C4—434no—
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—
475C22⋊C4—434no—
476C22⋊C4—434no—
477C22⋊C4—3441no—
478C22⋊C4—3441no—
479C22⋊C4—3441no—
480C22⋊C4—3441no—
481C42—432no—
482C42—432no—
483C42—3441no—
484C42—3441no—
485C42—3441no—
486C42—3441no—
487C42C2×C4×D4312yes—
488C42Q8×D4312yes—
489C23—432no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23—861no—
496C23C2×D4×D4311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—432no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
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×C4C4⋊C4×D4312yes—
539C2×C4C4⋊C4×D4312yes—
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×Q8×D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C2×C4C2×#1062190011yescharacteristic
544C2×C4C2×#1062190211yescharacteristic
545C2×C4C2×#1062190211yescharacteristic
546C8—862no—
547C8—862no—
548C8#1306328314yes—
549C8#1306328314yes—
550C22—862no—
551C22—862no—
552C22—862no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22C2×C4⋊C4×D4311yescharacteristic
558C22#1458344711yescharacteristic
559C22#1458345011yescharacteristic
560C22#1458370311yescharacteristic
561C22#1458370811yescharacteristic
562C22#1458370911yescharacteristic
563C22#1458371511yescharacteristic
564C4—22no—
565C4—22no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—862no—
571C4—862no—
572C4—862no—
573C4—3441no—
574C4—3441no—
575C4—3441no—
576C4—3441no—
577C4C2×#1306328311yescharacteristic
578C4C2×#1306328311yescharacteristic
579C4#1458345411yescharacteristic
580C4#1458345411yescharacteristic
581C2—1722no—
582C2#1913700011yescharacteristic
583C2#1914318911yescharacteristic
584C2#1914319411yescharacteristic
585C2#1914526011yescharacteristic
586C2#1914526811yescharacteristic
587C2#1914527511yescharacteristic
588C2#1914528311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1847C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1847D43
hypocenterC43#20822
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #19134763C2semidirect
5. #19134725C2semidirect
6. #19134722C2semidirect
11. #19134495C2semidirect
12. #19134494C2semidirect
13. #107×Dic43C2semidirect
14. #106×Dic43C2semidirect
15. C43×#1847C2semidirect
23. #14582856C4semidirect
291. #1847D43semidirect
354. C43#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#145828562
#191372052
#191372032
#191347632
#191347252
#191347222
#191346292
#191346252
#191346212
#191346172
#191344952
#191344942
#107×Dic432
#106×Dic432
C43×#18472
#2082243