Finite Group Databasebeta

← #24988657

Subgroups — #24988657

Order 11008.

794 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#19135573C211yesmaximal, characteristic, complemented
2C4×#13063252C211yesmaximal, characteristic, complemented
3C4×#13063252C211yesmaximal, characteristic, complemented
4#19133190C211yesmaximal, characteristic, complemented
5#19133034C211yesmaximal, characteristic, complemented
6#19133034C211yesmaximal, characteristic, complemented
7C43×#3482C211yesmaximal, characteristic
8#14582923C2211yescharacteristic
9C2×#13063252—21no—
10C2×#13063252—21no—
11C4×#10621877C2211yescharacteristic
12C4×#10621877C2211yescharacteristic
13C42×Dic43C2211yescharacteristic
14#14582658—22no—
15#14582658—21no—
16#14582658—21no—
17#14582641—22no—
18Q8⋊(C43⋊C8)—21no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#557C411yescharacteristic, complemented
23C43×#556—21no—
24C43×#556C411yescharacteristic, complemented
25C43×#552—22no—
26C43×#552—21no—
27D4×Q8×C43C411yescharacteristic, complemented
28C43×#548—21no—
29C43×#547—21no—
30C43×#547C411yescharacteristic, complemented
31C43×#533—21no—
32C43×#533C2211yescharacteristic
33C43×#529—21no—
34C43×#529—22no—
35C4×#41×C43—21no—
36C4×#41×C43C2211yescharacteristic
37C4×#41×C43C2211yescharacteristic
38C2×C4×Q8×C43—21no—
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47#13063252—24no—
48#13063252—24no—
49#13063236—21no—
50#13063236—21no—
51C4×C43⋊C8—21no—
52C4×C43⋊C8—21no—
53C2×#41×C43—21no—
54C2×#41×C43D411yescharacteristic
55C2×#41×C43D411yescharacteristic
56C22×Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43C2×C411yescharacteristic
60C4⋊Q8×C43C2×C411yescharacteristic
61#126×C43—22no—
62#126×C43—22no—
63#126×C43—22no—
64#125×C43—22no—
65#125×C43—22no—
66#125×C43—21no—
67#125×C43D412yes—
68#124×C43—22no—
69#124×C43—21no—
70#123×C43—22no—
71#123×C43—22no—
72#123×C43—22no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—21no—
80#121×C43—22no—
81#121×C43—21no—
82C4×Q8×C43—22no—
83C4×Q8×C43—22no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43C2×C411yescharacteristic
90C4×Q8×C43C2×C411yescharacteristic
91C4×Q8×C43D411yescharacteristic
92C4×Q8×C43D411yescharacteristic
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43C2×C411yescharacteristic
101C4×D4×C43C2×C411yescharacteristic
102C4×D4×C43D411yescharacteristic
103C4×D4×C43D411yescharacteristic
104#117×C43—22no—
105#117×C43—22no—
106#117×C43—21no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43D411yescharacteristic
110#117×C43D411yescharacteristic
111#117×C43D412yes—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—21no—
114C2×C42×C43—22no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#41×C43—22no—
119#41×C43—22no—
120#41×C43—41no—
121#41×C43—41no—
122#41×C43—42no—
123#41×C43—42no—
124C2×Q8×C43—22no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—42no—
128C2×Q8×C43—42no—
129C2×Q8×C43C22⋊C411yescharacteristic
130C2×Q8×C43C22⋊C411yescharacteristic
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22⋊C411yescharacteristic
135C2×D4×C43C22⋊C411yescharacteristic
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43—41no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43C22⋊C411yescharacteristic
163C4⋊C4×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C4⋊C4×C43C22⋊C411yescharacteristic
166C4⋊C4×C43C22⋊C412yes—
167C4⋊C4×C43C22⋊C412yes—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—22no—
187C42×C43—21no—
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198#10621877—22no—
199#10621877—22no—
200#10621877—41no—
201#10621877—41no—
202#10621877—42no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—41no—
205C2×C43⋊C8—41no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43#12011yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—44no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43#10412yescomplemented
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—44no—
224D4×C43#10412yescomplemented
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—44no—
242C2×C4×C43—44no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43#12011yescharacteristic
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C43⋊C8—42no—
261C43⋊C8—42no—
262C43⋊C8—81no—
263#8442—431nomaximal, Sylow
264C22×C43—21no—
265C22×C43—22no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43#37911yescharacteristic
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43C2×#10411yescharacteristic
286C4×C43C2×#10411yescharacteristic
287C4×C43#42111yescharacteristic
288C4×C43#42111yescharacteristic
289C4×C43#45411yescharacteristic
290C4×C43#45611yescharacteristic
291Dic43—44no—
292#3482D4311yescharacteristic
293#1994—431no—
294C4×#104—431no—
295C4×#104—431no—
296#1526—431no—
297#1489—431no—
298#1489—431no—
299C2×C43—41no—
300C2×C43—42no—
301C2×C43—81no—
302C2×C43#178911yescharacteristic
303C2×C43#178911yescharacteristic
304C2×C43#179311yescharacteristic
305#557Dic4311yescharacteristic, complemented
306#556—21no—
307#556Dic4311yescharacteristic, complemented
308#552—22no—
309#552—21no—
310D4×Q8Dic4311yescharacteristic, complemented
311#548—21no—
312#547—21no—
313#547Dic4311yescharacteristic, complemented
314#533—21no—
315#533C2×D4311yescharacteristic
316#529—21no—
317#529—22no—
318C4×#41—21no—
319C4×#41C2×D4311yescharacteristic
320C4×#41C2×D4311yescharacteristic
321C2×C4×Q8—21no—
322#423—431no—
323C2×#104—861no—
324C2×#104—861no—
325C4×M16—431no—
326C4×M16—431no—
327C43—431no—
328#339—862no—
329#339—861no—
330#339—861no—
331#330—862no—
332Q8⋊C8—861no—
333Q8⋊C8—861no—
334D4⋊C8—861no—
335D4⋊C8—861no—
336C43#844211yescharacteristic, complemented, Sylow
337C2×#41—21no—
338C2×#41C22⋊D4311yescharacteristic
339C2×#41C22⋊D4311yescharacteristic
340C22×Q8—21no—
341C2×M16—861no—
342C2×M16—861no—
343C2×M16—861no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8C2×Dic4311yescharacteristic
347C4⋊Q8C2×Dic4311yescharacteristic
348#126—22no—
349#126—22no—
350#126—22no—
351#125—22no—
352#125—22no—
353#125—21no—
354#125C22⋊D4312yes—
355#124—22no—
356#124—21no—
357#123—22no—
358#123—22no—
359#123—22no—
360C22⋊Q8—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—21no—
367#121—22no—
368#121—21no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C2×Dic4311yescharacteristic
377C4×Q8C2×Dic4311yescharacteristic
378C4×Q8C22⋊D4311yescharacteristic
379C4×Q8C22⋊D4311yescharacteristic
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C2×Dic4311yescharacteristic
388C4×D4C2×Dic4311yescharacteristic
389C4×D4C22⋊D4311yescharacteristic
390C4×D4C22⋊D4311yescharacteristic
391#117—22no—
392#117—22no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117C22⋊D4311yescharacteristic
397#117C22⋊D4311yescharacteristic
398#117C22⋊D4312yes—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C42—22no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408C4⋊C8—861no—
409C4⋊C8—861no—
410#104—864no—
411#104—864no—
412#97—861no—
413#97—861no—
414C4×C8—861no—
415C4×C8—861no—
416#41—22no—
417#41—22no—
418#41—41no—
419#41—41no—
420#41—42no—
421#41—42no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8C22⋊Dic4311yescharacteristic
428C2×Q8C22⋊Dic4311yescharacteristic
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C22⋊Dic4311yescharacteristic
433C2×D4C22⋊Dic4311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—1721no—
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446M16—862no—
447M16—862no—
448M16—1722no—
449M16—1721no—
450M16—1721no—
451C2×C8—1721no—
452C2×C8—1721no—
453C2×C8—1721no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4C22⋊Dic4311yescharacteristic
469C4⋊C4C22⋊Dic4311yescharacteristic
470C4⋊C4C22⋊Dic4311yescharacteristic
471C4⋊C4C22⋊Dic4311yescharacteristic
472C4⋊C4C22⋊Dic4312yes—
473C4⋊C4C22⋊Dic4312yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—22no—
494C42—862no—
495C42—862no—
496C42—862no—
497C42—1721no—
498C42—1721no—
499C42—1721no—
500C42C22×Dic4311yescharacteristic
501C42C2×C22⋊D4311yescharacteristic
502C42C2×C22⋊D4311yescharacteristic
503C42C2×C22⋊D4311yescharacteristic
504C23—21no—
505C23—21no—
506C23#1306329411yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—44no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8#1306325212yescomplemented
516D4—21no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4#1306325212yescomplemented
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—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4C2×C22⋊Dic4311yescharacteristic
553C2×C4C2×C22⋊Dic4311yescharacteristic
554C2×C4C2×C22⋊Dic4311yescharacteristic
555C2×C4#1306329411yescharacteristic
556C2×C4#1306329411yescharacteristic
557C2×C4#1306329411yescharacteristic
558C8—3441no—
559C8—1722no—
560C8—1722no—
561C22—21no—
562C22—21no—
563C22—22no—
564C22—21no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22#1458275511yescharacteristic
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—1724no—
583C4C2×#1306325211yescharacteristic
584C4C2×#1306325211yescharacteristic
585C4#1458291611yescharacteristic
586C4#1458291611yescharacteristic
587C4#1458307211yescharacteristic
588C4#1458308211yescharacteristic
589C2—41no—
590C2—42no—
591C2—81no—
592C2#1913453911yescharacteristic
593C2#1913453911yescharacteristic
594C2#1913455411yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3482C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3482D43
hypocenterC43#8442
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #19135573C2semidirect
2. C4×#13063252C2semidirect
3. C4×#13063252C2semidirect
4. #19133190C2semidirect
5. #19133034C2semidirect
6. #19133034C2semidirect
22. C43×#557C4semidirect
24. C43×#556C4semidirect
27. D4×Q8×C43C4semidirect
30. C43×#547C4semidirect
217. Q8×C43#104semidirect
224. D4×C43#104semidirect
305. #557Dic43semidirect
307. #556Dic43semidirect
310. D4×Q8Dic43semidirect
313. #547Dic43semidirect
336. C43#8442semidirect
515. Q8#13063252semidirect
522. D4#13063252semidirect

Maximal subgroups

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

subgroupindex
#191355732
C4×#130632522
#191331902
#191330342
C43×#34822
#844243