Finite Group Databasebeta

← #25153186

Subgroups — #25153186

Order 11008.

1406 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139088C212yesmaximal, complemented
2#19138912C211yesmaximal, characteristic, complemented
3#19135843C214yesmaximal, complemented
4#19135432C212yesmaximal, complemented
5#19134543C214yesmaximal, complemented
6C4×#13063240C211yesmaximal, characteristic, complemented
7C43×#3496C211yesmaximal, characteristic
8C22×C4⋊Dic43C2211yescharacteristic, complemented
9C2×#13063240C2212yes—
10C2×#13063240C2218yescomplemented
11#14582838—21no—
12#14582835—21no—
13#14582824—24no—
14#14582802—22no—
15#14582797—21no—
16#14582779C2212yes—
17#14582779C2218yescomplemented
18#14582771C2212yescomplemented
19#14582764—22no—
20#14582759—21no—
21#14582759C2211yescharacteristic, complemented
22C4×C22⋊Dic43C2212yescomplemented
23#14582666C2212yescomplemented
24C2×H(5,𝔽2)×C43C2212yes—
25C43×#547—22no—
26C43×#546—24no—
27D42×C43—22no—
28C43×#537—21no—
29C43×#534—21no—
30C43×#534C2212yes—
31C43×#532—21no—
32C2×#121×C43—21no—
33C2×#121×C43C2212yes—
34C2×C4×D4×C43C2211yescharacteristic
35C23×Dic43C2312yes—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—22no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43—21no—
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—28no—
43C2×C22⋊Dic43—22no—
44C2×C22⋊Dic43C2314yes—
45C2×C22⋊Dic43C2312yes—
46C2×C4×Dic43—22no—
47#13063240—24no—
48#13063240—48no—
49C43⋊#95—22no—
50C43⋊#95—22no—
51C43⋊#95—28no—
52C43⋊#95—21no—
53C43⋊#95—22no—
54H(5,𝔽2)×C43—28no—
55H(5,𝔽2)×C43—44no—
56C2×#41×C43—22no—
57C2×#41×C43—24no—
58C22×D4×C43—22no—
59C22×D4×C43—24no—
60C22×D4×C43—21no—
61C22×D4×C43D412yes—
62C22×D4×C43C2314yes—
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C4⋊Q8×C43—21no—
67#127×C43—21no—
68#124×C43—22no—
69#123×C43—24no—
70#123×C43—24no—
71C22⋊Q8×C43—24no—
72#121×C43—22no—
73#121×C43—22no—
74#121×C43—24no—
75#121×C43—22no—
76#121×C43—22no—
77#121×C43—22no—
78#121×C43—22no—
79#121×C43—22no—
80#121×C43—22no—
81#120×C43—24no—
82#120×C43—24no—
83C4×D4×C43—22no—
84C4×D4×C43—22no—
85C4×D4×C43—22no—
86C4×D4×C43—22no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43D411yescharacteristic
89C2×C4⋊C4×C43D412yes—
90C2×C22⋊C4×C43—22no—
91C2×C22⋊C4×C43D411yescharacteristic
92C2×C22⋊C4×C43D414yes—
93C2×C22⋊C4×C43C2311yescharacteristic
94C2×C42×C43D411yescharacteristic
95C24×C43—22no—
96C24×C43C2×D414yes—
97C24×C43C2×D411yescharacteristic
98C24×C43C2411yescharacteristic
99#41×C43—416no—
100#41×C43—44no—
101#41×C43—44no—
102C2×Q8×C43—22no—
103C2×D4×C43—24no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—24no—
111C2×D4×C43—24no—
112C2×D4×C43—28no—
113C2×D4×C43—22no—
114C2×D4×C43—28no—
115C2×D4×C43—416no—
116C2×D4×C43—44no—
117C2×D4×C43—44no—
118C2×D4×C43—44no—
119C2×D4×C43—82no—
120C2×D4×C43#4114yes—
121C22×C4×C43—22no—
122C22×C4×C43—24no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43C2×D414yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×Dic43—24no—
136C22×Dic43—22no—
137C22×Dic43—24no—
138C22×Dic43—22no—
139C22×Dic43—82no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C22⋊C4×C43—24no—
146C22⋊C4×C43—24no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—24no—
150C22⋊C4×C43—22no—
151C42×C43—21no—
152C42×C43—21no—
153C22⋊Dic43—24no—
154C22⋊Dic43—24no—
155C22⋊Dic43—24no—
156C22⋊Dic43—82no—
157C22⋊Dic43—88no—
158C4⋊Dic43—42no—
159C4⋊Dic43—41no—
160C4⋊Dic43—42no—
161C4⋊Dic43—41no—
162Dic43⋊C4—82no—
163C4×Dic43—44no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—24no—
167C23×C43—28no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—41no—
171C23×C43—41no—
172C23×C43—44no—
173C23×C43—44no—
174C23×C43—44no—
175C23×C43—82no—
176C23×C43—82no—
177C23×C43#12412yes—
178C23×C43C22×D411yescharacteristic
179C23×C43C22×D412yes—
180C23×C43C2×#4112yes—
181C23×C43H(5,𝔽2)12yes—
182Q8×C43—44no—
183D4×C43—28no—
184D4×C43—44no—
185D4×C43—48no—
186D4×C43—44no—
187D4×C43—44no—
188D4×C43—48no—
189D4×C43—44no—
190D4×C43—82no—
191D4×C43—82no—
192D4×C43—82no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—24no—
196C2×C4×C43—22no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—24no—
200C2×C4×C43—28no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—48no—
204C2×C4×C43—44no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—81no—
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12012yes—
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12412yes—
213C2×Dic43—44no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—44no—
218C2×Dic43—48no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—44no—
223#25900—431nomaximal, Sylow
224C22×C43—22no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—21no—
228C22×C43—22no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—44no—
235C22×C43—44no—
236C22×C43—44no—
237C22×C43—81no—
238C22×C43—88no—
239C22×C43—164no—
240C22×C43C2×#12011yescharacteristic
241C22×C43C2×#12411yescharacteristic
242C22×C43#53511yescharacteristic
243C22×C43#54614yes—
244C4×C43—22no—
245C4×C43—21no—
246C4×C43—22no—
247C4×C43—44no—
248C4×C43—41no—
249C4×C43—41no—
250C4×C43#45812yes—
251Dic43—82no—
252Dic43—84no—
253Dic43—82no—
254#3496D4311yescharacteristic
255#2504—432no—
256#2487—431no—
257#2044—434no—
258#1964—432no—
259#1790—434no—
260C4×#99—431no—
261C2×C43—21no—
262C2×C43—24no—
263C2×C43—21no—
264C2×C43—42no—
265C2×C43—84no—
266C2×C43#243511yescharacteristic
267C2×C43C2×#45811yescharacteristic
268C2×C43#302711yescharacteristic
269C2×H(5,𝔽2)C2×D4312yes—
270#547—22no—
271#546—24no—
272D42—22no—
273#537—21no—
274#534—21no—
275#534C2×D4312yes—
276#532—21no—
277C2×#121—21no—
278C2×#121C2×D4312yes—
279C2×C4×D4C2×D4311yescharacteristic
280C22×C4⋊C4—431no—
281C2×#99—432no—
282C2×#99—438no—
283#400—861no—
284#399—861no—
285#397—864no—
286#390—862no—
287#389—861no—
288#386—432no—
289#386—438no—
290#385—432no—
291#382—862no—
292#380—431no—
293#380—861no—
294C4×C22⋊C4—432no—
295#342—432no—
296C43#2590011yescharacteristic, complemented, Sylow
297H(5,𝔽2)—28no—
298H(5,𝔽2)—44no—
299C2×#41—22no—
300C2×#41—24no—
301C22×D4—22no—
302C22×D4—24no—
303C22×D4—21no—
304C22×D4C22⋊D4312yes—
305C22×D4C22×D4314yes—
306C22×D4C22×D4311yescharacteristic
307C23×C4—432no—
308C23×C4C22⋊D4311yescharacteristic
309C23×C4C22×D4311yescharacteristic
310C4⋊Q8—21no—
311#127—21no—
312#124—22no—
313#123—24no—
314#123—24no—
315C22⋊Q8—24no—
316#121—22no—
317#121—22no—
318#121—24no—
319#121—22no—
320#121—22no—
321#121—22no—
322#121—22no—
323#121—22no—
324#121—22no—
325#120—24no—
326#120—24no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—862no—
333C2×C4⋊C4—861no—
334C2×C4⋊C4—862no—
335C2×C4⋊C4—862no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4C22⋊D4311yescharacteristic
339C2×C4⋊C4C22⋊D4312yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—434no—
342C2×C22⋊C4—432no—
343C2×C22⋊C4—862no—
344C2×C22⋊C4—868no—
345C2×C22⋊C4C22⋊D4311yescharacteristic
346C2×C22⋊C4C22⋊D4314yes—
347C2×C22⋊C4C22×D4311yescharacteristic
348C2×C42—862no—
349C2×C42C22⋊D4311yescharacteristic
350#99—864no—
351#99—1728no—
352#95—862no—
353#95—861no—
354#95—862no—
355#95—868no—
356#95—862no—
357C24—22no—
358C24C2×C22⋊D4314yes—
359C24C2×C22⋊D4311yescharacteristic
360C24C23×D4311yescharacteristic
361#41—416no—
362#41—44no—
363#41—44no—
364C2×Q8—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—24no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—28no—
372C2×D4—28no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—44no—
378C2×D4—416no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—82no—
382C2×D4#1062190014yes—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—864no—
390C22×C4—862no—
391C22×C4—864no—
392C22×C4—862no—
393C22×C4—3442no—
394C22×C4C2×C22⋊D4314yes—
395C22×C4C2×C22⋊D4312yes—
396C22×C4C2×C22⋊D4311yescharacteristic
397C22×C4C2×C22⋊D4311yescharacteristic
398C22×C4C2×C22⋊D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400C22×C4C2×C22⋊D4312yes—
401C22×C4C2×C22⋊D4311yescharacteristic
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—3442no—
408C4⋊C4—1722no—
409C4⋊C4—1721no—
410C4⋊C4—1722no—
411C4⋊C4—1721no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—24no—
418C22⋊C4—864no—
419C22⋊C4—864no—
420C22⋊C4—864no—
421C22⋊C4—3448no—
422C22⋊C4—3442no—
423C42—21no—
424C42—21no—
425C42—1724no—
426C23—21no—
427C23—21no—
428C23—24no—
429C23—28no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—82no—
438C23—82no—
439C23#1306331212yes—
440C23C22×C22⋊D4311yescharacteristic
441C23C22×C22⋊D4312yes—
442C23C2×#1062190012yes—
443C23#1306337012yes—
444Q8—44no—
445D4—28no—
446D4—44no—
447D4—48no—
448D4—44no—
449D4—44no—
450D4—48no—
451D4—44no—
452D4—82no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—24no—
462C2×C4—28no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—48no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—1724no—
472C2×C4—1724no—
473C2×C4—1722no—
474C2×C4—1722no—
475C2×C4—1728no—
476C2×C4—1722no—
477C2×C4—1722no—
478C2×C4—1722no—
479C2×C4—1722no—
480C2×C4—1724no—
481C2×C4#1306329411yescharacteristic
482C2×C4#1306329412yes—
483C2×C4#1306329411yescharacteristic
484C2×C4#1306331212yes—
485C22—21no—
486C22—22no—
487C22—21no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—81no—
499C22—88no—
500C22—164no—
501C22C2×#1306329411yescharacteristic
502C22C2×#1306331211yescharacteristic
503C22#1458346611yescharacteristic
504C22#1458354314yes—
505C4—21no—
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—44no—
511C4—3442no—
512C4—3444no—
513C4—3442no—
514C4#1458308912yes—
515C2—21no—
516C2—24no—
517C2—21no—
518C2—42no—
519C2—84no—
520C2#1913824211yescharacteristic
521C2C2×#1458308911yescharacteristic
522C2#1914399711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
Fitting, prime radicalC43×#3496C2
socleC22×C43C2×#120
hypercenter#3496D43
hypocenterC43#25900
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #19139088C2semidirect
2. #19138912C2semidirect
3. #19135843C2semidirect
4. #19135432C2semidirect
5. #19134543C2semidirect
6. C4×#13063240C2semidirect
8. C22×C4⋊Dic43C22semidirect
10. C2×#13063240C22semidirect
17. #14582779C22semidirect
18. #14582771C22semidirect
21. #14582759C22semidirect
22. C4×C22⋊Dic43C22semidirect
23. #14582666C22semidirect
296. C43#25900semidirect

Maximal subgroups

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

subgroupindex
#191390882
#191389122
#191358432
#191354322
#191345432
C4×#130632402
C43×#34962
#2590043