Finite Group Databasebeta

← #24988390

Subgroups — #24988390

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135394C211yesmaximal, characteristic, complemented
2C4×#13063242C211yesmaximal, characteristic, complemented
3#19133183C212yesmaximal, complemented
4#19133008C212yesmaximal, complemented
5C43×#3459C211yesmaximal, characteristic
6C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
7C2×#13063242—21no—
8C2×C22⋊(C43⋊C8)—21no—
9C2×C22⋊(C43⋊C8)—21no—
10C4×#10621877C2212yescomplemented
11C2×#13063236C2211yescharacteristic, complemented
12#14582668—21no—
13#14582641—22no—
14#14582639—22no—
15Q8⋊(C43⋊C8)—22no—
16D4⋊(C43⋊C8)—22no—
17C43×#543C411yescharacteristic
18C43×#539—22no—
19C43×#539—21no—
20C43×#538—22no—
21C43×#538C412yes—
22C43×#534—21no—
23C43×#534C411yescharacteristic
24C43×#529—22no—
25C43×#529C2212yes—
26C43×#525—21no—
27C43×#525—22no—
28C2×C4×D4×C43—21no—
29C2×C4×D4×C43C2211yescharacteristic
30C2×#10621877—22no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C4⋊(C43⋊C8)—22no—
34#13063242—24no—
35C22⋊(C43⋊C8)—42no—
36C22⋊(C43⋊C8)—42no—
37#13063236—22no—
38#13063236—22no—
39C4×C43⋊C8—22no—
40C2×#41×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43D411yescharacteristic
43C23×C4×C43—21no—
44C23×C4×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46#126×C43—22no—
47#126×C43—22no—
48#126×C43—22no—
49#125×C43—22no—
50#125×C43D412yes—
51#124×C43—22no—
52#124×C43D412yes—
53#123×C43—22no—
54#123×C43—22no—
55#123×C43—22no—
56#123×C43—22no—
57#123×C43—22no—
58#123×C43—22no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43C2×C412yes—
65#121×C43—22no—
66#121×C43—21no—
67#121×C43—22no—
68#121×C43—22no—
69#121×C43—21no—
70#121×C43C2×C412yes—
71#120×C43—22no—
72#120×C43—22no—
73#120×C43—22no—
74C4×Q8×C43D412yes—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43—22no—
80C4×D4×C43—22no—
81C4×D4×C43—22no—
82C4×D4×C43D412yes—
83#117×C43—21no—
84#117×C43—22no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43C2×C411yescharacteristic
90C2×C22⋊C4×C43C2×C411yescharacteristic
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C24×C43—21no—
94C24×C43C22⋊C411yescharacteristic
95C24×C43C22⋊C411yescharacteristic
96#41×C43—81no—
97#41×C43—81no—
98C2×Q8×C43—21no—
99C2×Q8×C43C22⋊C412yes—
100C2×D4×C43—22no—
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43—21no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—41no—
108C2×D4×C43—42no—
109C2×D4×C43—42no—
110C2×D4×C43C22⋊C412yes—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—81no—
125C22×C4×C43—81no—
126C22×C4×C43C22⋊C411yescharacteristic
127C22×C4×C43C22⋊C411yescharacteristic
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C4⋊C4×C43—22no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43C22⋊C412yes—
141C4⋊C4×C43C22⋊C412yes—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—22no—
154C42×C43—22no—
155C42×C43—22no—
156C42×C43C2×D412yes—
157C42×C43C2×D412yes—
158#10621877—24no—
159#10621877—42no—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—41no—
162C2×C43⋊C8—42no—
163C2×C43⋊C8—41no—
164C2×C43⋊C8—41no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—41no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—22no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—42no—
178C23×C43—81no—
179C23×C43—81no—
180C23×C43#10412yes—
181C23×C43C2×C22⋊C411yescharacteristic
182Q8×C43—42no—
183Q8×C43—81no—
184D4×C43—44no—
185D4×C43—42no—
186D4×C43—44no—
187D4×C43—42no—
188D4×C43—42no—
189D4×C43—82no—
190D4×C43—81no—
191D4×C43—82no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—81no—
212C2×C4×C43—81no—
213C2×C4×C43—81no—
214C2×C4×C43—82no—
215C2×C4×C43—81no—
216C2×C4×C43C2×C22⋊C412yes—
217C2×C4×C43#12012yes—
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C43⋊C8—42no—
221C43⋊C8—44no—
222C43⋊C8—81no—
223#8401—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—42no—
233C22×C43—41no—
234C22×C43—42no—
235C22×C43—41no—
236C22×C43—42no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—84no—
240C22×C43#37911yescharacteristic
241C22×C43C2×#10411yescharacteristic
242C22×C43#42111yescharacteristic
243C4×C43—21no—
244C4×C43—22no—
245C4×C43—22no—
246C4×C43—41no—
247C4×C43—41no—
248C4×C43—42no—
249C4×C43—42no—
250C4×C43—42no—
251C4×C43#45311yescharacteristic
252C4×C43#45511yescharacteristic
253#3459D4311yescharacteristic
254#1955—431no—
255C4×#100—431no—
256#1524—432no—
257#1483—432no—
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—42no—
261C2×C43—81no—
262C2×C43—82no—
263C2×C43#178911yescharacteristic
264C2×C43#179111yescharacteristic
265C2×C43#179211yescharacteristic
266#543Dic4311yescharacteristic
267#539—22no—
268#539—21no—
269#538—22no—
270#538Dic4312yes—
271#534—21no—
272#534Dic4311yescharacteristic
273#529—22no—
274#529C2×D4312yes—
275#525—21no—
276#525—22no—
277C2×C4×D4—21no—
278C2×C4×D4C2×D4311yescharacteristic
279C2×C4⋊C8—431no—
280C2×#100—861no—
281C2×C22⋊C8—861no—
282C2×C22⋊C8—861no—
283C4×M16—432no—
284C2×#97—431no—
285#343—861no—
286#330—862no—
287#329—862no—
288Q8⋊C8—862no—
289D4⋊C8—862no—
290C43#840111yescharacteristic, complemented, Sylow
291C2×#41—21no—
292C22×D4—21no—
293C22×D4C22⋊D4311yescharacteristic
294C23×C4—21no—
295C23×C4C22⋊D4311yescharacteristic
296C23×C4C22⋊D4311yescharacteristic
297C2×M16—862no—
298C22×C8—861no—
299C22×C8—861no—
300#126—22no—
301#126—22no—
302#126—22no—
303#125—22no—
304#125C22⋊D4312yes—
305#124—22no—
306#124C22⋊D4312yes—
307#123—22no—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—22no—
313C22⋊Q8—21no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—21no—
317C22⋊Q8—22no—
318C22⋊Q8C2×Dic4312yes—
319#121—22no—
320#121—21no—
321#121—22no—
322#121—22no—
323#121—21no—
324#121C2×Dic4312yes—
325#120—22no—
326#120—22no—
327#120—22no—
328C4×Q8C22⋊D4312yes—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4C22⋊D4312yes—
337#117—21no—
338#117—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C22⋊D4311yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4C2×Dic4311yescharacteristic
344C2×C22⋊C4C2×Dic4311yescharacteristic
345C2×C42—21no—
346C2×C42C22×D4311yescharacteristic
347C4⋊C8—862no—
348#100—864no—
349C22⋊C8—1722no—
350C22⋊C8—1722no—
351#97—862no—
352#97—862no—
353C4×C8—862no—
354C24—21no—
355C24C22⋊Dic4311yescharacteristic
356C24C22⋊Dic4311yescharacteristic
357#41—81no—
358#41—81no—
359C2×Q8—21no—
360C2×Q8C22⋊Dic4312yes—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—41no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4C22⋊Dic4312yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4C22⋊Dic4311yescharacteristic
388C22×C4C22⋊Dic4311yescharacteristic
389C22×C4C22×Dic4311yescharacteristic
390C22×C4C2×C22⋊D4311yescharacteristic
391C22×C4C2×C22⋊D4311yescharacteristic
392M16—864no—
393M16—1722no—
394C2×C8—862no—
395C2×C8—1721no—
396C2×C8—1721no—
397C2×C8—1721no—
398C2×C8—1721no—
399C2×C8—1722no—
400C2×C8—1721no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4C22⋊Dic4312yes—
411C4⋊C4C22⋊Dic4312yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C42—22no—
425C42—22no—
426C42C2×C22⋊D4312yes—
427C42C2×C22⋊D4312yes—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—22no—
433C23—21no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—42no—
439C23—81no—
440C23—81no—
441C23#1306325212yes—
442C23C2×C22⋊Dic4311yescharacteristic
443Q8—42no—
444Q8—81no—
445D4—44no—
446D4—42no—
447D4—44no—
448D4—42no—
449D4—42no—
450D4—81no—
451D4—82no—
452D4—82no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—82no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4C2×C22⋊Dic4312yes—
478C2×C4#1306329412yes—
479C2×C4#1306329411yescharacteristic
480C2×C4#1306329411yescharacteristic
481C8—3441no—
482C8—1722no—
483C8—1724no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—42no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—84no—
500C22#1458275511yescharacteristic
501C22C2×#1306325211yescharacteristic
502C22#1458291611yescharacteristic
503C4—22no—
504C4—22no—
505C4—21no—
506C4—42no—
507C4—42no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4#1458306711yescharacteristic
512C4#1458307711yescharacteristic
513C2—21no—
514C2—21no—
515C2—42no—
516C2—81no—
517C2—82no—
518C2#1913453911yescharacteristic
519C2#1913454611yescharacteristic
520C2#1913454911yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3459C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3459D43
hypocenterC43#8401
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #19135394C2semidirect
2. C4×#13063242C2semidirect
3. #19133183C2semidirect
4. #19133008C2semidirect
6. C2×C4⋊(C43⋊C8)C22semidirect
10. C4×#10621877C22semidirect
11. C2×#13063236C22semidirect
290. C43#8401semidirect

Maximal subgroups

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

subgroupindex
#191353942
C4×#130632422
#191331832
#191330082
C43×#34592
#840143