Finite Group Databasebeta

← #25251070

Subgroups — #25251070

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583335C211yesmaximal, characteristic, complemented
2C22×#13063265C211yesmaximal, characteristic, complemented
3#19144176C211yesmaximal, characteristic, complemented
4#19136706C212yesmaximal, complemented
5#19136696C212yesmaximal, complemented
6#19136689C212yesmaximal, complemented
7#19136679C212yesmaximal, complemented
8#19136381C211yesmaximal, characteristic, complemented
9#19136311C211yesmaximal, characteristic, complemented
10#19136305C211yesmaximal, characteristic, complemented
11C2×C43×#466C211yesmaximal, characteristic, complemented
12C2×#13063347C2211yescharacteristic
13#14583410—21no—
14#14583335—24no—
15C2×#13063269C2212yescomplemented
16C2×#13063266C2212yescomplemented
17C2×#13063265—24no—
18C2×#13063265C2211yescharacteristic
19C2×#13063265C2211yescharacteristic
20C2×#13063265C2212yescomplemented
21C22×C43⋊C16C2212yescomplemented
22#14583140C2211yescharacteristic, complemented
23#14583140C2211yescharacteristic, complemented
24#14583135C2211yescharacteristic, complemented
25#14583135C2211yescharacteristic, complemented
26#14583128—21no—
27#14583128—21no—
28#14582937C2211yescharacteristic
29#14582896—21no—
30#14582726C2212yescomplemented
31#14582724C2212yescomplemented
32#14582702C2212yescomplemented
33#14582700C2212yescomplemented
34#14582700C2212yescomplemented
35#14582699C2212yescomplemented
36C22×D8×C43C2211yescharacteristic
37C23×C8×C43C2211yescharacteristic
38C2×#121×C43—21no—
39C43×#466—21no—
40C43×#466—21no—
41C43×#466C2212yes—
42C43×#466C2212yes—
43C2×#107×C43C2211yescharacteristic
44C2×#102×C43—21no—
45C2×#10621898—21no—
46#13063347—22no—
47#13063347—22no—
48C2×Dic172C2311yescharacteristic
49C2×#10621873—21no—
50C2×D344C2311yescharacteristic
51#13063308—41no—
52#13063304—21no—
53#13063304—21no—
54#13063299—21no—
55#13063299—21no—
56#13063294—41no—
57C4×C22⋊D43—41no—
58C4×C22⋊D43—41no—
59#13063284—21no—
60#13063269—24no—
61#13063266—24no—
62#13063265—22no—
63#13063265—24no—
64#13063265D414yescomplemented
65C2×C43⋊C16—24no—
66C2×C43⋊C16C2312yes—
67C2×C43⋊C16C2312yes—
68#13063259C2311yescharacteristic
69#13063259C2311yescharacteristic
70#13063257—21no—
71#13063250—21no—
72#13063250—21no—
73#13063247—21no—
74#13063247—21no—
75C22×D4×C43—21no—
76C22×D4×C43—41no—
77C23×C4×C43D411yescharacteristic
78C2×D8×C43—22no—
79C2×D8×C43—21no—
80C2×D8×C43—22no—
81C2×D8×C43C2312yes—
82C22×C8×C43—22no—
83C22×C8×C43—22no—
84C22×C8×C43D411yescharacteristic
85C22×C8×C43D411yescharacteristic
86C22×C8×C43D411yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—41no—
93#121×C43—41no—
94C2×C4⋊C4×C43—21no—
95C2×C22⋊C4×C43—41no—
96#107×C43—21no—
97#107×C43C2312yes—
98#102×C43—22no—
99#102×C43—22no—
100C24×C43—41no—
101C24×C43D811yescharacteristic
102C2×D4×C43—22no—
103C2×D4×C43—41no—
104C2×D4×C43—42no—
105C2×D4×C43—42no—
106C2×D4×C43—42no—
107C2×D4×C43—42no—
108C2×D4×C43—84no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—41no—
112C22×C4×C43D811yescharacteristic
113C22×C4×C43D811yescharacteristic
114C22×C4×C43D811yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121#10621898—42no—
122#10621898—42no—
123C2×D172—21no—
124C2×C4×D43—41no—
125C2×Dic86—21no—
126D8×C43—22no—
127D8×C43—22no—
128D8×C43—42no—
129C2×C8×C43—22no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—21no—
133C2×C8×C43—21no—
134C2×C8×C43—21no—
135C2×C8×C43—21no—
136C2×C8×C43C2×D412yes—
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43#4112yes—
141C2×C8×C43C2411yescharacteristic
142C4⋊C4×C43—22no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—42no—
145C22⋊C4×C43—42no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155C4×Dic43—41no—
156Dic172—21no—
157Dic172—21no—
158D344—21no—
159D344—21no—
160#10621873—42no—
161C43⋊C16—22no—
162C43⋊C16C2×D414yescomplemented
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—41no—
166C23×C43—42no—
167C23×C43—82no—
168C23×C43—82no—
169C23×C43—82no—
170C23×C43C2×D811yescharacteristic
171C23×C43C2×D811yescharacteristic
172C23×C43C2×D811yescharacteristic
173C22×D43—41no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—84no—
177D4×C43—84no—
178D4×C43—82no—
179C2×C4×C43—22no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—42no—
187C2×C4×C43—82no—
188C2×C4×C43#12112yes—
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43#13512yes—
193C2×C4×C43C22×D411yescharacteristic
194C22⋊D43—82no—
195C22⋊D43—82no—
196C22⋊D43—82no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200D172—41no—
201D172—41no—
202C4×D43—82no—
203Dic86—41no—
204Dic86—41no—
205C8×C43—21no—
206C8×C43—21no—
207C8×C43#12112yes—
208C8×C43C22×D411yescharacteristic
209C8×C43C2×#4111yescharacteristic
210#33605—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—44no—
219C22×C43—82no—
220C22×C43—82no—
221C22×C43—82no—
222C22×C43—164no—
223C22×C43#46612yes—
224C22×C43#50912yescomplemented
225C22×C43C22×D811yescharacteristic
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—82no—
232C4×C43#46612yes—
233C4×C43C2×#12111yescharacteristic
234C4×C43C2×#13511yescharacteristic
235Dic43—81no—
236Dic43—81no—
237Dic43—81no—
238C2×#509—431no—
239C22×M32—431no—
240#3050—431no—
241C2×#466D4311yescharacteristic, complemented
242#2220—432no—
243#2218—432no—
244#2217—432no—
245#2215—432no—
246#2159—431no—
247#2140—431no—
248#2139—431no—
249C2×C43—22no—
250C2×C43—22no—
251C2×C43—41no—
252C2×C43—162no—
253C2×C43C2×#46611yescharacteristic
254C2×C43C2×#50911yescharacteristic
255C2×C43#341411yescharacteristic
256D43—161no—
257C2×#135—431no—
258C22×D8C2×D4311yescharacteristic
259C23×C8C2×D4311yescharacteristic
260#525—861no—
261C2×#121—21no—
262#509—864no—
263C2×SD32—432no—
264C2×D16—432no—
265C2×M32—431no—
266C2×M32—431no—
267C2×M32—432no—
268C2×M32—864no—
269C22×C16—432no—
270#467—431no—
271#467—431no—
272#466—21no—
273#466—21no—
274#466—431no—
275#466—431no—
276#466C2×D4312yes—
277#466C2×D4312yes—
278#465—861no—
279#465—861no—
280#427—431no—
281C2×#107C2×D4311yescharacteristic
282#416—861no—
283C2×#102—21no—
284#367—432no—
285#366—432no—
286#358—432no—
287#357—432no—
288#357—432no—
289#357—432no—
290C43#3360511yescharacteristic, complemented, Sylow
291C2×#41—861no—
292C22×D4—21no—
293C22×D4—41no—
294C23×C4C22⋊D4311yescharacteristic
295#135—862no—
296#135—862no—
297C2×Q16—431no—
298C2×SD16—861no—
299C2×D8—22no—
300C2×D8—22no—
301C2×D8—21no—
302C2×D8—431no—
303C2×D8C22×D4312yes—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8C22⋊D4311yescharacteristic
307C22×C8C22⋊D4311yescharacteristic
308C22×C8C22⋊D4311yescharacteristic
309C22×C8C22×D4311yescharacteristic
310C22×C8C22×D4311yescharacteristic
311C22×C8C22×D4311yescharacteristic
312#123—1721no—
313C22⋊Q8—861no—
314C22⋊Q8—861no—
315#121—22no—
316#121—22no—
317#121—41no—
318#121—41no—
319#121—861no—
320#121—861no—
321#120—1721no—
322C4×D4—1721no—
323C4×D4—1721no—
324#117—861no—
325C2×C4⋊C4—21no—
326C2×C22⋊C4—41no—
327SD32—864no—
328D16—864no—
329M32—434no—
330M32—864no—
331M32—862no—
332C2×C16—432no—
333C2×C16—432no—
334C2×C16—864no—
335#107—21no—
336#107—431no—
337#107—431no—
338#107C22×D4312yes—
339#106—861no—
340#103—861no—
341#103—861no—
342#102—22no—
343#102—22no—
344#102—861no—
345#102—861no—
346C24—41no—
347C24#1062188211yescharacteristic
348#41—1722no—
349#41—1722no—
350C2×Q8—861no—
351C2×D4—22no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—84no—
358C2×D4—861no—
359C2×D4—1721no—
360C2×D4—1721no—
361C2×D4—1721no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—41no—
365C22×C4—1721no—
366C22×C4#1062188211yescharacteristic
367C22×C4#1062188211yescharacteristic
368C22×C4#1062188211yescharacteristic
369C22×C4C2×C22⋊D4311yescharacteristic
370C22×C4C2×C22⋊D4311yescharacteristic
371C22×C4C2×C22⋊D4311yescharacteristic
372Q16—861no—
373Q16—861no—
374SD16—1722no—
375D8—22no—
376D8—22no—
377D8—42no—
378D8—861no—
379D8—861no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8D4×D4312yes—
388C2×C8#1062190012yes—
389C2×C8C2×C22⋊D4311yescharacteristic
390C2×C8C2×C22⋊D4311yescharacteristic
391C2×C8C2×C22⋊D4311yescharacteristic
392C2×C8C23×D4311yescharacteristic
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—861no—
396C4⋊C4—861no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C42—1721no—
407C16—434no—
408C16—862no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—42no—
413C23—82no—
414C23—82no—
415C23—82no—
416C23—1721no—
417C23C2×#1062188211yescharacteristic
418C23C2×#1062188211yescharacteristic
419C23C2×#1062188211yescharacteristic
420Q8—1721no—
421Q8—1721no—
422D4—42no—
423D4—42no—
424D4—84no—
425D4—84no—
426D4—82no—
427D4—3442no—
428D4—3442no—
429D4—3442no—
430D4—1721no—
431D4—1721no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—3442no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4#1306329712yes—
446C2×C4C2×#1062188211yescharacteristic
447C2×C4C2×#1062188211yescharacteristic
448C2×C4C2×#1062188211yescharacteristic
449C2×C4#1306334512yes—
450C2×C4C22×C22⋊D4311yescharacteristic
451C8—21no—
452C8—21no—
453C8#1306329712yes—
454C8C2×D4×D4311yescharacteristic
455C8C2×#1062190011yescharacteristic
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22#1458313312yes—
472C22#1458333512yescomplemented
473C22C22×#1062188211yescharacteristic
474C4—21no—
475C4—21no—
476C4—82no—
477C4—3441no—
478C4—3441no—
479C4—3441no—
480C4#1458313312yes—
481C4C2×#1306329711yescharacteristic
482C4C2×#1306334511yescharacteristic
483C2—22no—
484C2—22no—
485C2—41no—
486C2—162no—
487C2—6881no—
488C2C2×#1458313311yescharacteristic
489C2C2×#1458333511yescharacteristic
490C2#1914772911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#466C2
socleC22×C43C22×D8
hypercenterC2×#466D43
hypocenterC43#33605
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#14583335C2semidirect
2. C22×#13063265C2semidirect
3. #19144176C2semidirect
4. #19136706C2semidirect
5. #19136696C2semidirect
6. #19136689C2semidirect
7. #19136679C2semidirect
8. #19136381C2semidirect
9. #19136311C2semidirect
10. #19136305C2semidirect
11. C2×C43×#466C2semidirect
15. C2×#13063269C22semidirect
16. C2×#13063266C22semidirect
20. C2×#13063265C22semidirect
21. C22×C43⋊C16C22semidirect
22. #14583140C22semidirect
23. #14583140C22semidirect
24. #14583135C22semidirect
25. #14583135C22semidirect
30. #14582726C22semidirect
31. #14582724C22semidirect
32. #14582702C22semidirect
33. #14582700C22semidirect
34. #14582700C22semidirect
35. #14582699C22semidirect
64. #13063265D4semidirect
162. C43⋊C16C2×D4semidirect
224. C22×C43#509semidirect
241. C2×#466D43semidirect
290. C43#33605semidirect
472. C22#14583335semidirect

Maximal subgroups

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

subgroupindex
C2×#145833352
C22×#130632652
#191441762
#191367062
#191366962
#191366892
#191366792
#191363812
#191363112
#191363052
C2×C43×#4662
#3360543