Finite Group Databasebeta

← #24995775

Subgroups — #24995775

Order 11008.

460 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135540C211yesmaximal, characteristic, complemented
2#19135515C211yesmaximal, characteristic
3C4×#13063259C211yesmaximal, characteristic, complemented
4#19133094C211yesmaximal, characteristic, complemented
5#19133090C211yesmaximal, characteristic
6#19132884C211yesmaximal, characteristic, complemented
7C43×#3167C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9C2×#13063259—21no—
10C2×#13063252—22no—
11C4×#10621877C2211yescharacteristic
12C4×C4⋊Dic43C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582662—21no—
15#14582658—22no—
16#14582636—22no—
17#14582633—22no—
18#14582621—21no—
19#14582620—21no—
20C43×#533C2211yescharacteristic
21C43×#532C2211yescharacteristic
22C43×#498C411yescharacteristic, complemented
23C43×#492C411yescharacteristic, complemented
24C43×#487C411yescharacteristic, complemented
25C43×#486C411yescharacteristic, complemented
26C43×#465—21no—
27C43×#465—21no—
28C4×SD16×C43—21no—
29C4×SD16×C43—21no—
30C2×C4×C8×C43C2211yescharacteristic
31C2×#10621877D412yes—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36#13063259—24no—
37C4⋊(C43⋊C8)—21no—
38#13063252—44no—
39C22⋊(C43⋊C8)D412yes—
40#13063236—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C2×#41×C43—21no—
46C2×SD16×C43—21no—
47C2×SD16×C43—21no—
48C22×C8×C43D411yescharacteristic
49C22×C8×C43D411yescharacteristic
50C4⋊Q8×C43C2×C411yescharacteristic
51C4⋊Q8×C43C2×C411yescharacteristic
52C4⋊Q8×C43C2×C411yescharacteristic
53#127×C43C2×C411yescharacteristic
54#125×C43—21no—
55#124×C43—21no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43—21no—
58#121×C43—21no—
59#121×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64#117×C43—21no—
65C2×C42×C43C2311yescharacteristic
66#106×C43—21no—
67#106×C43—21no—
68#103×C43—21no—
69#103×C43—21no—
70#102×C43—21no—
71#102×C43—21no—
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C4×C8×C43D411yescharacteristic
76#41×C43—42no—
77#41×C43—42no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—41no—
90C22×Dic43—41no—
91SD16×C43—42no—
92SD16×C43—42no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43#4111yescharacteristic
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4×Dic43—42no—
120C4×Dic43—42no—
121#10621877—22no—
122#10621877—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C23×C43—41no—
126C23×C43#12711yescharacteristic
127Q8×C43—41no—
128Q8×C43—41no—
129Q8×C43—42no—
130Q8×C43—81no—
131D4×C43—41no—
132D4×C43—41no—
133D4×C43—42no—
134D4×C43—81no—
135D4×C43—81no—
136D4×C43—81no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—82no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12411yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)12yes—
151C2×C4×C43#13712yes—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C8×C43—21no—
159C8×C43—21no—
160C8×C43—21no—
161C8×C43#10412yescomplemented
162C43⋊C8—42no—
163C43⋊C8—42no—
164#9722—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43#39011yescharacteristic
171C22×C43#49611yescharacteristic
172C22×C43#49711yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—81no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43C2×#10411yescharacteristic
180C4×C43#42111yescharacteristic
181C4×C43#44012yes—
182C4×C43#46812yes—
183Dic43—82no—
184Dic43—82no—
185#3167D4311yescharacteristic
186#1986—431no—
187#1980—431no—
188C4×#107—431no—
189#1503—431no—
190#1502—431no—
191#1451—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—161no—
195C2×C43#197311yescharacteristic
196C2×C43#197611yescharacteristic
197C2×C43#198011yescharacteristic
198#533C2×D4311yescharacteristic
199#532C2×D4311yescharacteristic
200#498Dic4311yescharacteristic, complemented
201#492Dic4311yescharacteristic, complemented
202#487Dic4311yescharacteristic, complemented
203#486Dic4311yescharacteristic, complemented
204#465—21no—
205#465—21no—
206C4×SD16—21no—
207C4×SD16—21no—
208#431—431no—
209C2×#107—861no—
210C2×#104—862no—
211C4×M16—431no—
212C2×C4×C8C2×D4311yescharacteristic
213C4×C4⋊C4—431no—
214C4×C4⋊C4—431no—
215#340—861no—
216#339—862no—
217#328—862no—
218#327—862no—
219#322—861no—
220#322—861no—
221C43#972211yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C2×SD16—21no—
224C2×SD16—21no—
225C2×M16—432no—
226C22×C8C22⋊D4311yescharacteristic
227C22×C8C22⋊D4311yescharacteristic
228C4⋊Q8C2×Dic4311yescharacteristic
229C4⋊Q8C2×Dic4311yescharacteristic
230C4⋊Q8C2×Dic4311yescharacteristic
231#127C2×Dic4311yescharacteristic
232#125—21no—
233#124—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242#117—21no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C42—861no—
246C2×C42—861no—
247C2×C42C22×D4311yescharacteristic
248#107—864no—
249#106—21no—
250#106—21no—
251C4⋊C8—861no—
252#104—1724no—
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257C22⋊C8—432no—
258#97—861no—
259C4×C8—861no—
260C4×C8—861no—
261C4×C8C2×Dic4311yescharacteristic
262C4×C8C2×Dic4311yescharacteristic
263C4×C8C22⋊D4311yescharacteristic
264C4×C8C22⋊D4311yescharacteristic
265#95—861no—
266#95—861no—
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C22×C4C2×C22⋊D4311yescharacteristic
282SD16—42no—
283SD16—42no—
284M16—862no—
285M16—862no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8C22⋊Dic4311yescharacteristic
291C2×C8C22⋊Dic4311yescharacteristic
292C2×C8C22⋊Dic4311yescharacteristic
293C2×C8C22⋊Dic4311yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—862no—
303C4⋊C4—862no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42—1722no—
311C42—1722no—
312C42#1062190011yescharacteristic
313C42#1062190011yescharacteristic
314C42C22×Dic4311yescharacteristic
315C42C2×C22⋊D4311yescharacteristic
316C23—41no—
317C23#1306332111yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4C2×C22⋊Dic4311yescharacteristic
342C2×C4D4×Dic4311yescharacteristic
343C2×C4D4×Dic4311yescharacteristic
344C2×C4#1306329611yescharacteristic
345C2×C4#1306329611yescharacteristic
346C2×C4#1306331211yescharacteristic
347C2×C4#1306335212yes—
348C2×C4#1306335412yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—1722no—
353C8—1722no—
354C8#1306325212yescomplemented
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1458280211yescharacteristic
361C22#1458328511yescharacteristic
362C22#1458329011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—3442no—
370C4—3442no—
371C4C2×#1306325211yescharacteristic
372C4#1458291611yescharacteristic
373C4#1458300012yes—
374C4#1458314212yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2#1913547811yescharacteristic
379C2#1913549411yescharacteristic
380C2#1913551511yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3167C2
socleC22×C43#390
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#3167D43
hypocenterC43#9722
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19135540C2semidirect
3. C4×#13063259C2semidirect
4. #19133094C2semidirect
6. #19132884C2semidirect
22. C43×#498C4semidirect
23. C43×#492C4semidirect
24. C43×#487C4semidirect
25. C43×#486C4semidirect
161. C8×C43#104semidirect
200. #498Dic43semidirect
201. #492Dic43semidirect
202. #487Dic43semidirect
203. #486Dic43semidirect
221. C43#9722semidirect
354. C8#13063252semidirect

Maximal subgroups

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

subgroupindex
#191355402
#191355152
C4×#130632592
#191330942
#191330902
#191328842
C43×#31672
#972243