Finite Group Databasebeta

← #25010104

Subgroups — #25010104

Order 11008.

378 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147569C211yesmaximal, characteristic, complemented
2#19136844C211yesmaximal, characteristic, complemented
3#19133952C211yesmaximal, characteristic, complemented
4#19132642C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132556C211yesmaximal, characteristic, complemented
7C43×#2206C211yesmaximal, characteristic, complemented
8#14583570—21no—
9C2×#13063266—22no—
10#14583276C2211yescharacteristic
11#14583274—21no—
12#14583096—21no—
13#14583094—21no—
14#14583093—22no—
15C8×Dic86C2211yescharacteristic
16#14582981—21no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582643—21no—
20C2×D16×C43—21no—
21C43×#493C2211yescharacteristic
22C4×D8×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#357—21no—
25C2×#10621898—41no—
26C2×#10621883—41no—
27C2×D344—21no—
28C2×D344D412yes—
29C2×#10621882—22no—
30#13063322—21no—
31#13063321—22no—
32#13063299—41no—
33#13063298—42no—
34C4×Dic86D411yescharacteristic
35#13063287—22no—
36#13063266—44no—
37C2×C43⋊C16—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063246—41no—
42#13063245—22no—
43C8×Dic43—21no—
44C2×D8×C43—21no—
45C2×D8×C43—21no—
46C2×D8×C43D411yescharacteristic
47#127×C43—21no—
48C4×D4×C43—21no—
49D16×C43—42no—
50C2×C16×C43—21no—
51#107×C43D411yescharacteristic
52#102×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×D4×C43—21no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C22×C4×C43—41no—
59C2×C22⋊D43—42no—
60C2×C22⋊D43—42no—
61#10621898—82no—
62#10621898—82no—
63C2×D172—22no—
64C2×D172—41no—
65C2×D172—41no—
66C2×C4×D43—42no—
67C2×Dic86D811yescharacteristic
68D8×C43—21no—
69D8×C43—21no—
70D8×C43—42no—
71D8×C43—41no—
72D8×C43—41no—
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43C2×D411yescharacteristic
75C4⋊C4×C43—21no—
76C22⋊C4×C43—41no—
77C42×C43C2×D411yescharacteristic
78#10621883—82no—
79#10621882—82no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43D811yescharacteristic
82Dic43⋊C4—21no—
83C4×Dic43—21no—
84C2×C43⋊C8—21no—
85C2×C43⋊C8—41no—
86D344—42no—
87D344—41no—
88D344—41no—
89C16×C43—41no—
90C43⋊C16—22no—
91C23×C43—41no—
92C23×C43—81no—
93C22×D43—42no—
94D4×C43—41no—
95D4×C43—41no—
96D4×C43—81no—
97D4×C43—81no—
98D4×C43—81no—
99D4×C43—81no—
100D4×C43—161no—
101C2×C4×C43—41no—
102C2×C4×C43—81no—
103C2×C4×C43—81no—
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43C2×D811yescharacteristic
106C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
107C22⋊D43—84no—
108C22⋊D43—162no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111D172—42no—
112D172—42no—
113D172—81no—
114D172—81no—
115D172—161no—
116C4×D43—84no—
117Dic86—21no—
118Dic86D1612yescomplemented
119C8×C43—21no—
120C8×C43#13511yescharacteristic
121C8×C43AGL(1,ℤ/8)11yescharacteristic
122C43⋊C8—41no—
123C43⋊C8—81no—
124#12328—431nomaximal, Sylow
125C22×C43—81no—
126C22×C43—81no—
127C22×C43—81no—
128C22×C43—161no—
129C22×C43—161no—
130C22×C43—161no—
131C22×C43#44711yescharacteristic
132C2×D43—82no—
133C2×D43—82no—
134C2×D43—82no—
135C4×C43—21no—
136C4×C43—81no—
137C4×C43#44911yescharacteristic
138C4×C43#45311yescharacteristic
139C4×C43C2×D1611yescharacteristic
140C4×C43#50911yescharacteristic
141Dic43—22no—
142Dic43—41no—
143#3391—431no—
144#2246—431no—
145#2206D4311yescharacteristic, complemented
146#1668—431no—
147#1361—431no—
148Q8⋊C16—431no—
149#1331—431no—
150C2×C43—161no—
151C2×C43—321no—
152C2×C43#162111yescharacteristic
153C2×C43#218411yescharacteristic
154C2×C43#219211yescharacteristic
155D43—162no—
156#550—861no—
157C2×D16—21no—
158C2×D16—862no—
159#493—431no—
160#493—861no—
161#493C2×D4311yescharacteristic
162#460—861no—
163#459—862no—
164#459—861no—
165C8×Q8—431no—
166C4×D8—861no—
167C4×D8C2×D4311yescharacteristic
168C4⋊C16C2×D4311yescharacteristic
169#357—21no—
170C4×C16—431no—
171#335—431no—
172#331—861no—
173C43#1232811yescharacteristic, complemented, Sylow
174C2×#41—1721no—
175C2×SD16—1721no—
176C2×D8—21no—
177C2×D8—21no—
178C2×D8—432no—
179C2×D8—862no—
180C2×D8—861no—
181C2×D8C22⋊D4311yescharacteristic
182#127—21no—
183#127—862no—
184#127—861no—
185#121—1722no—
186#121—1721no—
187C4×Q8—431no—
188C4×D4—21no—
189C4×D4—862no—
190D16—42no—
191D16—1724no—
192C2×C16—21no—
193C2×C16—861no—
194#107C22⋊D4311yescharacteristic
195C4⋊C8—431no—
196C4⋊C8—861no—
197C4⋊C8—861no—
198#102—21no—
199#102—862no—
200#102—1721no—
201C4×C8—861no—
202C4×C8C22×D4311yescharacteristic
203#41—3442no—
204#41—3442no—
205C2×Q8—431no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—862no—
211C2×D4—1722no—
212C2×D4—1722no—
213C2×D4—1721no—
214C2×D4—1721no—
215C22×C4—41no—
216C22×C4—1722no—
217SD16—3442no—
218D8—21no—
219D8—21no—
220D8—42no—
221D8—41no—
222D8—41no—
223D8—3442no—
224D8—1722no—
225D8—1721no—
226D8—1721no—
227C2×C8—861no—
228C2×C8—1721no—
229C2×C8D4×D4311yescharacteristic
230C2×C8C2×C22⋊D4311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—431no—
233C4⋊C4—861no—
234C22⋊C4—41no—
235C22⋊C4—1722no—
236C42—861no—
237C42D4×D4311yescharacteristic
238C16—41no—
239C16—862no—
240C23—41no—
241C23—81no—
242C23—1722no—
243Q8—432no—
244Q8—861no—
245D4—41no—
246D4—41no—
247D4—81no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—161no—
252D4—3444no—
253D4—3441no—
254D4—3441no—
255D4—1722no—
256D4—1722no—
257D4—6881no—
258D4—6882no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—3444no—
265C2×C4#1306329311yescharacteristic
266C2×C4D8×D4311yescharacteristic
267C2×C4#1306334911yescharacteristic
268C8—21no—
269C8—3441no—
270C8—1721no—
271C8#1306334511yescharacteristic
272C8#1306335111yescharacteristic
273C22—81no—
274C22—81no—
275C22—81no—
276C22—161no—
277C22—161no—
278C22—161no—
279C22—3442no—
280C22—3442no—
281C22—3442no—
282C22#1458303111yescharacteristic
283C4—21no—
284C4—81no—
285C4—862no—
286C4—1721no—
287C4#1458304211yescharacteristic
288C4#1458306511yescharacteristic
289C4D16×D4311yescharacteristic
290C4#1458333311yescharacteristic
291C2—161no—
292C2—321no—
293C2—6882no—
294C2#1913365911yescharacteristic
295C2#1913650511yescharacteristic
296C2#1913654911yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2206C2
socleC22×C43#447
hypercenter#2206D43
hypocenterC43#12328
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #19147569C2semidirect
2. #19136844C2semidirect
3. #19133952C2semidirect
4. #19132642C2semidirect
5. #19132573C2semidirect
6. #19132556C2semidirect
7. C43×#2206C2semidirect
118. Dic86D16semidirect
145. #2206D43semidirect
173. C43#12328semidirect

Maximal subgroups

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

subgroupindex
#191475692
#191368442
#191339522
#191326422
#191325732
#191325562
C43×#22062
#1232843