Finite Group Databasebeta

← #25010102

Subgroups — #25010102

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#19147568C211yesmaximal, characteristic, complemented
2#19136627C211yesmaximal, characteristic, complemented
3#19133952C211yesmaximal, characteristic, complemented
4#19132641C211yesmaximal, characteristic, complemented
5#19132575C211yesmaximal, characteristic, complemented
6#19132557C211yesmaximal, characteristic, complemented
7C43×#2246C211yesmaximal, characteristic, complemented
8#14583569—21no—
9C2×#13063266—21no—
10#14583274—21no—
11#14583096—21no—
12#14583092—22no—
13#14583091—21no—
14C8×Dic86C2211yescharacteristic
15C4×D344C2211yescharacteristic
16D8×Dic43—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582700—21no—
19#14582652C2211yescharacteristic
20#14582643—21no—
21C2×D16×C43—22no—
22C43×#493C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×#10621900—41no—
26C2×#10621883—41no—
27C2×D344D411yescharacteristic
28C2×#10621882—22no—
29#13063321—22no—
30#13063297—42no—
31#13063296—41no—
32C4×Dic86D411yescharacteristic
33C4×D172—21no—
34D4×Dic43—22no—
35#13063266—42no—
36C2×C43⋊C16—21no—
37#13063259D411yescharacteristic
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063247—21no—
42#13063246—22no—
43#13063246—41no—
44C8×Dic43—21no—
45C2×D8×C43—21no—
46C2×D8×C43—21no—
47C2×D8×C43—21no—
48C2×D8×C43D412yes—
49#127×C43—21no—
50#127×C43—21no—
51D16×C43—44no—
52C2×C16×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×D4×C43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×C22⋊D43—42no—
61C2×C22⋊D43—42no—
62C22×Dic43—42no—
63#10621900—82no—
64#10621900—82no—
65C2×D172—21no—
66C2×C4×D43—41no—
67C2×Dic86D811yescharacteristic
68D8×C43—42no—
69D8×C43—42no—
70D8×C43—41no—
71D8×C43—41no—
72D8×C43—41no—
73D8×C43—41no—
74C2×C8×C43C2×D411yescharacteristic
75C2×C8×C43C2×D411yescharacteristic
76C42×C43C2×D411yescharacteristic
77C22⋊Dic43—42no—
78#10621883—82no—
79#10621882—82no—
80(C2×D43)⋊C4—41no—
81C4⋊Dic43—21no—
82C4⋊Dic43D811yescharacteristic
83Dic43⋊C4—21no—
84C4×Dic43—21no—
85C2×C43⋊C8—21no—
86C2×C43⋊C8—41no—
87D344—21no—
88D344—21no—
89C16×C43—22no—
90C43⋊C16—41no—
91C23×C43—42no—
92C23×C43—81no—
93C22×D43—41no—
94D4×C43—42no—
95D4×C43—42no—
96D4×C43—81no—
97D4×C43—81no—
98D4×C43—81no—
99D4×C43—81no—
100D4×C43—81no—
101D4×C43—81no—
102D4×C43—161no—
103D4×C43—161no—
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—
111C2×Dic43—41no—
112C2×Dic43—84no—
113D172—41no—
114D172—41no—
115C4×D43—81no—
116C4×D43—81no—
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—82no—
126C22×C43—82no—
127C22×C43—82no—
128C22×C43—161no—
129C22×C43—161no—
130C22×C43—161no—
131C22×C43#44711yescharacteristic
132C2×D43—81no—
133C2×D43—81no—
134C2×D43—81no—
135C4×C43—21no—
136C4×C43#44911yescharacteristic
137C4×C43#45311yescharacteristic
138C4×C43C2×D1611yescharacteristic
139C4×C43#50911yescharacteristic
140Dic43—22no—
141Dic43—41no—
142Dic43—81no—
143#3391—431no—
144#2246D4311yescharacteristic, complemented
145#2206—431no—
146#1668—431no—
147#1361—431no—
148Q8⋊C16—431no—
149#1331—431no—
150C2×C43—162no—
151C2×C43—321no—
152C2×C43#162111yescharacteristic
153C2×C43#218411yescharacteristic
154C2×C43#219211yescharacteristic
155D43—161no—
156#550—861no—
157C2×D16—22no—
158C2×D16—861no—
159#493—861no—
160#493C2×D4311yescharacteristic
161#493C2×D4311yescharacteristic
162#460—861no—
163#459—861no—
164#459—862no—
165C8×Q8—431no—
166C4×D8—431no—
167C4×D8—861no—
168C4⋊C16—431no—
169#357—861no—
170C4×C16C2×D4311yescharacteristic
171#335—431no—
172#331—861no—
173C43#1232811yescharacteristic, complemented, Sylow
174C2×#41—1721no—
175C2×SD16—1721no—
176C2×D8—21no—
177C2×D8—21no—
178C2×D8—21no—
179C2×D8—431no—
180C2×D8—862no—
181C2×D8C22⋊D4312yes—
182#127—21no—
183#127—21no—
184#127—862no—
185#121—1721no—
186#121—1722no—
187C4×Q8—431no—
188C4×D4—862no—
189C4×D4—861no—
190D16—44no—
191D16—1722no—
192C2×C16—21no—
193C2×C16—861no—
194#107—431no—
195C4⋊C8—431no—
196C4⋊C8—861no—
197C4⋊C8—861no—
198#102—862no—
199#102—861no—
200#102—1721no—
201C4×C8—861no—
202C4×C8C22×D4311yescharacteristic
203#41—3442no—
204#41—3442no—
205C2×Q8—431no—
206C2×D4—22no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—861no—
213C2×D4—1722no—
214C2×D4—1722no—
215C22×C4—1722no—
216C22×C4—1721no—
217SD16—3442no—
218D8—42no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—41no—
223D8—41no—
224D8—861no—
225D8—861no—
226D8—3442no—
227C2×C8—861no—
228C2×C8—1721no—
229C2×C8D4×D4311yescharacteristic
230C2×C8C2×C22⋊D4311yescharacteristic
231C4⋊C4—431no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C22⋊C4—1722no—
235C22⋊C4—1721no—
236C42—861no—
237C42D4×D4311yescharacteristic
238C16—22no—
239C16—1721no—
240C23—42no—
241C23—81no—
242C23—1721no—
243Q8—432no—
244Q8—861no—
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—161no—
254D4—161no—
255D4—3444no—
256D4—1721no—
257D4—1721no—
258D4—6882no—
259C2×C4—861no—
260C2×C4—861no—
261C2×C4—3444no—
262C2×C4—3441no—
263C2×C4—3441no—
264C2×C4—1721no—
265C2×C4#1306329311yescharacteristic
266C2×C4D8×D4311yescharacteristic
267C2×C4#1306334911yescharacteristic
268C8—21no—
269C8—3441no—
270C8—1721no—
271C8#1306334411yescharacteristic
272C8#1306334911yescharacteristic
273C22—82no—
274C22—82no—
275C22—82no—
276C22—161no—
277C22—161no—
278C22—161no—
279C22—3441no—
280C22—3441no—
281C22—3441no—
282C22#1458303111yescharacteristic
283C4—21no—
284C4—862no—
285C4—3441no—
286C4—1721no—
287C4#1458304111yescharacteristic
288C4#1458306611yescharacteristic
289C4D16×D4311yescharacteristic
290C4#1458333311yescharacteristic
291C2—162no—
292C2—321no—
293C2—6881no—
294C2#1913365711yescharacteristic
295C2#1913650511yescharacteristic
296C2#1913655111yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2246C2
socleC22×C43#447
hypercenter#2246D43
hypocenterC43#12328
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #19147568C2semidirect
2. #19136627C2semidirect
3. #19133952C2semidirect
4. #19132641C2semidirect
5. #19132575C2semidirect
6. #19132557C2semidirect
7. C43×#2246C2semidirect
118. Dic86D16semidirect
144. #2246D43semidirect
173. C43#12328semidirect

Maximal subgroups

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

subgroupindex
#191475682
#191366272
#191339522
#191326412
#191325752
#191325572
C43×#22462
#1232843