Finite Group Databasebeta

← #25006461

Subgroups — #25006461

Order 11008.

318 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 91 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#19143573C211yesmaximal, characteristic
2#19136397C211yesmaximal, characteristic, complemented
3#19136188C211yesmaximal, characteristic, complemented
4#19132578C211yesmaximal, characteristic, complemented
5#19132576C211yesmaximal, characteristic, complemented
6#19132553C211yesmaximal, characteristic, complemented
7C43×#1330C211yesmaximal, characteristic, complemented
8#14583431C411yescharacteristic
9C2×#13063264—21no—
10#14583029C2211yescharacteristic
11#14583023C411yescharacteristic
12#14582968—21no—
13D4×C43⋊C8C411yescharacteristic
14(C22⋊D43)⋊C8—21no—
15#14582957—21no—
16#14582955C411yescharacteristic
17#14582857—21no—
18C4×C8×D43C2211yescharacteristic
19C4⋊(C43⋊C16)C2211yescharacteristic
20(C2×D43)⋊C16—21no—
21#14582675C2211yescharacteristic
22#14582674—21no—
23C16×Dic43—21no—
24C43×#436C2211yescharacteristic
25C43×C4⋊C16C2211yescharacteristic
26C43×#346C2211yescharacteristic
27C22×C43⋊C8—21no—
28C2×C8×D43D411yescharacteristic
29C2×C8×D43D411yescharacteristic
30#13063318—21no—
31#13063316C811yescharacteristic
32#13063312C811yescharacteristic
33#13063307—21no—
34#13063305C811yescharacteristic
35#13063296C811yescharacteristic
36C4×Dic86C2×C411yescharacteristic
37C4×C22⋊D43—21no—
38#13063284—21no—
39C42×D43C2×C411yescharacteristic
40#13063264—24no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16—21no—
43C4⋊(C43⋊C8)C2×C411yescharacteristic
44Dic43⋊C8—21no—
45Dic43⋊C8—21no—
46C22⋊(C43⋊C8)—21no—
47(C2×D43)⋊C8—21no—
48#13063235—21no—
49#13063235—21no—
50C4×C43⋊C8C2×C411yescharacteristic
51C8×Dic43—21no—
52C8×Dic43D411yescharacteristic
53C8×Dic43D411yescharacteristic
54C2×M16×C43—21no—
55C4×D4×C43C2×C411yescharacteristic
56C2×C16×C43—21no—
57C2×C16×C43—21no—
58C4⋊C8×C43C2×C411yescharacteristic
59C22⋊C8×C43—21no—
60C4×C8×C43C2311yescharacteristic
61C2×D4×C43C2×C811yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C4×D43C22⋊C411yescharacteristic
65C2×C4×D43C2×C811yescharacteristic
66C2×C4×D43M1611yescharacteristic
67C2×Dic86C2×C811yescharacteristic
68M16×C43—41no—
69M16×C43—41no—
70C2×C8×C43—21no—
71C2×C8×C43C2×D411yescharacteristic
72C2×C8×C43C2×D411yescharacteristic
73C4⋊C4×C43C2×C811yescharacteristic
74C22⋊C4×C43—21no—
75C42×C43C22×C411yescharacteristic
76C22⋊Dic43—21no—
77C22⋊Dic43—21no—
78C22⋊Dic43—21no—
79(C2×D43)⋊C4—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43C2×C811yescharacteristic
83Dic43⋊C4—21no—
84Dic43⋊C4—21no—
85C4×Dic43—21no—
86C4×Dic43C22⋊C411yescharacteristic
87C4×Dic43C2×C811yescharacteristic
88C4×Dic43M1611yescharacteristic
89C2×C43⋊C8—21no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8C22⋊C411yescharacteristic
92C2×C43⋊C8C22⋊C411yescharacteristic
93C8×D43—21no—
94C8×D43—21no—
95C8×D43—22no—
96C16×C43—22no—
97C16×C43—41no—
98C43⋊C16—22no—
99C43⋊C16—41no—
100C23×C43—21no—
101C22×D43C22⋊C811yescharacteristic
102D4×C43—41no—
103C2×C4×C43—21no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43C22×C811yescharacteristic
108C2×C4×C43C2×M1611yescharacteristic
109C22⋊D43—42no—
110C2×Dic43—21no—
111C2×Dic43—21no—
112C2×Dic43C22⋊C811yescharacteristic
113C2×Dic43C22⋊C811yescharacteristic
114C2×Dic43C22⋊C811yescharacteristic
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—41no—
118C4×D43—41no—
119Dic86—41no—
120C8×C43—21no—
121C8×C43—41no—
122C8×C43#13511yescharacteristic
123C8×C43#13511yescharacteristic
124C43⋊C8—21no—
125C43⋊C8—41no—
126C43⋊C8#10412yes—
127#11620—431nomaximal, Sylow
128C22×C43—41no—
129C22×C43—41no—
130C22×C43—41no—
131C22×C43C2×C22⋊C811yescharacteristic
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—41no—
138C4×C43#41611yescharacteristic
139C4×C43C2×#10411yescharacteristic
140Dic43—21no—
141Dic43—21no—
142Dic43—21no—
143Dic43—41no—
144Dic43—41no—
145#2966—431no—
146#2163—431no—
147C4×M32—431no—
148#1338—431no—
149#1338—431no—
150#1330—431no—
151#1330D4311yescharacteristic, complemented
152C2×C43—81no—
153C2×C43#147611yescharacteristic
154C2×C43#211511yescharacteristic
155C2×C43#211711yescharacteristic
156D43—41no—
157#529—431no—
158C2×M32—861no—
159#446—431no—
160C8×Q8—431no—
161#436C2×D4311yescharacteristic
162#435—861no—
163C8×D4—431no—
164C8×D4—861no—
165#433—861no—
166#432—431no—
167#405—861no—
168C2×C4×C8—431no—
169C4⋊C16—431no—
170C4⋊C16C2×D4311yescharacteristic
171C22⋊C16—861no—
172#346—431no—
173#346—861no—
174#346C2×D4311yescharacteristic
175C4×C16—861no—
176C43#1162011yescharacteristic, complemented, Sylow
177C2×M16—21no—
178C22×C8—431no—
179C22×C8—431no—
180C22×C8—861no—
181#126—861no—
182#125—431no—
183#124—431no—
184#123—861no—
185C22⋊Q8—431no—
186#121—431no—
187C4×Q8—431no—
188C4×D4—861no—
189C4×D4C4×D4311yescharacteristic
190#117—861no—
191C2×C42—431no—
192M32—864no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—861no—
196C2×C16—861no—
197C4⋊C8—431no—
198C4⋊C8—861no—
199C4⋊C8—861no—
200C4⋊C8C4×D4311yescharacteristic
201C22⋊C8—21no—
202C22⋊C8—861no—
203C22⋊C8—861no—
204#97—861no—
205#97—861no—
206C4×C8—431no—
207C4×C8—431no—
208C4×C8—431no—
209C4×C8—861no—
210C4×C8C22×D4311yescharacteristic
211C2×Q8—431no—
212C2×D4—861no—
213C2×D4C8×D4311yescharacteristic
214C22×C4—21no—
215C22×C4—431no—
216C22×C4—431no—
217C22×C4—431no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—431no—
222C2×C8—431no—
223C2×C8—862no—
224C2×C8—861no—
225C2×C8—861no—
226C2×C8—861no—
227C2×C8—1722no—
228C2×C8D4×D4311yescharacteristic
229C2×C8D4×D4311yescharacteristic
230C4⋊C4—431no—
231C4⋊C4—861no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4C8×D4311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C22⋊C4—861no—
241C42—431no—
242C42—431no—
243C42—431no—
244C42—861no—
245C42C2×C4×D4311yescharacteristic
246C16—22no—
247C16—41no—
248C16—862no—
249C16—1721no—
250C23—21no—
251C23—431no—
252Q8—1721no—
253D4—41no—
254D4—1722no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—431no—
261C2×C4—861no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—861no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4C22⋊C4×D4311yescharacteristic
268C2×C4C2×C8×D4311yescharacteristic
269C2×C4M16×D4311yescharacteristic
270C8—21no—
271C8—41no—
272C8—432no—
273C8—861no—
274C8—1721no—
275C8#1306334411yescharacteristic
276C8#1306334611yescharacteristic
277C22—41no—
278C22—41no—
279C22—41no—
280C22—861no—
281C22—861no—
282C22—861no—
283C22C22⋊C8×D4311yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—861no—
288C4—861no—
289C4—861no—
290C4—1721no—
291C4—1721no—
292C4#1458289211yescharacteristic
293C4#104×D4311yescharacteristic
294C2—81no—
295C2—1721no—
296C2#1913297411yescharacteristic
297C2#1913621411yescharacteristic
298C2#1913622111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC4×C8C22×D43
FittingC43×#1330C2
socleC22×C43C2×C22⋊C8
prime radical#13063296C8
cosocleC4×C8×C43C23
hypercenter#1330D43
hypocenterC43#11620
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #19136397C2semidirect
3. #19136188C2semidirect
4. #19132578C2semidirect
5. #19132576C2semidirect
6. #19132553C2semidirect
7. C43×#1330C2semidirect
151. #1330D43semidirect
176. C43#11620semidirect

Maximal subgroups

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

subgroupindex
#191435732
#191363972
#191361882
#191325782
#191325762
#191325532
C43×#13302
#1162043