Finite Group Databasebeta

← #25006498

Subgroups — #25006498

Order 11008.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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#19143569C211yesmaximal, characteristic
2#19136396C211yesmaximal, characteristic, complemented
3#19136349C211yesmaximal, characteristic, complemented
4#19132577C211yesmaximal, characteristic, complemented
5#19132554C211yesmaximal, characteristic, complemented
6#19132552C211yesmaximal, characteristic, complemented
7C43×#1338C211yesmaximal, characteristic, complemented
8#14583436C411yescharacteristic
9C2×#13063264—21no—
10Q8×C43⋊C8C411yescharacteristic
11#14582978C2211yescharacteristic
12#14582972—21no—
13#14582964—21no—
14#14582964C411yescharacteristic
15#14582959—21no—
16#14582955C411yescharacteristic
17#14582856—21no—
18C4×C8×D43C2211yescharacteristic
19C4⋊(C43⋊C16)C2211yescharacteristic
20Dic43⋊C16—21no—
21Dic43⋊C16—21no—
22(C2×D43)⋊C16—21no—
23#14582675C2211yescharacteristic
24C43×#446C2211yescharacteristic
25C43×C4⋊C16C2211yescharacteristic
26C43×#346C2211yescharacteristic
27C2×#10621872—21no—
28C2×C8×D43—21no—
29C2×C8×D43D411yescharacteristic
30C2×C8×D43D411yescharacteristic
31#13063320—21no—
32#13063316C811yescharacteristic
33#13063314C811yescharacteristic
34#13063310—21no—
35#13063301C811yescharacteristic
36#13063300C811yescharacteristic
37C4×D172—21no—
38C4×D172C2×C411yescharacteristic
39#13063282—21no—
40C42×D43C2×C411yescharacteristic
41#13063264—42no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C411yescharacteristic
46(C2×D43)⋊C8—21no—
47(C2×D43)⋊C8—21no—
48(C2×D43)⋊C8—21no—
49#13063235—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8C2×C411yescharacteristic
52C8×Dic43D411yescharacteristic
53C8×Dic43D411yescharacteristic
54C4×Q8×C43C2×C411yescharacteristic
55C2×C16×C43—21no—
56C2×C16×C43—21no—
57C4⋊C8×C43—21no—
58C4⋊C8×C43C2×C411yescharacteristic
59#97×C43—21no—
60C4×C8×C43C2311yescharacteristic
61C2×Q8×C43C2×C811yescharacteristic
62C2×D172—21no—
63C2×D172C2×C811yescharacteristic
64C2×C4×D43—21no—
65C2×C4×D43C22⋊C411yescharacteristic
66C2×C4×D43C2×C811yescharacteristic
67C2×C4×D43M1611yescharacteristic
68C2×C8×C43—21no—
69C2×C8×C43C2×D411yescharacteristic
70C2×C8×C43C2×D411yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43C2×C811yescharacteristic
73C42×C43—21no—
74C42×C43C22×C411yescharacteristic
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43C2×C811yescharacteristic
82Dic43⋊C4—21no—
83Dic43⋊C4—21no—
84C4×Dic43C22⋊C411yescharacteristic
85C4×Dic43C2×C811yescharacteristic
86C4×Dic43M1611yescharacteristic
87C2×C43⋊C8—21no—
88C2×C43⋊C8C22⋊C411yescharacteristic
89C2×C43⋊C8C22⋊C411yescharacteristic
90#10621872—41no—
91#10621872—41no—
92C8×D43—21no—
93C8×D43—21no—
94C8×D43—41no—
95C8×D43—42no—
96C16×C43—41no—
97C16×C43—41no—
98C43⋊C16—41no—
99C43⋊C16—41no—
100C22×D43—21no—
101C22×D43C22⋊C811yescharacteristic
102Q8×C43—41no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43C2×C22⋊C411yescharacteristic
106C2×C4×C43C22×C811yescharacteristic
107C2×C4×C43C2×M1611yescharacteristic
108C2×Dic43—21no—
109C2×Dic43C22⋊C811yescharacteristic
110C2×Dic43C22⋊C811yescharacteristic
111C2×Dic43C22⋊C811yescharacteristic
112D172—41no—
113D172—42no—
114C4×D43—21no—
115C4×D43—21no—
116C4×D43—41no—
117C4×D43—41no—
118C4×D43—41no—
119C4×D43—41no—
120C8×C43—21no—
121C8×C43—41no—
122C8×C43AGL(1,ℤ/8)11yescharacteristic
123C8×C43#13711yescharacteristic
124C43⋊C8—21no—
125C43⋊C8—21no—
126C43⋊C8—41no—
127#11627—431nomaximal, Sylow
128C22×C43C2×C22⋊C811yescharacteristic
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—21no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—41no—
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—41no—
138C4×C43—41no—
139C4×C43#41711yescharacteristic
140C4×C43#42111yescharacteristic
141Dic43—21no—
142Dic43—21no—
143Dic43—21no—
144Dic43—41no—
145#2966—431no—
146#2163—431no—
147#2150—431no—
148#1338—431no—
149#1338D4311yescharacteristic, complemented
150#1330—431no—
151#1330—431no—
152C2×C43#147711yescharacteristic
153C2×C43#211511yescharacteristic
154C2×C43#211711yescharacteristic
155D43—41no—
156D43—81no—
157#529—431no—
158C2×M32—861no—
159#446C2×D4311yescharacteristic
160C8×Q8—431no—
161#436—431no—
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⋊C16—861no—
171C4⋊C16—861no—
172C4⋊C16C2×D4311yescharacteristic
173C22⋊C16—861no—
174#346—431no—
175#346C2×D4311yescharacteristic
176C43#1162711yescharacteristic, complemented, Sylow
177C2×M16—861no—
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×Q8C4×D4311yescharacteristic
188C4×D4—431no—
189C4×D4—861no—
190#117—861no—
191C2×C42—431no—
192M32—1722no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—861no—
196C2×C16—861no—
197C4⋊C8—21no—
198C4⋊C8—431no—
199C4⋊C8—861no—
200C4⋊C8C4×D4311yescharacteristic
201C22⋊C8—861no—
202C22⋊C8—861no—
203C22⋊C8—861no—
204#97—21no—
205#97—861no—
206C4×C8—431no—
207C4×C8—431no—
208C4×C8—431no—
209C4×C8—861no—
210C4×C8C22×D4311yescharacteristic
211C2×Q8C8×D4311yescharacteristic
212C2×D4—431no—
213C2×D4—861no—
214C22×C4—431no—
215C22×C4—431no—
216C22×C4—431no—
217C22×C4—861no—
218M16—1721no—
219M16—1721no—
220C2×C8—21no—
221C2×C8—431no—
222C2×C8—431no—
223C2×C8—861no—
224C2×C8—861no—
225C2×C8—861no—
226C2×C8—1721no—
227C2×C8—1722no—
228C2×C8D4×D4311yescharacteristic
229C2×C8D4×D4311yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—431no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4C8×D4311yescharacteristic
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C22⋊C4—861no—
241C42—21no—
242C42—431no—
243C42—431no—
244C42—431no—
245C42C2×C4×D4311yescharacteristic
246C16—41no—
247C16—41no—
248C16—1721no—
249C16—1721no—
250C23—431no—
251C23—861no—
252Q8—41no—
253D4—1721no—
254D4—1722no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—431no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—861no—
261C2×C4—861no—
262C2×C4—861no—
263C2×C4—1721no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4C22⋊C4×D4311yescharacteristic
268C2×C4C2×C8×D4311yescharacteristic
269C2×C4M16×D4311yescharacteristic
270C8—21no—
271C8—41no—
272C8—861no—
273C8—861no—
274C8—1721no—
275C8#1306335211yescharacteristic
276C8#1306335711yescharacteristic
277C22—861no—
278C22—861no—
279C22—861no—
280C22—1721no—
281C22—1721no—
282C22—1721no—
283C22C22⋊C8×D4311yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—861no—
289C4—861no—
290C4—861no—
291C4—1721no—
292C4#1458289911yescharacteristic
293C4#1458291411yescharacteristic
294C2—3441no—
295C2—1721no—
296C2#1913298111yescharacteristic
297C2#1913621411yescharacteristic
298C2#1913622111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC4×C8C22×D43
FittingC43×#1338C2
socleC22×C43C2×C22⋊C8
prime radical#13063300C8
cosocleC4×C8×C43C23
hypercenter#1338D43
hypocenterC43#11627
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #19136396C2semidirect
3. #19136349C2semidirect
4. #19132577C2semidirect
5. #19132554C2semidirect
6. #19132552C2semidirect
7. C43×#1338C2semidirect
149. #1338D43semidirect
176. C43#11627semidirect

Maximal subgroups

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

subgroupindex
#191435692
#191363962
#191363492
#191325772
#191325542
#191325522
C43×#13382
#1162743