Finite Group Databasebeta

← #25005815

Subgroups — #25005815

Order 11008.

310 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 87 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#19143238C211yesmaximal, characteristic
2#19136395C211yesmaximal, characteristic, complemented
3#19136391C211yesmaximal, characteristic, complemented
4#19132537C211yesmaximal, characteristic, complemented
5#19132520C211yesmaximal, characteristic
6#19132520C211yesmaximal, characteristic
7C43×#1323C211yesmaximal, characteristic, complemented
8#14583367C411yescharacteristic
9#14582959—21no—
10#14582959—21no—
11#14582951—21no—
12#14582951—21no—
13#14582926C411yescharacteristic
14#14582867C411yescharacteristic
15#14582865C2211yescharacteristic
16M16×Dic43C411yescharacteristic
17C2×C8×Dic43C2211yescharacteristic
18Dic43⋊C16—21no—
19Dic43⋊C16—21no—
20C22⋊(C43⋊C16)C2211yescharacteristic
21C22⋊(C43⋊C16)C2211yescharacteristic
22#14582674—21no—
23C16×Dic43—21no—
24C43×#424C2211yescharacteristic
25C43×C22⋊C16C2211yescharacteristic
26C43×C22⋊C16C2211yescharacteristic
27C2×#10621898C2×C411yescharacteristic
28C2×#10621877C2×C411yescharacteristic
29C22×C43⋊C8C2×C411yescharacteristic
30#13063290C811yescharacteristic
31#13063290C811yescharacteristic
32#13063287C811yescharacteristic
33#13063287C811yescharacteristic
34(C22⋊D43)⋊C4—21no—
35(C22⋊D43)⋊C4—21no—
36#13063282—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C42×D43—21no—
39C2×C43⋊C16—21no—
40C2×C43⋊C16—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43(C2×D43)⋊C8—21no—
44(C2×D43)⋊C8—21no—
45(C2×D43)⋊C8—21no—
46(C2×D43)⋊C8—21no—
47#13063235—21no—
48C8×Dic43—21no—
49C8×Dic43D411yescharacteristic
50C8×Dic43D411yescharacteristic
51C8×Dic43D411yescharacteristic
52C8×Dic43D411yescharacteristic
53C2×M16×C43C2×C411yescharacteristic
54C22×C8×C43C2311yescharacteristic
55#117×C43C2×C411yescharacteristic
56C2×C16×C43—21no—
57C2×C16×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C22×C4×C43C22×C411yescharacteristic
61C2×C22⋊D43—21no—
62C22×Dic43M1611yescharacteristic
63C22×Dic43M1611yescharacteristic
64#10621898—41no—
65#10621898—41no—
66C2×D172C2×C811yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×Dic86C2×C811yescharacteristic
71M16×C43—41no—
72C2×C8×C43—21no—
73C2×C8×C43—41no—
74C2×C8×C43C2×D411yescharacteristic
75C2×C8×C43C2×D411yescharacteristic
76C4⋊C4×C43C2×C811yescharacteristic
77C4⋊C4×C43C2×C811yescharacteristic
78C22⋊C4×C43—21no—
79C42×C43—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82Dic43⋊C4—21no—
83Dic43⋊C4—21no—
84C4×Dic43—21no—
85C4×Dic43—21no—
86C4×Dic43C22⋊C411yescharacteristic
87C4×Dic43C22⋊C411yescharacteristic
88C4×Dic43C2×C811yescharacteristic
89C4×Dic43C2×C811yescharacteristic
90#10621877—41no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8C22⋊C411yescharacteristic
94C2×C43⋊C8C22⋊C411yescharacteristic
95C16×C43—41no—
96C16×C43—41no—
97C43⋊C16—41no—
98C43⋊C16—41no—
99C23×C43C2×M1611yescharacteristic
100C22×D43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43C2×C22⋊C411yescharacteristic
106C2×C4×C43C22×C811yescharacteristic
107C22⋊D43—42no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43—41no—
111C2×Dic43C22⋊C811yescharacteristic
112C2×Dic43C22⋊C811yescharacteristic
113C2×Dic43C22⋊C811yescharacteristic
114C2×Dic43C22⋊C811yescharacteristic
115D172—41no—
116C4×D43—42no—
117C4×D43—41no—
118C4×D43—41no—
119C4×D43—42no—
120Dic86—41no—
121C8×C43—21no—
122C8×C43—21no—
123C8×C43—41no—
124C43⋊C8—21no—
125C43⋊C8—21no—
126C43⋊C8—41no—
127#11464—431nomaximal, Sylow
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43C2×C22⋊C811yescharacteristic
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—41no—
135C4×C43—21no—
136C4×C43—41no—
137C4×C43—41no—
138C4×C43#41011yescharacteristic
139C4×C43#41311yescharacteristic
140Dic43—21no—
141Dic43—21no—
142Dic43—21no—
143Dic43—41no—
144Dic43#35012yes—
145#2922—431no—
146#2163—431no—
147#2162—431no—
148#1323—431no—
149#1323D4311yescharacteristic, complemented
150#1315—431no—
151#1315—431no—
152C2×C43—41no—
153C2×C43#145811yescharacteristic
154C2×C43C2×#35011yescharacteristic
155C2×C43#211711yescharacteristic
156D43—81no—
157C4×#41—431no—
158#433—861no—
159#433—861no—
160#431—861no—
161#431—861no—
162#424—431no—
163#424C2×D4311yescharacteristic
164#408—431no—
165#408—431no—
166C4×M16—431no—
167C2×C4×C8—431no—
168C4⋊C16—861no—
169C4⋊C16—861no—
170C22⋊C16—431no—
171C22⋊C16—431no—
172C22⋊C16C2×D4311yescharacteristic
173C22⋊C16C2×D4311yescharacteristic
174#346—861no—
175C4×C16—861no—
176C43#1146411yescharacteristic, complemented, Sylow
177C2×#41—431no—
178C2×M16—431no—
179C2×M16C4×D4311yescharacteristic
180C22×C8—431no—
181C22×C8C22×D4311yescharacteristic
182C4×Q8—431no—
183C4×Q8—431no—
184C4×D4—431no—
185C4×D4—431no—
186C4×D4—861no—
187C4×D4—861no—
188#117—861no—
189#117C4×D4311yescharacteristic
190C2×C42—431no—
191C2×C42—861no—
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—861no—
195C2×C16—861no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—861no—
199C4⋊C8—861no—
200C22⋊C8—861no—
201C22⋊C8—861no—
202C22⋊C8—861no—
203C22⋊C8—861no—
204#97—861no—
205C4×C8—431no—
206C4×C8—431no—
207C4×C8—431no—
208C4×C8—431no—
209C4×C8—861no—
210#41—1721no—
211#41—1721no—
212C2×Q8—431no—
213C2×D4—431no—
214C2×D4—861no—
215C22×C4—431no—
216C22×C4—431no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4—861no—
220C22×C4C2×C4×D4311yescharacteristic
221M16—41no—
222M16—1721no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—431no—
226C2×C8—431no—
227C2×C8—861no—
228C2×C8—1721no—
229C2×C8D4×D4311yescharacteristic
230C2×C8D4×D4311yescharacteristic
231C4⋊C4—861no—
232C4⋊C4—861no—
233C4⋊C4C8×D4311yescharacteristic
234C4⋊C4C8×D4311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C42—21no—
239C42—431no—
240C42—431no—
241C42—431no—
242C42—431no—
243C42—861no—
244C42—861no—
245C16—41no—
246C16—41no—
247C16—1721no—
248C16—1721no—
249C23—861no—
250C23M16×D4311yescharacteristic
251Q8—1721no—
252D4—1721no—
253D4—1722no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—431no—
261C2×C4—431no—
262C2×C4—862no—
263C2×C4—861no—
264C2×C4—1722no—
265C2×C4—1722no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4C22⋊C4×D4311yescharacteristic
270C2×C4C2×C8×D4311yescharacteristic
271C8—21no—
272C8—21no—
273C8—41no—
274C8—861no—
275C8—861no—
276C8—1721no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—1721no—
281C22—1721no—
282C22—1721no—
283C22C22⋊C8×D4311yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—432no—
288C4—861no—
289C4—861no—
290C4—861no—
291C4—1721no—
292C4#1458287111yescharacteristic
293C4#1458288211yescharacteristic
294C2—41no—
295C2—3441no—
296C2#1913290811yescharacteristic
297C2#350×D4311yescharacteristic
298C2#1913622111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1323C2
socleC22×C43C2×C22⋊C8
prime radicalC2×#10621898C2×C4
cosocleC22×C8×C43C23
hypercenter#1323D43
hypocenterC43#11464
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #19136395C2semidirect
3. #19136391C2semidirect
4. #19132537C2semidirect
7. C43×#1323C2semidirect
149. #1323D43semidirect
176. C43#11464semidirect

Maximal subgroups

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

subgroupindex
#191432382
#191363952
#191363912
#191325372
#191325202
C43×#13232
#1146443