Finite Group Databasebeta

← #25007525

Subgroups — #25007525

Order 11008.

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

normal subgroups only

This group has 368 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#19134678C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic
3#19132622C212yesmaximal, complemented
4#19132601C212yesmaximal, complemented
5C43×#2611C211yesmaximal, characteristic
6#14582952—21no—
7#14582863—21no—
8#14582668—21no—
9#14582668C2212yes—
10#14582625C2212yes—
11#14582623—21no—
12C2×#125×C43C411yescharacteristic
13C2×#117×C43C2211yescharacteristic
14C43×#400C2211yescharacteristic
15C43×#399C411yescharacteristic
16C43×#398C2211yescharacteristic
17C43×#397C411yescharacteristic
18C43×#389—21no—
19C43×#388—21no—
20C43×#387—21no—
21C43×#385—21no—
22C43×#376C411yescharacteristic
23C2×#10621877—22no—
24C4⋊(C43⋊C8)—41no—
25C22⋊(C43⋊C8)—22no—
26C22⋊(C43⋊C8)—41no—
27C22⋊(C43⋊C8)—41no—
28C4×C43⋊C8—41no—
29C23×C4×C43D411yescharacteristic
30#125×C43—41no—
31#125×C43—41no—
32#117×C43—41no—
33#117×C43—41no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C42×C43—21no—
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43C2×C411yescharacteristic
55#95×C43C2×C411yescharacteristic
56C24×C43C22⋊C411yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—42no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—42no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—42no—
89#10621877—42no—
90#10621877—42no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43C2×C22⋊C411yescharacteristic
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43#9911yescharacteristic
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#13512yes—
128C43⋊C8—82no—
129C43⋊C8—82no—
130#11853—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—42no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—81no—
138C22×C43C2×#9911yescharacteristic
139C22×C43#41611yescharacteristic
140C22×C43#42111yescharacteristic
141C4×C43—22no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—42no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—81no—
150C4×C43—81no—
151C4×C43—81no—
152#2611D4311yescharacteristic
153#1822—431no—
154#1458—431no—
155#1353—432no—
156#1346—432no—
157C2×C43—21no—
158C2×C43—21no—
159C2×C43—81no—
160C2×C43#151611yescharacteristic
161C2×C43#212311yescharacteristic
162C2×C43#213211yescharacteristic
163C2×#125Dic4311yescharacteristic
164C2×#117C2×D4311yescharacteristic
165#431—861no—
166#407—861no—
167#400C2×D4311yescharacteristic
168#399Dic4311yescharacteristic
169#398C2×D4311yescharacteristic
170#397Dic4311yescharacteristic
171#389—21no—
172#388—21no—
173#387—21no—
174#385—21no—
175#376Dic4311yescharacteristic
176#343—432no—
177#343—861no—
178#324—432no—
179#323—861no—
180C43#1185311yescharacteristic, complemented, Sylow
181C23×C4C22⋊D4311yescharacteristic
182C2×M16—862no—
183#125—41no—
184#125—41no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic4311yescharacteristic
192C2×C4⋊C4C2×Dic4311yescharacteristic
193C2×C4⋊C4C22⋊D4311yescharacteristic
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4C2×Dic4311yescharacteristic
198C2×C22⋊C4C22⋊D4311yescharacteristic
199C2×C42—21no—
200C2×C42C2×Dic4311yescharacteristic
201C2×C42C22⋊D4311yescharacteristic
202C4⋊C8—1721no—
203C22⋊C8—862no—
204C22⋊C8—1721no—
205C22⋊C8—1721no—
206C4×C8—1721no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95C2×Dic4311yescharacteristic
213#95C2×Dic4311yescharacteristic
214C24C22⋊Dic4311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C22⋊Dic4311yescharacteristic
224C22×C4C22⋊Dic4311yescharacteristic
225C22×C4C22⋊Dic4311yescharacteristic
226C22×C4C22×Dic4311yescharacteristic
227C22×C4C2×C22⋊D4311yescharacteristic
228C22×C4C2×C22⋊D4311yescharacteristic
229M16—1722no—
230M16—1722no—
231C2×C8—1722no—
232C2×C8—1722no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—42no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×C22⋊Dic4311yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4#1306324011yescharacteristic
284C2×C4#1306324011yescharacteristic
285C2×C4#1306334512yes—
286C8—3442no—
287C8—3442no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×#1306324011yescharacteristic
296C22#1458289511yescharacteristic
297C22#1458291611yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—81no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2#1913315111yescharacteristic
313C2#1913624911yescharacteristic
314C2#1913628011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2611C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2611D43
hypocenterC43#11853
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2611

Complements

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

NH ≅ G/Ntype
3. #19132622C2semidirect
4. #19132601C2semidirect
180. C43#11853semidirect

Maximal subgroups

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

subgroupindex
#191346782
#191329092
#191326222
#191326012
C43×#26112
#1185343