Finite Group Databasebeta

← #25007470

Subgroups — #25007470

Order 11008.

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

normal subgroups only

This group has 390 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#19134672C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic
3#19132616C212yesmaximal
4#19132595C212yesmaximal
5C43×#2599C211yesmaximal, characteristic
6#14582952—21no—
7#14582762—21no—
8#14582666—21no—
9#14582666C2212yes—
10#14582625—21no—
11#14582623C2212yes—
12C2×C4×Q8×C43C411yescharacteristic, complemented
13C2×#117×C43C2211yescharacteristic
14C43×#398C411yescharacteristic, complemented
15C43×#397C2211yescharacteristic
16C43×#395C411yescharacteristic, complemented
17C43×#393C2211yescharacteristic
18C43×#388—21no—
19C43×#387—21no—
20C43×#387—21no—
21C43×#385—21no—
22C43×#383C411yescharacteristic, complemented
23C2×C22⋊Dic43—22no—
24C4⋊(C43⋊C8)—41no—
25C22⋊(C43⋊C8)—22no—
26C4×C43⋊C8—41no—
27C43⋊#95—41no—
28C43⋊#95—41no—
29C22×Q8×C43C2×C411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C4×Q8×C43—41no—
32C4×Q8×C43—41no—
33#117×C43—41no—
34#117×C43—41no—
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×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43D411yescharacteristic
44C2×C22⋊C4×C43C2311yescharacteristic
45C2×C42×C43—21no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43D411yescharacteristic
48#95×C43—21no—
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×C43C2×D411yescharacteristic
57C2×Q8×C43—42no—
58C2×Q8×C43—41no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—42no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—42no—
90C22⋊Dic43—42no—
91C22⋊Dic43—42no—
92C2×C43⋊C8—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43C2×C22⋊C411yescharacteristic
98C23×C43#13512yes—
99Q8×C43—42no—
100Q8×C43—42no—
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—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
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—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43#9911yescharacteristic
129C2×C4×C43#9911yescharacteristic
130C2×Dic43—82no—
131C2×Dic43—82no—
132C2×Dic43—82no—
133C43⋊C8—82no—
134#11842—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—22no—
138C22×C43—42no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—81no—
142C22×C43C2×#9911yescharacteristic
143C22×C43#41611yescharacteristic
144C22×C43#42111yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—41no—
148C4×C43—42no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—81no—
154C4×C43—81no—
155C4×C43—81no—
156Dic43—162no—
157#2599D4311yescharacteristic
158#1820—431no—
159#1458—431no—
160#1351—432no—
161#1344—432no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—42no—
165C2×C43#151611yescharacteristic
166C2×C43#212011yescharacteristic
167C2×C43#212911yescharacteristic
168C2×C4×Q8Dic4311yescharacteristic, complemented
169C2×#117C2×D4311yescharacteristic
170#431—861no—
171#398Dic4311yescharacteristic, complemented
172#397C2×D4311yescharacteristic
173#395Dic4311yescharacteristic, complemented
174#393C2×D4311yescharacteristic
175#388—21no—
176#387—21no—
177#387—21no—
178#385—21no—
179#383Dic4311yescharacteristic, complemented
180#381—861no—
181#342—432no—
182#342—861no—
183#324—861no—
184#323—432no—
185C43#1184211yescharacteristic, complemented, Sylow
186C22×Q8C2×Dic4311yescharacteristic
187C23×C4C22⋊D4311yescharacteristic
188C4×Q8—41no—
189C4×Q8—41no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×Dic4311yescharacteristic
196C2×C4⋊C4C2×Dic4311yescharacteristic
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—862no—
201C2×C22⋊C4C22⋊D4311yescharacteristic
202C2×C22⋊C4C22×D4311yescharacteristic
203C2×C42—21no—
204C2×C42C2×Dic4311yescharacteristic
205C2×C42C22⋊D4311yescharacteristic
206C4⋊C8—1721no—
207C22⋊C8—862no—
208C4×C8—1721no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—1721no—
216#95—1721no—
217#95C2×Dic4311yescharacteristic
218#95C2×Dic4311yescharacteristic
219C24C2×C22⋊D4311yescharacteristic
220C2×Q8—42no—
221C2×Q8—41no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—1722no—
231C22×C4C22⋊Dic4311yescharacteristic
232C22×C4C22⋊Dic4311yescharacteristic
233C22×C4C22⋊Dic4311yescharacteristic
234C22×C4C22⋊Dic4311yescharacteristic
235C22×C4C22×Dic4311yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C2×C8—1722no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—1722no—
250C22⋊C4—1722no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—42no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23C2×C22⋊Dic4311yescharacteristic
261C23#1306334512yes—
262Q8—42no—
263Q8—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—3442no—
292C2×C4—3442no—
293C2×C4—3442no—
294C2×C4#1306324011yescharacteristic
295C2×C4#1306324011yescharacteristic
296C8—3442no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22C2×#1306324011yescharacteristic
305C22#1458289511yescharacteristic
306C22#1458291611yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—42no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—6882no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2#1913315111yescharacteristic
323C2#1913623611yescharacteristic
324C2#1913627011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2599C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#2599D43
hypocenterC43#11842
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2599

Complements

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

NH ≅ G/Ntype
12. C2×C4×Q8×C43C4semidirect
14. C43×#398C4semidirect
16. C43×#395C4semidirect
22. C43×#383C4semidirect
168. C2×C4×Q8Dic43semidirect
171. #398Dic43semidirect
173. #395Dic43semidirect
179. #383Dic43semidirect
185. C43#11842semidirect

Maximal subgroups

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

subgroupindex
#191346722
#191329092
#191326162
#191325952
C43×#25992
#1184243