Finite Group Databasebeta

← #25006149

Subgroups — #25006149

Order 11008.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#19138878C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic
3#19132542C212yesmaximal
4#19132524C212yesmaximal
5C43×#1464C211yesmaximal, characteristic
6C22×Dic43⋊C4C411yescharacteristic
7#14582952—21no—
8#14582837—21no—
9#14582830—21no—
10#14582783—21no—
11#14582783—21no—
12#14582771C411yescharacteristic
13#14582771C2211yescharacteristic
14#14582762C411yescharacteristic
15#14582760C411yescharacteristic
16#14582760C2211yescharacteristic
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C23×Dic43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C2×Dic43⋊C4—21no—
26C2×Dic43⋊C4—21no—
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—41no—
30C2×Dic43⋊C4—41no—
31C2×C22⋊Dic43C2×C411yescharacteristic
32C2×C22⋊Dic43C2×C411yescharacteristic
33C4⋊(C43⋊C8)—41no—
34C22⋊(C43⋊C8)—22no—
35C4×C43⋊C8—41no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43C2×C411yescharacteristic
50C2×C22⋊C4×C43C2311yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55#97×C43—41no—
56C24×C43C22×C411yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—22no—
72C22×Dic43—41no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43—42no—
76C2×C8×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C22⋊Dic43—22no—
86C22⋊Dic43—41no—
87Dic43⋊C4—42no—
88Dic43⋊C4—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92C2×C43⋊C8—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43C2×C22⋊C411yescharacteristic
98C23×C43#13112yes—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
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#9911yescharacteristic
115C2×C4×C43#9911yescharacteristic
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—42no—
119C2×Dic43—41no—
120C2×Dic43—42no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—82no—
131C8×C43—82no—
132C43⋊C8—82no—
133#11548—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—22no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43#40811yescharacteristic
142C22×C43C2×#9911yescharacteristic
143C22×C43#41311yescharacteristic
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151Dic43—42no—
152Dic43—81no—
153Dic43—81no—
154Dic43—81no—
155#2484—431no—
156#1464D4311yescharacteristic
157#1458—431no—
158#1326—432no—
159#1317—432no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—42no—
163C2×C43#146811yescharacteristic
164C2×C43#212011yescharacteristic
165C2×C43#212311yescharacteristic
166C2×#117C2×D4311yescharacteristic
167C22×C4⋊C4—431no—
168#432—21no—
169#431—861no—
170#400—861no—
171#398—861no—
172#387—861no—
173#387—861no—
174#385—431no—
175#385—431no—
176#381—431no—
177#381—431no—
178#381—431no—
179#324—21no—
180#324—861no—
181#323—432no—
182#323C2×D4312yes—
183C43#1154811yescharacteristic, complemented, Sylow
184C23×C4—431no—
185C23×C4—431no—
186C23×C4C4×D4311yescharacteristic
187#117—41no—
188#117—41no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—1721no—
194C2×C4⋊C4—1721no—
195C2×C4⋊C4D17211yescharacteristic
196C2×C4⋊C4C22⋊D4311yescharacteristic
197C2×C22⋊C4—431no—
198C2×C22⋊C4—431no—
199C2×C22⋊C4C4×D4311yescharacteristic
200C2×C22⋊C4C22×D4311yescharacteristic
201C2×C42D17211yescharacteristic
202C2×C42C22⋊D4311yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—1721no—
205C22⋊C8—22no—
206C22⋊C8—862no—
207#97—41no—
208C4×C8—1721no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217C24C2×C4×D4311yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—861no—
223C22×C4—862no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—1722no—
228C22×C4—1721no—
229C22×C4—1721no—
230C22×C4—1721no—
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4(C2×D43)⋊C411yescharacteristic
234C22×C4(C2×D43)⋊C411yescharacteristic
235C22×C4C2×D17211yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C2×C8—42no—
238C2×C8—1722no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—1722no—
242C4⋊C4—1722no—
243C4⋊C4—1722no—
244C4⋊C4—1721no—
245C4⋊C4—1721no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—862no—
249C22⋊C4—1721no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×(C2×D43)⋊C411yescharacteristic
259C23#1306333312yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—862no—
276C2×C4—3442no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1722no—
288C2×C4—1721no—
289C2×C4—1722no—
290C2×C4#1306323911yescharacteristic
291C2×C4#1306323911yescharacteristic
292C8—82no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1458286711yescharacteristic
302C22C2×#1306323911yescharacteristic
303C22#1458288111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—3441no—
312C4—3441no—
313C4—3441no—
314C4—1722no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1913294411yescharacteristic
319C2#1913623411yescharacteristic
320C2#1913625011yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutator, prime radicalC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
cosocleC2×C22⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11548
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
183. C43#11548semidirect

Maximal subgroups

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

subgroupindex
#191388782
#191329092
#191325422
#191325242
C43×#14642
#1154843