Finite Group Databasebeta

← #25006189

Subgroups — #25006189

Order 11008.

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

normal subgroups only

This group has 366 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#19139044C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic
3#19132538C212yesmaximal, complemented
4#19132528C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7#14582952—21no—
8#14582827—21no—
9#14582827—21no—
10#14582804C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582783—21no—
13#14582783—21no—
14#14582768C411yescharacteristic
15#14582764C2211yescharacteristic
16C4×C22⋊Dic43C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24#13063304—41no—
25#13063304—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C4⋊(C43⋊C8)—41no—
35C22⋊(C43⋊C8)—22no—
36C4×C43⋊C8—41no—
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×C43C2×C411yescharacteristic
48C2×C4⋊C4×C43C2311yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
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—
71C2×Dic86—22no—
72C2×Dic86—41no—
73C2×Dic86—41no—
74C2×C8×C43—42no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C22⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85C4⋊Dic43—41no—
86Dic43⋊C4—42no—
87Dic43⋊C4—42no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—22no—
91C4×Dic43—41no—
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—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43#9911yescharacteristic
114C2×C4×C43#9911yescharacteristic
115C2×C4×C43#13112yes—
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128Dic86—82no—
129C8×C43—82no—
130C43⋊C8—82no—
131#11556—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43#40811yescharacteristic
140C22×C43C2×#9911yescharacteristic
141C22×C43#41311yescharacteristic
142C4×C43—22no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—41no—
149Dic43—42no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153#2499—431no—
154#1464D4311yescharacteristic
155#1458—431no—
156#1324—432no—
157#1319—432no—
158C2×C43—21no—
159C2×C43—21no—
160C2×C43—81no—
161C2×C43#146811yescharacteristic
162C2×C43#212911yescharacteristic
163C2×C43#213211yescharacteristic
164C2×C22⋊Q8—431no—
165C2×#117C2×D4311yescharacteristic
166#432—21no—
167#431—861no—
168#397—861no—
169#397—861no—
170#391—431no—
171#391—431no—
172#387—861no—
173#387—861no—
174#384—431no—
175#382—431no—
176C4×C22⋊C4—431no—
177#324—432no—
178#324C2×D4312yes—
179#323—21no—
180#323—861no—
181C43#1155611yescharacteristic, complemented, Sylow
182C22×Q8—431no—
183C23×C4C4×D4311yescharacteristic
184C22⋊Q8—1721no—
185C22⋊Q8—1721no—
186#117—41no—
187#117—41no—
188C2×C4⋊C4—431no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4C4×D4311yescharacteristic
193C2×C4⋊C4C22×D4311yescharacteristic
194C2×C22⋊C4—861no—
195C2×C22⋊C4—861no—
196C2×C22⋊C4D17211yescharacteristic
197C2×C22⋊C4C22⋊D4311yescharacteristic
198C2×C42—431no—
199C2×C42—431no—
200C2×C42D17211yescharacteristic
201C2×C42C22⋊D4311yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—1721no—
204C22⋊C8—22no—
205C22⋊C8—862no—
206#97—41no—
207C4×C8—1721no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215C24(C2×D43)⋊C411yescharacteristic
216C2×Q8—862no—
217C2×Q8—1721no—
218C2×Q8—1721no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—41no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4(C2×D43)⋊C411yescharacteristic
228C22×C4(C2×D43)⋊C411yescharacteristic
229C22×C4(C2×D43)⋊C411yescharacteristic
230C22×C4C2×C4×D4311yescharacteristic
231C22×C4C2×D17211yescharacteristic
232C22×C4C2×C22⋊D4311yescharacteristic
233C2×C8—42no—
234C2×C8—1722no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—1721no—
238C4⋊C4—1722no—
239C4⋊C4—1722no—
240C4⋊C4—1721no—
241C4⋊C4—1721no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—862no—
251C42—1721no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×(C2×D43)⋊C411yescharacteristic
258Q8—3442no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—862no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
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#1306323911yescharacteristic
286C2×C4#1306323911yescharacteristic
287C2×C4#1306333312yes—
288C8—82no—
289C8—3442no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1458286711yescharacteristic
298C22C2×#1306323911yescharacteristic
299C22#1458288111yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—3441no—
308C4—3441no—
309C4—3441no—
310C4—1722no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1913294411yescharacteristic
315C2#1913626911yescharacteristic
316C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11556
LCSG ▷ C22×C4×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
3. #19132538C2semidirect
4. #19132528C2semidirect
181. C43#11556semidirect

Maximal subgroups

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

subgroupindex
#191390442
#191329092
#191325382
#191325282
C43×#14642
#1155643