Finite Group Databasebeta

← #25007209

Subgroups — #25007209

Order 11008.

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

normal subgroups only

This group has 462 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#19138912C211yesmaximal, characteristic
2#19132936C211yesmaximal, characteristic
3#19132618C214yesmaximal, complemented
4C4×#99×C43C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic, complemented
6#14582956—21no—
7#14582838C412yescomplemented
8#14582835C2212yes—
9#14582797—21no—
10#14582779—21no—
11#14582771—21no—
12#14582759—21no—
13#14582759C411yescharacteristic, complemented
14#14582623—21no—
15#14582623C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C2×#99×C43—21no—
18C4×C22⋊C4×C43—21no—
19C43×#342C2212yes—
20C23×Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—41no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43C2×C412yes—
26C2×Dic43⋊C4—22no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29C4⋊(C43⋊C8)—41no—
30C22⋊(C43⋊C8)—22no—
31#13063236—41no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95C2×C412yes—
35C22×D4×C43D411yescharacteristic
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C4×D4×C43—41no—
39C4×D4×C43—41no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43C2311yescharacteristic
44C2×C42×C43—41no—
45C2×C42×C43D411yescharacteristic
46#99×C43—24no—
47#95×C43—41no—
48C24×C43C22⋊C411yescharacteristic
49C24×C43C2×D411yescharacteristic
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43—41no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67C22×Dic43—42no—
68C22×Dic43—82no—
69C4⋊C4×C43—41no—
70C22⋊C4×C43—24no—
71C22⋊C4×C43—41no—
72C22⋊C4×C43—41no—
73C22⋊C4×C43—42no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—82no—
77C22⋊Dic43—42no—
78C22⋊Dic43—82no—
79C4⋊Dic43—42no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82C4⋊Dic43—42no—
83Dic43⋊C4—82no—
84C2×C43⋊C8—42no—
85C23×C43—21no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43—41no—
90C23×C43—41no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43#10412yes—
94C23×C43C2×C22⋊C411yescharacteristic
95C23×C43#13712yes—
96D4×C43—44no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—44no—
111C2×C4×C43—81no—
112C2×C4×C43—82no—
113C2×C4×C43—82no—
114C2×C4×C43#9911yescharacteristic
115C2×C4×C43#9911yescharacteristic
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—84no—
123C43⋊C8—82no—
124#11786—431nomaximal, Sylow
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—22no—
128C22×C43—22no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—81no—
137C22×C43C2×#9911yescharacteristic
138C22×C43#41911yescharacteristic
139C22×C43C2×#10411yescharacteristic
140C4×C43—21no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—84no—
146C4×C43#35212yes—
147Dic43—82no—
148Dic43—82no—
149#2487—431no—
150C4×#99D4311yescharacteristic
151#1466—431no—
152#1352—434no—
153C2×C43—21no—
154C2×C43—21no—
155C2×C43—42no—
156C2×C43—42no—
157C2×C43#150811yescharacteristic
158C2×C43C2×#35211yescharacteristic
159C2×C43#212811yescharacteristic
160C2×C4×D4C2×D4311yescharacteristic
161C22×C4⋊C4—431no—
162#432—861no—
163C2×#99—21no—
164#400—432no—
165#399—432no—
166#389—861no—
167#386—861no—
168#385—861no—
169#380—431no—
170#380—861no—
171C4×C22⋊C4—21no—
172#342C2×D4312yes—
173#323—432no—
174#323—861no—
175C43#1178611yescharacteristic, complemented, Sylow
176C22×D4C22⋊D4311yescharacteristic
177C23×C4—861no—
178C23×C4C4×D4311yescharacteristic
179C23×C4C22⋊D4311yescharacteristic
180C4×D4—41no—
181C4×D4—41no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—862no—
184C2×C4⋊C4—861no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—1721no—
187C2×C4⋊C4—1721no—
188C2×C4⋊C4C4×D4311yescharacteristic
189C2×C22⋊C4—22no—
190C2×C22⋊C4—862no—
191C2×C22⋊C4—861no—
192C2×C22⋊C4D17211yescharacteristic
193C2×C22⋊C4C22×D4311yescharacteristic
194C2×C42—41no—
195C2×C42D17211yescharacteristic
196C4⋊C8—1721no—
197#99—24no—
198C22⋊C8—862no—
199#97—1721no—
200#95—41no—
201#95—432no—
202#95—862no—
203#95—862no—
204C24(C2×D43)⋊C411yescharacteristic
205C24C2×C22⋊D4311yescharacteristic
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4—3442no—
219C22×C4—1722no—
220C22×C4(C2×D43)⋊C411yescharacteristic
221C22×C4(C2×D43)⋊C411yescharacteristic
222C22×C4(C2×D43)⋊C411yescharacteristic
223C22×C4C2×C4×D4311yescharacteristic
224C22×C4C2×D17211yescharacteristic
225C2×C8—1722no—
226C4⋊C4—41no—
227C4⋊C4—3442no—
228C4⋊C4—1722no—
229C4⋊C4—1722no—
230C4⋊C4—1721no—
231C4⋊C4—1721no—
232C22⋊C4—24no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—42no—
236C22⋊C4—3442no—
237C22⋊C4—1722no—
238C42—21no—
239C42—21no—
240C42—82no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23#1306325312yes—
250C23C2×(C2×D43)⋊C411yescharacteristic
251C23#1306335512yes—
252D4—44no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—3444no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4—1722no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4—1722no—
277C2×C4#1306323911yescharacteristic
278C2×C4#1306323911yescharacteristic
279C8—3442no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22C2×#1306323911yescharacteristic
293C22#1458290711yescharacteristic
294C22C2×#1306325311yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—84no—
301C4—3442no—
302C4—3442no—
303C4#1458268812yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#1913311411yescharacteristic
309C2C2×#1458268811yescharacteristic
310C2#1913626611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC4×#99×C43C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenterC4×#99D43
hypocenterC43#11786
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #19132618C2semidirect
5. C22×C4⋊Dic43C4semidirect
7. #14582838C4semidirect
13. #14582759C4semidirect
175. C43#11786semidirect

Maximal subgroups

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

subgroupindex
#191389122
#191329362
#191326182
C4×#99×C432
#1178643