Finite Group Databasebeta

← #24990006

Subgroups — #24990006

Order 11008.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137001C211yesmaximal, characteristic
2#19134358C212yesmaximal
3#19132477C212yesmaximal, complemented
4#19132476C211yesmaximal, characteristic, complemented
5C43×#1295C211yesmaximal, characteristic, complemented
6C2×#13063283C411yescharacteristic
7C2×#13063283C411yescharacteristic
8C2×C42×D43C2211yescharacteristic
9C2×(C2×D43)⋊C8—22no—
10C2×#13063236C2212yes—
11#14582768C411yescharacteristic
12#14582768C411yescharacteristic
13#14582765C2211yescharacteristic
14#14582758—22no—
15#14582750—22no—
16#14582653—22no—
17C2×#97×C43C2212yes—
18C43×#382C2211yescharacteristic
19C22×C4×D43C2×C411yescharacteristic
20C22×C4×D43D412yes—
21C22×C43⋊C8—22no—
22#13063283—42no—
23#13063283—42no—
24C2×C4⋊Dic43C2×C411yescharacteristic
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28C2×(C2×D43)⋊C4—21no—
29C2×(C2×D43)⋊C4—21no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43D412yes—
34C42×D43—22no—
35C42×D43—21no—
36C42×D43—21no—
37(C2×D43)⋊C8—28no—
38#13063236—22no—
39#13063236—22no—
40C43⋊#95—22no—
41C22×C8×C43—22no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C42×C43C2311yescharacteristic
45#97×C43—22no—
46#97×C43—22no—
47#95×C43—22no—
48C23×D43C22⋊C411yescharacteristic
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—21no—
54C22×Dic43—21no—
55C22×Dic43C22⋊C411yescharacteristic
56C22×Dic43C22⋊C412yes—
57C2×C4×D43—21no—
58C2×C4×D43—21no—
59C2×C4×D43—22no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×C4×D43—24no—
63C2×C4×D43—22no—
64C2×C4×D43—42no—
65C2×C8×C43—24no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C42×C43#4112yes—
71C42×C43#4111yescharacteristic
72C42×C43#4111yescharacteristic
73(C2×D43)⋊C4—42no—
74(C2×D43)⋊C4—42no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77Dic43⋊C4—44no—
78Dic43⋊C4—44no—
79C4×Dic43—21no—
80C4×Dic43—21no—
81C4×Dic43—22no—
82C4×Dic43—22no—
83C4×Dic43—42no—
84C4×Dic43—42no—
85C2×C43⋊C8—24no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—42no—
88C23×C43C2×C22⋊C411yescharacteristic
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43#10112yes—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43#11711yescharacteristic
103C2×C4×C43#11711yescharacteristic
104C2×C4×C43#12312yes—
105C2×C4×C43#12312yes—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43#10012yes—
115C2×Dic43#10414yes—
116C4×D43—24no—
117C4×D43—24no—
118C4×D43—44no—
119C4×D43—44no—
120C8×C43—44no—
121C43⋊C8—44no—
122#8721—431nomaximal, Sylow
123C22×C43#38111yescharacteristic
124C22×C43C2×#10011yescharacteristic
125C22×C43C2×#10111yescharacteristic
126C22×C43C2×#10412yes—
127C22×C43#42112yes—
128C2×D43—22no—
129C2×D43—24no—
130C2×D43—41no—
131C2×D43—42no—
132C2×D43—41no—
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—22no—
136C4×C43—22no—
137C4×C43—81no—
138C4×C43—81no—
139Dic43—22no—
140Dic43—24no—
141Dic43—81no—
142Dic43—81no—
143#2285—431no—
144#1749—432no—
145#1295—432no—
146#1295—431no—
147#1295D4311yescharacteristic, complemented
148C2×C43#152511yescharacteristic
149C2×C43#153112yes—
150C2×C43#153611yescharacteristic
151C2×C43#182111yescharacteristic
152C2×C43#182612yes—
153D43—42no—
154C2×#117—431no—
155C2×#117—431no—
156C22×C42—431no—
157C2×C22⋊C8—862no—
158C2×#97—432no—
159C2×#97C2×D4312yes—
160#384—431no—
161#384—431no—
162#382—431no—
163#382C2×D4311yescharacteristic
164#380—862no—
165C4×C4⋊C4—862no—
166#336—862no—
167C43#872111yescharacteristic, complemented, Sylow
168C23×C4—431no—
169C23×C4—432no—
170C22×C8—22no—
171C22×C8—862no—
172#117—1722no—
173#117—1722no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4—431no—
176C2×C4⋊C4—862no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4C4×D4311yescharacteristic
179C2×C4⋊C4C4×D4311yescharacteristic
180C2×C22⋊C4—861no—
181C2×C22⋊C4—861no—
182C2×C42—431no—
183C2×C42—432no—
184C2×C42—862no—
185C2×C42—861no—
186C2×C42—861no—
187C2×C42—861no—
188C2×C42—861no—
189C2×C42C22×D4311yescharacteristic
190C22⋊C8—868no—
191#97—22no—
192#97—22no—
193#97—862no—
194#97—862no—
195#95—22no—
196#95—862no—
197C24—431no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—431no—
201C22×C4—432no—
202C22×C4—862no—
203C22×C4—864no—
204C22×C4—862no—
205C22×C4—861no—
206C22×C4—861no—
207C22×C4—862no—
208C22×C4—862no—
209C22×C4—861no—
210C22×C4—861no—
211C22×C4—1722no—
212C22×C4C2×C4×D4311yescharacteristic
213C22×C4D4×D4312yes—
214C2×C8—24no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—864no—
218C2×C8—1722no—
219C2×C8—1722no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—1721no—
223C4⋊C4—1721no—
224C4⋊C4—1724no—
225C4⋊C4—1724no—
226C22⋊C4—1722no—
227C22⋊C4—1722no—
228C42—861no—
229C42—861no—
230C42—862no—
231C42—862no—
232C42—1722no—
233C42—1722no—
234C42#1062189812yes—
235C42#1062190011yescharacteristic
236C42#1062190211yescharacteristic
237C23—432no—
238C23—861no—
239C23—862no—
240C23—862no—
241C23—861no—
242C23C22⋊C4×D4311yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—432no—
252C2×C4—434no—
253C2×C4—864no—
254C2×C4—864no—
255C2×C4—861no—
256C2×C4—862no—
257C2×C4—861no—
258C2×C4—862no—
259C2×C4—1724no—
260C2×C4—1724no—
261C2×C4—1721no—
262C2×C4—1721no—
263C2×C4—1722no—
264C2×C4—1722no—
265C2×C4#1306328211yescharacteristic
266C2×C4#1306328311yescharacteristic
267C2×C4#1306330712yes—
268C2×C4#1306331012yes—
269C8—44no—
270C8—1724no—
271C22—864no—
272C22—862no—
273C22—1721no—
274C22—1721no—
275C22—1722no—
276C22#1458276111yescharacteristic
277C22#100×D4311yescharacteristic
278C22#101×D4311yescharacteristic
279C22#104×D4312yes—
280C22#1458291412yes—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—81no—
286C4—81no—
287C4—862no—
288C4—864no—
289C4—3441no—
290C4—3441no—
291C2—1722no—
292C2#1913318511yescharacteristic
293C2#1913320812yes—
294C2#1913322811yescharacteristic
295C2#1913467411yescharacteristic
296C2#1913469312yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#8721
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #19132477C2semidirect
4. #19132476C2semidirect
5. C43×#1295C2semidirect
147. #1295D43semidirect
167. C43#8721semidirect

Maximal subgroups

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

subgroupindex
#191370012
#191343582
#191324772
#191324762
C43×#12952
#872143