Finite Group Databasebeta

← #24991263

Subgroups — #24991263

Order 11008.

558 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 131 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#19143636C211yesmaximal, characteristic
2#19132990C212yesmaximal, complemented
3#19132916C211yesmaximal, characteristic
4#19132428C212yesmaximal, complemented
5C4×#124×C43C211yesmaximal, characteristic
6#14582977—24no—
7#14582952C2212yes—
8#14582952C2212yes—
9#14582863—22no—
10Q8⋊(C43⋊C8)—24no—
11#14582623—22no—
12C2×#124×C43C411yescharacteristic
13C2×C4×Q8×C43C2211yescharacteristic
14C2×C4×D4×C43C2211yescharacteristic
15C43×#391C411yescharacteristic
16C43×#390C411yescharacteristic
17C43×#388—22no—
18C43×#382C411yescharacteristic
19C4×C22⋊C4×C43—22no—
20C43×C43C2211yescharacteristic
21C2×#10621877—24no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)D414yes—
24C22⋊(C43⋊C8)—24no—
25C22⋊(C43⋊C8)—22no—
26C22⋊(C43⋊C8)—22no—
27C4×C43⋊C8—22no—
28C4×C43⋊C8—22no—
29C22×Q8×C43C2×C411yescharacteristic
30C22×D4×C43C2×C411yescharacteristic
31C23×C4×C43D412yes—
32#124×C43—22no—
33#124×C43—22no—
34C4×Q8×C43—22no—
35C4×Q8×C43—22no—
36C4×D4×C43—22no—
37C4×D4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43D412yes—
44C2×C42×C43—21no—
45C2×C42×C43—21no—
46C2×C42×C43—21no—
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50#95×C43—22no—
51#95×C43—22no—
52C24×C43C22⋊C412yes—
53C2×Q8×C43—21no—
54C2×Q8×C43—22no—
55C2×Q8×C43—22no—
56C2×Q8×C43M1612yescomplemented
57C2×D4×C43—22no—
58C2×D4×C43—21no—
59C2×D4×C43—21no—
60C2×D4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—44no—
68C22×C4×C43C22⋊C412yes—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—42no—
75C22⋊C4×C43—28no—
76C22⋊C4×C43—24no—
77C22⋊C4×C43—44no—
78C42×C43—21no—
79C42×C43—22no—
80C42×C43—42no—
81C42×C43—42no—
82C42×C43—41no—
83C42×C43—41no—
84C42×C43M1612yescomplemented
85C42×C43C2×D412yes—
86C42×C43#4112yes—
87#10621877—84no—
88C2×C43⋊C8—24no—
89C2×C43⋊C8—42no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43C2×C22⋊C411yescharacteristic
96Q8×C43—24no—
97Q8×C43—42no—
98D4×C43—42no—
99D4×C43—42no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—44no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—41no—
116C2×C4×C43—82no—
117C2×C4×C43C4×D412yes—
118C2×C4×C43#12011yescharacteristic
119C2×C4×C43#12112yes—
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43C2×M1611yescharacteristic
122C2×C4×C43C2×M1611yescharacteristic
123C2×C4×C43#13112yes—
124C43⋊C8—44no—
125C43⋊C8—82no—
126#8961—431nomaximal, Sylow
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—44no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—82no—
134C22×C43#38611yescharacteristic
135C22×C43#40711yescharacteristic
136C22×C43#40811yescharacteristic
137C4×C43—22no—
138C4×C43—21no—
139C4×C43—42no—
140C4×C43—42no—
141C4×C43—42no—
142C4×C43—42no—
143C4×C43—81no—
144C4×C43#43512yes—
145C4×C43#43612yes—
146C4×C43#45512yes—
147#2975—431no—
148C4×#124D4311yescharacteristic
149#1479—432no—
150#1460—431no—
151#1276—432no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—82no—
155C2×C43#187011yescharacteristic
156C2×C43#188411yescharacteristic
157C2×C43#188511yescharacteristic
158C2×#124Dic4311yescharacteristic
159C2×C4×Q8C2×D4311yescharacteristic
160C2×C4×D4C2×D4311yescharacteristic
161#436—864no—
162#431—432no—
163#431—432no—
164#407—862no—
165#391Dic4311yescharacteristic
166#390Dic4311yescharacteristic
167#388—22no—
168#382Dic4311yescharacteristic
169C4×C22⋊C4—22no—
170C43C2×D4311yescharacteristic
171Q8⋊C8—864no—
172#323—862no—
173C43#896111yescharacteristic, complemented, Sylow
174C22×Q8C2×Dic4311yescharacteristic
175C22×D4C2×Dic4311yescharacteristic
176C23×C4C22⋊D4312yes—
177C2×M16—864no—
178#124—22no—
179#124—22no—
180C4×Q8—22no—
181C4×Q8—22no—
182C4×D4—22no—
183C4×D4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×Dic4311yescharacteristic
186C2×C4⋊C4C2×Dic4311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4C22⋊D4312yes—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42C2×Dic4311yescharacteristic
194C2×C42C2×Dic4311yescharacteristic
195C2×C42C22×D4311yescharacteristic
196C4⋊C8—434no—
197C4⋊C8—862no—
198C22⋊C8—864no—
199C22⋊C8—862no—
200C22⋊C8—862no—
201C4×C8—862no—
202C4×C8—862no—
203#95—22no—
204#95—22no—
205C24C22⋊Dic4312yes—
206C2×Q8—21no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8#1062187712yescomplemented
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—44no—
221C22×C4C22⋊Dic4312yes—
222C22×C4C22×Dic4311yescharacteristic
223C22×C4C2×C22⋊D4311yescharacteristic
224C22×C4C2×C22⋊D4311yescharacteristic
225M16—3444no—
226C2×C8—864no—
227C2×C8—1722no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C22⋊C4—28no—
232C22⋊C4—24no—
233C22⋊C4—44no—
234C42—21no—
235C42—22no—
236C42—42no—
237C42—42no—
238C42—41no—
239C42—41no—
240C42#1062187712yescomplemented
241C42D4×D4312yes—
242C42#1062190012yes—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23C2×C22⋊Dic4311yescharacteristic
249Q8—24no—
250Q8—42no—
251D4—42no—
252D4—42no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—82no—
270C2×C4D4×Dic4312yes—
271C2×C4#1306329311yescharacteristic
272C2×C4#1306329712yes—
273C2×C4#1306330611yescharacteristic
274C2×C4C2×#1062187711yescharacteristic
275C2×C4C2×#1062187711yescharacteristic
276C2×C4#1306333212yes—
277C8—3442no—
278C8—1724no—
279C22—21no—
280C22—21no—
281C22—44no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—82no—
286C22#1458277911yescharacteristic
287C22#1458286311yescharacteristic
288C22#1458286611yescharacteristic
289C4—22no—
290C4—21no—
291C4—42no—
292C4—42no—
293C4—42no—
294C4—42no—
295C4—81no—
296C4#1458297112yes—
297C4#1458297712yes—
298C4#1458307612yes—
299C2—21no—
300C2—21no—
301C2—82no—
302C2#1913489311yescharacteristic
303C2#1913497911yescharacteristic
304C2#1913498411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#124×C43C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#124D43
hypocenterC43#8961
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #19132990C2semidirect
4. #19132428C2semidirect
56. C2×Q8×C43M16semidirect
84. C42×C43M16semidirect
173. C43#8961semidirect
209. C2×Q8#10621877semidirect
240. C42#10621877semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191329902
#191329162
#191324282
C4×#124×C432
#896143