Finite Group Databasebeta

← #25000992

Subgroups — #25000992

Order 11008.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#19135581C212yesmaximal
2#19135019C212yesmaximal
3#19134772C211yesmaximal, characteristic
4#19132463C211yesmaximal, characteristic
5C43×#3189C211yesmaximal, characteristic
6C23×C43⋊C8C2211yescharacteristic
7C2×Dic43⋊C8—21no—
8C2×#13063249—22no—
9#14582759C2212yes—
10C4×C22⋊Dic43C2211yescharacteristic
11#14582666—22no—
12#14582666—22no—
13#14582661—22no—
14#14582653—21no—
15C2×C22⋊Q8×C43C2212yes—
16C43×#484—22no—
17C43×#467—21no—
18C43×#467—21no—
19C43×#451—22no—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×C43⋊C8—22no—
22C22×C43⋊C8—21no—
23C22×C43⋊C8—42no—
24C2×C4⋊Dic43—22no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43D411yescharacteristic
27C2×C22⋊Dic43D411yescharacteristic
28C2×C4×Dic43—21no—
29Dic43⋊C8—42no—
30#13063249—44no—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C22×Q8×C43D412yes—
34C23×C4×C43C2311yescharacteristic
35C2×Q16×C43—21no—
36C2×Q16×C43—21no—
37C22×C8×C43D411yescharacteristic
38C22×C8×C43D411yescharacteristic
39C22⋊Q8×C43—22no—
40C22⋊Q8×C43—22no—
41C22⋊Q8×C43—22no—
42C22⋊Q8×C43—22no—
43C2×C4⋊C4×C43—22no—
44C2×C4⋊C4×C43D412yes—
45C2×C22⋊C4×C43—22no—
46#107×C43—21no—
47#107×C43—21no—
48#103×C43—22no—
49#103×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43C2×D411yescharacteristic
52C2×Q8×C43—22no—
53C2×Q8×C43—22no—
54C2×Q8×C43—42no—
55C2×Q8×C43—42no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43C2×D412yes—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×C4×C43#4112yes—
64C22×Dic43—21no—
65C22×Dic43—21no—
66C22×Dic43—42no—
67Q16×C43—81no—
68Q16×C43—81no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C22⋊Dic43—21no—
80C22⋊Dic43—22no—
81C22⋊Dic43—42no—
82C22⋊Dic43—42no—
83C22⋊Dic43Q1612yescomplemented
84C4⋊Dic43—42no—
85C4⋊Dic43—42no—
86C4×Dic43—41no—
87C4×Dic43—41no—
88C2×C43⋊C8—24no—
89C2×C43⋊C8—22no—
90C2×C43⋊C8—41no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—41no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43#12111yescharacteristic
96C23×C43#12112yes—
97C23×C43C2×Q1611yescharacteristic
98C23×C43#13511yescharacteristic
99C23×C43#13712yes—
100Q8×C43—44no—
101Q8×C43—42no—
102Q8×C43—42no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—82no—
112C2×C4×C43—82no—
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43#12312yes—
115C2×C4×C43#12411yescharacteristic
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—82no—
123C2×Dic43—82no—
124C2×Dic43—82no—
125C8×C43—41no—
126C8×C43—41no—
127C43⋊C8—42no—
128#10566—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—22no—
131C22×C43—21no—
132C22×C43—22no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43—42no—
136C22×C43#39411yescharacteristic
137C22×C43#46212yes—
138C22×C43#46412yes—
139C22×C43#46711yescharacteristic
140C22×C43#47011yescharacteristic
141C4×C43—22no—
142C4×C43—21no—
143C4×C43—82no—
144C4×C43—82no—
145C4×C43B(4,𝔽2)11yescharacteristic
146C4×C43#45811yescharacteristic
147Dic43—42no—
148Dic43—81no—
149Dic43—162no—
150#3189D4311yescharacteristic
151#1996—432no—
152#1892—432no—
153#1850—431no—
154#1289—431no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43—22no—
158C2×C43—22no—
159C2×C43#204411yescharacteristic
160C2×C43#205311yescharacteristic
161C2×C43#205611yescharacteristic
162C23×C8—431no—
163C2×C22⋊Q8C2×D4312yes—
164#484—22no—
165#467—21no—
166#467—21no—
167#451—22no—
168C2×C4⋊C8—861no—
169C2×#103—862no—
170C2×C22⋊C8C2×D4311yescharacteristic
171#380—432no—
172C4×C22⋊C4—431no—
173#342—862no—
174#342—862no—
175#340—862no—
176#336—861no—
177C43#1056611yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4312yes—
179C23×C4C22×D4311yescharacteristic
180C2×Q16—21no—
181C2×Q16—21no—
182C22×C8—861no—
183C22×C8—862no—
184C22×C8—1722no—
185C22×C8C22⋊D4311yescharacteristic
186C22×C8C22⋊D4311yescharacteristic
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4C22⋊D4312yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—431no—
197C2×C22⋊C4—862no—
198C2×C42—861no—
199#107—21no—
200#107—21no—
201C4⋊C8—1722no—
202#103—22no—
203#103—22no—
204#103—1724no—
205C22⋊C8—22no—
206#95—861no—
207#95—862no—
208C24D4×D4311yescharacteristic
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4—1722no—
220C22×C4#1062190011yescharacteristic
221C22×C4#1062190012yes—
222C22×C4C2×C22⋊D4312yes—
223C22×C4C2×C22⋊D4311yescharacteristic
224Q16—81no—
225Q16—81no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—864no—
231C2×C8—862no—
232C2×C8—1721no—
233C2×C8—1722no—
234C2×C8—1721no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—1722no—
240C4⋊C4—1722no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—432no—
244C22⋊C4—861no—
245C22⋊C4—862no—
246C22⋊C4—1722no—
247C22⋊C4—1722no—
248C42—1721no—
249C42—1721no—
250C23—41no—
251C23—41no—
252C23#1306329611yescharacteristic
253C23#1306329712yes—
254C23Q16×D4311yescharacteristic
255C23#1306334811yescharacteristic
256C23#1306335712yes—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—862no—
271C2×C4—3442no—
272C2×C4—3442no—
273C2×C4—3442no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4#1306329411yescharacteristic
280C2×C4#1306330612yes—
281C2×C4#1306331211yescharacteristic
282C8—41no—
283C8—41no—
284C8—1722no—
285C22—22no—
286C22—21no—
287C22—22no—
288C22—21no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22#1458281311yescharacteristic
293C22#1458310712yes—
294C22#1458312312yes—
295C22#1458313711yescharacteristic
296C22#1458315411yescharacteristic
297C4—22no—
298C4—21no—
299C4—82no—
300C4—82no—
301C4—3441no—
302C4—1722no—
303C4—6882no—
304C4#1458308611yescharacteristic
305C4#1458308911yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2#1913584311yescharacteristic
311C2#1913589811yescharacteristic
312C2#1913591511yescharacteristic
subgroupG/H
centerC22#14582813
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3189C2
socleC22×C43#394
prime radicalC24×C43C2×D4
hypercenter#3189D43
hypocenterC43#10566
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
83. C22⋊Dic43Q16semidirect
177. C43#10566semidirect

Maximal subgroups

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

subgroupindex
#191355812
#191350192
#191347722
#191324632
C43×#31892
#1056643