Finite Group Databasebeta

← #24992593

Subgroups — #24992593

Order 11008.

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

normal subgroups only

This group has 436 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#19143680C211yesmaximal, characteristic
2#19140471C211yesmaximal, characteristic
3#19133196C212yesmaximal
4#19132460C212yesmaximal
5C4×#101×C43C211yesmaximal, characteristic
6C2×#13063317C2211yescharacteristic
7#14583030—24no—
8#14582956—21no—
9#14582956C2212yes—
10#14582952—21no—
11#14582838C411yescharacteristic
12#14582838C411yescharacteristic
13#14582837—21no—
14#14582829C411yescharacteristic
15#14582829C411yescharacteristic
16#14582818—21no—
17#14582783—21no—
18#14582783—21no—
19#14582767C2211yescharacteristic
20#14582640—24no—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×#101×C43—21no—
23C4×M16×C43C2212yes—
24C43×#343—21no—
25#13063317—22no—
26#13063317—22no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37#13063236—22no—
38#13063236D414yes—
39C4×C43⋊C8—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95C2×C411yescharacteristic
49C43⋊#95C2×C411yescharacteristic
50C22×Q8×C43D411yescharacteristic
51C2×M16×C43—22no—
52C4×Q8×C43—22no—
53C4×Q8×C43—22no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#101×C43—24no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C2×Q8×C43—22no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77M16×C43—24no—
78M16×C43—42no—
79C2×C8×C43—42no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—22no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43C2×D412yes—
88C42×C43#4112yes—
89C4⋊Dic43—22no—
90C4⋊Dic43—22no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93Dic43⋊C4—41no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96C2×C43⋊C8—24no—
97C23×C43C2×C22⋊C411yescharacteristic
98Q8×C43—44no—
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—21no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43#10412yes—
113C2×C4×C43C4×D412yes—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43#12112yes—
116C2×C4×C43#12311yescharacteristic
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—42no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C8×C43—44no—
129C43⋊C8—44no—
130#9190—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43#38611yescharacteristic
134C22×C43C2×#10411yescharacteristic
135C22×C43#42111yescharacteristic
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—22no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—41no—
144Dic43—81no—
145Dic43—81no—
146Dic43—81no—
147Dic43—81no—
148#2983—431no—
149#2634—431no—
150C4×#101D4311yescharacteristic
151#1528—432no—
152#1288—432no—
153C2×C43—21no—
154C2×C43—21no—
155C2×C43#187111yescharacteristic
156C2×C43#191211yescharacteristic
157C2×C43#191511yescharacteristic
158C2×#125—431no—
159C2×C4×Q8C2×D4311yescharacteristic
160#446—864no—
161#432—432no—
162#432—861no—
163#431—861no—
164C2×#101—21no—
165C4×M16C2×D4312yes—
166#400—431no—
167#400—431no—
168#400—861no—
169#398—431no—
170#398—431no—
171#395—861no—
172#387—861no—
173#387—861no—
174#383—431no—
175#343—21no—
176#330—864no—
177C43#919011yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4311yescharacteristic
179C2×M16—22no—
180#125—862no—
181#125—862no—
182C4×Q8—22no—
183C4×Q8—22no—
184C2×C4⋊C4—431no—
185C2×C4⋊C4—431no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4—861no—
188C2×C4⋊C4—861no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4C4×D4311yescharacteristic
191C2×C4⋊C4C4×D4311yescharacteristic
192C2×C4⋊C4C22⋊D4311yescharacteristic
193C2×C42D17211yescharacteristic
194C2×C42D17211yescharacteristic
195C2×C42C22×D4311yescharacteristic
196C4⋊C8—862no—
197C4⋊C8—862no—
198C4⋊C8—862no—
199#101—24no—
200C22⋊C8—862no—
201#97—22no—
202#97—434no—
203#97—862no—
204C4×C8—22no—
205C4×C8—862no—
206#95—431no—
207#95—431no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—861no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4(C2×D43)⋊C411yescharacteristic
224C22×C4(C2×D43)⋊C411yescharacteristic
225C22×C4(C2×D43)⋊C411yescharacteristic
226C22×C4(C2×D43)⋊C411yescharacteristic
227C22×C4C2×C4×D4311yescharacteristic
228C22×C4C2×D17211yescharacteristic
229C22×C4C2×C22⋊D4311yescharacteristic
230M16—24no—
231M16—42no—
232C2×C8—42no—
233C2×C8—864no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—862no—
238C4⋊C4—862no—
239C4⋊C4—1722no—
240C4⋊C4—1722no—
241C4⋊C4—1721no—
242C4⋊C4—1722no—
243C4⋊C4—1721no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42D4×D4312yes—
249C42#1062190012yes—
250C23C2×(C2×D43)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1722no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4#1306325312yes—
277C2×C4(C22⋊D43)⋊C412yes—
278C2×C4#1306329511yescharacteristic
279C2×C4#1306329712yes—
280C2×C4#1306330911yescharacteristic
281C8—44no—
282C8—1724no—
283C22—21no—
284C22—21no—
285C22#1458277611yescharacteristic
286C22C2×#1306325311yescharacteristic
287C22#1458291711yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3441no—
297C4—3441no—
298C4—3441no—
299C4—3441no—
300C2—21no—
301C2—21no—
302C2#1913489511yescharacteristic
303C2#1913513011yescharacteristic
304C2#1913514511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#101×C43C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenterC4×#101D43
hypocenterC43#9190
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
177. C43#9190semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191404712
#191331962
#191324602
C4×#101×C432
#919043