Finite Group Databasebeta

← #25013445

Subgroups — #25013445

Order 11008.

416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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#19143662C211yesmaximal, characteristic
2#19136280C211yesmaximal, characteristic
3#19134815C212yesmaximal, complemented
4#19132723C212yesmaximal, complemented
5C43×#1884C211yesmaximal, characteristic
6#14582977—22no—
7D4×C43⋊C8—22no—
8#14582952—21no—
9#14582947—22no—
10#14582883C2212yes—
11#14582866—21no—
12#14582866C2212yes—
13#14582698C412yescomplemented
14#14582696C412yescomplemented
15#14582663—22no—
16C43×#568C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C43×#421—21no—
19C43×#410C2211yescharacteristic
20C43×#339—21no—
21C2×#10621877—21no—
22C2×#10621877—22no—
23C2×#10621877D412yes—
24C22×C43⋊C8—21no—
25C22×C43⋊C8D412yes—
26#13063260—44no—
27C4⋊(C43⋊C8)—21no—
28C4⋊(C43⋊C8)—21no—
29#13063244C2×C414yes—
30#13063242—22no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C4×C43⋊C8—22no—
35C2×#41×C43D411yescharacteristic
36C2×#41×C43C2311yescharacteristic
37#131×C43—42no—
38C2×M16×C43—21no—
39C2×M16×C43—22no—
40C4⋊Q8×C43C2×C411yescharacteristic
41#127×C43Q811yescharacteristic
42#124×C43C2×C411yescharacteristic
43#124×C43Q811yescharacteristic
44#121×C43—22no—
45C4×D4×C43—22no—
46#117×C43—21no—
47C2×C42×C43D411yescharacteristic
48#104×C43—42no—
49#99×C43—22no—
50#41×C43—41no—
51#41×C43—41no—
52#41×C43—41no—
53#41×C43—41no—
54C2×Q8×C43C4⋊C411yescharacteristic
55C2×Q8×C43C22×C411yescharacteristic
56C2×D4×C43—22no—
57C2×D4×C43—21no—
58C2×D4×C43C4⋊C411yescharacteristic
59C2×D4×C43C2×Q811yescharacteristic
60C2×D4×C43#4112yes—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65M16×C43—22no—
66M16×C43—24no—
67M16×C43—41no—
68C2×C8×C43—42no—
69C2×C8×C43—41no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—41no—
72C22⋊C4×C43—22no—
73C22⋊C4×C43—22no—
74C22⋊C4×C43—41no—
75C42×C43—21no—
76C42×C43—41no—
77C42×C43C4⋊C411yescharacteristic
78C42×C43C4⋊C411yescharacteristic
79#10621877—24no—
80#10621877—42no—
81#10621877—42no—
82#10621877—81no—
83C2×C43⋊C8—22no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—81no—
88C23×C43—21no—
89C23×C43C22⋊Q812yes—
90C23×C43#12311yescharacteristic
91Q8×C43—41no—
92Q8×C43—41no—
93D4×C43—41no—
94D4×C43—42no—
95D4×C43—41no—
96D4×C43—44no—
97D4×C43—81no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—81no—
109C2×C4×C43C2×C4⋊C411yescharacteristic
110C2×C4×C43C4×D412yes—
111C2×C4×C43#12011yescharacteristic
112C8×C43—42no—
113C43⋊C8—44no—
114C43⋊C8—42no—
115C43⋊C8—42no—
116#12975—431nomaximal, Sylow
117C22×C43—22no—
118C22×C43—21no—
119C22×C43—42no—
120C22×C43—41no—
121C22×C43—42no—
122C22×C43—41no—
123C22×C43#38511yescharacteristic
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—21no—
127C4×C43—41no—
128C4×C43—41no—
129C4×C43—161no—
130C4×C43B(4,𝔽2)11yescharacteristic
131C4×C43#45811yescharacteristic
132#2979—431no—
133#2132—431no—
134#1884D4311yescharacteristic
135#1858—432no—
136#1395—432no—
137C2×C43—21no—
138C2×C43—41no—
139C2×C43—42no—
140C2×C43—81no—
141C2×C43#186711yescharacteristic
142#568C2×D4311yescharacteristic
143#532C2×D4311yescharacteristic
144#436—862no—
145C8×D4—862no—
146#431—861no—
147#430—862no—
148#421—21no—
149#413—432no—
150#410C2×D4311yescharacteristic
151#408—432no—
152#408—861no—
153#356—432no—
154#355—432no—
155#341—862no—
156#339—21no—
157C43#1297511yescharacteristic, complemented, Sylow
158C2×#41C22⋊D4311yescharacteristic
159C2×#41C22×D4311yescharacteristic
160#131—42no—
161C2×M16—22no—
162C2×M16—21no—
163C2×M16—432no—
164C2×M16—861no—
165C2×M16—862no—
166C22×C8—432no—
167C22×C8—861no—
168C4⋊Q8C4×D4311yescharacteristic
169#127Dic8611yescharacteristic
170#124Dic8611yescharacteristic
171#124C4×D4311yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—21no—
175C2×C42C22⋊D4311yescharacteristic
176#108—1724no—
177C4⋊C8—861no—
178C4⋊C8—861no—
179#104—42no—
180#101—434no—
181#100—862no—
182#99—22no—
183C22⋊C8—862no—
184C22⋊C8—862no—
185C22⋊C8—862no—
186C4×C8—862no—
187#41—41no—
188#41—41no—
189#41—41no—
190#41—41no—
191C2×Q8Dic43⋊C411yescharacteristic
192C2×Q8C2×C4×D4311yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4Dic43⋊C411yescharacteristic
196C2×D4C2×Dic8611yescharacteristic
197C2×D4#1062190012yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4D4×D4312yes—
201C22×C4C2×C22⋊D4311yescharacteristic
202M16—22no—
203M16—24no—
204M16—41no—
205M16—864no—
206M16—3441no—
207M16—1722no—
208M16—1722no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—862no—
212C2×C8—862no—
213C2×C8—3441no—
214C2×C8—1722no—
215C2×C8—1722no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C22⋊C4—41no—
221C42—21no—
222C42—41no—
223C42Dic43⋊C411yescharacteristic
224C42Dic43⋊C411yescharacteristic
225C23—21no—
226C23#1306330212yes—
227C23#1306330611yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—44no—
234D4—81no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4C2×Dic43⋊C411yescharacteristic
247C2×C4(C22⋊D43)⋊C412yes—
248C2×C4#1306329311yescharacteristic
249C8—42no—
250C8—1724no—
251C8—1722no—
252C8—1722no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22#1458277111yescharacteristic
260C4—22no—
261C4—22no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—161no—
266C4#1458308511yescharacteristic
267C4#1458308811yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2#1913487511yescharacteristic
subgroupG/H
centerC4#14583085
commutatorC2×Q8×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#1884C2
socleC2×C43#1867
prime radicalC43×#532C22
cosocleC2×#41×C43C23
hypercenter#1884D43
hypocenterC43#12975
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1884

Complements

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

NH ≅ G/Ntype
3. #19134815C2semidirect
4. #19132723C2semidirect
13. #14582698C4semidirect
14. #14582696C4semidirect
157. C43#12975semidirect

Maximal subgroups

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

subgroupindex
#191436622
#191362802
#191348152
#191327232
C43×#18842
#1297543