Finite Group Databasebeta

← #25012628

Subgroups — #25012628

Order 11008.

420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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#19143307C211yesmaximal, characteristic
2#19136280C211yesmaximal, characteristic
3#19134643C212yesmaximal, complemented
4#19132717C212yesmaximal, complemented
5C43×#2132C211yesmaximal, characteristic
6C2×#13063332C411yescharacteristic
7C2×#13063332C2211yescharacteristic
8#14582977—22no—
9D4×C43⋊C8—22no—
10C2×#13063260—22no—
11#14582923C411yescharacteristic
12#14582883C2212yes—
13#14582866C411yescharacteristic
14#14582866C2211yescharacteristic
15C2×C4×C43⋊C8C411yescharacteristic
16#14582698—21no—
17#14582696—21no—
18C43⋊#338—22no—
19C43×#532C2211yescharacteristic
20C43×#413C2212yes—
21C43×#356—21no—
22C43×#355—21no—
23#13063332—42no—
24#13063332—42no—
25C2×#10621877—21no—
26C2×#10621877—22no—
27C2×#10621877C2×C411yescharacteristic
28C2×#10621877C2×C411yescharacteristic
29C2×#10621877D412yes—
30C22×C43⋊C8—21no—
31C22×C43⋊C8C2×C411yescharacteristic
32C22×C43⋊C8C2×C411yescharacteristic
33C22×C43⋊C8D412yes—
34#13063260—44no—
35C4⋊(C43⋊C8)—22no—
36#13063244—22no—
37#13063242—22no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C2×#41×C43C2×C411yescharacteristic
43C2×#41×C43C2311yescharacteristic
44C2×M16×C43—22no—
45C4⋊Q8×C43D411yescharacteristic
46#127×C43Q811yescharacteristic
47#124×C43D411yescharacteristic
48#124×C43Q811yescharacteristic
49#121×C43—22no—
50C4×D4×C43—22no—
51C2×C42×C43C2×C411yescharacteristic
52#101×C43—22no—
53#100×C43—22no—
54#41×C43—41no—
55#41×C43—41no—
56#41×C43—41no—
57#41×C43—41no—
58C2×Q8×C43C4⋊C411yescharacteristic
59C2×Q8×C43C2×D411yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—22no—
62C2×D4×C43C4⋊C411yescharacteristic
63C2×D4×C43C2×Q811yescharacteristic
64C2×D4×C43#4112yes—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D412yes—
69M16×C43—42no—
70M16×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—22no—
73C22⋊C4×C43—22no—
74C22⋊C4×C43—22no—
75C42×C43—21no—
76C42×C43C4⋊C411yescharacteristic
77C42×C43C4⋊C411yescharacteristic
78#10621877—41no—
79#10621877—42no—
80#10621877—42no—
81#10621877—41no—
82#10621877—42no—
83#10621877—42no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—21no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—41no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8C22⋊C411yescharacteristic
92C2×C43⋊C8C22⋊C412yes—
93C2×C43⋊C8C22⋊C411yescharacteristic
94C23×C43—21no—
95C23×C43#11711yescharacteristic
96C23×C43C22⋊Q812yes—
97Q8×C43—41no—
98Q8×C43—41no—
99D4×C43—41no—
100D4×C43—42no—
101D4×C43—41no—
102D4×C43—44no—
103D4×C43—42no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43C2×C4⋊C411yescharacteristic
116C2×C4×C43#12112yes—
117C8×C43—82no—
118C43⋊C8—22no—
119C43⋊C8—21no—
120C43⋊C8—41no—
121C43⋊C8—41no—
122C43⋊C8—82no—
123C43⋊C8#9912yes—
124#12809—431nomaximal, Sylow
125C22×C43—21no—
126C22×C43—22no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—41no—
131C22×C43#38011yescharacteristic
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—21no—
135C4×C43—41no—
136C4×C43—41no—
137C4×C43C2×#9911yescharacteristic
138C4×C43#41011yescharacteristic
139#2931—431no—
140#2132—431no—
141#2132D4311yescharacteristic
142#1813—432no—
143#1392—432no—
144C2×C43—21no—
145C2×C43—41no—
146C2×C43—42no—
147C2×C43—81no—
148C2×C43#179911yescharacteristic
149C2×#131—431no—
150C2×#131—431no—
151#532C2×D4311yescharacteristic
152#436—862no—
153C8×D4—862no—
154C2×#108—862no—
155#423—431no—
156#413—432no—
157#413C2×D4312yes—
158#408—431no—
159#408—431no—
160C2×C4×C8—431no—
161#356—21no—
162#356—861no—
163#355—21no—
164#355—861no—
165#338—862no—
166C43#1280911yescharacteristic, complemented, Sylow
167C2×#41C4×D4311yescharacteristic
168C2×#41C22×D4311yescharacteristic
169#131—1722no—
170#131—1722no—
171C2×M16—22no—
172C2×M16—431no—
173C2×M16—432no—
174C2×M16—431no—
175C2×M16—861no—
176C2×M16—862no—
177C22×C8—431no—
178C22×C8—432no—
179C22×C8—431no—
180C22×C8—861no—
181C4⋊Q8C22⋊D4311yescharacteristic
182#127Dic8611yescharacteristic
183#124Dic8611yescharacteristic
184#124C22⋊D4311yescharacteristic
185#121—22no—
186C4×D4—22no—
187C2×C42C4×D4311yescharacteristic
188#108—1724no—
189C4⋊C8—862no—
190#101—22no—
191#101—862no—
192#100—22no—
193#100—862no—
194C22⋊C8—862no—
195C22⋊C8—862no—
196C4×C8—861no—
197C4×C8—861no—
198#41—41no—
199#41—41no—
200#41—41no—
201#41—41no—
202C2×Q8Dic43⋊C411yescharacteristic
203C2×Q8C2×C22⋊D4311yescharacteristic
204C2×D4—21no—
205C2×D4—22no—
206C2×D4Dic43⋊C411yescharacteristic
207C2×D4C2×Dic8611yescharacteristic
208C2×D4#1062190012yes—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C2×C4×D4311yescharacteristic
212C22×C4D4×D4312yes—
213M16—42no—
214M16—42no—
215M16—1722no—
216M16—1721no—
217M16—1722no—
218M16—1722no—
219M16—1722no—
220M16—1721no—
221C2×C8—42no—
222C2×C8—431no—
223C2×C8—431no—
224C2×C8—432no—
225C2×C8—864no—
226C2×C8—862no—
227C2×C8—861no—
228C2×C8—861no—
229C2×C8—1722no—
230C2×C8—1722no—
231C2×C8—1721no—
232C4⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C42—21no—
236C42Dic43⋊C411yescharacteristic
237C42Dic43⋊C411yescharacteristic
238C23—21no—
239C23#1306328111yescharacteristic
240C23#1306330212yes—
241Q8—41no—
242Q8—41no—
243D4—41no—
244D4—42no—
245D4—41no—
246D4—44no—
247D4—42no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4C22⋊C4×D4311yescharacteristic
259C2×C4C2×Dic43⋊C411yescharacteristic
260C2×C4#1306329712yes—
261C8—82no—
262C8—432no—
263C8—861no—
264C8—862no—
265C8—3442no—
266C8—1721no—
267C8—1721no—
268C22—21no—
269C22—22no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22#1458275711yescharacteristic
275C4—22no—
276C4—22no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4#99×D4311yescharacteristic
281C4#1458287111yescharacteristic
282C2—21no—
283C2—41no—
284C2—42no—
285C2—81no—
286C2#1913458111yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#2132C2
socleC2×C43#1799
prime radicalC43×#532C22
cosocleC2×#41×C43C23
hypercenter#2132D43
hypocenterC43#12809
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #19134643C2semidirect
4. #19132717C2semidirect
166. C43#12809semidirect

Maximal subgroups

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

subgroupindex
#191433072
#191362802
#191346432
#191327172
C43×#21322
#1280943