Finite Group Databasebeta

← #24994023

Subgroups — #24994023

Order 11008.

706 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 123 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, complemented
2#19134587C211yesmaximal, characteristic, complemented
3#19133263C212yesmaximal, complemented
4#19132498C212yesmaximal, complemented
5C43×#2541C211yesmaximal, characteristic
6#14582977—24no—
7#14582952C2212yes—
8#14582923C2212yes—
9C2×#13063242—21no—
10#14582863—22no—
11#14582668—21no—
12#14582643—24no—
13C2×#127×C43—21no—
14C2×#127×C43C2211yescharacteristic
15C2×#121×C43—22no—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#392C414yes—
18C43×#390—21no—
19C4×C4⋊C4×C43C2211yescharacteristic
20C2×#10621877—24no—
21C2×#10621877—22no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)D414yescomplemented
25#13063242—42no—
26C22⋊(C43⋊C8)—24no—
27C22⋊(C43⋊C8)—22no—
28C4×C43⋊C8—22no—
29C22×D4×C43—24no—
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43C2×C412yes—
33C22×D4×C43D411yescharacteristic
34C23×C4×C43D412yes—
35#127×C43—22no—
36#127×C43—22no—
37#127×C43—44no—
38#121×C43—48no—
39C4×D4×C43—22no—
40C4×D4×C43—22no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43—24no—
44C2×C22⋊C4×C43C2×C412yes—
45C2×C42×C43—21no—
46C2×C42×C43C2311yescharacteristic
47#95×C43C2×C412yes—
48C24×C43—22no—
49C24×C43C22⋊C412yes—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43—21no—
53C2×D4×C43—21no—
54C2×D4×C43—24no—
55C2×D4×C43—48no—
56C2×D4×C43—48no—
57C2×D4×C43—44no—
58C2×D4×C43—41no—
59C2×D4×C43—42no—
60C2×D4×C43—41no—
61C2×D4×C43—42no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43—82no—
65C2×D4×C43—84no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—44no—
70C22×C4×C43C22⋊C412yes—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C4⋊C4×C43—24no—
75C4⋊C4×C43—22no—
76C22⋊C4×C43—24no—
77C22⋊C4×C43—48no—
78C42×C43—42no—
79C42×C43C2×D412yes—
80C42×C43#4112yes—
81#10621877—42no—
82#10621877—42no—
83#10621877—84no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—42no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43—22no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43—44no—
92C23×C43—44no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43C2×C22⋊C411yescharacteristic
97D4×C43—42no—
98D4×C43—42no—
99D4×C43—84no—
100D4×C43—82no—
101D4×C43—816no—
102D4×C43—82no—
103D4×C43—82no—
104D4×C43—82no—
105C2×C4×C43—22no—
106C2×C4×C43—24no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—44no—
112C2×C4×C43—42no—
113C2×C4×C43—82no—
114C2×C4×C43C4×D412yes—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43#12112yes—
117C2×C4×C43#12311yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)12yes—
120C2×C4×C43#13711yescharacteristic
121C43⋊C8—44no—
122C43⋊C8—82no—
123#9405—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—82no—
131C22×C43—84no—
132C22×C43—84no—
133C22×C43—82no—
134C22×C43—82no—
135C22×C43—82no—
136C22×C43#38611yescharacteristic
137C22×C43#41711yescharacteristic
138C22×C43#41811yescharacteristic
139C4×C43—21no—
140C4×C43—22no—
141C4×C43—44no—
142C4×C43—42no—
143C4×C43#45312yes—
144C4×C43#46812yes—
145C4×C43#46912yes—
146#2975—431no—
147#2541D4311yescharacteristic
148#1800—431no—
149#1545—432no—
150#1303—432no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—82no—
154C2×C43—162no—
155C2×C43#188711yescharacteristic
156C2×C43#189511yescharacteristic
157C2×C43#191411yescharacteristic
158C2×#127—21no—
159C2×#127C2×D4311yescharacteristic
160C2×#121—22no—
161C2×C4×D4C2×D4311yescharacteristic
162#436—864no—
163#431—432no—
164#423—432no—
165C2×#100—861no—
166#407—862no—
167#392Dic4314yes—
168#390—21no—
169C4×C4⋊C4C2×D4311yescharacteristic
170#343—861no—
171#331—864no—
172C43#940511yescharacteristic, complemented, Sylow
173C22×D4—24no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4C2×Dic4312yes—
177C22×D4C22⋊D4311yescharacteristic
178C23×C4C22⋊D4312yes—
179C2×M16—864no—
180C2×M16—862no—
181#127—22no—
182#127—22no—
183#127—44no—
184#121—48no—
185C4×D4—22no—
186C4×D4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C22⋊D4311yescharacteristic
189C2×C22⋊C4—24no—
190C2×C22⋊C4C2×Dic4312yes—
191C2×C42—21no—
192C2×C42C22×D4311yescharacteristic
193C4⋊C8—434no—
194C4⋊C8—862no—
195C4⋊C8—862no—
196#100—1722no—
197C22⋊C8—864no—
198C22⋊C8—862no—
199C4×C8—862no—
200#95C2×Dic4312yes—
201C24—22no—
202C24C22⋊Dic4312yes—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—44no—
209C2×D4—48no—
210C2×D4—48no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—42no—
216C2×D4—41no—
217C2×D4—84no—
218C2×D4—82no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—44no—
223C22×C4C22⋊Dic4312yes—
224C22×C4C22×Dic4311yescharacteristic
225C22×C4C2×C22⋊D4311yescharacteristic
226C22×C4C2×C22⋊D4311yescharacteristic
227M16—3444no—
228M16—1722no—
229M16—1722no—
230C2×C8—864no—
231C2×C8—1722no—
232C4⋊C4—24no—
233C4⋊C4—22no—
234C22⋊C4—24no—
235C22⋊C4—48no—
236C42—42no—
237C42D4×D4312yes—
238C42#1062190012yes—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—44no—
245C23—44no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊Dic4311yescharacteristic
250D4—42no—
251D4—42no—
252D4—84no—
253D4—82no—
254D4—816no—
255D4—82no—
256D4—82no—
257D4—82no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4D4×Dic4312yes—
268C2×C4#1306329311yescharacteristic
269C2×C4#1306329712yes—
270C2×C4#1306330611yescharacteristic
271C2×C4#1306335011yescharacteristic
272C2×C4#1306335112yes—
273C2×C4#1306335511yescharacteristic
274C8—3442no—
275C8—1724no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—82no—
283C22—84no—
284C22—84no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22#1458277911yescharacteristic
289C22#1458290011yescharacteristic
290C22#1458290411yescharacteristic
291C4—21no—
292C4—22no—
293C4—44no—
294C4—42no—
295C4#1458306612yes—
296C4#1458314312yes—
297C4#1458315012yes—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—162no—
302C2#1913499411yescharacteristic
303C2#1913503411yescharacteristic
304C2#1913514311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2541C2
socleC22×C43#386
cosocleC2×C42×C43C23
hypercenter#2541D43
hypocenterC43#9405
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #19143636C2semidirect
2. #19134587C2semidirect
3. #19133263C2semidirect
4. #19132498C2semidirect
24. C4⋊(C43⋊C8)D4semidirect
172. C43#9405semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191345872
#191332632
#191324982
C43×#25412
#940543