Finite Group Databasebeta

← #24994466

Subgroups — #24994466

Order 11008.

602 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 115 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#19139492C211yesmaximal, characteristic
2#19134587C211yesmaximal, characteristic, complemented
3#19133021C212yesmaximal, complemented
4#19132454C212yesmaximal, complemented
5C43×#2975C211yesmaximal, characteristic, complemented
6C2×#13063296—21no—
7C2×C4×D172C2211yescharacteristic
8#14582923C2212yes—
9C2×#13063242—21no—
10#14582824C412yes—
11#14582808C412yes—
12#14582778—22no—
13#14582765C2211yescharacteristic
14#14582756—21no—
15#14582668—21no—
16#14582628—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C43×#436—24no—
19C43×#431C2212yes—
20C43×#407—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—22no—
23C22×C4×D43—21no—
24C2×#10621877—22no—
25#13063296—44no—
26C4×D172—22no—
27C4×D172—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C22⋊Dic43—22no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—22no—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35#13063242—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95C2×C412yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43D412yes—
41C2×M16×C43—24no—
42C4×D4×C43—22no—
43C4×D4×C43—22no—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43C2×C412yes—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—22no—
48C22⋊C8×C43—24no—
49C22⋊C8×C43—22no—
50C4×C8×C43D414yescomplemented
51C24×C43C22⋊C412yes—
52C23×D43—21no—
53C2×D4×C43—22no—
54C2×D4×C43—21no—
55C2×D4×C43—22no—
56C2×D4×C43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—82no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C2×C22⋊D43—44no—
65C2×C22⋊D43—44no—
66C2×C22⋊D43—82no—
67C22×Dic43—22no—
68C22×Dic43—21no—
69C2×D172—22no—
70C2×D172—42no—
71C2×C4×D43—42no—
72C2×C4×D43—42no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75M16×C43—84no—
76C2×C8×C43—24no—
77C4⋊C4×C43—22no—
78C22⋊C4×C43—24no—
79C42×C43C2×D412yes—
80C42×C43#4112yes—
81C22⋊Dic43—44no—
82(C2×D43)⋊C4—41no—
83(C2×D43)⋊C4—41no—
84(C2×D43)⋊C4—82no—
85C4⋊Dic43—22no—
86C4⋊Dic43—42no—
87#10621877—42no—
88#10621877—42no—
89C2×C43⋊C8—42no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43—22no—
97C22×D43—41no—
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—41no—
102C22×D43—41no—
103D4×C43—42no—
104D4×C43—42no—
105C2×C4×C43—22no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—44no—
109C2×C4×C43—42no—
110C2×C4×C43—82no—
111C2×C4×C43C4×D412yes—
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12112yes—
114C2×C4×C43#12311yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)12yes—
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C43#13711yescharacteristic
118C22⋊D43—88no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43—41no—
125D172—24no—
126D172—42no—
127C4×D43—82no—
128C4×D43—82no—
129C8×C43—44no—
130C43⋊C8—82no—
131#9489—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—44no—
135C22×C43—42no—
136C22×C43—42no—
137C22×C43—42no—
138C22×C43—82no—
139C22×C43#38611yescharacteristic
140C22×C43#41711yescharacteristic
141C22×C43#41811yescharacteristic
142C2×D43—42no—
143C2×D43—42no—
144C2×D43—42no—
145C2×D43—81no—
146C2×D43—81no—
147C2×D43—81no—
148C2×D43—81no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—42no—
153C4×C43#46812yes—
154C4×C43#46912yes—
155Dic43—82no—
156Dic43—81no—
157#2975D4311yescharacteristic, complemented
158#2535—431no—
159#1800—431no—
160#1486—432no—
161#1286—432no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—82no—
165C2×C43#189111yescharacteristic
166C2×C43#189511yescharacteristic
167C2×C43#191111yescharacteristic
168D43—82no—
169C2×#121—861no—
170C2×C4×D4—431no—
171C2×C4×D4C2×D4311yescharacteristic
172#436—24no—
173#431C2×D4312yes—
174#423—432no—
175C2×#100—861no—
176#407—22no—
177#397—432no—
178#392—432no—
179#386—862no—
180#382—431no—
181#380—861no—
182#343—861no—
183D4⋊C8—864no—
184C43#948911yescharacteristic, complemented, Sylow
185C22×D4—431no—
186C22×D4—862no—
187C22×D4D17211yescharacteristic
188C23×C4—861no—
189C23×C4C22⋊D4312yes—
190C2×M16—24no—
191C2×M16—862no—
192#121—1724no—
193C4×D4—22no—
194C4×D4—22no—
195C4×D4—862no—
196C4×D4—862no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4D17211yescharacteristic
200C2×C22⋊C4—862no—
201C2×C22⋊C4—862no—
202C2×C22⋊C4—861no—
203C2×C22⋊C4C4×D4312yes—
204C2×C42C22×D4311yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—862no—
207C4⋊C8—862no—
208#100—1722no—
209C22⋊C8—24no—
210C22⋊C8—22no—
211C4×C8C22⋊D4314yescomplemented
212#95—432no—
213#95—862no—
214#95—861no—
215C24—861no—
216C24(C2×D43)⋊C412yes—
217C2×D4—22no—
218C2×D4—21no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—862no—
222C2×D4—3442no—
223C2×D4—1722no—
224C2×D4—1724no—
225C2×D4—1724no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—82no—
229C22×C4—862no—
230C22×C4—861no—
231C22×C4—1722no—
232C22×C4—1722no—
233C22×C4—1721no—
234C22×C4—1721no—
235C22×C4(C2×D43)⋊C412yes—
236C22×C4C2×C4×D4311yescharacteristic
237C22×C4C2×D17211yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239M16—84no—
240M16—1722no—
241M16—1722no—
242C2×C8—24no—
243C2×C8—1722no—
244C4⋊C4—22no—
245C4⋊C4—862no—
246C4⋊C4—1722no—
247C22⋊C4—24no—
248C22⋊C4—3442no—
249C22⋊C4—1724no—
250C22⋊C4—1721no—
251C22⋊C4—1721no—
252C42#1062189812yes—
253C42C2×C22⋊D4312yes—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—862no—
260C23—1721no—
261C23—1721no—
262C23—1721no—
263C23—1721no—
264C23—1721no—
265C23—1721no—
266C23C2×(C2×D43)⋊C411yescharacteristic
267D4—42no—
268D4—42no—
269D4—864no—
270D4—3448no—
271D4—1722no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—3442no—
279C2×C4—3442no—
280C2×C4—1722no—
281C2×C4—1722no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1722no—
285C2×C4—1721no—
286C2×C4C4×C22⋊D4312yes—
287C2×C4#1306329411yescharacteristic
288C2×C4#1306329912yes—
289C2×C4#1306330811yescharacteristic
290C2×C4#1306335312yes—
291C2×C4#1306335311yescharacteristic
292C2×C4#1306335811yescharacteristic
293C8—44no—
294C8—3442no—
295C22—21no—
296C22—21no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—3441no—
303C22—3441no—
304C22—3441no—
305C22—3441no—
306C22—1722no—
307C22—1722no—
308C22—1722no—
309C22#1458277811yescharacteristic
310C22#1458290111yescharacteristic
311C22#1458290511yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—3442no—
317C4—3441no—
318C4#1458314512yes—
319C4#1458315212yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—3442no—
324C2#1913501311yescharacteristic
325C2#1913503311yescharacteristic
326C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2975C2
socleC22×C43#386
prime radical#19139492C2
cosocleC2×C42×C43C23
hypercenter#2975D43
hypocenterC43#9489
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #19134587C2semidirect
3. #19133021C2semidirect
4. #19132454C2semidirect
5. C43×#2975C2semidirect
50. C4×C8×C43D4semidirect
157. #2975D43semidirect
184. C43#9489semidirect
211. C4×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191394922
#191345872
#191330212
#191324542
C43×#29752
#948943