Finite Group Databasebeta

← #24994446

Subgroups — #24994446

Order 11008.

626 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2972C211yesmaximal, 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
18C8×D4×C43—24no—
19C43×#431C2212yes—
20C2×C22⋊C8×C43—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—22no—
23C22×C4×D43—21no—
24C2×#10621877—22no—
25#13063296—42no—
26#13063296—42no—
27C4×D172—22no—
28C4×D172—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C22⋊Dic43—22no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—22no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)—22no—
36#13063242—42no—
37C43⋊#95—22no—
38C43⋊#95—21no—
39C43⋊#95C2×C412yes—
40C22×D4×C43D411yescharacteristic
41C23×C4×C43D412yes—
42C22×C8×C43—24no—
43C4×D4×C43—22no—
44C4×D4×C43—22no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43C2×C412yes—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49C22⋊C8×C43—24no—
50C22⋊C8×C43—22no—
51C4×C8×C43D414yescomplemented
52C24×C43C22⋊C412yes—
53C23×D43—21no—
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43D812yes—
57C2×D4×C43SD1612yes—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—82no—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C2×C22⋊D43—44no—
66C2×C22⋊D43—44no—
67C2×C22⋊D43—82no—
68C22×Dic43—22no—
69C22×Dic43—21no—
70C2×D172—22no—
71C2×D172—42no—
72C2×C4×D43—42no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C2×C4×D43—42no—
76C2×C8×C43—24no—
77C2×C8×C43—84no—
78C4⋊C4×C43—22no—
79C22⋊C4×C43—24no—
80C42×C43C2×D412yes—
81C42×C43#4112yes—
82C22⋊Dic43—44no—
83(C2×D43)⋊C4—41no—
84(C2×D43)⋊C4—41no—
85(C2×D43)⋊C4—82no—
86C4⋊Dic43—22no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89#10621877—42no—
90#10621877—42no—
91C2×C43⋊C8—42no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43#10214yes—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—22no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105D4×C43—24no—
106D4×C43—24no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—44no—
111C2×C4×C43—42no—
112C2×C4×C43—82no—
113C2×C4×C43C4×D412yes—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43#12112yes—
116C2×C4×C43#12311yescharacteristic
117C2×C4×C43C2×D811yescharacteristic
118C2×C4×C43C2×SD1611yescharacteristic
119C2×C4×C43#13512yes—
120C22⋊D43—88no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127D172—24no—
128D172—42no—
129C4×D43—82no—
130C4×D43—82no—
131C8×C43—44no—
132C43⋊C8—82no—
133#9485—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—24no—
137C22×C43—44no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43—82no—
141C22×C43#38611yescharacteristic
142C22×C43C2×#10211yescharacteristic
143C22×C43#41611yescharacteristic
144C2×D43—42no—
145C2×D43—42no—
146C2×D43—42no—
147C2×D43—81no—
148C2×D43—81no—
149C2×D43—81no—
150C2×D43—81no—
151C4×C43—22no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—42no—
155C4×C43#46512yes—
156C4×C43#46612yes—
157Dic43—82no—
158Dic43—81no—
159#2972D4311yescharacteristic, complemented
160#2535—431no—
161#1800—431no—
162#1486—432no—
163#1286—432no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—44no—
167C2×C43#189111yescharacteristic
168C2×C43#189311yescharacteristic
169C2×C43#191111yescharacteristic
170D43—82no—
171C2×#121—861no—
172C2×C4×D4—431no—
173C2×C4×D4C2×D4311yescharacteristic
174C8×D4—24no—
175#431C2×D4312yes—
176#423—432no—
177C2×#100—861no—
178C2×C22⋊C8—22no—
179#397—432no—
180#392—432no—
181#386—862no—
182#382—431no—
183#380—861no—
184#343—861no—
185D4⋊C8—864no—
186C43#948511yescharacteristic, complemented, Sylow
187C22×D4—431no—
188C22×D4—862no—
189C22×D4D17211yescharacteristic
190C23×C4—861no—
191C23×C4C22⋊D4312yes—
192C2×M16—862no—
193C22×C8—24no—
194#121—1722no—
195#121—1722no—
196C4×D4—22no—
197C4×D4—22no—
198C4×D4—862no—
199C4×D4—862no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4D17211yescharacteristic
203C2×C22⋊C4—862no—
204C2×C22⋊C4—862no—
205C2×C22⋊C4—861no—
206C2×C22⋊C4C4×D4312yes—
207C2×C42C22×D4311yescharacteristic
208C4⋊C8—22no—
209C4⋊C8—862no—
210C4⋊C8—862no—
211#100—1722no—
212C22⋊C8—24no—
213C22⋊C8—22no—
214C4×C8C22⋊D4314yescomplemented
215#95—432no—
216#95—862no—
217#95—861no—
218C24—861no—
219C24(C2×D43)⋊C412yes—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—862no—
223C2×D4—3442no—
224C2×D4—1722no—
225C2×D4—1724no—
226C2×D4—1724no—
227C2×D4#1062187312yes—
228C2×D4D34412yes—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—82no—
232C22×C4—862no—
233C22×C4—861no—
234C22×C4—1722no—
235C22×C4—1721no—
236C22×C4—1721no—
237C22×C4—1722no—
238C22×C4(C2×D43)⋊C412yes—
239C22×C4C2×C4×D4311yescharacteristic
240C22×C4C2×D17211yescharacteristic
241C22×C4C2×C22⋊D4311yescharacteristic
242M16—1722no—
243M16—1722no—
244C2×C8—24no—
245C2×C8—84no—
246C2×C8—1722no—
247C4⋊C4—22no—
248C4⋊C4—862no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C22⋊C4—24no—
252C22⋊C4—3442no—
253C22⋊C4—1724no—
254C22⋊C4—1721no—
255C22⋊C4—1721no—
256C42#1062189812yes—
257C42C2×C22⋊D4312yes—
258C23—22no—
259C23—22no—
260C23—42no—
261C23—42no—
262C23—862no—
263C23—1721no—
264C23—1721no—
265C23—1721no—
266C23—1721no—
267C23—1721no—
268C23—1721no—
269C23#1306324714yes—
270C23C2×(C2×D43)⋊C411yescharacteristic
271D4—24no—
272D4—24no—
273D4—864no—
274D4—3448no—
275D4—1722no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—3442no—
283C2×C4—3442no—
284C2×C4—1722no—
285C2×C4—1722no—
286C2×C4—1721no—
287C2×C4—1722no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4C4×C22⋊D4312yes—
291C2×C4#1306329411yescharacteristic
292C2×C4#1306329912yes—
293C2×C4#1306330811yescharacteristic
294C2×C4C2×D34411yescharacteristic
295C2×C4C2×#1062187311yescharacteristic
296C2×C4#1306334712yes—
297C8—44no—
298C8—3442no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—3441no—
307C22—3441no—
308C22—3441no—
309C22—3441no—
310C22—1722no—
311C22—1722no—
312C22—1722no—
313C22#1458277811yescharacteristic
314C22C2×#1306324711yescharacteristic
315C22#1458289611yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—42no—
320C4—3442no—
321C4—3441no—
322C4#1458312812yes—
323C4#1458313512yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—3442no—
328C2#1913501311yescharacteristic
329C2#1913502311yescharacteristic
330C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2972C2
socleC22×C43#386
prime radical#19139492C2
cosocleC2×C42×C43C23
hypercenter#2972D43
hypocenterC43#9485
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #19134587C2semidirect
3. #19133021C2semidirect
4. #19132454C2semidirect
5. C43×#2972C2semidirect
51. C4×C8×C43D4semidirect
159. #2972D43semidirect
186. C43#9485semidirect
214. 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×#29722
#948543