Finite Group Databasebeta

← #25000935

Subgroups — #25000935

Order 11008.

500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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#19135059C212yesmaximal, complemented
2#19134777C211yesmaximal, characteristic, complemented
3#19133111C212yesmaximal, complemented
4#19132472C211yesmaximal, characteristic, complemented
5C43×#3186C211yesmaximal, characteristic
6C22×#10621877C2211yescharacteristic
7C2×Dic43⋊C8—21no—
8C2×#13063242—22no—
9#14582863C2212yes—
10C4×C22⋊Dic43C2211yescharacteristic
11#14582668—22no—
12#14582653—21no—
13#14582633—22no—
14#14582633—22no—
15C2×#121×C43C2212yes—
16C43×#480—22no—
17C43×#466—21no—
18C43×#466—21no—
19C43×#447—22no—
20C2×C22⋊C8×C43C2211yescharacteristic
21C2×#10621877—22no—
22C2×#10621877—22no—
23C2×#10621877—42no—
24C22×C43⋊C8—21no—
25C2×C22⋊Dic43—21no—
26C2×C4×Dic43—21no—
27Dic43⋊C8—42no—
28#13063242—44no—
29C22⋊(C43⋊C8)—22no—
30C22⋊(C43⋊C8)—22no—
31C43⋊#95D411yescharacteristic
32C43⋊#95D411yescharacteristic
33C22×D4×C43—22no—
34C22×D4×C43D412yes—
35C23×C4×C43C2311yescharacteristic
36C2×D8×C43—21no—
37C2×D8×C43—21no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40#121×C43—22no—
41#121×C43—22no—
42#121×C43—22no—
43#121×C43—22no—
44C2×C4⋊C4×C43D412yes—
45C2×C22⋊C4×C43—22no—
46#107×C43—21no—
47#107×C43—21no—
48#102×C43—22no—
49#102×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43—22no—
52C24×C43#4111yescharacteristic
53C2×D4×C43—22no—
54C2×D4×C43—22no—
55C2×D4×C43—42no—
56C2×D4×C43—42no—
57C2×D4×C43—42no—
58C2×D4×C43—42no—
59C2×D4×C43—82no—
60C2×D4×C43—82no—
61C22×C4×C43—22no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D412yes—
67C22×C4×C43#4112yes—
68C22×Dic43—21no—
69C22×Dic43—21no—
70D8×C43—81no—
71D8×C43—81no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C22⋊Dic43—42no—
81C4×Dic43—41no—
82C4×Dic43—41no—
83#10621877—24no—
84#10621877—42no—
85#10621877—42no—
86#10621877—42no—
87C2×C43⋊C8—22no—
88C2×C43⋊C8—41no—
89C2×C43⋊C8—41no—
90C2×C43⋊C8—42no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43—44no—
96C23×C43—42no—
97C23×C43—82no—
98C23×C43—82no—
99C23×C43#12111yescharacteristic
100C23×C43#12312yes—
101D4×C43—42no—
102D4×C43—42no—
103D4×C43—82no—
104D4×C43—84no—
105D4×C43—82no—
106D4×C43—82no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—82no—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43#12112yes—
117C2×C4×C43#12411yescharacteristic
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C8×C43—41no—
125C8×C43—41no—
126C43⋊C8—42no—
127C43⋊C8—82no—
128#10557—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—22no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—81no—
135C22×C43—81no—
136C22×C43—82no—
137C22×C43—82no—
138C22×C43—82no—
139C22×C43—164no—
140C22×C43#39411yescharacteristic
141C22×C43#47211yescharacteristic
142C22×C43#47211yescharacteristic
143C4×C43—22no—
144C4×C43—21no—
145C4×C43—82no—
146C4×C43B(4,𝔽2)11yescharacteristic
147C4×C43#45811yescharacteristic
148Dic43—42no—
149Dic43—81no—
150#3186D4311yescharacteristic
151#1900—432no—
152#1851—431no—
153#1507—432no—
154#1293—431no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43—42no—
158C2×C43—162no—
159C2×C43#204411yescharacteristic
160C2×C43#204511yescharacteristic
161C2×C43#205011yescharacteristic
162C22×M16—431no—
163C2×#121C2×D4312yes—
164#480—22no—
165#466—21no—
166#466—21no—
167#447—22no—
168C2×C4⋊C8—861no—
169C2×#100—862no—
170#407—432no—
171C2×C22⋊C8C2×D4311yescharacteristic
172C4×C22⋊C4—431no—
173#343—862no—
174#336—861no—
175#327—862no—
176#327—862no—
177C43#1055711yescharacteristic, complemented, Sylow
178C22×D4—22no—
179C22×D4C22⋊D4312yes—
180C23×C4C22×D4311yescharacteristic
181C2×D8—21no—
182C2×D8—21no—
183C2×M16—862no—
184C2×M16—862no—
185C2×M16—1722no—
186C22×C8—861no—
187C22×C8C22⋊D4311yescharacteristic
188C22×C8C22⋊D4311yescharacteristic
189#121—22no—
190#121—22no—
191#121—22no—
192#121—22no—
193C2×C4⋊C4C22⋊D4312yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—861no—
196C2×C42—861no—
197#107—21no—
198#107—21no—
199C4⋊C8—1722no—
200#102—22no—
201#102—22no—
202#100—1724no—
203C22⋊C8—22no—
204C22⋊C8—862no—
205C22⋊C8—862no—
206#95—431no—
207#95—431no—
208C24—22no—
209C24#1062190011yescharacteristic
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—82no—
217C2×D4—82no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4D4×D4311yescharacteristic
224C22×C4#1062190012yes—
225C22×C4C2×C22⋊D4312yes—
226C22×C4C2×C22⋊D4311yescharacteristic
227D8—81no—
228D8—81no—
229M16—864no—
230M16—1722no—
231M16—1722no—
232M16—1722no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—862no—
238C2×C8—1722no—
239C2×C8—1721no—
240C2×C8—1721no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—1722no—
246C42—1721no—
247C42—1721no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—44no—
253C23—42no—
254C23—82no—
255C23—82no—
256C23#1306329611yescharacteristic
257C23#1306330612yes—
258D4—42no—
259D4—42no—
260D4—82no—
261D4—84no—
262D4—82no—
263D4—82no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—862no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4#1306329411yescharacteristic
279C2×C4#1306329712yes—
280C2×C4#1306331211yescharacteristic
281C8—41no—
282C8—41no—
283C8—3442no—
284C8—1722no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—81no—
291C22—81no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—164no—
296C22#1458281311yescharacteristic
297C22#1458316611yescharacteristic
298C22#1458316611yescharacteristic
299C4—22no—
300C4—21no—
301C4—82no—
302C4—3441no—
303C4—1722no—
304C4#1458308611yescharacteristic
305C4#1458308911yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—162no—
310C2#1913584311yescharacteristic
311C2#1913584811yescharacteristic
312C2#1913587911yescharacteristic
subgroupG/H
centerC22#14582813
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3186C2
socleC22×C43#394
hypercenter#3186D43
hypocenterC43#10557
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #19135059C2semidirect
2. #19134777C2semidirect
3. #19133111C2semidirect
4. #19132472C2semidirect
177. C43#10557semidirect

Maximal subgroups

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

subgroupindex
#191350592
#191347772
#191331112
#191324722
C43×#31862
#1055743