Finite Group Databasebeta

← #25007745

Subgroups — #25007745

Order 11008.

568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137960C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3#19132624C214yesmaximal, complemented
4C43×#1800C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic
6C2×#13063304—21no—
7C2×C22⋊(C43⋊C8)—21no—
8#14582819C2212yes—
9#14582811C412yes—
10#14582805—21no—
11#14582779—21no—
12#14582771—21no—
13#14582759C411yescharacteristic
14#14582625C2212yes—
15#14582623—21no—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#423—21no—
18C2×#100×C43—21no—
19C43×#343C2212yes—
20C22×Dic86—21no—
21C22×Dic86—44no—
22C22×Dic86—41no—
23C22×Dic86—41no—
24C22×Dic86C2×C412yes—
25C23×Dic43—21no—
26C22×C43⋊C8—41no—
27#13063304—44no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—22no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—21no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—41no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95C2×C412yes—
37C22×D4×C43D411yescharacteristic
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C2×M16×C43—22no—
41C4×D4×C43—41no—
42C4×D4×C43—41no—
43C2×C4⋊C4×C43C2311yescharacteristic
44C2×C22⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C4⋊C8×C43—41no—
48C4⋊C8×C43—41no—
49#100×C43—42no—
50C24×C43C22⋊C411yescharacteristic
51C24×C43C22⋊C411yescharacteristic
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43SD1612yes—
55C2×D4×C43Q1612yes—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—42no—
70C22×Dic43—44no—
71C2×Dic86—24no—
72C2×Dic86—42no—
73C2×Dic86—48no—
74C2×Dic86—44no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—42no—
78C2×Dic86—44no—
79C2×Dic86—44no—
80M16×C43—42no—
81M16×C43—42no—
82C2×C8×C43—42no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C42×C43—21no—
87C42×C43—21no—
88C22⋊Dic43—42no—
89C22⋊Dic43—44no—
90C4⋊Dic43—42no—
91Dic43⋊C4—44no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—82no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43#10312yes—
103C23×C43#10312yes—
104C23×C43C2×C22⋊C411yescharacteristic
105D4×C43—42no—
106D4×C43—42no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—81no—
120C2×C4×C43#9911yescharacteristic
121C2×C4×C43#9911yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43C2×Q1611yescharacteristic
124C2×Dic43—24no—
125C2×Dic43—42no—
126C2×Dic43—48no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129C2×Dic43—42no—
130C2×Dic43—42no—
131Dic86—44no—
132Dic86—44no—
133Dic86—44no—
134Dic86—44no—
135C8×C43—82no—
136C43⋊C8—82no—
137#11904—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—22no—
141C22×C43—22no—
142C22×C43—42no—
143C22×C43—42no—
144C22×C43—42no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—81no—
150C22×C43C2×#9911yescharacteristic
151C22×C43C2×#10311yescharacteristic
152C22×C43#42111yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43AΣL(1,𝔽16)12yes—
160Dic43—44no—
161Dic43—82no—
162#2409—431no—
163#1800D4311yescharacteristic
164#1459—431no—
165#1354—434no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—42no—
169C2×C43—42no—
170C2×C43#152011yescharacteristic
171C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
172C2×C43#213511yescharacteristic
173C23×Q8—431no—
174C2×C22⋊Q8—861no—
175C2×C4×D4C2×D4311yescharacteristic
176#423—21no—
177C2×#100—21no—
178C2×C22⋊C8—861no—
179#395—432no—
180#393—432no—
181#391—861no—
182#386—861no—
183#385—861no—
184#380—431no—
185#343C2×D4312yes—
186#324—432no—
187#323—861no—
188C43#1190411yescharacteristic, complemented, Sylow
189C22×Q8—432no—
190C22×Q8—861no—
191C22×Q8—1721no—
192C22×Q8—1721no—
193C22×Q8—1724no—
194C22×D4C22⋊D4311yescharacteristic
195C23×C4—861no—
196C23×C4C4×D4311yescharacteristic
197C23×C4D17211yescharacteristic
198C2×M16—22no—
199C22×C8—1721no—
200C22⋊Q8—1724no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4C22×D4311yescharacteristic
206C2×C22⋊C4—862no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4C4×D4311yescharacteristic
209C2×C22⋊C4D17211yescharacteristic
210C2×C42C22⋊D4311yescharacteristic
211C4⋊C8—41no—
212C4⋊C8—41no—
213#100—42no—
214C22⋊C8—862no—
215C22⋊C8—1721no—
216#95—432no—
217#95—862no—
218#95—862no—
219C24(C2×D43)⋊C411yescharacteristic
220C24(C2×D43)⋊C411yescharacteristic
221C2×Q8—864no—
222C2×Q8—1722no—
223C2×Q8—1722no—
224C2×Q8—1724no—
225C2×Q8—1724no—
226C2×Q8—1728no—
227C2×Q8—1724no—
228C2×Q8—1721no—
229C2×Q8—1721no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4#1062188312yes—
233C2×D4#1062188512yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—862no—
241C22×C4—862no—
242C22×C4—1724no—
243C22×C4—1722no—
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4C2×C4×D4311yescharacteristic
247C22×C4C2×D17211yescharacteristic
248C22×C4C2×C22⋊D4311yescharacteristic
249M16—42no—
250M16—42no—
251C2×C8—42no—
252C2×C8—3442no—
253C2×C8—1722no—
254C4⋊C4—41no—
255C4⋊C4—1722no—
256C4⋊C4—1724no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—1724no—
260C22⋊C4—1722no—
261C42—21no—
262C42—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#1306324812yes—
272C23#1306324812yes—
273C23C2×(C2×D43)⋊C411yescharacteristic
274Q8—1724no—
275Q8—1724no—
276Q8—1724no—
277Q8—1724no—
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—864no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4—1728no—
299C2×C4—1722no—
300C2×C4#1306323911yescharacteristic
301C2×C4#1306323911yescharacteristic
302C2×C4C2×#1062188311yescharacteristic
303C2×C4C2×#1062188511yescharacteristic
304C8—82no—
305C8—3442no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#1306323911yescharacteristic
319C22C2×#1306324811yescharacteristic
320C22#1458291711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—3442no—
328C4—1724no—
329C4#1458268712yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1913316611yescharacteristic
335C2C2×#1458268711yescharacteristic
336C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1800C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#1800D43
hypocenterC43#11904
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #19132624C2semidirect
188. C43#11904semidirect

Maximal subgroups

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

subgroupindex
#191379602
#191329132
#191326242
C43×#18002
#1190443