Finite Group Databasebeta

← #25007232

Subgroups — #25007232

Order 11008.

572 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 87 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
2C4×#13063242C211yesmaximal, characteristic
3#19132626C214yesmaximal, complemented
4C43×#1465C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic
6C2×#13063304—21no—
7C2×#13063242—21no—
8C4×#10621877—21no—
9#14582819C2212yes—
10#14582811C412yes—
11#14582805—21no—
12#14582779—21no—
13#14582771—21no—
14#14582759C411yescharacteristic
15#14582668C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324C2212yes—
19C43×#323—21no—
20C22×Dic86—21no—
21C22×Dic86—44no—
22C22×Dic86—41no—
23C22×Dic86—41no—
24C22×Dic86C2×C412yes—
25C23×Dic43—21no—
26C2×#10621877—22no—
27#13063304—44no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—22no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—21no—
32#13063242—24no—
33#13063236—41no—
34C4×C43⋊C8—41no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95C2×C412yes—
38C22×D4×C43D411yescharacteristic
39C23×C4×C43C2×C411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C2×M16×C43—41no—
42C4×D4×C43—41no—
43C4×D4×C43—41no—
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C22⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C22⋊C8×C43—22no—
49C22⋊C8×C43—41no—
50C24×C43C22⋊C411yescharacteristic
51C24×C43C22⋊C411yescharacteristic
52C2×D4×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43—41no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—22no—
67C22×Dic43—22no—
68C22×Dic43—42no—
69C22×Dic43—44no—
70C2×Dic86—24no—
71C2×Dic86—42no—
72C2×Dic86—48no—
73C2×Dic86—44no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—42no—
77C2×Dic86—44no—
78C2×Dic86—44no—
79M16×C43—82no—
80C2×C8×C43—42no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C42×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—44no—
87C22⋊Dic43—42no—
88C4⋊Dic43—42no—
89Dic43⋊C4—44no—
90#10621877—24no—
91#10621877—42no—
92C2×C43⋊C8—42no—
93C23×C43—21no—
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#10412yes—
103C23×C43C2×C22⋊C411yescharacteristic
104D4×C43—44no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—81no—
118C2×C4×C43#9911yescharacteristic
119C2×C4×C43#9911yescharacteristic
120C2×C4×C43#13712yes—
121C2×Dic43—24no—
122C2×Dic43—42no—
123C2×Dic43—48no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128Dic86—44no—
129Dic86—44no—
130Dic86—44no—
131Dic86—44no—
132C8×C43—82no—
133C43⋊C8—44no—
134#11791—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—22no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43—42no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—81no—
147C22×C43C2×#9911yescharacteristic
148C22×C43#41911yescharacteristic
149C22×C43C2×#10411yescharacteristic
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43AΣL(1,𝔽16)12yes—
156Dic43—44no—
157Dic43—82no—
158#2409—431no—
159C4×#100—431no—
160#1465D4311yescharacteristic
161#1354—434no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—42no—
165C2×C43—81no—
166C2×C43#150811yescharacteristic
167C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
168C2×C43#213511yescharacteristic
169C23×Q8—431no—
170C2×C22⋊Q8—861no—
171C2×C4×D4C2×D4311yescharacteristic
172C2×#100—861no—
173#407—21no—
174C4×M16—861no—
175#395—432no—
176#393—432no—
177#391—861no—
178#386—861no—
179#385—861no—
180#380—431no—
181#343—432no—
182#324C2×D4312yes—
183#323—21no—
184C43#1179111yescharacteristic, complemented, Sylow
185C22×Q8—432no—
186C22×Q8—861no—
187C22×Q8—1721no—
188C22×Q8—1721no—
189C22×Q8—1724no—
190C22×D4D17211yescharacteristic
191C23×C4—861no—
192C23×C4C4×D4311yescharacteristic
193C23×C4C22⋊D4311yescharacteristic
194C2×M16—41no—
195C2×M16—862no—
196C22⋊Q8—1724no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—862no—
201C2×C4⋊C4C22×D4311yescharacteristic
202C2×C22⋊C4—862no—
203C2×C22⋊C4—861no—
204C2×C22⋊C4C4×D4311yescharacteristic
205C2×C22⋊C4C22⋊D4311yescharacteristic
206C2×C42D17211yescharacteristic
207#100—864no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210#97—1721no—
211C4×C8—1721no—
212#95—432no—
213#95—862no—
214#95—862no—
215C24(C2×D43)⋊C411yescharacteristic
216C24(C2×D43)⋊C411yescharacteristic
217C2×Q8—864no—
218C2×Q8—1722no—
219C2×Q8—1722no—
220C2×Q8—1724no—
221C2×Q8—1724no—
222C2×Q8—1728no—
223C2×Q8—1724no—
224C2×Q8—1721no—
225C2×Q8—1721no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—862no—
236C22×C4—862no—
237C22×C4—1724no—
238C22×C4—1722no—
239C22×C4(C2×D43)⋊C411yescharacteristic
240C22×C4(C2×D43)⋊C411yescharacteristic
241C22×C4C2×C4×D4311yescharacteristic
242C22×C4C2×D17211yescharacteristic
243C22×C4C2×C22⋊D4311yescharacteristic
244M16—82no—
245M16—864no—
246M16—1722no—
247C2×C8—42no—
248C2×C8—1722no—
249C4⋊C4—41no—
250C4⋊C4—1722no—
251C4⋊C4—1724no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—1724no—
255C22⋊C4—1722no—
256C42—21no—
257C42—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23#1306325112yes—
268C23C2×(C2×D43)⋊C411yescharacteristic
269Q8—1724no—
270Q8—1724no—
271Q8—1724no—
272Q8—1724no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—864no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4—1722no—
291C2×C4—1722no—
292C2×C4—1728no—
293C2×C4—1722no—
294C2×C4#1306323911yescharacteristic
295C2×C4#1306323911yescharacteristic
296C2×C4#1306335812yes—
297C8—82no—
298C8—1724no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#1306323911yescharacteristic
312C22#1458290911yescharacteristic
313C22C2×#1306325111yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—3442no—
320C4—1724no—
321C4#1458268512yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2#1913311611yescharacteristic
327C2C2×#1458268511yescharacteristic
328C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11791
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #19132626C2semidirect
184. C43#11791semidirect

Maximal subgroups

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

subgroupindex
#191379602
C4×#130632422
#191326262
C43×#14652
#1179143