Finite Group Databasebeta

← #25006987

Subgroups — #25006987

Order 11008.

400 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140455C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic, complemented
3#19132626C212yesmaximal, complemented
4#19132599C212yesmaximal
5C43×#1461C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic
7C2×#13063244—21no—
8C4×#10621877—21no—
9#14582834—21no—
10#14582819C411yescharacteristic
11#14582819C2211yescharacteristic
12#14582816C411yescharacteristic
13#14582816C2211yescharacteristic
14#14582810—21no—
15#14582790—21no—
16#14582790—21no—
17#14582767C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C22×D172C2×C411yescharacteristic
25C2×#10621877—22no—
26#13063313—41no—
27#13063313—41no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36#13063244—24no—
37#13063236—41no—
38C4×C43⋊C8—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C4×Q8×C43—41no—
47C4×Q8×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56C4×C8×C43—41no—
57C23×D43—21no—
58C2×Q8×C43—22no—
59C2×Q8×C43—22no—
60C2×Q8×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×D172—41no—
72C2×D172—81no—
73C2×Dic86—41no—
74C2×Dic86—81no—
75C2×C8×C43—42no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85(C2×D43)⋊C4—42no—
86(C2×D43)⋊C4—41no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—81no—
91(C2×D43)⋊C4—81no—
92Dic43⋊C4—81no—
93Dic43⋊C4—81no—
94#10621877—24no—
95#10621877—42no—
96C2×C43⋊C8—42no—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105Q8×C43—44no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43#9911yescharacteristic
121C2×C4×C43#9911yescharacteristic
122C2×C4×C43#10412yes—
123C2×C4×C43#13512yes—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133D172—82no—
134Dic86—82no—
135C8×C43—82no—
136C43⋊C8—44no—
137#11738—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43C2×#9911yescharacteristic
141C22×C43#41611yescharacteristic
142C22×C43C2×#10411yescharacteristic
143C2×D43—81no—
144C2×D43—81no—
145C2×D43—81no—
146C2×D43—81no—
147C2×D43—81no—
148C2×D43—81no—
149C2×D43—81no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158Dic43—81no—
159Dic43—81no—
160Dic43—81no—
161#2632—431no—
162C4×#101—431no—
163#1461D4311yescharacteristic, complemented
164#1354—432no—
165#1345—432no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43#150111yescharacteristic
169C2×C43#212211yescharacteristic
170C2×C43#213311yescharacteristic
171D43—161no—
172C2×#124—431no—
173C2×C4×Q8C2×D4311yescharacteristic
174#431—21no—
175C2×#101—861no—
176C4×M16—861no—
177#399—861no—
178#395—431no—
179#395—431no—
180#394—431no—
181#394—431no—
182#393—861no—
183#388—861no—
184#388—861no—
185#383—431no—
186#343—432no—
187#324—21no—
188#324C2×D4312yes—
189C43#1173811yescharacteristic, complemented, Sylow
190C22×Q8—431no—
191C22×Q8D17211yescharacteristic
192C22×D4—431no—
193C2×M16—862no—
194#124—1721no—
195#124—1721no—
196C4×Q8—41no—
197C4×Q8—41no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4C4×D4311yescharacteristic
201C2×C4⋊C4C22⋊D4311yescharacteristic
202C2×C4⋊C4C22×D4311yescharacteristic
203C2×C22⋊C4—861no—
204C2×C22⋊C4—861no—
205C2×C22⋊C4—861no—
206C2×C22⋊C4—861no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—861no—
209C2×C42C4×D4311yescharacteristic
210C2×C42D17211yescharacteristic
211C2×C42C22⋊D4311yescharacteristic
212C4⋊C8—41no—
213#101—864no—
214C22⋊C8—22no—
215#97—1721no—
216C4×C8—41no—
217C4×C8—1721no—
218#95—431no—
219#95—431no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224C24—861no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—3441no—
229C2×Q8—1721no—
230C2×D4—3441no—
231C2×D4—1721no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4(C2×D43)⋊C411yescharacteristic
236C22×C4(C2×D43)⋊C411yescharacteristic
237C22×C4(C2×D43)⋊C411yescharacteristic
238C22×C4(C2×D43)⋊C411yescharacteristic
239C22×C4C2×C4×D4311yescharacteristic
240C22×C4C2×D17211yescharacteristic
241C22×C4C2×C22⋊D4311yescharacteristic
242M16—864no—
243M16—1722no—
244C2×C8—42no—
245C2×C8—1722no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—3441no—
250C4⋊C4—3441no—
251C22⋊C4—3441no—
252C22⋊C4—3441no—
253C22⋊C4—1722no—
254C22⋊C4—1721no—
255C22⋊C4—1721no—
256C22⋊C4—1722no—
257C22⋊C4—1722no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C23—1721no—
265C23—1721no—
266C23—1721no—
267C23—1721no—
268C23—1721no—
269C23—1721no—
270C23—1721no—
271C23C2×(C2×D43)⋊C411yescharacteristic
272Q8—44no—
273Q8—3442no—
274D4—3442no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4#1306323911yescharacteristic
299C2×C4#1306323911yescharacteristic
300C2×C4#1306325112yes—
301C2×C4#1306334712yes—
302C8—82no—
303C8—1724no—
304C22—21no—
305C22—21no—
306C22—3441no—
307C22—3441no—
308C22—3441no—
309C22—3441no—
310C22—3441no—
311C22—3441no—
312C22—3441no—
313C22C2×#1306323911yescharacteristic
314C22#1458289611yescharacteristic
315C22C2×#1306325111yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3441no—
325C4—3441no—
326C4—3441no—
327C2—21no—
328C2—21no—
329C2—6881no—
330C2#1913308711yescharacteristic
331C2#1913624411yescharacteristic
332C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11738
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. C4×#13063244C2semidirect
3. #19132626C2semidirect
5. C43×#1461C2semidirect
163. #1461D43semidirect
189. C43#11738semidirect

Maximal subgroups

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

subgroupindex
#191404552
C4×#130632442
#191326262
#191325992
C43×#14612
#1173843