Finite Group Databasebeta

← #24988336

Subgroups — #24988336

Order 11008.

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

normal subgroups only

This group has 706 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
1C2×#14583627C211yesmaximal, characteristic
2#19133268C212yesmaximal
3#19133023C212yesmaximal
4#19132919C211yesmaximal, characteristic
5C43×#1801C211yesmaximal, characteristic
6#14583627—24no—
7#14583627—24no—
8C2×#13063325C2211yescharacteristic
9C2×#13063323—21no—
10C2×#13063317C412yes—
11C2×#13063315—22no—
12C2×C4×Dic86C412yes—
13C2×C4×Dic86C2211yescharacteristic
14C2×#13063290—21no—
15#14582952C2212yes—
16#14582646—24no—
17#14582629—24no—
18#14582625—22no—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#423C2212yes—
21C2×#101×C43—21no—
22C43×#343—21no—
23C22×Dic86—21no—
24C22×Dic86C2×C411yescharacteristic
25#13063325—22no—
26#13063325D414yes—
27#13063323—28no—
28#13063317—24no—
29#13063317—24no—
30#13063315—216no—
31C4×Dic86—24no—
32C4×Dic86—22no—
33C4×Dic86—24no—
34C4×Dic86D414yes—
35#13063290—28no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C412yes—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—21no—
43C2×C4×Dic43—22no—
44C2×C4×Dic43—21no—
45C4⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—22no—
47C4×C43⋊C8—22no—
48C22×Q8×C43D411yescharacteristic
49C2×M16×C43—22no—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C2×C4⋊C4×C43D412yes—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C42×C43C2×C412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C4⋊C8×C43—22no—
58#101×C43—42no—
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43—21no—
62C2×Q8×C43—21no—
63C22×C4×C43C22⋊C412yes—
64C22×C4×C43C22⋊C412yes—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—22no—
71C2×Dic86—21no—
72C2×Dic86—24no—
73C2×Dic86—24no—
74C2×Dic86—42no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86C22⋊C412yes—
78M16×C43—42no—
79M16×C43—42no—
80C2×C8×C43—42no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—24no—
83C42×C43—22no—
84C42×C43—22no—
85C42×C43C2×D412yes—
86C42×C43C2×D412yes—
87C4⋊Dic43—21no—
88C4⋊Dic43—22no—
89C4⋊Dic43—24no—
90C4⋊Dic43C22⋊C414yes—
91C4⋊Dic43C22⋊C412yes—
92Dic43⋊C4—28no—
93Dic43⋊C4—28no—
94Dic43⋊C4—28no—
95Dic43⋊C4—24no—
96C4×Dic43—28no—
97C4×Dic43—24no—
98C2×C43⋊C8—42no—
99C23×C43C2×C22⋊C411yescharacteristic
100Q8×C43—42no—
101Q8×C43—42no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43C2×C22⋊C411yescharacteristic
110C2×C4×C43C2×C22⋊C411yescharacteristic
111C2×C4×C43#12012yes—
112C2×C4×C43#12012yes—
113C2×C4×C43#13512yes—
114C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C43#13711yescharacteristic
116C2×Dic43—24no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—24no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123Dic86—24no—
124Dic86—22no—
125Dic86—44no—
126Dic86—44no—
127Dic86#10114yescomplemented
128C8×C43—82no—
129C43⋊C8—82no—
130#8390—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43#37911yescharacteristic
134C22×C43#41611yescharacteristic
135C22×C43#41711yescharacteristic
136C4×C43—22no—
137C4×C43—21no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43C2×#10112yes—
141C4×C43#44912yes—
142C4×C43#45212yes—
143Dic43—24no—
144Dic43—42no—
145Dic43—44no—
146C2×#557—431no—
147#1801D4311yescharacteristic
148#1546—432no—
149#1487—432no—
150#1461—431no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43#178411yescharacteristic
154C2×C43#178811yescharacteristic
155C2×C43#179611yescharacteristic
156#557—864no—
157#557—864no—
158C2×C4⋊Q8—431no—
159C2×C4⋊Q8—861no—
160C2×#125—432no—
161C2×#125—862no—
162C2×C4×Q8—431no—
163C2×C4×Q8—432no—
164C2×C4×Q8—861no—
165C2×C4×Q8C2×D4311yescharacteristic
166#431—432no—
167#423C2×D4312yes—
168C2×#101—21no—
169#343—21no—
170#332—864no—
171Q8⋊C8—864no—
172#324—862no—
173C43#839011yescharacteristic, complemented, Sylow
174C22×Q8—431no—
175C22×Q8—861no—
176C22×Q8C22⋊D4311yescharacteristic
177C2×M16—22no—
178C4⋊Q8—434no—
179C4⋊Q8—868no—
180C4⋊Q8—862no—
181#125—864no—
182#125—864no—
183#125—8616no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8—434no—
187C4×Q8—864no—
188C4×Q8—864no—
189C4×Q8—868no—
190C4×Q8—862no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—432no—
193C2×C4⋊C4—862no—
194C2×C4⋊C4—862no—
195C2×C4⋊C4—862no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4D17212yes—
199C2×C4⋊C4C22⋊D4311yescharacteristic
200C2×C42—862no—
201C2×C42—861no—
202C2×C42C4×D4312yes—
203C2×C42C22×D4311yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—862no—
207#101—42no—
208C22⋊C8—862no—
209C4×C8—862no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—432no—
215C2×Q8—864no—
216C2×Q8—861no—
217C2×Q8—864no—
218C2×Q8—1722no—
219C2×Q8—1721no—
220C2×Q8—1721no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—862no—
224C22×C4(C2×D43)⋊C412yes—
225C22×C4(C2×D43)⋊C412yes—
226C22×C4C2×C4×D4311yescharacteristic
227C22×C4C2×D17211yescharacteristic
228C22×C4C2×C22⋊D4311yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—1722no—
233C4⋊C4—22no—
234C4⋊C4—24no—
235C4⋊C4—432no—
236C4⋊C4—434no—
237C4⋊C4—868no—
238C4⋊C4—868no—
239C4⋊C4—868no—
240C4⋊C4—861no—
241C4⋊C4—862no—
242C4⋊C4—864no—
243C4⋊C4—864no—
244C42—22no—
245C42—22no—
246C42—868no—
247C42—864no—
248C42D4×D4312yes—
249C42D4×D4312yes—
250C23C2×(C2×D43)⋊C411yescharacteristic
251Q8—42no—
252Q8—42no—
253Q8—434no—
254Q8—864no—
255Q8—862no—
256Q8—1724no—
257Q8—1724no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—864no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—864no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4—1722no—
272C2×C4C22⋊C4×D4311yescharacteristic
273C2×C4C22⋊C4×D4311yescharacteristic
274C2×C4#1306329312yes—
275C2×C4#1306329512yes—
276C2×C4#1306334512yes—
277C2×C4#1306335111yescharacteristic
278C2×C4#1306335611yescharacteristic
279C8—82no—
280C8—3442no—
281C22—21no—
282C22—21no—
283C22#1458275411yescharacteristic
284C22#1458289311yescharacteristic
285C22#1458289811yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—864no—
291C4—1724no—
292C4—1722no—
293C4#101×D4312yes—
294C4#1458304212yes—
295C4#1458305912yes—
296C2—21no—
297C2—21no—
298C2#1913451711yescharacteristic
299C2#1913453311yescharacteristic
300C2#1913457111yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1801C2
socleC22×C43#379
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1801D43
hypocenterC43#8390
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
127. Dic86#101semidirect
173. C43#8390semidirect

Maximal subgroups

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

subgroupindex
C2×#145836272
#191332682
#191330232
#191329192
C43×#18012
#839043