Finite Group Databasebeta

← #24988333

Subgroups — #24988333

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#19134591C211yesmaximal, characteristic
3#19133266C212yesmaximal
4#19133025C212yesmaximal
5C43×#1461C211yesmaximal, 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#14582923C2212yes—
16C2×#13063244—21no—
17#14582668—21no—
18#14582644—24no—
19#14582631—24no—
20C2×C4×Q8×C43C2211yescharacteristic
21C43×#431C2212yes—
22C43×#324—22no—
23C22×Dic86—21no—
24C22×Dic86C2×C411yescharacteristic
25C2×#10621877—22no—
26#13063325—22no—
27#13063325D414yes—
28#13063323—28no—
29#13063317—24no—
30#13063317—24no—
31#13063315—216no—
32C4×Dic86—24no—
33C4×Dic86—22no—
34C4×Dic86—24no—
35C4×Dic86D414yes—
36#13063290—28no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C412yes—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—22no—
43C2×Dic43⋊C4—21no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43—21no—
46C4⋊(C43⋊C8)—22no—
47C4⋊(C43⋊C8)—22no—
48#13063244—42no—
49C22×Q8×C43D411yescharacteristic
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43D412yes—
54C2×C42×C43C2×C412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58C4×C8×C43—22no—
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—
78C2×C8×C43—42no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—24no—
81C42×C43—22no—
82C42×C43—22no—
83C42×C43C2×D412yes—
84C42×C43C2×D412yes—
85C4⋊Dic43—21no—
86C4⋊Dic43—22no—
87C4⋊Dic43—24no—
88C4⋊Dic43C22⋊C414yes—
89C4⋊Dic43C22⋊C412yes—
90Dic43⋊C4—28no—
91Dic43⋊C4—28no—
92Dic43⋊C4—28no—
93Dic43⋊C4—24no—
94C4×Dic43—28no—
95C4×Dic43—24no—
96#10621877—42no—
97#10621877—42no—
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#1801—431no—
148#1546—432no—
149#1487—432no—
150#1461D4311yescharacteristic
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#431C2×D4312yes—
167#423—432no—
168C2×#101—861no—
169#343—861no—
170#332—864no—
171Q8⋊C8—864no—
172#324—22no—
173C43#839011yescharacteristic, complemented, Sylow
174C22×Q8—431no—
175C22×Q8—861no—
176C22×Q8D17211yescharacteristic
177C2×M16—862no—
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⋊C4D17211yescharacteristic
199C2×C4⋊C4C22⋊D4312yes—
200C2×C42—862no—
201C2×C42—861no—
202C2×C42C4×D4312yes—
203C2×C42C22×D4311yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—862no—
206C4⋊C8—862no—
207#101—1722no—
208C22⋊C8—22no—
209C4×C8—22no—
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—1722no—
230M16—1722no—
231C2×C8—42no—
232C2×C8—1722no—
233C4⋊C4—24no—
234C4⋊C4—22no—
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#1306334712yes—
277C2×C4#1306335311yescharacteristic
278C2×C4#1306335811yescharacteristic
279C8—82no—
280C8—3442no—
281C22—21no—
282C22—21no—
283C22#1458275411yescharacteristic
284C22#1458289611yescharacteristic
285C22#1458290111yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—864no—
291C4—1724no—
292C4—1722no—
293C4#101×D4312yes—
294C4#1458304612yes—
295C4#1458306312yes—
296C2—21no—
297C2—21no—
298C2#1913451711yescharacteristic
299C2#1913453611yescharacteristic
300C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1461C2
socleC22×C43#379
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1461D43
hypocenterC43#8390
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

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
#191345912
#191332662
#191330252
C43×#14612
#839043