Finite Group Databasebeta

← #24988328

Subgroups — #24988328

Order 11008.

738 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14583619C211yesmaximal, characteristic
2#19134587C211yesmaximal, characteristic
3#19133266C212yesmaximal, complemented
4#19133025C212yesmaximal, complemented
5C43×#1460C211yesmaximal, characteristic
6#14583619—24no—
7#14583619—24no—
8C2×#13063325C2211yescharacteristic
9C2×#13063318—22no—
10C2×#13063312—21no—
11C2×#13063304C412yes—
12C2×C4×Dic86C2211yescharacteristic
13C2×#13063290—21no—
14C2×#13063284C412yes—
15#14582923C2212yes—
16C2×#13063242—21no—
17#14582668—21no—
18#14582644—24no—
19#14582631—24no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#431C2212yes—
22C43×#323—22no—
23C22×Dic86—21no—
24C22×Dic86C2×C411yescharacteristic
25C2×#10621877—22no—
26#13063325—22no—
27#13063325D414yes—
28#13063318—216no—
29#13063312—28no—
30#13063304—24no—
31#13063304—24no—
32C4×Dic86—22no—
33C4×Dic86D414yes—
34#13063290—28no—
35#13063284—24no—
36#13063284—24no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43C2×C412yes—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43—21no—
46C4⋊(C43⋊C8)—22no—
47C4⋊(C43⋊C8)—22no—
48#13063242—42no—
49C22×D4×C43D411yescharacteristic
50C23×C4×C43C2×C412yes—
51C4×D4×C43—22no—
52C4×D4×C43—22no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58C4×C8×C43—22no—
59C24×C43C22⋊C412yes—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—44no—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—22no—
74C2×Dic86—21no—
75C2×Dic86—24no—
76C2×Dic86—42no—
77C2×Dic86—42no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86C22⋊C412yes—
81C2×C8×C43—42no—
82C4⋊C4×C43—22no—
83C22⋊C4×C43—24no—
84C42×C43C2×D412yes—
85C42×C43C2×D412yes—
86C22⋊Dic43—28no—
87C22⋊Dic43—28no—
88C4⋊Dic43—21no—
89C4⋊Dic43—22no—
90C4⋊Dic43—24no—
91C4⋊Dic43C22⋊C412yes—
92C4⋊Dic43C22⋊C414yes—
93Dic43⋊C4—28no—
94Dic43⋊C4—24no—
95C4×Dic43—28no—
96C4×Dic43—24no—
97#10621877—42no—
98#10621877—42no—
99C2×C43⋊C8—42no—
100C23×C43—22no—
101C23×C43—22no—
102C23×C43—22no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43C2×C22⋊C411yescharacteristic
106D4×C43—42no—
107D4×C43—42no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—41no—
111C2×C4×C43—44no—
112C2×C4×C43—44no—
113C2×C4×C43—42no—
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43C2×C22⋊C411yescharacteristic
116C2×C4×C43#12012yes—
117C2×C4×C43#12012yes—
118C2×C4×C43#13512yes—
119C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—24no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128Dic86—24no—
129Dic86—42no—
130Dic86—44no—
131Dic86—44no—
132C8×C43—82no—
133C43⋊C8—82no—
134#8389—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43—82no—
141C22×C43—82no—
142C22×C43#37911yescharacteristic
143C22×C43#41611yescharacteristic
144C22×C43#41711yescharacteristic
145C4×C43—22no—
146C4×C43—21no—
147C4×C43—42no—
148C4×C43#41312yes—
149C4×C43#44912yes—
150C4×C43#45212yes—
151Dic43—42no—
152Dic43—42no—
153Dic43—44no—
154C2×#556—431no—
155#1800—431no—
156#1546—432no—
157#1487—432no—
158#1460D4311yescharacteristic
159C2×C43—21no—
160C2×C43—21no—
161C2×C43—82no—
162C2×C43#178511yescharacteristic
163C2×C43#178811yescharacteristic
164C2×C43#179611yescharacteristic
165#556—864no—
166#556—864no—
167C2×C4⋊Q8—431no—
168C2×#126—862no—
169C2×#124—861no—
170C2×C22⋊Q8—432no—
171C2×C4×Q8—431no—
172C2×C4×Q8—861no—
173C2×C4×D4C2×D4311yescharacteristic
174C2×#117—432no—
175#431C2×D4312yes—
176#423—432no—
177C2×#100—861no—
178#343—861no—
179#332—864no—
180Q8⋊C8—864no—
181#323—22no—
182C43#838911yescharacteristic, complemented, Sylow
183C22×Q8—431no—
184C22×Q8—861no—
185C22×D4D17211yescharacteristic
186C23×C4C4×D4312yes—
187C2×M16—862no—
188C4⋊Q8—434no—
189C4⋊Q8—862no—
190#126—8616no—
191#124—868no—
192C22⋊Q8—864no—
193C22⋊Q8—864no—
194C4×Q8—434no—
195C4×Q8—868no—
196C4×Q8—862no—
197C4×D4—22no—
198C4×D4—22no—
199#117—864no—
200#117—864no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—432no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4D17211yescharacteristic
207C2×C22⋊C4—862no—
208C2×C22⋊C4—862no—
209C2×C22⋊C4C22⋊D4312yes—
210C2×C42—862no—
211C2×C42—861no—
212C2×C42C22×D4311yescharacteristic
213C4⋊C8—22no—
214C4⋊C8—862no—
215C4⋊C8—862no—
216#100—1722no—
217C22⋊C8—22no—
218C4×C8—22no—
219C24(C2×D43)⋊C412yes—
220C2×Q8—432no—
221C2×Q8—861no—
222C2×Q8—864no—
223C2×Q8—1722no—
224C2×Q8—1722no—
225C2×Q8—1721no—
226C2×Q8—1721no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—21no—
230C2×D4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—44no—
234C22×C4—861no—
235C22×C4—862no—
236C22×C4—861no—
237C22×C4(C2×D43)⋊C412yes—
238C22×C4C2×C4×D4311yescharacteristic
239C22×C4C2×D17211yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241M16—1722no—
242M16—1722no—
243C2×C8—42no—
244C2×C8—1722no—
245C4⋊C4—22no—
246C4⋊C4—432no—
247C4⋊C4—434no—
248C4⋊C4—868no—
249C4⋊C4—861no—
250C4⋊C4—862no—
251C4⋊C4—864no—
252C4⋊C4—864no—
253C22⋊C4—24no—
254C22⋊C4—868no—
255C22⋊C4—868no—
256C42—868no—
257C42—864no—
258C42D4×D4312yes—
259C42D4×D4312yes—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—42no—
264C23—42no—
265C23C2×(C2×D43)⋊C411yescharacteristic
266Q8—864no—
267Q8—1722no—
268Q8—1724no—
269Q8—1724no—
270D4—42no—
271D4—42no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—862no—
279C2×C4—864no—
280C2×C4—862no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4—1722no—
284C2×C4—1722no—
285C2×C4C22⋊C4×D4311yescharacteristic
286C2×C4C22⋊C4×D4311yescharacteristic
287C2×C4#1306329312yes—
288C2×C4#1306329512yes—
289C2×C4#1306334712yes—
290C2×C4#1306335311yescharacteristic
291C2×C4#1306335811yescharacteristic
292C8—82no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—82no—
300C22—82no—
301C22#1458275411yescharacteristic
302C22#1458289611yescharacteristic
303C22#1458290111yescharacteristic
304C4—21no—
305C4—22no—
306C4—42no—
307C4—1722no—
308C4—1724no—
309C4—1722no—
310C4#1458288012yes—
311C4#1458304612yes—
312C4#1458306312yes—
313C2—21no—
314C2—21no—
315C2—82no—
316C2#1913452011yescharacteristic
317C2#1913453611yescharacteristic
318C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1460C2
socleC22×C43#379
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#1460D43
hypocenterC43#8389
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #19133266C2semidirect
4. #19133025C2semidirect
182. C43#8389semidirect

Maximal subgroups

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

subgroupindex
C2×#145836192
#191345872
#191332662
#191330252
C43×#14602
#838943