Finite Group Databasebeta

← #25012479

Subgroups — #25012479

Order 11008.

740 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14583649C211yesmaximal, characteristic
2C2×#14582697C212yesmaximal, complemented
3#19134999C211yesmaximal, characteristic
4#19134986C212yesmaximal, complemented
5C2×C43×#355C211yesmaximal, characteristic
6#14583649—24no—
7#14583649—22no—
8#14583649C414yescomplemented
9C2×#13063323C2212yes—
10C2×#13063318—22no—
11C2×#13063317—21no—
12C2×#13063306—21no—
13C2×#13063302—22no—
14#14583377C2211yescharacteristic
15#14582909—22no—
16#14582904—21no—
17C2×#13063244C2211yescharacteristic
18#14582697—24no—
19#14582660—22no—
20#14582659—21no—
21C2×#124×C43C2211yescharacteristic
22C2×#101×C43C2212yes—
23C43×#355—22no—
24C22×Dic86D412yes—
25C23×Dic43—21no—
26C2×#10621877—21no—
27#13063323—22no—
28#13063323—22no—
29#13063323C2×C414yes—
30#13063323D414yes—
31#13063318—28no—
32#13063318—28no—
33#13063317—24no—
34#13063317—24no—
35#13063306—24no—
36#13063306—24no—
37#13063302—28no—
38#13063302—28no—
39Q8×Dic43—42no—
40#13063284—21no—
41#13063284—22no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—22no—
45C2×Dic43⋊C4—22no—
46C2×Dic43⋊C4—22no—
47C2×C22⋊Dic43—22no—
48C2×C22⋊Dic43—21no—
49C2×C4×Dic43D412yes—
50#13063250—44no—
51#13063246—42no—
52#13063244—22no—
53C22×Q8×C43C2311yescharacteristic
54C22×D4×C43D411yescharacteristic
55C2×M16×C43—22no—
56#124×C43—22no—
57#124×C43C2×C412yes—
58#124×C43D412yes—
59C2×C22⋊C4×C43—22no—
60C2×C42×C43D411yescharacteristic
61#101×C43—22no—
62#101×C43—22no—
63C24×C43—21no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43C22×C411yescharacteristic
67C2×Q8×C43C2×D412yes—
68C2×Q8×C43C2×D411yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43C22⋊C412yes—
73C22×C4×C43—21no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D412yes—
76C22×Dic43—24no—
77C22×Dic43—22no—
78C22×Dic43—22no—
79C22×Dic43—81no—
80C22×Dic43—81no—
81C2×Dic86—22no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86C22⋊C414yes—
85M16×C43—42no—
86M16×C43—42no—
87C2×C8×C43—42no—
88C22⋊C4×C43—24no—
89C22⋊C4×C43—24no—
90C42×C43—21no—
91C42×C43C22⋊C412yes—
92C22⋊Dic43—28no—
93C22⋊Dic43—24no—
94C22⋊Dic43—41no—
95C4⋊Dic43—24no—
96C4⋊Dic43—24no—
97C4⋊Dic43—22no—
98C4⋊Dic43—24no—
99Dic43⋊C4—28no—
100Dic43⋊C4—24no—
101Dic43⋊C4—24no—
102Dic43⋊C4—24no—
103Dic43⋊C4—24no—
104C4×Dic43—22no—
105C4×Dic43—41no—
106C4×Dic43—42no—
107C4×Dic43C22⋊C414yes—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—41no—
111C23×C43—22no—
112C23×C43—44no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43#12011yescharacteristic
116Q8×C43—41no—
117Q8×C43—42no—
118Q8×C43—41no—
119D4×C43—42no—
120D4×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—42no—
127C2×C4×C43C2×C22⋊C412yes—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43#12012yes—
130C2×C4×C43#12011yescharacteristic
131C2×Dic43—24no—
132C2×Dic43—24no—
133C2×Dic43—44no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—84no—
138Dic86—44no—
139Dic86—82no—
140C8×C43—82no—
141C43⋊C8—81no—
142#12775—431nomaximal, Sylow
143C22×C43—22no—
144C22×C43—44no—
145C22×C43—42no—
146C22×C43—82no—
147C22×C43—82no—
148C22×C43#37911yescharacteristic
149C22×C43B(4,𝔽2)11yescharacteristic
150C22×C43#45811yescharacteristic
151C4×C43—21no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—21no—
155C4×C43—42no—
156Dic43—44no—
157Dic43—44no—
158Dic43—82no—
159C2×#563—431no—
160C2×#356—432no—
161C2×#355D4311yescharacteristic
162#1888—431no—
163#1886—432no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—82no—
167C2×C43#179011yescharacteristic
168C2×C43#220312yes—
169#563—434no—
170#563—864no—
171#563—862no—
172C2×C4⋊Q8—432no—
173C2×#126—862no—
174C2×#125—861no—
175C2×#124C2×D4311yescharacteristic
176C2×#123—861no—
177C2×C22⋊Q8—862no—
178#519—431no—
179#419—862no—
180#418—861no—
181C2×#101—431no—
182C2×#101C2×D4312yes—
183#356—864no—
184#355—22no—
185#339—862no—
186#339—861no—
187C43#1277511yescharacteristic, complemented, Sylow
188C22×Q8—432no—
189C22×Q8C22×D4311yescharacteristic
190C22×D4D17211yescharacteristic
191C23×C4—861no—
192C2×M16—22no—
193C2×M16—861no—
194C4⋊Q8—434no—
195C4⋊Q8—434no—
196C4⋊Q8—862no—
197C4⋊Q8—862no—
198#126—868no—
199#126—868no—
200#125—864no—
201#125—864no—
202#124—22no—
203#124C4×D4312yes—
204#124C22⋊D4312yes—
205#123—864no—
206#123—864no—
207C22⋊Q8—868no—
208C22⋊Q8—868no—
209C4×Q8—1722no—
210#117—861no—
211#117—862no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—862no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—862no—
216C2×C4⋊C4—862no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—862no—
219C2×C22⋊C4—861no—
220C2×C42—432no—
221C2×C42D17211yescharacteristic
222#103—1724no—
223#102—1722no—
224#101—22no—
225#101—22no—
226#101—862no—
227C24—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—434no—
231C2×Q8—862no—
232C2×Q8—1722no—
233C2×Q8—1722no—
234C2×Q8C2×C4×D4311yescharacteristic
235C2×Q8D4×D4312yes—
236C2×Q8C2×C22⋊D4311yescharacteristic
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4(C2×D43)⋊C412yes—
241C22×C4—21no—
242C22×C4—864no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4—3441no—
246C22×C4—3441no—
247C22×C4C2×D17211yescharacteristic
248C22×C4D4×D4312yes—
249M16—42no—
250M16—42no—
251M16—1721no—
252M16—1721no—
253C2×C8—42no—
254C2×C8—1721no—
255C4⋊C4—864no—
256C4⋊C4—868no—
257C4⋊C4—864no—
258C4⋊C4—862no—
259C4⋊C4—864no—
260C4⋊C4—864no—
261C4⋊C4—864no—
262C4⋊C4—864no—
263C4⋊C4—864no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—868no—
267C22⋊C4—864no—
268C22⋊C4—1721no—
269C42—21no—
270C42—434no—
271C42—862no—
272C42—1722no—
273C42—1721no—
274C42(C2×D43)⋊C412yes—
275C23—22no—
276C23—44no—
277C23—41no—
278C23—41no—
279C23#1306329511yescharacteristic
280Q8—41no—
281Q8—42no—
282Q8—41no—
283Q8—3442no—
284Q8—1724no—
285D4—42no—
286D4—81no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—864no—
294C2×C4—864no—
295C2×C4—3444no—
296C2×C4—1722no—
297C2×C4—1724no—
298C2×C4—1722no—
299C2×C4—1722no—
300C2×C4C22⋊C4×D4312yes—
301C2×C4C2×(C2×D43)⋊C411yescharacteristic
302C2×C4#1306329312yes—
303C2×C4#1306329511yescharacteristic
304C8—82no—
305C8—3441no—
306C22—22no—
307C22—44no—
308C22—42no—
309C22—82no—
310C22—82no—
311C22#1458275411yescharacteristic
312C22#1458308711yescharacteristic
313C22#1458309011yescharacteristic
314C4—22no—
315C4—21no—
316C4—22no—
317C4—21no—
318C4—42no—
319C4—3442no—
320C4—1724no—
321C4—1724no—
322C2—21no—
323C2—21no—
324C2—82no—
325C2#1913454111yescharacteristic
326C2#1913661812yes—
subgroupG/H
centerC22#14583087
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#355C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
cosocleC22×Q8×C43C23
hypercenterC2×#355D43
hypocenterC43#12775
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
2. C2×#14582697C2semidirect
4. #19134986C2semidirect
8. #14583649C4semidirect
187. C43#12775semidirect

Maximal subgroups

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

subgroupindex
C2×#145836492
C2×#145826972
#191349992
#191349862
C2×C43×#3552
#1277543