Finite Group Databasebeta

← #25012486

Subgroups — #25012486

Order 11008.

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

normal subgroups only

This group has 784 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×#14583629C211yesmaximal, characteristic
2C2×#14582698C211yesmaximal, characteristic
3C2×#14582697C212yesmaximal
4#19134988C212yesmaximal
5C43×#1886C211yesmaximal, characteristic
6#14583629—24no—
7#14583629—22no—
8#14583629C414yescomplemented
9C2×#13063324—22no—
10C2×#13063323—21no—
11C2×#13063323C2212yes—
12C2×C4×Dic86—21no—
13C2×#13063290—22no—
14#14582907—22no—
15C2×#13063244C2212yes—
16#14582698—22no—
17#14582697—24no—
18#14582658—22no—
19C2×C4⋊Q8×C43C2211yescharacteristic
20C43×#519C2211yescharacteristic
21C43×#419—21no—
22C2×#101×C43C2211yescharacteristic
23C43×#339—21no—
24C22×Dic86—21no—
25C22×Dic86—21no—
26C22×Dic86D412yes—
27C2×#10621877—22no—
28#13063324—28no—
29#13063324—28no—
30#13063323—24no—
31#13063323—24no—
32#13063323—22no—
33#13063323—22no—
34#13063323C2×C414yes—
35#13063323D414yes—
36C4×Dic86—24no—
37C4×Dic86—24no—
38#13063290—28no—
39#13063290—28no—
40C2×C4⋊Dic43—21no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—22no—
43C2×Dic43⋊C4—22no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—22no—
46C2×C4×Dic43D412yes—
47#13063248—44no—
48#13063244—22no—
49#13063244—22no—
50C22×Q8×C43D411yescharacteristic
51C22×Q8×C43C2311yescharacteristic
52C2×M16×C43—21no—
53C4⋊Q8×C43—22no—
54C4⋊Q8×C43C2×C412yes—
55C4⋊Q8×C43D412yes—
56C4×Q8×C43—42no—
57#117×C43—21no—
58#117×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C42×C43D411yescharacteristic
61#103×C43—42no—
62#101×C43—22no—
63C2×Q8×C43—21no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43C22⋊C412yes—
69C2×Q8×C43C22×C411yescharacteristic
70C2×Q8×C43C2×D411yescharacteristic
71C2×Q8×C43C2×D412yes—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2×D412yes—
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—22no—
77C22×Dic43—22no—
78C2×Dic86—24no—
79C2×Dic86—28no—
80C2×Dic86—24no—
81C2×Dic86—22no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86—81no—
85C2×Dic86—81no—
86C2×Dic86C22⋊C414yes—
87M16×C43—41no—
88M16×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—24no—
91C4⋊C4×C43—24no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—24no—
94C22⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43—42no—
97C42×C43—41no—
98C42×C43C22⋊C412yes—
99C4⋊Dic43—24no—
100Dic43⋊C4—28no—
101Dic43⋊C4—24no—
102Dic43⋊C4—24no—
103Dic43⋊C4—24no—
104Dic43⋊C4—24no—
105C4×Dic43—24no—
106C4×Dic43—28no—
107C4×Dic43—22no—
108C4×Dic43C22⋊C414yes—
109#10621877—42no—
110#10621877—42no—
111C2×C43⋊C8—42no—
112C23×C43#12011yescharacteristic
113Q8×C43—41no—
114Q8×C43—41no—
115Q8×C43—42no—
116Q8×C43—42no—
117Q8×C43—81no—
118C2×C4×C43—24no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43C2×C22⋊C412yes—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12012yes—
132C2×Dic43—28no—
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137Dic86—216no—
138Dic86—44no—
139Dic86—82no—
140Dic86—84no—
141C8×C43—81no—
142C43⋊C8—82no—
143#12777—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43#37911yescharacteristic
146C22×C43B(4,𝔽2)11yescharacteristic
147C22×C43#45811yescharacteristic
148C4×C43—24no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—21no—
153C4×C43—42no—
154C4×C43—82no—
155Dic43—28no—
156Dic43—44no—
157C2×Q82—431no—
158C2×#356—432no—
159C2×#356—431no—
160#1886—432no—
161#1886D4311yescharacteristic
162C2×C43—21no—
163C2×C43—21no—
164C2×C43#179011yescharacteristic
165C2×C43#220512yes—
166Q82—434no—
167Q82—864no—
168Q82—862no—
169C2×C4⋊Q8—432no—
170C2×C4⋊Q8—862no—
171C2×C4⋊Q8—861no—
172C2×C4⋊Q8C2×D4311yescharacteristic
173#519C2×D4311yescharacteristic
174C2×C4×Q8—862no—
175C2×C4×Q8—861no—
176#419—21no—
177#419—862no—
178C2×#101—432no—
179C2×#101C2×D4311yescharacteristic
180#356—864no—
181#356—862no—
182#339—21no—
183#339—862no—
184C43#1277711yescharacteristic, complemented, Sylow
185C22×Q8—432no—
186C22×Q8—861no—
187C22×Q8—861no—
188C22×Q8C22⋊D4311yescharacteristic
189C22×Q8C22×D4311yescharacteristic
190C2×M16—21no—
191C2×M16—862no—
192C4⋊Q8—22no—
193C4⋊Q8—434no—
194C4⋊Q8—434no—
195C4⋊Q8—868no—
196C4⋊Q8—868no—
197C4⋊Q8—864no—
198C4⋊Q8—864no—
199C4⋊Q8—862no—
200C4⋊Q8—862no—
201C4⋊Q8C4×D4312yes—
202C4⋊Q8D17212yes—
203C4×Q8—42no—
204C4×Q8—864no—
205C4×Q8—868no—
206C4×Q8—868no—
207C4×Q8—864no—
208#117—22no—
209#117—21no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—862no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—862no—
214C2×C4⋊C4—862no—
215C2×C42—432no—
216C2×C42—862no—
217C2×C42—861no—
218C2×C42C22⋊D4311yescharacteristic
219#103—42no—
220#103—1724no—
221#101—22no—
222#101—862no—
223#101—862no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—434no—
230C2×Q8—864no—
231C2×Q8—868no—
232C2×Q8—864no—
233C2×Q8—862no—
234C2×Q8—3441no—
235C2×Q8—3441no—
236C2×Q8—1722no—
237C2×Q8—1722no—
238C2×Q8(C2×D43)⋊C412yes—
239C2×Q8C2×C4×D4311yescharacteristic
240C2×Q8C2×D17211yescharacteristic
241C2×Q8D4×D4312yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—862no—
245C22×C4—862no—
246C22×C4D4×D4312yes—
247C22×C4C2×C22⋊D4311yescharacteristic
248M16—41no—
249M16—41no—
250M16—1722no—
251M16—1722no—
252C2×C8—41no—
253C2×C8—1722no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—868no—
259C4⋊C4—864no—
260C4⋊C4—864no—
261C4⋊C4—864no—
262C4⋊C4—864no—
263C4⋊C4—864no—
264C22⋊C4—41no—
265C42—21no—
266C42—41no—
267C42—42no—
268C42—434no—
269C42—868no—
270C42—864no—
271C42—862no—
272C42(C2×D43)⋊C412yes—
273C23#1306329311yescharacteristic
274Q8—41no—
275Q8—41no—
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—8616no—
280Q8—3442no—
281Q8—3444no—
282Q8—1724no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—868no—
294C2×C4—864no—
295C2×C4—864no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4C22⋊C4×D4312yes—
299C2×C4C2×(C2×D43)⋊C411yescharacteristic
300C2×C4#1306329311yescharacteristic
301C2×C4#1306329512yes—
302C8—81no—
303C8—3442no—
304C22—22no—
305C22#1458275411yescharacteristic
306C22#1458308511yescharacteristic
307C22#1458308811yescharacteristic
308C4—24no—
309C4—21no—
310C4—22no—
311C4—22no—
312C4—21no—
313C4—42no—
314C4—82no—
315C4—868no—
316C4—1724no—
317C2—21no—
318C2—21no—
319C2#1913454211yescharacteristic
320C2#1913662412yes—
subgroupG/H
centerC22#14583085
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1886C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
cosocleC22×Q8×C43C23
hypercenter#1886D43
hypocenterC43#12777
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1886

Complements

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

NH ≅ G/Ntype
8. #14583629C4semidirect
184. C43#12777semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
C2×#145826982
C2×#145826972
#191349882
C43×#18862
#1277743