Finite Group Databasebeta

← #25016995

Subgroups — #25016995

Order 11008.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#19145673C211yesmaximal, characteristic
2#19136281C211yesmaximal, characteristic
3#19136268C211yesmaximal, characteristic
4#19132771C211yesmaximal, characteristic, complemented
5#19132769C211yesmaximal, characteristic, complemented
6#19132755C211yesmaximal, characteristic, complemented
7C43×#1407C211yesmaximal, characteristic, complemented
8#14583510C411yescharacteristic, complemented
9#14583469C2211yescharacteristic
10#14583278C411yescharacteristic, complemented
11#14583268C411yescharacteristic, complemented
12#14583253C2211yescharacteristic
13#14583119—21no—
14#14583107—21no—
15#14583058—21no—
16#14583053—21no—
17#14582961C411yescharacteristic, complemented
18#101×D43—21no—
19#14582871—21no—
20#14582697—21no—
21#14582696C2211yescharacteristic
22#14582694C2211yescharacteristic
23#14582693—21no—
24C43×#497C2211yescharacteristic
25C43×#355C2211yescharacteristic
26C43×#354C2211yescharacteristic
27C2×#10621900D411yescharacteristic
28C2×Q8×D43D411yescharacteristic
29C2×#10621885—21no—
30C2×#10621885—21no—
31M16×D43—41no—
32#13063325C2×C411yescharacteristic
33#13063323D411yescharacteristic
34#13063320—41no—
35#13063317C2×C411yescharacteristic
36#13063315—41no—
37#13063312D411yescharacteristic
38#13063307—41no—
39#13063302—41no—
40#13063301—21no—
41Q8×Dic43—21no—
42#13063282C2×C411yescharacteristic
43#13063281—41no—
44Dic43⋊C8—21no—
45#13063250—21no—
46#13063250—21no—
47#13063249—21no—
48#13063246—21no—
49#13063244—21no—
50#13063243—41no—
51#13063240—21no—
52#13063239—41no—
53(C2×D43)⋊C8—21no—
54C4×C43⋊C8C2×C411yescharacteristic
55C2×Q16×C43—21no—
56C2×SD16×C43—21no—
57C4⋊Q8×C43C2×C411yescharacteristic
58#124×C43C2311yescharacteristic
59#101×C43—21no—
60#99×C43—21no—
61#97×C43C2×C411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43C2×D411yescharacteristic
64C2×D4×C43C2×D411yescharacteristic
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67Q8×D43—81no—
68#10621900—81no—
69C2×C4×D43—21no—
70C2×C4×D43C22⋊C411yescharacteristic
71C2×Dic86—21no—
72C2×Dic86C22⋊C411yescharacteristic
73C2×Dic86C22⋊C411yescharacteristic
74Q16×C43—81no—
75SD16×C43—81no—
76M16×C43—41no—
77C2×C8×C43—21no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C42×C43C22×C411yescharacteristic
82C22⋊Dic43—41no—
83C22⋊Dic43—41no—
84#10621885—81no—
85#10621885—81no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—41no—
88C4⋊Dic43—21no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91Dic43⋊C4—21no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—81no—
96C4×Dic43—41no—
97C4×Dic43—81no—
98C4×Dic43C22⋊C411yescharacteristic
99#10621877—41no—
100C2×C43⋊C8—21no—
101#10621872—81no—
102C8×D43—81no—
103C23×C43—21no—
104C22×D43#9911yescharacteristic
105Q8×C43—41no—
106Q8×C43—41no—
107Q8×C43—41no—
108D4×C43—41no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43C2×C22⋊C411yescharacteristic
114C22⋊D43—81no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—81no—
122C2×Dic43#9911yescharacteristic
123C4×D43—41no—
124C4×D43—41no—
125C4×D43—41no—
126Dic86—41no—
127Dic86—41no—
128Dic86—81no—
129C8×C43—41no—
130C8×C43—81no—
131C43⋊C8—41no—
132C43⋊C8—81no—
133#13608—431nomaximal, Sylow
134C22×C43—41no—
135C22×C43—81no—
136C22×C43C2×#9911yescharacteristic
137C2×D43—21no—
138C2×D43—41no—
139C4×C43—21no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43—81no—
143C4×C43—161no—
144Dic43—21no—
145Dic43—41no—
146Dic43—41no—
147Dic43—41no—
148Dic43—81no—
149Dic43—161no—
150#3223—431no—
151#2133—431no—
152#2129—431no—
153#1414—431no—
154#1414—431no—
155#1407—431no—
156#1407D4311yescharacteristic, complemented
157C2×C43—21no—
158C2×C43—81no—
159C2×C43#212711yescharacteristic
160D43—41no—
161#541—431no—
162#536—431no—
163#497C2×D4311yescharacteristic
164#494—431no—
165#491—431no—
166#488—431no—
167#464—861no—
168#462—861no—
169#452—861no—
170#451—861no—
171#433—431no—
172C2×#101—861no—
173#410—861no—
174#356—861no—
175#355—431no—
176#355C2×D4311yescharacteristic
177#354—431no—
178#354—861no—
179#354C2×D4311yescharacteristic
180C43#1360811yescharacteristic, complemented, Sylow
181C2×#41—431no—
182C22×Q8—431no—
183C2×Q16—21no—
184C2×Q16—861no—
185C2×Q16—861no—
186C2×SD16—21no—
187C2×M16—1721no—
188C4⋊Q8—431no—
189C4⋊Q8—431no—
190C4⋊Q8C4×D4311yescharacteristic
191#126—1721no—
192#125—431no—
193#125—1721no—
194#124—431no—
195#124C22×D4311yescharacteristic
196#123—1721no—
197C22⋊Q8—861no—
198C22⋊Q8—1721no—
199C4×Q8—861no—
200#117—431no—
201#117—1721no—
202C4⋊C8—861no—
203#103—861no—
204#103—861no—
205#103—861no—
206#102—861no—
207#101—21no—
208#101—861no—
209#101—1721no—
210#99—21no—
211#99—861no—
212#99—1721no—
213C22⋊C8—861no—
214#97C4×D4311yescharacteristic
215C4×C8—431no—
216#41—3441no—
217C2×Q8—21no—
218C2×Q8—431no—
219C2×Q8—431no—
220C2×Q8—861no—
221C2×Q8—3441no—
222C2×Q8D4×D4311yescharacteristic
223C2×D4—861no—
224C2×D4D4×D4311yescharacteristic
225C22×C4—431no—
226C22×C4—861no—
227C22×C4—861no—
228Q16—81no—
229Q16—3441no—
230Q16—3441no—
231SD16—81no—
232M16—41no—
233M16—3441no—
234M16—1721no—
235C2×C8—21no—
236C2×C8—861no—
237C2×C8—3441no—
238C4⋊C4—41no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—3441no—
242C4⋊C4—1721no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—861no—
250C22⋊C4—1721no—
251C22⋊C4—1721no—
252C22⋊C4—1721no—
253C42—431no—
254C42—3441no—
255C42—1721no—
256C42C2×C4×D4311yescharacteristic
257C23—21no—
258C23—431no—
259Q8—41no—
260Q8—41no—
261Q8—41no—
262Q8—3441no—
263Q8—1721no—
264Q8—1721no—
265D4—41no—
266D4—3441no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—431no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—3441no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4C22⋊C4×D4311yescharacteristic
283C8—41no—
284C8—81no—
285C8—3441no—
286C8—1721no—
287C22—41no—
288C22—81no—
289C22—861no—
290C22—1721no—
291C22#99×D4311yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—161no—
297C4—861no—
298C4—3441no—
299C4—1721no—
300C4—1721no—
301C4—1721no—
302C4—6881no—
303C2—21no—
304C2—81no—
305C2—1721no—
306C2#1913626111yescharacteristic
subgroupG/H
centerC2#19136261
commutatorC42×C43C22×C4
Frattini#124C22×D43
FittingC43×#1407C2
socleC2×C43#2127
prime radicalC2×#10621900D4
cosocle#124×C43C23
hypercenter#1407D43
hypocenterC43#13608
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1407

Complements

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

NH ≅ G/Ntype
4. #19132771C2semidirect
5. #19132769C2semidirect
6. #19132755C2semidirect
7. C43×#1407C2semidirect
8. #14583510C4semidirect
10. #14583278C4semidirect
11. #14583268C4semidirect
17. #14582961C4semidirect
156. #1407D43semidirect
180. C43#13608semidirect

Maximal subgroups

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

subgroupindex
#191456732
#191362812
#191362682
#191327712
#191327692
#191327552
C43×#14072
#1360843