Finite Group Databasebeta

← #25074495

Subgroups — #25074495

Order 11008.

868 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 868 conjugacy classes of subgroups — too many to draw. Only its 179 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#19145986C212yesmaximal, complemented
2#19144917C211yesmaximal, characteristic
3#19133816C214yesmaximal, complemented
4#19133781C214yesmaximal, complemented
5#19133330C211yesmaximal, characteristic
6#19133050C212yesmaximal, complemented
7C43×#3550C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583253—22no—
10#14583249C2212yes—
11#14583245C2212yes—
12#14583184C2214yes—
13#14583181—22no—
14#14583155—24no—
15#14583109C2214yes—
16#14583106—22no—
17#14582923C2212yes—
18#14582895—22no—
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582648C2212yes—
21#14582643C2212yes—
22Q8⋊(C43⋊C8)C2218yes—
23C43×#563—22no—
24C43×#559C2212yes—
25Q82×C43C2212yes—
26C43×#556—22no—
27D4×Q8×C43—22no—
28C43×#542—24no—
29C43×#536—22no—
30C43×#533C2212yes—
31C43×#532C2211yescharacteristic
32C2×#10621885—24no—
33C2×#10621877—22no—
34C22×C43⋊C8—21no—
35#13063325C2312yes—
36#13063317—21no—
37#13063304—22no—
38C4×Dic86—22no—
39#13063284—21no—
40#13063256—24no—
41C4⋊(C43⋊C8)—22no—
42C4⋊(C43⋊C8)C2314yes—
43#13063249—24no—
44#13063249—24no—
45#13063248—24no—
46#13063246—24no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8C2312yes—
49C2×#41×C43D412yes—
50C22×Q8×C43—22no—
51C4⋊Q8×C43—24no—
52C4⋊Q8×C43—24no—
53C4⋊Q8×C43D412yes—
54C4⋊Q8×C43D412yes—
55C4⋊Q8×C43C2311yescharacteristic
56#127×C43C2311yescharacteristic
57#126×C43—28no—
58#125×C43—22no—
59#124×C43—24no—
60#124×C43—24no—
61#124×C43D412yes—
62#123×C43—24no—
63#123×C43—24no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43—28no—
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43D414yes—
68#121×C43—22no—
69C4×Q8×C43—24no—
70C4×Q8×C43—22no—
71C4×Q8×C43C2314yes—
72C4×D4×C43—24no—
73C4×D4×C43—22no—
74#117×C43—22no—
75#117×C43—22no—
76C2×C42×C43C2311yescharacteristic
77#41×C43—44no—
78C2×Q8×C43—24no—
79C2×Q8×C43—22no—
80C2×Q8×C43—84no—
81C2×Q8×C43C2×D414yes—
82C2×Q8×C43C2×D412yes—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43C2×D412yes—
86C22×C4×C43—24no—
87C22×C4×C43—22no—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D411yescharacteristic
90C2×Dic86—22no—
91C4⋊C4×C43—28no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43C2×D414yes—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—28no—
101C22⋊C4×C43—24no—
102C22⋊C4×C43—24no—
103C42×C43—24no—
104C42×C43—24no—
105C42×C43C2×D412yes—
106C42×C43C2×D411yescharacteristic
107C42×C43C2411yescharacteristic
108C22⋊Dic43—41no—
109#10621885—84no—
110C4⋊Dic43—22no—
111C4⋊Dic43—22no—
112Dic43⋊C4—42no—
113C4×Dic43—41no—
114#10621877—82no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—24no—
117C2×C43⋊C8—42no—
118C23×C43—22no—
119C23×C43#12011yescharacteristic
120Q8×C43—24no—
121Q8×C43—24no—
122Q8×C43—42no—
123Q8×C43—44no—
124Q8×C43—84no—
125D4×C43—42no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—82no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—24no—
133C2×C4×C43—22no—
134C2×C4×C43—24no—
135C2×C4×C43—44no—
136C2×C4×C43—84no—
137C2×C4×C43#12012yes—
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C22×D412yes—
141C2×Dic43—42no—
142Dic86—42no—
143Dic86—42no—
144C43⋊C8—42no—
145C43⋊C8—44no—
146#18693—431nomaximal, Sylow
147C22×C43—22no—
148C22×C43—21no—
149C22×C43—44no—
150C22×C43—42no—
151C22×C43C2×#12011yescharacteristic
152C4×C43—22no—
153C4×C43—21no—
154C4×C43—44no—
155C4×C43—42no—
156C4×C43—44no—
157C4×C43#45512yes—
158C4×C43#57712yes—
159C4×C43#57812yes—
160Dic43—82no—
161#3550D4311yescharacteristic
162#3255—432no—
163#3131—431no—
164#1645—434no—
165#1640—434no—
166#1560—431no—
167#1493—432no—
168C2×C43—41no—
169C2×C43—82no—
170C2×C43#301312yes—
171C2×C43C2×#45511yescharacteristic
172#563—22no—
173#559C2×D4312yes—
174Q82C2×D4312yes—
175#556—22no—
176D4×Q8—22no—
177#542—24no—
178#536—22no—
179#533—431no—
180#533C2×D4312yes—
181#532C2×D4311yescharacteristic
182#488—862no—
183#487—432no—
184#486—432no—
185#475—434no—
186#475—862no—
187#470—864no—
188#462—434no—
189#462—862no—
190#423—432no—
191#416—862no—
192C2×C4×C8—431no—
193#333—432no—
194#331—432no—
195Q8⋊C8—438no—
196C43#1869311yescharacteristic, complemented, Sylow
197C2×#41C22⋊D4312yes—
198C22×Q8—22no—
199C2×Q16—864no—
200C2×M16—862no—
201C22×C8—861no—
202C4⋊Q8—24no—
203C4⋊Q8—24no—
204C4⋊Q8—432no—
205C4⋊Q8C22⋊D4312yes—
206C4⋊Q8C22⋊D4312yes—
207C4⋊Q8C22×D4311yescharacteristic
208#127C22×D4311yescharacteristic
209#126—28no—
210#125—22no—
211#125—861no—
212#124—24no—
213#124—24no—
214#124C22⋊D4312yes—
215#123—24no—
216#123—24no—
217C22⋊Q8—24no—
218C22⋊Q8—28no—
219C22⋊Q8—22no—
220C22⋊Q8—862no—
221C22⋊Q8C22⋊D4314yes—
222#121—22no—
223C4×Q8—24no—
224C4×Q8—22no—
225C4×Q8—862no—
226C4×Q8C22×D4314yes—
227C4×D4—24no—
228C4×D4—22no—
229#117—22no—
230#117—22no—
231#117—861no—
232C2×C42C22×D4311yescharacteristic
233#106—864no—
234C4⋊C8—434no—
235C4⋊C8—862no—
236#103—864no—
237#103—864no—
238#103—864no—
239#102—864no—
240C4×C8—432no—
241C4×C8—861no—
242#41—44no—
243C2×Q8—24no—
244C2×Q8—22no—
245C2×Q8—84no—
246C2×Q8—862no—
247C2×Q8C2×C22⋊D4314yes—
248C2×Q8C2×C22⋊D4312yes—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4C2×C22⋊D4312yes—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4C2×C22⋊D4312yes—
255C22×C4C2×C22⋊D4311yescharacteristic
256Q16—3444no—
257M16—3442no—
258C2×C8—862no—
259C2×C8—864no—
260C2×C8—1722no—
261C4⋊C4—28no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—862no—
269C4⋊C4—862no—
270C4⋊C4—1722no—
271C4⋊C4C2×C22⋊D4314yes—
272C22⋊C4—24no—
273C22⋊C4—28no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—1721no—
277C42—24no—
278C42—24no—
279C42—1721no—
280C42C2×C22⋊D4311yescharacteristic
281C42C2×C22⋊D4312yes—
282C42C23×D4311yescharacteristic
283C23—22no—
284C23#1306329411yescharacteristic
285Q8—24no—
286Q8—24no—
287Q8—42no—
288Q8—44no—
289Q8—84no—
290Q8—1722no—
291Q8—1722no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—44no—
303C2×C4—84no—
304C2×C4—1722no—
305C2×C4#1306329412yes—
306C2×C4#1306329411yescharacteristic
307C2×C4C22×C22⋊D4311yescharacteristic
308C2×C4C22×C22⋊D4312yes—
309C8—1722no—
310C8—1724no—
311C22—22no—
312C22—21no—
313C22—44no—
314C22—42no—
315C22C2×#1306329411yescharacteristic
316C4—22no—
317C4—21no—
318C4—44no—
319C4—42no—
320C4—44no—
321C4—3442no—
322C4#1458307712yes—
323C4#1458370712yes—
324C4#1458371412yes—
325C2—41no—
326C2—82no—
327C2#1914391012yes—
328C2C2×#1458307711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3550C2
socleC22×C43C2×#120
prime radicalC43×#532C22
hypercenter#3550D43
hypocenterC43#18693
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #19145986C2semidirect
3. #19133816C2semidirect
4. #19133781C2semidirect
6. #19133050C2semidirect
196. C43#18693semidirect

Maximal subgroups

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

subgroupindex
#191459862
#191449172
#191338162
#191337812
#191333302
#191330502
C43×#35502
#1869343