Finite Group Databasebeta

← #25069729

Subgroups — #25069729

Order 11008.

890 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 187 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#19148405C211yesmaximal, characteristic
2#19144634C212yesmaximal
3#19133636C214yesmaximal
4#19133568C214yesmaximal
5#19133158C212yesmaximal
6#19132919C211yesmaximal, characteristic
7C43×#2581C211yesmaximal, characteristic
8Q8×Dic86—22no—
9#14583628—22no—
10#14583625—24no—
11#14583530—21no—
12#14583530C2214yes—
13#14583456—22no—
14#14583456C2212yes—
15#14583377—21no—
16#14583234C2214yes—
17#14583194—22no—
18#14583109—22no—
19#14583055C2214yes—
20C4×#10621885—24no—
21#14582952C2212yes—
22#14582635C2218yes—
23#14582625C2214yes—
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#400C2212yes—
27C43×#395C2212yes—
28C43×#391—21no—
29C43×#389—21no—
30C43×#387—22no—
31C43×#382C2211yescharacteristic
32C2×#10621885—24no—
33#13063325—22no—
34#13063325—22no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063324—28no—
39#13063317—24no—
40#13063317—22no—
41#13063316—24no—
42#13063316—28no—
43#13063304—22no—
44#13063304—24no—
45#13063304C2314yes—
46Q8×Dic43—24no—
47Q8×Dic43—24no—
48C4×Dic86—24no—
49C4×Dic86—24no—
50C4×Dic86—22no—
51C4×Dic86D414yes—
52#13063284—24no—
53#13063284—22no—
54#13063258—24no—
55C4⋊(C43⋊C8)—22no—
56#13063249—24no—
57#13063248—24no—
58C22⋊(C43⋊C8)C2314yes—
59C4×C43⋊C8—22no—
60C22×Q8×C43D411yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C4×Q8×C43—22no—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C4⋊C4×C43C2311yescharacteristic
71C2×C4⋊C4×C43C2312yes—
72C2×C42×C43—21no—
73C2×C42×C43D412yes—
74C2×C42×C43C2311yescharacteristic
75#95×C43—21no—
76#95×C43—22no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43C2312yes—
80C2×Q8×C43—22no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—42no—
84C2×Q8×C43Q1614yescomplemented
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2411yescharacteristic
93C2×Dic86—22no—
94C2×Dic86—24no—
95C2×Dic86C2×D414yes—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—44no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—42no—
103C42×C43—22no—
104C42×C43—22no—
105C42×C43—42no—
106C42×C43C2×D412yes—
107C42×C43C2×D412yes—
108C22⋊Dic43—24no—
109#10621885—48no—
110C4⋊Dic43—24no—
111C4⋊Dic43—24no—
112C4⋊Dic43—24no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43C2×D414yes—
117Dic43⋊C4—28no—
118Dic43⋊C4—24no—
119Dic43⋊C4—24no—
120C4×Dic43—28no—
121C4×Dic43—24no—
122C2×C43⋊C8—24no—
123C23×C43C22×D411yescharacteristic
124Q8×C43—28no—
125Q8×C43—24no—
126Q8×C43—42no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12012yes—
144C2×C4×C43C2×Q1614yes—
145C2×C4×C43C2×Q1612yes—
146C2×C4×C43#13712yes—
147C2×C4×C43C22×D412yes—
148C2×Dic43—24no—
149C2×Dic43—24no—
150Dic86—44no—
151Dic86—44no—
152Dic86—84no—
153C43⋊C8—44no—
154#18221—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43C2×#12011yescharacteristic
158C22×C43C22×Q1611yescharacteristic
159C22×C43C2×#13711yescharacteristic
160C4×C43—24no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43—82no—
167C4×C43—81no—
168C4×C43#45114yes—
169Dic43—44no—
170Dic43—44no—
171#3502—431no—
172#3104—432no—
173#2581D4311yescharacteristic
174#1617—434no—
175#1605—434no—
176#1518—432no—
177#1461—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43C2×#45111yescharacteristic
181C2×C43#302011yescharacteristic
182C2×C43#302511yescharacteristic
183Q82—862no—
184#557—864no—
185#557—862no—
186#544—434no—
187#544—861no—
188#533—432no—
189#533—862no—
190#519—861no—
191C2×C4×Q8C2×D4311yescharacteristic
192C2×C4×Q8C2×D4311yescharacteristic
193#484—434no—
194#477—862no—
195#462—862no—
196#451—434no—
197C4×Q16—864no—
198#431—432no—
199#400C2×D4312yes—
200#395C2×D4312yes—
201#391—21no—
202#389—21no—
203#387—22no—
204#382C2×D4311yescharacteristic
205#328—438no—
206#324—434no—
207C43#1822111yescharacteristic, complemented, Sylow
208C22×Q8C22⋊D4311yescharacteristic
209C22×Q8C22×D4311yescharacteristic
210C2×Q16—864no—
211C4⋊Q8—432no—
212C4⋊Q8—432no—
213C4⋊Q8—862no—
214C4⋊Q8—862no—
215C4⋊Q8—868no—
216C4⋊Q8—864no—
217#125—864no—
218#125—868no—
219#125—864no—
220#125—862no—
221C22⋊Q8—434no—
222C22⋊Q8—862no—
223C22⋊Q8—864no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—434no—
229C4×Q8—864no—
230C4×Q8—864no—
231C4×Q8—864no—
232C4×Q8—864no—
233C4×Q8—862no—
234#117—862no—
235#117—864no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4C22⋊D4311yescharacteristic
240C2×C4⋊C4C22×D4311yescharacteristic
241C2×C4⋊C4C22×D4312yes—
242C2×C42—21no—
243C2×C42C22⋊D4312yes—
244C2×C42C22×D4311yescharacteristic
245#107—864no—
246C4⋊C8—862no—
247#103—864no—
248#103—864no—
249C22⋊C8—434no—
250C4×C8—862no—
251#95—21no—
252#95—22no—
253#95—22no—
254#95—22no—
255#95C22×D4312yes—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—42no—
260C2×Q8—434no—
261C2×Q8—864no—
262C2×Q8—862no—
263C2×Q8#1062188514yescomplemented
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4C2×C22⋊D4312yes—
268C22×C4C2×C22⋊D4312yes—
269C22×C4C2×C22⋊D4311yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271C22×C4C23×D4311yescharacteristic
272Q16—1728no—
273C2×C8—864no—
274C4⋊C4—22no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—44no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—434no—
282C4⋊C4—864no—
283C4⋊C4—864no—
284C4⋊C4—864no—
285C4⋊C4—868no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—864no—
289C4⋊C4—862no—
290C4⋊C4—864no—
291C22⋊C4—864no—
292C42—22no—
293C42—22no—
294C42—42no—
295C42—868no—
296C42—864no—
297C42D4×D4312yes—
298C42D4×D4312yes—
299C23C22×C22⋊D4311yescharacteristic
300Q8—28no—
301Q8—24no—
302Q8—42no—
303Q8—3444no—
304Q8—1724no—
305Q8—1724no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—864no—
321C2×C4—864no—
322C2×C4#1306329311yescharacteristic
323C2×C4#1306329311yescharacteristic
324C2×C4#1306329312yes—
325C2×C4C2×#1062188514yes—
326C2×C4C2×#1062188512yes—
327C2×C4#1306335512yes—
328C2×C4C2×D4×D4312yes—
329C8—1724no—
330C22—21no—
331C22—21no—
332C22C2×#1306329311yescharacteristic
333C22C22×#1062188511yescharacteristic
334C22C2×#1306335511yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—24no—
339C4—42no—
340C4—42no—
341C4—82no—
342C4—81no—
343C4—1724no—
344C4—1724no—
345C4#1458305414yes—
346C2—21no—
347C2—21no—
348C2C2×#1458305411yescharacteristic
349C2#1914395811yescharacteristic
350C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2581C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#2581D43
hypocenterC43#18221
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
84. C2×Q8×C43Q16semidirect
207. C43#18221semidirect
263. C2×Q8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191446342
#191336362
#191335682
#191331582
#191329192
C43×#25812
#1822143