Finite Group Databasebeta

← #25069730

Subgroups — #25069730

Order 11008.

890 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 203 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#19144630C212yesmaximal
2#19139957C211yesmaximal, characteristic
3#19133637C214yesmaximal
4#19133569C214yesmaximal
5#19133159C212yesmaximal
6#19132919C211yesmaximal, characteristic
7C43×#3502C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583232C2214yes—
10#14583191—22no—
11#14583106—22no—
12#14583054C2214yes—
13C4×#10621885—24no—
14#14582952C2212yes—
15#14582838C2212yes—
16#14582819C2212yes—
17#14582806—21no—
18#14582795—21no—
19#14582783—22no—
20#14582765C2211yescharacteristic
21#14582636C2218yes—
22#14582625C2214yes—
23Q82×C43—22no—
24C43×#557—22no—
25C43×#557—24no—
26C43×#544—21no—
27C43×#544C2214yes—
28C43×#533—22no—
29C43×#533C2212yes—
30C43×#519—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C22×Dic86C2311yescharacteristic
33C2×#10621885—24no—
34C4×Dic86—22no—
35C4×Dic86—22no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2311yescharacteristic
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—21no—
40C2×C4×Dic43—21no—
41#13063258—24no—
42C4⋊(C43⋊C8)—22no—
43#13063249—24no—
44#13063248—24no—
45C22⋊(C43⋊C8)C2314yes—
46C4×C43⋊C8—22no—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95—21no—
51C43⋊#95C2312yes—
52C22×Q8×C43D411yescharacteristic
53C4⋊Q8×C43—22no—
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43—24no—
56C4⋊Q8×C43—28no—
57C4⋊Q8×C43D412yes—
58C4⋊Q8×C43D412yes—
59#125×C43—24no—
60#125×C43—24no—
61#125×C43—28no—
62#125×C43—22no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43C2314yes—
66C4×Q8×C43—24no—
67C4×Q8×C43—24no—
68C4×Q8×C43—24no—
69C4×Q8×C43—24no—
70C4×Q8×C43—22no—
71C4×Q8×C43—22no—
72C4×Q8×C43—22no—
73C4×Q8×C43D414yes—
74#117×C43—24no—
75#117×C43—22no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C4⋊C4×C43C2312yes—
78C2×C42×C43D412yes—
79C2×C42×C43C2311yescharacteristic
80C2×Q8×C43—24no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—22no—
84C2×Q8×C43Q1614yescomplemented
85C2×Q8×C43C2×D414yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2411yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—22no—
93C22×Dic43—21no—
94C2×Dic86—22no—
95C2×Dic86—42no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—28no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—24no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43—24no—
107C4⋊C4×C43C2×D414yes—
108C22⋊C4×C43—24no—
109C42×C43—28no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—24no—
113C42×C43C2×D412yes—
114C42×C43C2×D412yes—
115#10621885—48no—
116C4⋊Dic43—22no—
117C4⋊Dic43—42no—
118Dic43⋊C4—44no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121C4×Dic43—42no—
122C2×C43⋊C8—24no—
123C23×C43C22×D411yescharacteristic
124Q8×C43—28no—
125Q8×C43—44no—
126Q8×C43—44no—
127Q8×C43—84no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12012yes—
139C2×C4×C43C2×Q1614yes—
140C2×C4×C43C2×Q1612yes—
141C2×C4×C43#13712yes—
142C2×C4×C43C22×D412yes—
143C2×Dic43—22no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—41no—
150C2×Dic43—42no—
151Dic86—24no—
152Dic86—42no—
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—44no—
165C4×C43—42no—
166C4×C43—44no—
167C4×C43#45114yes—
168Dic43—42no—
169Dic43—82no—
170Dic43—81no—
171#3502D4311yescharacteristic
172#3104—432no—
173#2581—431no—
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—22no—
184#557—22no—
185#557—24no—
186#544—21no—
187#544C2×D4314yes—
188#533—22no—
189#533C2×D4312yes—
190#519—21no—
191C2×C4×Q8—431no—
192C2×C4×Q8C2×D4311yescharacteristic
193#484—434no—
194#477—862no—
195#462—862no—
196#451—434no—
197C4×Q16—864no—
198#431—432no—
199#400—432no—
200#395—432no—
201#391—861no—
202#389—861no—
203#387—862no—
204#382—431no—
205#328—438no—
206#324—434no—
207C43#1822111yescharacteristic, complemented, Sylow
208C22×Q8—431no—
209C22×Q8C22⋊D4311yescharacteristic
210C2×Q16—864no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—24no—
214C4⋊Q8—28no—
215C4⋊Q8C22⋊D4312yes—
216C4⋊Q8C22⋊D4312yes—
217#125—24no—
218#125—24no—
219#125—28no—
220#125—22no—
221C22⋊Q8—22no—
222C22⋊Q8—24no—
223C22⋊Q8C22×D4314yes—
224C4×Q8—24no—
225C4×Q8—24no—
226C4×Q8—24no—
227C4×Q8—24no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8—862no—
232C4×Q8—862no—
233C4×Q8C22⋊D4314yes—
234#117—24no—
235#117—22no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—862no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C4⋊C4C22×D4312yes—
242C2×C42—861no—
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—432no—
252#95—861no—
253#95—862no—
254#95—862no—
255#95—862no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—862no—
261C2×Q8—1722no—
262C2×Q8#1062188514yescomplemented
263C2×Q8C2×C22⋊D4314yes—
264C22×C4—861no—
265C22×C4—862no—
266C22×C4—861no—
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—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—28no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—862no—
286C4⋊C4—1724no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1722no—
290C4⋊C4C2×C22⋊D4314yes—
291C22⋊C4—24no—
292C42—28no—
293C42—22no—
294C42—22no—
295C42—24no—
296C42—1722no—
297C42C2×C22⋊D4312yes—
298C42C2×C22⋊D4312yes—
299C23C22×C22⋊D4311yescharacteristic
300Q8—28no—
301Q8—44no—
302Q8—44no—
303Q8—84no—
304Q8—864no—
305Q8—1722no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—862no—
315C2×C4—1722no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1721no—
319C2×C4—1722no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4#1306329411yescharacteristic
323C2×C4#1306329411yescharacteristic
324C2×C4#1306329412yes—
325C2×C4C2×#1062188514yes—
326C2×C4C2×#1062188512yes—
327C2×C4#1306335612yes—
328C2×C4C22×C22⋊D4312yes—
329C8—1724no—
330C22—21no—
331C22—21no—
332C22C2×#1306329411yescharacteristic
333C22C22×#1062188511yescharacteristic
334C22C2×#1306335611yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—24no—
339C4—44no—
340C4—42no—
341C4—44no—
342C4—3442no—
343C4—3441no—
344C4—1722no—
345C4#1458305514yes—
346C2—21no—
347C2—21no—
348C2C2×#1458305511yescharacteristic
349C2#1914395911yescharacteristic
350C2#1914398711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3502C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#3502D43
hypocenterC43#18221
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

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

Maximal subgroups

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

subgroupindex
#191446302
#191399572
#191336372
#191335692
#191331592
#191329192
C43×#35022
#1822143