Finite Group Databasebeta

← #24992643

Subgroups — #24992643

Order 11008.

560 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 127 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#19140408C211yesmaximal, characteristic
2#19137213C211yesmaximal, characteristic
3#19133168C212yesmaximal
4#19132463C212yesmaximal
5C2×C43×#324C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7C2×#13063284—21no—
8#14582838C412yescomplemented
9#14582832—22no—
10#14582819C412yescomplemented
11#14582798—24no—
12#14582772—21no—
13#14582762—21no—
14#14582759—21no—
15#14582759C2211yescharacteristic
16#14582759C2212yes—
17#14582637—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2212yes—
20C43×#324—22no—
21C22×Dic86C2×C411yescharacteristic
22#13063304—22no—
23#13063304—22no—
24#13063284—42no—
25#13063284—42no—
26C2×C4⋊Dic43—22no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C4×Dic43—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95C2×C412yes—
42C43⋊#95D414yes—
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C22×C8×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43C2×C412yes—
50C2×C4⋊C4×C43D412yes—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C24×C43C2×D411yescharacteristic
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—81no—
61C22×C4×C43—81no—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22⋊C412yes—
64C22×C4×C43SD1612yes—
65C22×C4×C43Q1612yes—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D412yes—
69C22×C4×C43#4112yes—
70C22×Dic43—21no—
71C22×Dic43—22no—
72C22×Dic43—21no—
73C22×Dic43—24no—
74C2×Dic86—22no—
75C2×Dic86—81no—
76C2×C8×C43—42no—
77C2×C8×C43—82no—
78C4⋊C4×C43—24no—
79C4⋊C4×C43—24no—
80C22⋊Dic43—41no—
81C22⋊Dic43—41no—
82C22⋊Dic43—42no—
83C22⋊Dic43—41no—
84C22⋊Dic43—42no—
85C22⋊Dic43—41no—
86C4⋊Dic43—22no—
87C4⋊Dic43—44no—
88C4⋊Dic43—81no—
89C4⋊Dic43—82no—
90C4⋊Dic43—82no—
91Dic43⋊C4—42no—
92Dic43⋊C4—82no—
93C4×Dic43—44no—
94C23×C43—41no—
95C23×C43—41no—
96C23×C43C2×C22⋊C411yescharacteristic
97C23×C43#12011yescharacteristic
98C23×C43#12311yescharacteristic
99C23×C43C2×SD1611yescharacteristic
100C23×C43C2×Q1611yescharacteristic
101C23×C43AGL(1,ℤ/8)11yescharacteristic
102C23×C43#13711yescharacteristic
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—42no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43—81no—
117C2×C4×C43#10314yes—
118C2×C4×C43C4×D412yes—
119C2×C4×C43#12112yes—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—44no—
123C2×Dic43—42no—
124C2×Dic43—44no—
125C2×Dic43—42no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—44no—
130Dic86—82no—
131C8×C43—82no—
132#9200—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—21no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43#38611yescharacteristic
144C22×C43C2×#10311yescharacteristic
145C22×C43#41711yescharacteristic
146C22×C43#45011yescharacteristic
147C22×C43#45111yescharacteristic
148C22×C43#48311yescharacteristic
149C22×C43#48411yescharacteristic
150C4×C43—24no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—42no—
154Dic43—84no—
155Dic43—82no—
156Dic43—81no—
157Dic43—81no—
158#2627—431no—
159#2316—431no—
160#1520—432no—
161C2×#324D4311yescharacteristic
162#1289—432no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#187211yescharacteristic
170C2×C43#191211yescharacteristic
171C2×C43#191311yescharacteristic
172C2×C22⋊Q8—431no—
173C2×#117—861no—
174C22×C4⋊C4C2×D4311yescharacteristic
175C2×C22⋊C8C2×D4312yes—
176#400—432no—
177#398—862no—
178#395—432no—
179#389—864no—
180#385—861no—
181#381—861no—
182#380—431no—
183#380—432no—
184#380—861no—
185#328—864no—
186#324—22no—
187C43#920011yescharacteristic, complemented, Sylow
188C22×Q8—431no—
189C23×C4D17211yescharacteristic
190C23×C4D17211yescharacteristic
191C23×C4C22×D4311yescharacteristic
192C22×C8—22no—
193C22⋊Q8—862no—
194C22⋊Q8—862no—
195#117—1722no—
196#117—1722no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—862no—
201C2×C4⋊C4—862no—
202C2×C4⋊C4—862no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4C4×D4312yes—
207C2×C4⋊C4C22⋊D4312yes—
208C2×C22⋊C4—862no—
209C2×C22⋊C4—861no—
210C2×C22⋊C4—861no—
211C2×C42—862no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214#95—432no—
215#95—434no—
216#95—862no—
217#95—862no—
218#95—862no—
219#95—862no—
220C24C2×D17211yescharacteristic
221C2×Q8—862no—
222C2×Q8—3441no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—81no—
230C22×C4—81no—
231C22×C4—862no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—864no—
235C22×C4#1062187312yes—
236C22×C4Dic17212yes—
237C22×C4(C2×D43)⋊C412yes—
238C22×C4(C2×D43)⋊C412yes—
239C22×C4C2×C4×D4311yescharacteristic
240C22×C4D4×D4312yes—
241C22×C4#1062190012yes—
242C22×C4C2×C22⋊D4311yescharacteristic
243C2×C8—42no—
244C2×C8—82no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—862no—
248C4⋊C4—3442no—
249C4⋊C4—3442no—
250C4⋊C4—3441no—
251C4⋊C4—3442no—
252C4⋊C4—1724no—
253C4⋊C4—1722no—
254C22⋊C4—1721no—
255C22⋊C4—1721no—
256C22⋊C4—1722no—
257C22⋊C4—1722no—
258C22⋊C4—1721no—
259C22⋊C4—1721no—
260C42—1724no—
261C23—41no—
262C23—41no—
263C23C2×(C2×D43)⋊C411yescharacteristic
264C23#1306329511yescharacteristic
265C23#1306330911yescharacteristic
266C23C2×#1062187311yescharacteristic
267C23C2×Dic17211yescharacteristic
268C23#1306335311yescharacteristic
269C23#1306335811yescharacteristic
270Q8—3442no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—1722no—
286C2×C4—1724no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4—1724no—
290C2×C4—1722no—
291C2×C4—1724no—
292C2×C4—1722no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4#1306325014yes—
296C2×C4(C22⋊D43)⋊C412yes—
297C2×C4#1306329712yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1458277611yescharacteristic
310C22C2×#1306325011yescharacteristic
311C22#1458290111yescharacteristic
312C22#1458305211yescharacteristic
313C22#1458305711yescharacteristic
314C22#1458323011yescharacteristic
315C22#1458323511yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—3444no—
321C4—3442no—
322C4—3441no—
323C4—3441no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1913490011yescharacteristic
331C2#1913513011yescharacteristic
332C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#9200
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #14582838C4semidirect
10. #14582819C4semidirect
187. C43#9200semidirect

Maximal subgroups

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

subgroupindex
#191404082
#191372132
#191331682
#191324632
C2×C43×#3242
#920043