Finite Group Databasebeta

← #24994484

Subgroups — #24994484

Order 11008.

458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143233C211yesmaximal, characteristic
2#19140172C211yesmaximal, characteristic
3#19133041C212yesmaximal, complemented
4#19132461C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14582960—24no—
8#14582923—21no—
9#14582863—21no—
10C4×#10621877C2212yes—
11#14582829C411yescharacteristic
12#14582824C411yescharacteristic
13#14582819C411yescharacteristic
14#14582811C411yescharacteristic
15#14582787—21no—
16#14582783—21no—
17#14582780—21no—
18#14582772—21no—
19#14582767C2211yescharacteristic
20#14582629—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#432C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C22×Dic86C2×C411yescharacteristic
26C2×#10621877—22no—
27C4×Dic86—22no—
28C4×Dic86—22no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—24no—
37C22⋊(C43⋊C8)—24no—
38#13063236—22no—
39C4×C43⋊C8D414yes—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95C2×C411yescharacteristic
47C43⋊#95C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49#117×C43—22no—
50#117×C43—22no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—22no—
58C22⋊C8×C43—22no—
59#97×C43—22no—
60C24×C43C22⋊C411yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×Dic86—22no—
76C2×Dic86—42no—
77C2×C8×C43—42no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C22⋊C4×C43—22no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43C2×D412yes—
85C42×C43#4112yes—
86C22⋊Dic43—42no—
87C22⋊Dic43—42no—
88C4⋊Dic43—22no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93C4×Dic43—42no—
94#10621877—42no—
95#10621877—42no—
96C2×C43⋊C8—24no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43C4×D412yes—
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43#12112yes—
119C2×C4×C43#12311yescharacteristic
120C2×Dic43—22no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132Dic86—24no—
133Dic86—42no—
134C8×C43—82no—
135C43⋊C8—44no—
136#9493—431nomaximal, Sylow
137C22×C43—21no—
138C22×C43—21no—
139C22×C43—42no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—81no—
144C22×C43#38611yescharacteristic
145C22×C43#42111yescharacteristic
146C22×C43#42111yescharacteristic
147C4×C43—22no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—22no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—41no—
154Dic43—42no—
155Dic43—81no—
156Dic43—81no—
157Dic43—81no—
158#2921—431no—
159#2599—431no—
160#1491—432no—
161#1464D4311yescharacteristic
162#1288—432no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—81no—
166C2×C43#189111yescharacteristic
167C2×C43#189711yescharacteristic
168C2×C43#190911yescharacteristic
169C2×C4×Q8—431no—
170C2×#117C2×D4311yescharacteristic
171#433—864no—
172#432C2×D4312yes—
173#423—861no—
174#407—861no—
175C4×M16—432no—
176#398—431no—
177#397—431no—
178#395—431no—
179#393—431no—
180#388—861no—
181#387—861no—
182#387—861no—
183#385—861no—
184#383—431no—
185Q8⋊C8—864no—
186#324—21no—
187#323—21no—
188C43#949311yescharacteristic, complemented, Sylow
189C22×Q8—431no—
190C23×C4D17211yescharacteristic
191C2×M16—862no—
192C4×Q8—862no—
193C4×Q8—862no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4C4×D4311yescharacteristic
201C2×C4⋊C4C22⋊D4311yescharacteristic
202C2×C22⋊C4—861no—
203C2×C22⋊C4—861no—
204C2×C22⋊C4C4×D4311yescharacteristic
205C2×C22⋊C4C22⋊D4311yescharacteristic
206C2×C42—861no—
207C2×C42D17211yescharacteristic
208C2×C42C22×D4311yescharacteristic
209C4⋊C8—22no—
210C4⋊C8—864no—
211C22⋊C8—22no—
212C22⋊C8—864no—
213#97—22no—
214#97—862no—
215C4×C8—434no—
216#95—431no—
217#95—431no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224C24(C2×D43)⋊C411yescharacteristic
225C2×Q8—862no—
226C2×Q8—1722no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4(C2×D43)⋊C411yescharacteristic
236C22×C4(C2×D43)⋊C411yescharacteristic
237C22×C4(C2×D43)⋊C411yescharacteristic
238C22×C4C2×C4×D4311yescharacteristic
239C22×C4C2×D17211yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241M16—1722no—
242M16—1722no—
243C2×C8—42no—
244C2×C8—864no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—862no—
248C4⋊C4—1722no—
249C4⋊C4—1722no—
250C4⋊C4—1721no—
251C4⋊C4—1721no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—1722no—
255C22⋊C4—1722no—
256C42—21no—
257C42—21no—
258C42—1722no—
259C42D4×D4312yes—
260C42#1062190012yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×(C2×D43)⋊C411yescharacteristic
267Q8—864no—
268Q8—1722no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—862no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4(C22⋊D43)⋊C412yes—
295C2×C4#1306329511yescharacteristic
296C2×C4#1306329712yes—
297C2×C4#1306330911yescharacteristic
298C8—82no—
299C8—1724no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1458277611yescharacteristic
308C22#1458291511yescharacteristic
309C22#1458291511yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—3441no—
318C4—3441no—
319C4—3441no—
320C4—1722no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1913501111yescharacteristic
325C2#1913504111yescharacteristic
326C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#386
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#9493
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #19133041C2semidirect
4. #19132461C2semidirect
188. C43#9493semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191401722
#191330412
#191324612
C43×#14642
#949343