Finite Group Databasebeta

← #25007471

Subgroups — #25007471

Order 11008.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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#19140172C211yesmaximal, characteristic
2#19134672C211yesmaximal, characteristic
3#19132617C212yesmaximal
4#19132596C212yesmaximal
5C43×#1458C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic, complemented
7#14582829C411yescharacteristic, complemented
8#14582824C2211yescharacteristic
9#14582819C411yescharacteristic, complemented
10#14582811C2211yescharacteristic
11#14582787—21no—
12#14582783—21no—
13#14582780—21no—
14#14582772—21no—
15#14582767C411yescharacteristic, complemented
16#14582762—21no—
17#14582666—21no—
18#14582666C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C4×Dic86—41no—
25C4×Dic86—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×C4×Dic43—21no—
34C43⋊#95—21no—
35C43⋊#95—21no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—41no—
41C43⋊#95—41no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55C4×C8×C43—41no—
56C24×C43C2×D411yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—42no—
72C2×Dic86—41no—
73C2×Dic86—42no—
74C2×C8×C43—42no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C22⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C4⋊Dic43—41no—
88Dic43⋊C4—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92C4×Dic43—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43C2×C22⋊C411yescharacteristic
98C23×C43#13512yes—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43#9911yescharacteristic
115C2×C4×C43#9911yescharacteristic
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—82no—
129C2×Dic43—82no—
130C2×Dic43—82no—
131Dic86—42no—
132Dic86—42no—
133C8×C43—82no—
134#11842—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—22no—
138C22×C43—42no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—81no—
142C22×C43C2×#9911yescharacteristic
143C22×C43#41611yescharacteristic
144C22×C43#42111yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152Dic43—42no—
153Dic43—81no—
154Dic43—81no—
155Dic43—81no—
156Dic43—162no—
157#2599—431no—
158#1820—431no—
159#1458D4311yescharacteristic
160#1351—432no—
161#1344—432no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—42no—
165C2×C43#151611yescharacteristic
166C2×C43#212011yescharacteristic
167C2×C43#212911yescharacteristic
168C2×C4×Q8—431no—
169C2×#117C2×D4311yescharacteristic
170#431—21no—
171#398—431no—
172#397—431no—
173#395—431no—
174#393—431no—
175#388—861no—
176#387—861no—
177#387—861no—
178#385—861no—
179#383—431no—
180#381—861no—
181#342—432no—
182#342—861no—
183#324—21no—
184#323C2×D4312yes—
185C43#1184211yescharacteristic, complemented, Sylow
186C22×Q8—431no—
187C23×C4D17211yescharacteristic
188C4×Q8—1721no—
189C4×Q8—1721no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4C4×D4311yescharacteristic
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C22⋊C4—861no—
199C2×C22⋊C4—861no—
200C2×C22⋊C4—862no—
201C2×C22⋊C4D17211yescharacteristic
202C2×C22⋊C4C22×D4311yescharacteristic
203C2×C42—861no—
204C2×C42C4×D4311yescharacteristic
205C2×C42C22⋊D4311yescharacteristic
206C4⋊C8—41no—
207C22⋊C8—22no—
208C4×C8—41no—
209#95—431no—
210#95—431no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—1721no—
218#95—1721no—
219C24C2×D17211yescharacteristic
220C2×Q8—1721no—
221C2×Q8—1722no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—1722no—
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4(C2×D43)⋊C411yescharacteristic
234C22×C4(C2×D43)⋊C411yescharacteristic
235C22×C4C2×C4×D4311yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C2×C8—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—1721no—
241C4⋊C4—1722no—
242C4⋊C4—1722no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—1722no—
248C22⋊C4—1722no—
249C22⋊C4—1722no—
250C22⋊C4—1722no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—1722no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23C2×(C2×D43)⋊C411yescharacteristic
261C23#1306334712yes—
262Q8—1722no—
263Q8—1722no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—862no—
280C2×C4—3442no—
281C2×C4—3442no—
282C2×C4—3442no—
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#1306323911yescharacteristic
295C2×C4#1306323911yescharacteristic
296C8—82no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22C2×#1306323911yescharacteristic
305C22#1458289611yescharacteristic
306C22#1458291511yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—3441no—
315C4—3441no—
316C4—3441no—
317C4—1722no—
318C4—6882no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2#1913315211yescharacteristic
323C2#1913623711yescharacteristic
324C2#1913626911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1458C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1458D43
hypocenterC43#11842
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
6. C2×C4×Dic86C4semidirect
7. #14582829C4semidirect
9. #14582819C4semidirect
15. #14582767C4semidirect
185. C43#11842semidirect

Maximal subgroups

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

subgroupindex
#191401722
#191346722
#191326172
#191325962
C43×#14582
#1184243