Finite Group Databasebeta

← #25006252

Subgroups — #25006252

Order 11008.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139783C211yesmaximal, characteristic
2#19132937C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132541C211yesmaximal, characteristic
5#19132538C211yesmaximal, characteristic
6#19132538C211yesmaximal, characteristic
7C43×#1325C211yesmaximal, characteristic
8C2×#13063316C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582953—21no—
11#14582949—21no—
12#14582830—21no—
13#14582830—21no—
14#14582805C411yescharacteristic
15#14582804C411yescharacteristic
16#14582785—21no—
17#14582785—21no—
18#14582764C2211yescharacteristic
19C4×Dic43⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#384C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28#13063316—41no—
29#13063316—41no—
30#13063290—41no—
31#13063290—41no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4D411yescharacteristic
37C2×Dic43⋊C4D411yescharacteristic
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42Dic43⋊C8—41no—
43Dic43⋊C8—41no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46#13063235—41no—
47C8×Dic43—41no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C42×C43C2×C411yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C42×C43—21no—
84C42×C43—21no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92C4×Dic43—21no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C23×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43#13111yescharacteristic
116C2×C4×C43#13111yescharacteristic
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—42no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43#9911yescharacteristic
131C2×Dic43#9911yescharacteristic
132C2×Dic43#10112yes—
133Dic86—42no—
134Dic86—42no—
135C8×C43—81no—
136C8×C43—81no—
137C43⋊C8—81no—
138C43⋊C8—81no—
139#11571—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#40811yescharacteristic
143C22×C43C2×#9911yescharacteristic
144C22×C43C2×#10111yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—42no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—81no—
151Dic43—21no—
152Dic43—21no—
153Dic43—22no—
154Dic43—41no—
155Dic43—41no—
156Dic43—81no—
157Dic43—81no—
158#2565—431no—
159#1467—431no—
160#1461—431no—
161#1325—431no—
162#1325D4311yescharacteristic
163#1324—431no—
164#1324—431no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#147211yescharacteristic
168C2×C43#212611yescharacteristic
169C2×C43#213311yescharacteristic
170C2×#125—431no—
171C2×C4×Q8—431no—
172#432—861no—
173#431—861no—
174#398—861no—
175#398—861no—
176#391—431no—
177#391—431no—
178#387—861no—
179#387—861no—
180#384C2×D4311yescharacteristic
181#382—431no—
182C4×C4⋊C4—431no—
183#324—431no—
184#324—431no—
185#324—861no—
186#324—861no—
187#324C2×D4311yescharacteristic
188#324C2×D4311yescharacteristic
189C43#1157111yescharacteristic, complemented, Sylow
190C22×Q8—431no—
191#125—1721no—
192#125—1721no—
193C4×Q8—1721no—
194C4×Q8—1721no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4C4×D4311yescharacteristic
204C2×C4⋊C4C22×D4311yescharacteristic
205C2×C42—431no—
206C2×C42—431no—
207C2×C42—431no—
208C2×C42—431no—
209C2×C42C4×D4311yescharacteristic
210C4⋊C8—1721no—
211C4⋊C8—1721no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—861no—
215C22⋊C8—861no—
216#97—1721no—
217C4×C8—1721no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225C2×Q8—862no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—1721no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—431no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—431no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4C2×C4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—1721no—
243C2×C8—1721no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C4⋊C4—1722no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C4⋊C4—1722no—
255C42—21no—
256C42—21no—
257C42—861no—
258C42—861no—
259C42—861no—
260C42—861no—
261C42—861no—
262C42—861no—
263C42—861no—
264C42—861no—
265C23C22⋊C4×D4311yescharacteristic
266Q8—1722no—
267Q8—1722no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—431no—
281C2×C4—431no—
282C2×C4—432no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1722no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4#1306333111yescharacteristic
297C2×C4#1306333311yescharacteristic
298C8—81no—
299C8—81no—
300C8—3441no—
301C8—3441no—
302C22—21no—
303C22—21no—
304C22#1458286411yescharacteristic
305C22#99×D4311yescharacteristic
306C22#101×D4311yescharacteristic
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—861no—
314C4—861no—
315C4—862no—
316C4—3441no—
317C4—3441no—
318C4—1721no—
319C4—1721no—
320C2—21no—
321C2—21no—
322C2#1913295711yescharacteristic
323C2#1913625711yescharacteristic
324C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1325D43
hypocenterC43#11571
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
189. C43#11571semidirect

Maximal subgroups

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

subgroupindex
#191397832
#191329372
#191329172
#191325412
#191325382
C43×#13252
#1157143