Finite Group Databasebeta

← #25006993

Subgroups — #25006993

Order 11008.

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

normal subgroups only

This group has 358 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#19140476C211yesmaximal, characteristic
2#19134390C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic
5#19132621C211yesmaximal, characteristic
6#19132601C211yesmaximal, characteristic
7C43×#1346C211yesmaximal, characteristic
8C2×#13063316C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582949—21no—
11C2×#13063243—21no—
12M16×Dic43—21no—
13#14582840—21no—
14#14582839C411yescharacteristic
15#14582838C2211yescharacteristic
16#14582830C411yescharacteristic
17#14582819—21no—
18#14582786—21no—
19#14582785—21no—
20#14582766C411yescharacteristic
21#14582668C2211yescharacteristic
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29#13063316—41no—
30#13063316—41no—
31#13063290—41no—
32#13063290—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4C2×C411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42Dic43⋊C8—41no—
43#13063243—24no—
44C22⋊(C43⋊C8)—21no—
45#13063235—41no—
46C8×Dic43—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—
55C43⋊#95C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—22no—
77C2×Dic86—41no—
78M16×C43—22no—
79M16×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99#10621877—22no—
100#10621877—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43C2×C22⋊C411yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
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—41no—
116C2×C4×C43#13511yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43#9911yescharacteristic
132C2×Dic43#9911yescharacteristic
133C2×Dic43#10412yes—
134Dic86—42no—
135Dic86—42no—
136C8×C43—42no—
137C8×C43—81no—
138C43⋊C8—42no—
139C43⋊C8—81no—
140#11740—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43C2×#9911yescharacteristic
144C22×C43#41611yescharacteristic
145C22×C43C2×#10411yescharacteristic
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—81no—
151C4×C43—81no—
152Dic43—21no—
153Dic43—21no—
154Dic43—22no—
155Dic43—41no—
156Dic43—41no—
157Dic43—81no—
158Dic43—81no—
159#2634—431no—
160C4×#101—431no—
161#1461—431no—
162#1353—431no—
163#1353—431no—
164#1346—431no—
165#1346D4311yescharacteristic
166C2×C43—21no—
167C2×C43—21no—
168C2×C43#150111yescharacteristic
169C2×C43#212311yescharacteristic
170C2×C43#213311yescharacteristic
171C2×#125—431no—
172C2×C4×Q8—431no—
173#431—861no—
174C2×#101—861no—
175C4×M16—861no—
176#400—431no—
177#400—431no—
178#400—861no—
179#398—431no—
180#398C2×D4311yescharacteristic
181#395—861no—
182#387—861no—
183#387—861no—
184#383—431no—
185#343—431no—
186#343C2×D4311yescharacteristic
187#324—431no—
188#324—861no—
189#324C2×D4311yescharacteristic
190C43#1174011yescharacteristic, complemented, Sylow
191C22×Q8—431no—
192C2×M16—21no—
193C2×M16—861no—
194#125—1721no—
195#125—1721no—
196C4×Q8—1721no—
197C4×Q8—1721no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4C4×D4311yescharacteristic
206C2×C4⋊C4C22×D4311yescharacteristic
207C2×C42—431no—
208C2×C42—431no—
209C2×C42—431no—
210C4⋊C8—1721no—
211#101—864no—
212C22⋊C8—21no—
213C22⋊C8—861no—
214#97—1721no—
215C4×C8—1721no—
216C4×C8—1721no—
217#95—21no—
218#95—431no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95C4×D4311yescharacteristic
227C2×Q8—862no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8—1721no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—431no—
234C22×C4—431no—
235C22×C4—431no—
236C22×C4—431no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4C2×C4×D4311yescharacteristic
240C22×C4D4×D4311yescharacteristic
241C22×C4D4×D4311yescharacteristic
242M16—22no—
243M16—41no—
244M16—862no—
245M16—1721no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—1721no—
249C2×C8—1721no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1722no—
260C4⋊C4—1722no—
261C42—861no—
262C42—861no—
263C42—861no—
264C42—861no—
265C42—861no—
266C42—861no—
267C23C22⋊C4×D4311yescharacteristic
268Q8—1722no—
269Q8—1722no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—431no—
283C2×C4—431no—
284C2×C4—432no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1722no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4#1306334411yescharacteristic
299C2×C4#1306334611yescharacteristic
300C8—42no—
301C8—81no—
302C8—3441no—
303C8—1722no—
304C22—21no—
305C22—21no—
306C22#99×D4311yescharacteristic
307C22#1458289211yescharacteristic
308C22#104×D4311yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—861no—
316C4—861no—
317C4—862no—
318C4—3441no—
319C4—3441no—
320C4—1721no—
321C4—1721no—
322C2—21no—
323C2—21no—
324C2#1913308311yescharacteristic
325C2#1913624711yescharacteristic
326C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43#11740
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
190. C43#11740semidirect

Maximal subgroups

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

subgroupindex
#191404762
#191343902
#191329172
#191326232
#191326212
#191326012
C43×#13462
#1174043