Finite Group Databasebeta

← #25005958

Subgroups — #25005958

Order 11008.

662 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 77 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#19136973C211yesmaximal, characteristic
2#19132926C212yesmaximal, complemented
3#19132524C212yesmaximal, complemented
4#19132523C211yesmaximal, characteristic
5C43×#1316C211yesmaximal, characteristic
6C24×Dic43C411yescharacteristic
7C2×#13063281C411yescharacteristic
8C2×#13063281C2211yescharacteristic
9#14582953—22no—
10#14582760C411yescharacteristic
11#14582760C2211yescharacteristic
12#14582757—22no—
13#14582755C411yescharacteristic
14C22⋊C4×Dic43—22no—
15#14582624—22no—
16#14582623C2212yes—
17C43×#379C2211yescharacteristic
18C43×#323C2212yes—
19C23×Dic43—22no—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C23×Dic43—22no—
23C23×Dic43—42no—
24C23×Dic43—42no—
25C23×Dic43C2×C411yescharacteristic
26C23×Dic43C2×C411yescharacteristic
27#13063281—42no—
28#13063281—42no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4D412yes—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43C2×C411yescharacteristic
33C2×C22⋊Dic43C2×C411yescharacteristic
34C2×C4×Dic43—21no—
35C2×C4×Dic43D412yes—
36Dic43⋊C8—42no—
37C22⋊(C43⋊C8)—22no—
38#13063235—42no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C25×C43C2×C411yescharacteristic
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43C2311yescharacteristic
45C22⋊C8×C43—22no—
46C24×C43—21no—
47C24×C43—21no—
48C24×C43—44no—
49C24×C43—41no—
50C24×C43—41no—
51C24×C43M1612yes—
52C24×C43C22×C411yescharacteristic
53C22×C4×C43—21no—
54C22×C4×C43C2×D412yes—
55C22×Dic43—22no—
56C22×Dic43—22no—
57C22×Dic43—24no—
58C22×Dic43—24no—
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—41no—
65C22×Dic43—41no—
66C22×Dic43—48no—
67C22×Dic43—48no—
68C22×Dic43—42no—
69C22×Dic43—42no—
70C22×Dic43—42no—
71C22×Dic43—42no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C412yes—
75C22×Dic43M1612yes—
76C2×C8×C43—42no—
77C22⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—44no—
80C22⋊Dic43—41no—
81C22⋊Dic43—41no—
82C22⋊Dic43—44no—
83Dic43⋊C4—42no—
84Dic43⋊C4—42no—
85C4×Dic43—22no—
86C4×Dic43—22no—
87C4×Dic43—42no—
88C2×C43⋊C8—42no—
89C23×C43—24no—
90C23×C43—22no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—42no—
94C23×C43—44no—
95C23×C43—42no—
96C23×C43—42no—
97C23×C43—42no—
98C23×C43—44no—
99C23×C43—44no—
100C23×C43—48no—
101C23×C43—44no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43C2×M1611yescharacteristic
106C23×C43C2×M1611yescharacteristic
107C2×C4×C43—22no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×Dic43—24no—
112C2×Dic43—24no—
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—48no—
120C2×Dic43—48no—
121C2×Dic43—42no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—41no—
128C2×Dic43#9912yes—
129C2×Dic43#10012yes—
130C8×C43—82no—
131C43⋊C8—82no—
132#11501—431nomaximal, Sylow
133C22×C43—22no—
134C22×C43—24no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—44no—
140C22×C43—42no—
141C22×C43—42no—
142C22×C43—44no—
143C22×C43—44no—
144C22×C43—48no—
145C22×C43—44no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43#40711yescharacteristic
149C22×C43C2×#9911yescharacteristic
150C22×C43C2×#10011yescharacteristic
151C4×C43—42no—
152C4×C43—81no—
153Dic43—22no—
154Dic43—22no—
155Dic43—42no—
156Dic43—42no—
157Dic43—81no—
158#2280—431no—
159#1464—432no—
160#1317—432no—
161#1316—431no—
162#1316D4311yescharacteristic
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—44no—
166C2×C43—41no—
167C2×C43—41no—
168C2×C43#146211yescharacteristic
169C2×C43#212012yes—
170C24×C4—431no—
171C2×#117—431no—
172C2×#117—431no—
173#432—862no—
174#381—431no—
175#381—431no—
176#380—862no—
177#379—431no—
178#379C2×D4311yescharacteristic
179C4×C22⋊C4—862no—
180#324—862no—
181#323—432no—
182#323C2×D4312yes—
183C43#1150111yescharacteristic, complemented, Sylow
184C25C4×D4311yescharacteristic
185C23×C4—431no—
186C23×C4—431no—
187C23×C4—861no—
188C23×C4—861no—
189C23×C4—862no—
190C23×C4—862no—
191C23×C4—1722no—
192C23×C4—1722no—
193#117—1722no—
194#117—1722no—
195C2×C4⋊C4—432no—
196C2×C4⋊C4—861no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—431no—
199C2×C22⋊C4—431no—
200C2×C22⋊C4—862no—
201C2×C22⋊C4C4×D4311yescharacteristic
202C2×C22⋊C4C22×D4311yescharacteristic
203C2×C42—432no—
204C2×C42—861no—
205C4⋊C8—1722no—
206C22⋊C8—22no—
207C22⋊C8—862no—
208#97—1722no—
209#95—862no—
210#95—862no—
211C24—21no—
212C24—21no—
213C24—41no—
214C24—41no—
215C24—44no—
216C24#1062187212yes—
217C24C2×C4×D4311yescharacteristic
218C22×C4—21no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—432no—
222C22×C4—432no—
223C22×C4—862no—
224C22×C4—862no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—864no—
228C22×C4—864no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—1722no—
233C22×C4—1722no—
234C22×C4—1728no—
235C22×C4—1728no—
236C22×C4—1722no—
237C22×C4—1722no—
238C22×C4—1721no—
239C22×C4—1721no—
240C22×C4D4×D4312yes—
241C2×C8—42no—
242C2×C8—1722no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C22⋊C4—41no—
246C22⋊C4—44no—
247C22⋊C4—41no—
248C22⋊C4—1721no—
249C22⋊C4—1724no—
250C22⋊C4—1721no—
251C42—862no—
252C42—862no—
253C42—1722no—
254C23—24no—
255C23—22no—
256C23—21no—
257C23—21no—
258C23—42no—
259C23—44no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—44no—
264C23—44no—
265C23—48no—
266C23—44no—
267C23—41no—
268C23—41no—
269C23C22⋊C4×D4311yescharacteristic
270C23M16×D4311yescharacteristic
271C23C2×#1062187211yescharacteristic
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—432no—
277C2×C4—432no—
278C2×C4—864no—
279C2×C4—864no—
280C2×C4—861no—
281C2×C4—861no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—862no—
285C2×C4—862no—
286C2×C4—1728no—
287C2×C4—1728no—
288C2×C4—1722no—
289C2×C4—1721no—
290C2×C4—1722no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1722no—
294C2×C4—1722no—
295C8—82no—
296C8—3442no—
297C22—22no—
298C22—24no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—44no—
307C22—44no—
308C22—48no—
309C22—44no—
310C22—42no—
311C22—42no—
312C22#1458286111yescharacteristic
313C22#99×D4311yescharacteristic
314C22#100×D4311yescharacteristic
315C4—42no—
316C4—81no—
317C4—862no—
318C4—862no—
319C4—3441no—
320C4—1722no—
321C4—1722no—
322C2—21no—
323C2—21no—
324C2—44no—
325C2—41no—
326C2—41no—
327C2#1913292011yescharacteristic
328C2#1913623312yes—
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1316C2
socleC22×C43C2×#99
prime radicalC25×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1316D43
hypocenterC43#11501
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #19132926C2semidirect
3. #19132524C2semidirect
183. C43#11501semidirect

Maximal subgroups

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

subgroupindex
#191369732
#191329262
#191325242
#191325232
C43×#13162
#1150143