Finite Group Databasebeta

← #25005680

Subgroups — #25005680

Order 11008.

678 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 93 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#19132906C212yesmaximal, complemented
3#19132524C212yesmaximal, complemented
4#19132523C211yesmaximal, characteristic
5C43×#1316C211yesmaximal, characteristic
6C24×Dic43C411yescharacteristic
7C2×#13063281C411yescharacteristic
8C2×#13063281C2211yescharacteristic
9#14582949—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—21no—
20C23×Dic43—21no—
21C23×Dic43—22no—
22C23×Dic43—41no—
23C23×Dic43—41no—
24C23×Dic43—42no—
25C23×Dic43C814yescomplemented
26C23×Dic43C2×C411yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28#13063281—41no—
29#13063281—41no—
30#13063281—42no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4D412yes—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×C4×Dic43—21no—
37C2×C4×Dic43D412yes—
38Dic43⋊C8—42no—
39C22⋊(C43⋊C8)—22no—
40C8×Dic43—42no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C25×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43C2311yescharacteristic
47C22⋊C8×C43—22no—
48C24×C43—21no—
49C24×C43—21no—
50C24×C43—44no—
51C24×C43—41no—
52C24×C43—41no—
53C24×C43C2×C812yes—
54C24×C43C22×C411yescharacteristic
55C22×C4×C43—21no—
56C22×C4×C43C2×D412yes—
57C22×Dic43—21no—
58C22×Dic43—21no—
59C22×Dic43—22no—
60C22×Dic43—24no—
61C22×Dic43—24no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—41no—
66C22×Dic43—41no—
67C22×Dic43—44no—
68C22×Dic43—44no—
69C22×Dic43—44no—
70C22×Dic43—44no—
71C22×Dic43—42no—
72C22×Dic43—42no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43—42no—
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C412yes—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C2×C812yes—
80C22×Dic43C2×C812yes—
81C22×Dic43M1612yes—
82C2×C8×C43—42no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—44no—
86C22⋊Dic43—41no—
87C22⋊Dic43—41no—
88C22⋊Dic43—44no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91C4×Dic43—22no—
92C4×Dic43—22no—
93C4×Dic43—42no—
94C2×C43⋊C8—42no—
95C23×C43—24no—
96C23×C43—22no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—42no—
100C23×C43—44no—
101C23×C43—42no—
102C23×C43—42no—
103C23×C43—42no—
104C23×C43—44no—
105C23×C43—44no—
106C23×C43—48no—
107C23×C43—44no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111C23×C43C22×C811yescharacteristic
112C23×C43C2×M1611yescharacteristic
113C2×C4×C43—22no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43—41no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—48no—
126C2×Dic43—42no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—44no—
130C2×Dic43—44no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134C2×Dic43—41no—
135C2×Dic43C22⋊C812yes—
136C2×Dic43C22⋊C812yes—
137C2×Dic43#9911yescharacteristic
138C2×Dic43#9911yescharacteristic
139C2×Dic43#10012yes—
140C8×C43—82no—
141C43⋊C8—82no—
142#11425—431nomaximal, Sylow
143C22×C43—22no—
144C22×C43—24no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—44no—
150C22×C43—42no—
151C22×C43—42no—
152C22×C43—44no—
153C22×C43—44no—
154C22×C43—48no—
155C22×C43—44no—
156C22×C43—42no—
157C22×C43—42no—
158C22×C43C2×C22⋊C811yescharacteristic
159C22×C43C2×#9911yescharacteristic
160C22×C43C2×#10011yescharacteristic
161C4×C43—42no—
162C4×C43—81no—
163Dic43—22no—
164Dic43—42no—
165Dic43—42no—
166Dic43—81no—
167Dic43#32312yes—
168Dic43#32312yes—
169#2280—431no—
170#1458—432no—
171#1317—432no—
172#1316—431no—
173#1316D4311yescharacteristic
174C2×C43—21no—
175C2×C43—21no—
176C2×C43—44no—
177C2×C43—41no—
178C2×C43—41no—
179C2×C43C2×#32311yescharacteristic
180C2×C43#212012yes—
181C24×C4—431no—
182C2×#117—431no—
183C2×#117—431no—
184#431—862no—
185#381—431no—
186#381—431no—
187#380—862no—
188#379—431no—
189#379C2×D4311yescharacteristic
190C4×C22⋊C4—862no—
191#324—862no—
192#323—432no—
193#323C2×D4312yes—
194C43#1142511yescharacteristic, complemented, Sylow
195C25C4×D4311yescharacteristic
196C23×C4—431no—
197C23×C4—434no—
198C23×C4—431no—
199C23×C4—861no—
200C23×C4—861no—
201C23×C4—862no—
202C23×C4—1721no—
203C23×C4—1721no—
204C23×C4—1722no—
205#117—1721no—
206#117—1721no—
207#117—1722no—
208C2×C4⋊C4—432no—
209C2×C4⋊C4—861no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—431no—
212C2×C22⋊C4—431no—
213C2×C22⋊C4—862no—
214C2×C22⋊C4C4×D4311yescharacteristic
215C2×C22⋊C4C22×D4311yescharacteristic
216C2×C42—432no—
217C2×C42—861no—
218C4⋊C8—1722no—
219C22⋊C8—22no—
220C22⋊C8—862no—
221C4×C8—1722no—
222#95—862no—
223#95—862no—
224C24—21no—
225C24—21no—
226C24—41no—
227C24—41no—
228C24—44no—
229C24C8×D4312yes—
230C24C2×C4×D4311yescharacteristic
231C22×C4—21no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—432no—
235C22×C4—432no—
236C22×C4—432no—
237C22×C4—432no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—862no—
241C22×C4—864no—
242C22×C4—864no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—1721no—
247C22×C4—1721no—
248C22×C4—1722no—
249C22×C4—1724no—
250C22×C4—1724no—
251C22×C4—1722no—
252C22×C4—1722no—
253C22×C4—1724no—
254C22×C4—1724no—
255C22×C4—1721no—
256C22×C4—1721no—
257C22×C4D4×D4312yes—
258C2×C8—42no—
259C2×C8—1722no—
260C4⋊C4—1722no—
261C4⋊C4—1722no—
262C22⋊C4—41no—
263C22⋊C4—44no—
264C22⋊C4—41no—
265C22⋊C4—1721no—
266C22⋊C4—1724no—
267C22⋊C4—1721no—
268C42—862no—
269C42—862no—
270C42—1722no—
271C23—24no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23—42no—
276C23—44no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—44no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23—41no—
285C23—41no—
286C23C22⋊C4×D4311yescharacteristic
287C23C2×C8×D4311yescharacteristic
288C23M16×D4311yescharacteristic
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—432no—
294C2×C4—431no—
295C2×C4—431no—
296C2×C4—432no—
297C2×C4—432no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—862no—
301C2×C4—862no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—1724no—
307C2×C4—1724no—
308C2×C4—1728no—
309C2×C4—1722no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1722no—
315C2×C4—1722no—
316C8—82no—
317C8—3442no—
318C22—22no—
319C22—24no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—44no—
325C22—42no—
326C22—42no—
327C22—44no—
328C22—44no—
329C22—48no—
330C22—42no—
331C22—44no—
332C22—42no—
333C22C22⋊C8×D4311yescharacteristic
334C22#99×D4311yescharacteristic
335C22#100×D4311yescharacteristic
336C4—42no—
337C4—81no—
338C4—432no—
339C4—432no—
340C4—862no—
341C4—3441no—
342C4—1722no—
343C4—1722no—
344C2—21no—
345C2—21no—
346C2—44no—
347C2—41no—
348C2—41no—
349C2#323×D4311yescharacteristic
350C2#1913623312yes—
subgroupG/H
centerC22#99×D43
commutatorC23×C43C22×C8
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1316C2
socleC22×C43C2×#99
prime radicalC25×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1316D43
hypocenterC43#11425
LCSG ▷ C23×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. #19132906C2semidirect
3. #19132524C2semidirect
25. C23×Dic43C8semidirect
194. C43#11425semidirect

Maximal subgroups

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

subgroupindex
#191369732
#191329062
#191325242
#191325232
C43×#13162
#1142543