Finite Group Databasebeta

← #24987926

Subgroups — #24987926

Order 11008.

1502 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 207 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
1C23×Dic43⋊C4C211yesmaximal, characteristic
2#19134505C211yesmaximal, characteristic
3C2×#14582624C214yesmaximal, complemented
4C43×#1779C211yesmaximal, characteristic
5C24×Dic43C411yescharacteristic
6C24×Dic43C411yescharacteristic
7C22×Dic43⋊C4—28no—
8C22×Dic43⋊C4—22no—
9C22×Dic43⋊C4—22no—
10C22×Dic43⋊C4C412yes—
11C22×Dic43⋊C4C2212yes—
12C2×C22⋊(C43⋊C8)—22no—
13C2×C22⋊(C43⋊C8)C2212yes—
14#14582624—28no—
15C24×C4×C43C2211yescharacteristic
16C2×C22⋊C8×C43—22no—
17C2×C22⋊C8×C43C2212yes—
18C23×Dic43—22no—
19C23×Dic43—22no—
20C23×Dic43—24no—
21C23×Dic43—24no—
22C23×Dic43—22no—
23C23×Dic43—24no—
24C23×Dic43—44no—
25C23×Dic43C814yescomplemented
26C23×Dic43C2×C412yes—
27C23×Dic43C2×C412yes—
28C22×C43⋊C8—22no—
29C2×Dic43⋊C4—216no—
30C2×Dic43⋊C4—216no—
31C2×Dic43⋊C4—24no—
32C2×Dic43⋊C4—22no—
33C2×Dic43⋊C4—24no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—24no—
36C2×Dic43⋊C4—24no—
37C2×Dic43⋊C4D418yes—
38C22⋊(C43⋊C8)—24no—
39C22⋊(C43⋊C8)—44no—
40C25×C43C2×C411yescharacteristic
41C23×C4×C43—24no—
42C23×C4×C43—44no—
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43D412yes—
45C23×C4×C43D412yes—
46C23×C4×C43C2311yescharacteristic
47C22×C8×C43—22no—
48C22⋊C8×C43—24no—
49C22⋊C8×C43—44no—
50C24×C43—24no—
51C24×C43—24no—
52C24×C43—22no—
53C24×C43—22no—
54C24×C43C22⋊C412yes—
55C24×C43C2×C812yes—
56C24×C43M1612yes—
57C24×C43C22×C411yescharacteristic
58C22×C4×C43—24no—
59C22×C4×C43—24no—
60C22×C4×C43—24no—
61C22×C4×C43—24no—
62C22×C4×C43—22no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—416no—
68C22×C4×C43C22⋊C412yes—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D414yes—
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—28no—
73C22×Dic43—28no—
74C22×Dic43—216no—
75C22×Dic43—216no—
76C22×Dic43—28no—
77C22×Dic43—28no—
78C22×Dic43—22no—
79C22×Dic43—22no—
80C22×Dic43—22no—
81C22×Dic43—22no—
82C22×Dic43—22no—
83C22×Dic43—22no—
84C22×Dic43—44no—
85C22×Dic43—416no—
86C22×Dic43—44no—
87C22×Dic43—44no—
88C22×Dic43C22⋊C414yes—
89C22×Dic43C22⋊C414yes—
90C22×Dic43C2×C814yes—
91C22×Dic43M1614yes—
92C2×C8×C43—44no—
93C2×C8×C43—42no—
94Dic43⋊C4—216no—
95Dic43⋊C4—28no—
96Dic43⋊C4—28no—
97C2×C43⋊C8—44no—
98C2×C43⋊C8—42no—
99C23×C43—28no—
100C23×C43—216no—
101C23×C43—28no—
102C23×C43—28no—
103C23×C43—28no—
104C23×C43—22no—
105C23×C43—24no—
106C23×C43—22no—
107C23×C43—24no—
108C23×C43—22no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43C22⋊C814yes—
113C23×C43#9914yes—
114C23×C43#10114yes—
115C23×C43C2×C22⋊C412yes—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43C22×C811yescharacteristic
118C23×C43C2×M1612yes—
119C23×C43C2×M1611yescharacteristic
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—44no—
126C2×C4×C43—48no—
127C2×C4×C43—48no—
128C2×C4×C43—44no—
129C2×C4×C43#12012yes—
130C2×C4×C43#12012yes—
131C2×Dic43—232no—
132C2×Dic43—24no—
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—24no—
136C2×Dic43—24no—
137C2×Dic43—24no—
138C2×Dic43—24no—
139C2×Dic43—416no—
140C2×Dic43—44no—
141C2×Dic43—44no—
142C2×Dic43—44no—
143C2×Dic43C22⋊C818yescomplemented
144C8×C43—82no—
145C43⋊C8—82no—
146#8299—431nomaximal, Sylow
147C22×C43—216no—
148C22×C43—216no—
149C22×C43—24no—
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—24no—
153C22×C43—24no—
154C22×C43—24no—
155C22×C43—24no—
156C22×C43—24no—
157C22×C43—22no—
158C22×C43—24no—
159C22×C43—22no—
160C22×C43#32418yescomplemented
161C22×C43#37911yescharacteristic
162C22×C43C2×C22⋊C812yes—
163C22×C43C2×C22⋊C811yescharacteristic
164C22×C43#40712yes—
165C22×C43#40711yescharacteristic
166C22×C43C2×#9912yes—
167C22×C43C2×#10112yes—
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—42no—
171Dic43—28no—
172Dic43—44no—
173C23×C4⋊C4—431no—
174#1779—431no—
175#1779D4311yescharacteristic
176C2×#324—434no—
177C2×C43—28no—
178C2×C43—22no—
179C2×C43—22no—
180C2×C43C2×#32412yes—
181C2×C43#146312yes—
182C2×C43#177911yescharacteristic
183C2×C43#178111yescharacteristic
184C2×C43#178411yescharacteristic
185C24×C4—431no—
186C24×C4—431no—
187C24×C4C2×D4311yescharacteristic
188C22×C4⋊C4—432no—
189C22×C4⋊C4—432no—
190C22×C4⋊C4—868no—
191C22×C4⋊C4—862no—
192C22×C4⋊C4—862no—
193C2×C22⋊C8—22no—
194C2×C22⋊C8—432no—
195C2×C22⋊C8—862no—
196C2×C22⋊C8C2×D4312yes—
197#324—868no—
198C43#829911yescharacteristic, complemented, Sylow
199C25C4×D4311yescharacteristic
200C23×C4—24no—
201C23×C4—44no—
202C23×C4—432no—
203C23×C4—434no—
204C23×C4—432no—
205C23×C4—864no—
206C23×C4—864no—
207C23×C4—864no—
208C23×C4—862no—
209C23×C4—862no—
210C23×C4—862no—
211C23×C4—1724no—
212C23×C4C4×D4311yescharacteristic
213C23×C4D17212yes—
214C23×C4C22⋊D4312yes—
215C23×C4C22×D4311yescharacteristic
216C22×C8—22no—
217C22×C8—862no—
218C2×C4⋊C4—438no—
219C2×C4⋊C4—864no—
220C2×C4⋊C4—864no—
221C2×C4⋊C4—8616no—
222C2×C4⋊C4—8616no—
223C2×C4⋊C4—864no—
224C2×C4⋊C4—862no—
225C2×C4⋊C4—864no—
226C2×C4⋊C4—862no—
227C22⋊C8—24no—
228C22⋊C8—44no—
229C22⋊C8—864no—
230C22⋊C8—1724no—
231C24—24no—
232C24—24no—
233C24—22no—
234C24—22no—
235C24C8×D4312yes—
236C24#1062187212yes—
237C24(C2×D43)⋊C412yes—
238C24C2×C4×D4311yescharacteristic
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—416no—
249C22×C4—434no—
250C22×C4—434no—
251C22×C4—434no—
252C22×C4—434no—
253C22×C4—8616no—
254C22×C4—868no—
255C22×C4—8616no—
256C22×C4—868no—
257C22×C4—868no—
258C22×C4—862no—
259C22×C4—862no—
260C22×C4—862no—
261C22×C4—862no—
262C22×C4—868no—
263C22×C4—862no—
264C22×C4—862no—
265C22×C4—17216no—
266C22×C4—1724no—
267C22×C4—1724no—
268C22×C4—1724no—
269C22×C4(C2×D43)⋊C412yes—
270C22×C4C2×D17211yescharacteristic
271C22×C4D4×D4314yes—
272C22×C4C2×C22⋊D4311yescharacteristic
273C2×C8—44no—
274C2×C8—42no—
275C2×C8—1724no—
276C2×C8—1722no—
277C4⋊C4—8616no—
278C4⋊C4—868no—
279C4⋊C4—868no—
280C23—28no—
281C23—28no—
282C23—216no—
283C23—24no—
284C23—24no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—28no—
291C23—28no—
292C23—22no—
293C23(C2×D43)⋊C814yes—
294C23#1306323914yes—
295C23#1306324314yes—
296C23C22⋊C4×D4312yes—
297C23C2×(C2×D43)⋊C411yescharacteristic
298C23C2×C8×D4311yescharacteristic
299C23M16×D4312yes—
300C23C2×#1062187211yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—44no—
307C2×C4—48no—
308C2×C4—48no—
309C2×C4—44no—
310C2×C4—438no—
311C2×C4—8632no—
312C2×C4—864no—
313C2×C4—864no—
314C2×C4—864no—
315C2×C4—864no—
316C2×C4—864no—
317C2×C4—864no—
318C2×C4—864no—
319C2×C4—17216no—
320C2×C4—1724no—
321C2×C4—1724no—
322C2×C4—1724no—
323C2×C4#1306329312yes—
324C2×C4#1306329512yes—
325C8—82no—
326C8—3442no—
327C22—216no—
328C22—216no—
329C22—24no—
330C22—24no—
331C22—22no—
332C22—24no—
333C22—22no—
334C22—24no—
335C22—22no—
336C22—22no—
337C22—24no—
338C22—24no—
339C22—24no—
340C22#1458262418yescomplemented
341C22#1458275411yescharacteristic
342C22C22⋊C8×D4312yes—
343C22C2×(C2×D43)⋊C811yescharacteristic
344C22#1458286112yes—
345C22#1458286211yescharacteristic
346C22C2×#1306323912yes—
347C22C2×#1306324312yes—
348C4—22no—
349C4—22no—
350C4—42no—
351C4—868no—
352C4—1724no—
353C2—22no—
354C2—22no—
355C2—28no—
356C2C2×#1458262412yes—
357C2#1913292412yes—
358C2#1913450411yescharacteristic
359C2#1913450911yescharacteristic
360C2#1913451811yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1779C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43C2×C4
cosocleC23×C4×C43C23
hypercenter#1779D43
hypocenterC43#8299
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#14582624C2semidirect
25. C23×Dic43C8semidirect
143. C2×Dic43C22⋊C8semidirect
160. C22×C43#324semidirect
198. C43#8299semidirect
340. C22#14582624semidirect

Maximal subgroups

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

subgroupindex
C23×Dic43⋊C42
#191345052
C2×#145826242
C43×#17792
#829943