Finite Group Databasebeta

← #24984745

Subgroups — #24984745

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134663C211yesmaximal, characteristic
2#19134289C211yesmaximal, characteristic
3#19132418C214yesmaximal, complemented
4C2×C43×#389C211yesmaximal, characteristic
5C22×#10621877—21no—
6C2×C22⋊(C43⋊C8)—21no—
7#14582654—21no—
8#14582654—21no—
9#14582654C2212yes—
10#14582654C2212yes—
11C22×C4⋊C4×C43—21no—
12C22×C4⋊C4×C43C411yescharacteristic
13C22×C4⋊C4×C43C411yescharacteristic
14C22×C42×C43C2211yescharacteristic
15C43×#389—21no—
16C43×#389—21no—
17C43×#389C412yes—
18C43×#389C2212yes—
19C2×#95×C43—21no—
20C2×#10621877—24no—
21C2×#10621877—42no—
22C2×#10621877—42no—
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C22⋊(C43⋊C8)—42no—
26C23×C4×C43—21no—
27C23×C4×C43—21no—
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43D411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—24no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—42no—
37C2×C4⋊C4×C43—42no—
38C2×C4⋊C4×C43—42no—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C4⋊C4×C43C2×C412yes—
41C2×C42×C43—42no—
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43C2311yescharacteristic
46#95×C43—22no—
47#95×C43—22no—
48C24×C43C22⋊C411yescharacteristic
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—24no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—41no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43D812yes—
69C22×C4×C43SD1612yes—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C4⋊C4×C43—24no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—44no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43M1614yescomplemented
81C42×C43—41no—
82C42×C43—41no—
83C42×C43—41no—
84C42×C43—41no—
85#10621877—48no—
86C2×C43⋊C8—24no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43#9912yes—
97C23×C43#10212yes—
98C23×C43#10412yes—
99C23×C43C2×C22⋊C411yescharacteristic
100C2×C4×C43—28no—
101C2×C4×C43—24no—
102C2×C4×C43—24no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—24no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—44no—
118C2×C4×C43—48no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—84no—
125C2×C4×C43#10112yes—
126C2×C4×C43#10212yes—
127C2×C4×C43C2×M1612yes—
128C2×C4×C43C2×D811yescharacteristic
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43#13712yes—
131C43⋊C8—44no—
132C43⋊C8—82no—
133#7610—431nomaximal, Sylow
134C22×C43—22no—
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43#32714yes—
141C22×C43#40711yescharacteristic
142C22×C43C2×#9911yescharacteristic
143C22×C43C2×#10111yescharacteristic
144C22×C43C2×#10211yescharacteristic
145C22×C43#41911yescharacteristic
146C22×C43C2×#10411yescharacteristic
147C22×C43#42111yescharacteristic
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—21no—
153C4×C43—22no—
154C4×C43—44no—
155C4×C43—41no—
156C4×C43—82no—
157C2×#389D4311yescharacteristic
158#1817—431no—
159#1728—431no—
160#1271—434no—
161C2×C43—24no—
162C2×C43#146311yescharacteristic
163C2×C43#148611yescharacteristic
164C2×C43#149111yescharacteristic
165C2×C43C2×#32711yescharacteristic
166C2×C43#151111yescharacteristic
167C2×C43#152811yescharacteristic
168C2×C43#154611yescharacteristic
169C22×M16—861no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4Dic4311yescharacteristic
172C22×C4⋊C4Dic4311yescharacteristic
173C22×C42C2×D4311yescharacteristic
174C2×C22⋊C8—861no—
175#389—21no—
176#389—21no—
177#389Dic4312yes—
178#389C2×D4312yes—
179C2×#95—21no—
180#336—432no—
181#336—432no—
182#336—861no—
183#336—861no—
184C43#761011yescharacteristic, complemented, Sylow
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C2×Dic4311yescharacteristic
188C23×C4C22⋊D4311yescharacteristic
189C23×C4C22⋊D4311yescharacteristic
190C2×M16—864no—
191C2×M16—1722no—
192C2×M16—1722no—
193C22×C8—862no—
194C22×C8—862no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4C2×Dic4312yes—
204C2×C4⋊C4C2×Dic4312yes—
205C2×C42—42no—
206C2×C42C2×Dic4311yescharacteristic
207C2×C42C22⋊D4311yescharacteristic
208C2×C42C22⋊D4311yescharacteristic
209C2×C42C22×D4311yescharacteristic
210C22⋊C8—1722no—
211#95—22no—
212#95—22no—
213C24C22⋊Dic4311yescharacteristic
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4#1062188212yes—
231C22×C4#1062188312yes—
232C22×C4C22⋊Dic4311yescharacteristic
233C22×C4C22⋊Dic4311yescharacteristic
234C22×C4C22⋊Dic4311yescharacteristic
235C22×C4C22×Dic4311yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C22×C4C2×C22⋊D4311yescharacteristic
238M16—1728no—
239C2×C8—864no—
240C2×C8—1722no—
241C2×C8—1722no—
242C2×C8—1722no—
243C2×C8—1722no—
244C2×C8—1722no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4#1062187714yescomplemented
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23#1306324012yes—
262C23#1306324612yes—
263C23#1306325212yes—
264C23C2×C22⋊Dic4311yescharacteristic
265C2×C4—28no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—44no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4#1306324412yes—
291C2×C4#1306324612yes—
292C2×C4C2×#1062187712yes—
293C2×C4C2×#1062188211yescharacteristic
294C2×C4C2×#1062188311yescharacteristic
295C2×C4#1306335612yes—
296C8—3442no—
297C8—1724no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22#1458263314yes—
305C22#1458286311yescharacteristic
306C22C2×#1306324011yescharacteristic
307C22C2×#1306324411yescharacteristic
308C22C2×#1306324611yescharacteristic
309C22#1458290811yescharacteristic
310C22C2×#1306325211yescharacteristic
311C22#1458291611yescharacteristic
312C4—21no—
313C4—22no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—44no—
319C4—41no—
320C4—82no—
321C2—24no—
322C2#1913292511yescharacteristic
323C2#1913302011yescharacteristic
324C2#1913304211yescharacteristic
325C2C2×#1458263311yescharacteristic
326C2#1913312811yescharacteristic
327C2#1913319711yescharacteristic
328C2#1913326711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#389C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#389D43
hypocenterC43#7610
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #19132418C2semidirect
80. C4⋊C4×C43M16semidirect
184. C43#7610semidirect
252. C4⋊C4#10621877semidirect

Maximal subgroups

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

subgroupindex
#191346632
#191342892
#191324182
C2×C43×#3892
#761043