Finite Group Databasebeta

← #25005842

Subgroups — #25005842

Order 11008.

392 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136206C211yesmaximal, characteristic, complemented
2C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
3#19132537C212yesmaximal, complemented
4#19132521C212yesmaximal, complemented
5C43×#2929C211yesmaximal, characteristic
6C2×#13063265—21no—
7C22×C43⋊C16—21no—
8C22⋊(C43⋊C16)—21no—
9C22⋊(C43⋊C16)—21no—
10C22⋊(C43⋊C16)C2212yes—
11C22⋊(C43⋊C16)C2212yes—
12C2×#131×C43C411yescharacteristic
13C23×C8×C43C2211yescharacteristic
14C43×#525C411yescharacteristic
15C43×#435—21no—
16C43×#435—21no—
17C8×D4×C43—21no—
18C8×D4×C43—21no—
19C43×#424C2211yescharacteristic
20C43×#408C2211yescharacteristic
21C43×#407C411yescharacteristic
22C43×#405C411yescharacteristic
23#13063265—42no—
24C2×C43⋊C16—22no—
25C2×C43⋊C16—22no—
26C2×C43⋊C16—42no—
27C2×#41×C43C2×C411yescharacteristic
28C23×C4×C43C2×C411yescharacteristic
29#131×C43—42no—
30C2×M16×C43—21no—
31C2×M16×C43C2×C411yescharacteristic
32C2×M16×C43C2×C411yescharacteristic
33C22×C8×C43—21no—
34C22×C8×C43—42no—
35C22×C8×C43C2×C411yescharacteristic
36C22×C8×C43D411yescharacteristic
37C22×C8×C43D411yescharacteristic
38C22×C8×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40C22×C8×C43C2311yescharacteristic
41#123×C43—21no—
42C22⋊Q8×C43C811yescharacteristic
43C22⋊Q8×C43C811yescharacteristic
44#121×C43C811yescharacteristic
45#121×C43C811yescharacteristic
46#120×C43—21no—
47C4×D4×C43—21no—
48C4×D4×C43—21no—
49#117×C43C2×C411yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C22⋊C8×C43—21no—
53C22⋊C8×C43—21no—
54C22⋊C8×C43—21no—
55C22⋊C8×C43—21no—
56#97×C43—21no—
57C4×C8×C43—21no—
58C24×C43M1611yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43C2×C811yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2×C811yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C2×C811yescharacteristic
72C22×C4×C43C2×C811yescharacteristic
73C22×C4×C43M1611yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75M16×C43—42no—
76M16×C43—41no—
77M16×C43—41no—
78C2×C8×C43—22no—
79C2×C8×C43—22no—
80C2×C8×C43—22no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—42no—
87C2×C8×C43C22⋊C411yescharacteristic
88C2×C8×C43C22⋊C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2×C811yescharacteristic
94C4⋊C4×C43C2×C811yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C42×C43—21no—
101C43⋊C16—42no—
102C43⋊C16—42no—
103C23×C43—22no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43C22⋊C811yescharacteristic
108C23×C43C22⋊C811yescharacteristic
109C23×C43C2×M1611yescharacteristic
110Q8×C43—41no—
111D4×C43—41no—
112D4×C43—42no—
113D4×C43—42no—
114D4×C43—42no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43C22⋊C811yescharacteristic
130C2×C4×C43C22⋊C811yescharacteristic
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C22×C811yescharacteristic
133C8×C43—21no—
134C8×C43—21no—
135C8×C43—21no—
136C8×C43—41no—
137C8×C43—41no—
138C8×C43#9912yes—
139#11470—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—44no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43#35012yes—
153C22×C43C2×C22⋊C811yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43C2×#9911yescharacteristic
161C4×C43#41311yescharacteristic
162#2929D4311yescharacteristic
163#2112—431no—
164C2×C22⋊C16—431no—
165#1323—432no—
166#1315—432no—
167C2×C43—22no—
168C2×C43—41no—
169C2×C43—41no—
170C2×C43—81no—
171C2×C43#145911yescharacteristic
172C2×C43C2×#35011yescharacteristic
173C2×C43#211711yescharacteristic
174C2×#131Dic4311yescharacteristic
175C23×C8C2×D4311yescharacteristic
176#525Dic4311yescharacteristic
177C2×M32—861no—
178C22×C16—861no—
179#435—21no—
180#435—21no—
181C8×D4—21no—
182C8×D4—21no—
183#424C2×D4311yescharacteristic
184#408C2×D4311yescharacteristic
185#407Dic4311yescharacteristic
186#405Dic4311yescharacteristic
187C22⋊C16—432no—
188C22⋊C16—432no—
189C22⋊C16—861no—
190C22⋊C16—861no—
191C43#1147011yescharacteristic, complemented, Sylow
192C2×#41C2×Dic4311yescharacteristic
193C23×C4C2×Dic4311yescharacteristic
194#131—42no—
195C2×M16—21no—
196C2×M16C2×Dic4311yescharacteristic
197C2×M16C2×Dic4311yescharacteristic
198C22×C8—21no—
199C22×C8—42no—
200C22×C8C2×Dic4311yescharacteristic
201C22×C8C22⋊D4311yescharacteristic
202C22×C8C22⋊D4311yescharacteristic
203C22×C8C22⋊D4311yescharacteristic
204C22×C8C22⋊D4311yescharacteristic
205C22×C8C22×D4311yescharacteristic
206#123—21no—
207C22⋊Q8C43⋊C811yescharacteristic
208C22⋊Q8C43⋊C811yescharacteristic
209#121C43⋊C811yescharacteristic
210#121C43⋊C811yescharacteristic
211#120—21no—
212C4×D4—21no—
213C4×D4—21no—
214#117C2×Dic4311yescharacteristic
215M32—1722no—
216C2×C16—862no—
217C2×C16—862no—
218C2×C16—1722no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C24#1062187711yescharacteristic
228#41—41no—
229#41—41no—
230C2×Q8C2×C43⋊C811yescharacteristic
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C2×C43⋊C811yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4C2×C43⋊C811yescharacteristic
239C22×C4C2×C43⋊C811yescharacteristic
240C22×C4#1062187711yescharacteristic
241C22×C4C22⋊Dic4311yescharacteristic
242C22×C4C22⋊Dic4311yescharacteristic
243C22×C4C22×Dic4311yescharacteristic
244M16—42no—
245M16—41no—
246M16—41no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—42no—
256C2×C8C22⋊Dic4311yescharacteristic
257C2×C8C22⋊Dic4311yescharacteristic
258C2×C8C2×C22⋊D4311yescharacteristic
259C2×C8C2×C22⋊D4311yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4C2×C43⋊C811yescharacteristic
263C4⋊C4C2×C43⋊C811yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C42—21no—
270C16—1722no—
271C16—1722no—
272C23—22no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C22⋊(C43⋊C8)11yescharacteristic
277C23C22⋊(C43⋊C8)11yescharacteristic
278C23C2×#1062187711yescharacteristic
279Q8—41no—
280D4—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C22⋊(C43⋊C8)11yescharacteristic
299C2×C4C22⋊(C43⋊C8)11yescharacteristic
300C2×C4C2×C22⋊Dic4311yescharacteristic
301C2×C4C22×C43⋊C811yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—41no—
306C8—41no—
307C8#1306324012yes—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—44no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1458268312yes—
321C22C2×C22⋊(C43⋊C8)11yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4C2×#1306324011yescharacteristic
329C4#1458288311yescharacteristic
330C2—22no—
331C2—41no—
332C2—41no—
333C2—81no—
334C2#1913291311yescharacteristic
335C2C2×#1458268311yescharacteristic
336C2#1913622311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#2929C2
socleC22×C43C2×C22⋊C8
prime radicalC43×#525C4
cosocleC22×C8×C43C23
hypercenter#2929D43
hypocenterC43#11470
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #19136206C2semidirect
2. C2×C22⋊(C43⋊C16)C2semidirect
3. #19132537C2semidirect
4. #19132521C2semidirect
191. C43#11470semidirect

Maximal subgroups

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

subgroupindex
#191362062
C2×C22⋊(C43⋊C16)2
#191325372
#191325212
C43×#29292
#1147043