Finite Group Databasebeta

← #25006228

Subgroups — #25006228

Order 11008.

412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139571C211yesmaximal, characteristic
2#19132919C211yesmaximal, characteristic, complemented
3#19132528C212yesmaximal, complemented
4#19132526C212yesmaximal
5C43×#1467C211yesmaximal, characteristic, complemented
6C2×#13063323C411yescharacteristic
7C2×#13063314C411yescharacteristic
8C2×#13063313C411yescharacteristic
9#14582952—21no—
10#14582821—21no—
11#14582821—21no—
12#14582804C2211yescharacteristic
13#14582800C2211yescharacteristic
14#14582790—21no—
15#14582790—21no—
16C4×C4⋊Dic43C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C22×D172C2×C411yescharacteristic
25#13063323—42no—
26#13063314—42no—
27#13063313—41no—
28#13063313—41no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C4⋊(C43⋊C8)—41no—
41C22⋊(C43⋊C8)—22no—
42C4×C43⋊C8—41no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×Q8×C43C2×C411yescharacteristic
47C4×Q8×C43—41no—
48C4×Q8×C43—41no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43C2311yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C4⋊C8×C43—41no—
56C22⋊C8×C43—22no—
57#97×C43—41no—
58C23×D43—21no—
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×D172—22no—
73C2×D172—41no—
74C2×D172—41no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—42no—
95C4⋊Dic43—42no—
96Dic43⋊C4—42no—
97Dic43⋊C4—42no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100C2×C43⋊C8—42no—
101C23×C43C2×C22⋊C411yescharacteristic
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109Q8×C43—44no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#9911yescharacteristic
126C2×C4×C43#10012yes—
127C2×C4×C43#13112yes—
128C2×Dic43—22no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137D172—82no—
138Dic86—82no—
139C8×C43—82no—
140C43⋊C8—82no—
141#11565—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43#40811yescharacteristic
145C22×C43C2×#9911yescharacteristic
146C22×C43C2×#10011yescharacteristic
147C2×D43—81no—
148C2×D43—81no—
149C2×D43—81no—
150C2×D43—81no—
151C2×D43—81no—
152C2×D43—81no—
153C2×D43—81no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—22no—
157C4×C43—22no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165#2545—431no—
166#1467D4311yescharacteristic, complemented
167#1461—431no—
168#1319—432no—
169#1318—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43#147111yescharacteristic
173C2×C43#212611yescharacteristic
174C2×C43#213311yescharacteristic
175D43—161no—
176C2×C4⋊Q8—431no—
177C2×#124—431no—
178C2×#124—431no—
179C2×C4×Q8C2×D4311yescharacteristic
180#432—21no—
181#431—861no—
182#396—861no—
183#396—861no—
184#391—431no—
185#390—431no—
186#388—861no—
187#388—861no—
188C4×C4⋊C4—431no—
189#324—21no—
190#324—432no—
191#324—861no—
192#324C2×D4312yes—
193C43#1156511yescharacteristic, complemented, Sylow
194C22×Q8—431no—
195C22×Q8C4×D4311yescharacteristic
196C22×D4—431no—
197C4⋊Q8—1722no—
198#124—1721no—
199#124—1721no—
200#124—1722no—
201C4×Q8—41no—
202C4×Q8—41no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4D17211yescharacteristic
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C4⋊C4C22×D4311yescharacteristic
209C2×C22⋊C4—861no—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C42—431no—
216C2×C42—431no—
217C2×C42C4×D4311yescharacteristic
218C2×C42D17211yescharacteristic
219C2×C42C22⋊D4311yescharacteristic
220C4⋊C8—41no—
221C4⋊C8—1721no—
222C22⋊C8—22no—
223C22⋊C8—862no—
224#97—41no—
225C4×C8—1721no—
226#95—861no—
227#95—861no—
228#95—861no—
229C24—861no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—862no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C2×D4—862no—
237C2×D4—1721no—
238C2×D4—1721no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4C2×C4×D4311yescharacteristic
247C22×C4C2×D17211yescharacteristic
248C22×C4C2×C22⋊D4311yescharacteristic
249C2×C8—42no—
250C2×C8—1722no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C4⋊C4—1722no—
257C22⋊C4—1722no—
258C22⋊C4—1722no—
259C22⋊C4—1722no—
260C22⋊C4—1722no—
261C22⋊C4—1721no—
262C22⋊C4—1721no—
263C22⋊C4—1722no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—1721no—
271C42—1721no—
272C23—1721no—
273C23—1721no—
274C23—1721no—
275C23—1721no—
276C23—1721no—
277C23—1721no—
278C23—1721no—
279C23C2×(C2×D43)⋊C411yescharacteristic
280Q8—44no—
281Q8—3442no—
282D4—3442no—
283C2×C4—21no—
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—862no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4#1306323911yescharacteristic
307C2×C4#1306323911yescharacteristic
308C2×C4#1306324112yes—
309C2×C4#1306333312yes—
310C8—82no—
311C8—3442no—
312C22—21no—
313C22—21no—
314C22—3441no—
315C22—3441no—
316C22—3441no—
317C22—3441no—
318C22—3441no—
319C22—3441no—
320C22—3441no—
321C22#1458286711yescharacteristic
322C22C2×#1306323911yescharacteristic
323C22C2×#1306324111yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—3441no—
333C4—3441no—
334C4—1722no—
335C2—21no—
336C2—21no—
337C2—6881no—
338C2#1913295611yescharacteristic
339C2#1913625811yescharacteristic
340C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1467C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1467D43
hypocenterC43#11565
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #19132919C2semidirect
3. #19132528C2semidirect
5. C43×#1467C2semidirect
166. #1467D43semidirect
193. C43#11565semidirect

Maximal subgroups

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

subgroupindex
#191395712
#191329192
#191325282
#191325262
C43×#14672
#1156543