Finite Group Databasebeta

← #25005996

Subgroups — #25005996

Order 11008.

578 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#14582768C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132540C214yesmaximal, complemented
4C43×#1463C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic
6C22×Dic43⋊C4—21no—
7C22×Dic43⋊C4—21no—
8C22×C4×Dic43C411yescharacteristic
9#14582863—21no—
10#14582768—21no—
11#14582768—21no—
12#14582768C412yes—
13#14582768C2212yes—
14#14582625—21no—
15#14582625C2212yes—
16C22×C4⋊C4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C2×#10621877—41no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43—41no—
26C2×C4⋊Dic43C2×C412yes—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—44no—
32C2×Dic43⋊C4—44no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—24no—
35C2×C4×Dic43C2×C412yes—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—41no—
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C2×M16×C43—41no—
42C2×C4⋊C4×C43—41no—
43C2×C4⋊C4×C43—41no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43C2311yescharacteristic
48C22⋊C8×C43—22no—
49C22⋊C8×C43—41no—
50C24×C43C22⋊C411yescharacteristic
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—24no—
68C22×Dic43—24no—
69C22×Dic43—24no—
70C22×Dic43—22no—
71C22×Dic43—22no—
72C22×Dic43—42no—
73C22×Dic43—42no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76M16×C43—82no—
77C2×C8×C43—42no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊Dic43—42no—
83C4⋊Dic43—42no—
84Dic43⋊C4—44no—
85Dic43⋊C4—44no—
86Dic43⋊C4—44no—
87Dic43⋊C4—44no—
88C4×Dic43—24no—
89C4×Dic43—22no—
90C4×Dic43M1614yescomplemented
91#10621877—82no—
92C2×C43⋊C8—42no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43#9911yescharacteristic
98C23×C43#9911yescharacteristic
99C23×C43C2×C22⋊C411yescharacteristic
100C2×C4×C43—24no—
101C2×C4×C43—24no—
102C2×C4×C43—21no—
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—42no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—81no—
117C2×C4×C43—81no—
118C2×C4×C43#10112yes—
119C2×C4×C43C2×M1612yes—
120C2×Dic43—24no—
121C2×Dic43—216no—
122C2×Dic43—24no—
123C2×Dic43—24no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—82no—
128C2×Dic43—82no—
129C8×C43—82no—
130C43⋊C8—82no—
131#11512—431nomaximal, Sylow
132C22×C43—24no—
133C22×C43—24no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—21no—
139C22×C43—21no—
140C22×C43#35312yes—
141C22×C43#35612yes—
142C22×C43#40711yescharacteristic
143C22×C43C2×#9911yescharacteristic
144C22×C43C2×#10111yescharacteristic
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151Dic43—28no—
152Dic43—82no—
153C2×#384—431no—
154#1463—431no—
155#1463D4311yescharacteristic
156#1325—434no—
157C2×C43—21no—
158C2×C43—22no—
159C2×C43—22no—
160C2×C43—21no—
161C2×C43#146311yescharacteristic
162C2×C43C2×#35311yescharacteristic
163C2×C43C2×#35611yescharacteristic
164C22×C4⋊C4—431no—
165C22×C4⋊C4—861no—
166C22×C4⋊C4—861no—
167C22×C4⋊C4C2×D4311yescharacteristic
168C22×C42—431no—
169#407—21no—
170#407—861no—
171#384—432no—
172#384—432no—
173#384—861no—
174#384—861no—
175#324—21no—
176#324—432no—
177#324—861no—
178#324C2×D4312yes—
179C43#1151211yescharacteristic, complemented, Sylow
180C23×C4—861no—
181C23×C4—861no—
182C23×C4C4×D4311yescharacteristic
183C23×C4D17211yescharacteristic
184C23×C4C22⋊D4311yescharacteristic
185C2×M16—41no—
186C2×M16—1721no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—432no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—862no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4—862no—
194C2×C4⋊C4—862no—
195C2×C4⋊C4—1721no—
196C2×C4⋊C4—1721no—
197C2×C4⋊C4—1724no—
198C2×C4⋊C4—1724no—
199C2×C4⋊C4C4×D4311yescharacteristic
200C2×C4⋊C4D17211yescharacteristic
201C2×C4⋊C4C22⋊D4311yescharacteristic
202C2×C4⋊C4C22×D4311yescharacteristic
203C2×C42—432no—
204C2×C42—864no—
205C2×C42—861no—
206C22⋊C8—22no—
207C22⋊C8—41no—
208C22⋊C8—862no—
209C22⋊C8—1721no—
210C24(C2×D43)⋊C411yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—864no—
222C22×C4—864no—
223C22×C4—864no—
224C22×C4—862no—
225C22×C4—862no—
226C22×C4—1722no—
227C22×C4—1722no—
228C22×C4—1721no—
229C22×C4—1721no—
230C22×C4(C2×D43)⋊C411yescharacteristic
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4C2×C4×D4311yescharacteristic
234C22×C4C2×D17211yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236M16—82no—
237M16—3442no—
238C2×C8—42no—
239C2×C8—1722no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C4⋊C4—1724no—
247C4⋊C4—1724no—
248C4⋊C4—1724no—
249C4⋊C4—1724no—
250C42—434no—
251C42—864no—
252C42—862no—
253C23—21no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23#1306323911yescharacteristic
258C23#1306323911yescharacteristic
259C23C2×(C2×D43)⋊C411yescharacteristic
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—864no—
279C2×C4—8616no—
280C2×C4—864no—
281C2×C4—864no—
282C2×C4—3442no—
283C2×C4—3442no—
284C2×C4—1722no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4#1306324312yes—
288C2×C4M16×D4312yes—
289C8—82no—
290C8—3442no—
291C22—24no—
292C22—24no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22#1458269112yes—
300C22#1458269712yes—
301C22#1458286211yescharacteristic
302C22C2×#1306323911yescharacteristic
303C22C2×#1306324311yescharacteristic
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—868no—
311C4—3442no—
312C2—21no—
313C2—21no—
314C2—22no—
315C2—22no—
316C2#1913292411yescharacteristic
317C2C2×#1458269111yescharacteristic
318C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1463C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1463D43
hypocenterC43#11512
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
90. C4×Dic43M16semidirect
179. C43#11512semidirect

Maximal subgroups

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

subgroupindex
C2×#145827682
#191329252
#191325402
C43×#14632
#1151243