Finite Group Databasebeta

← #25005976

Subgroups — #25005976

Order 11008.

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

normal subgroups only

This group has 598 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×#14582804C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132528C214yesmaximal, complemented
4C43×#1463C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic
6C22×C4×Dic43C411yescharacteristic
7#14582863—21no—
8#14582804—21no—
9#14582804—21no—
10#14582804C412yes—
11#14582804C2212yes—
12C2×C43⋊#95—21no—
13C2×C43⋊#95—21no—
14#14582625—21no—
15#14582625C2212yes—
16C22×C4⋊C4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C22×Dic86—21no—
21C22×Dic86—24no—
22C22×Dic86—41no—
23C22×Dic86—41no—
24C22×Dic86—42no—
25C22×Dic86C2×C412yes—
26C23×Dic43—21no—
27C23×Dic43—21no—
28C2×#10621877—41no—
29C2×C4×Dic43—21no—
30C2×C4×Dic43—42no—
31C2×C4×Dic43C2×C412yes—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—41no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
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—22no—
70C22×Dic43—22no—
71C22×Dic43—42no—
72C22×Dic43—42no—
73C22×Dic43—42no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76C2×Dic86—24no—
77C2×Dic86—22no—
78C2×Dic86—42no—
79C2×Dic86—48no—
80C2×Dic86—48no—
81C2×Dic86—42no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86M1614yescomplemented
85M16×C43—82no—
86C2×C8×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4×Dic43—42no—
92C4×Dic43—42no—
93#10621877—82no—
94C2×C43⋊C8—42no—
95C23×C43—22no—
96C23×C43—22no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43#9911yescharacteristic
100C23×C43#9911yescharacteristic
101C23×C43C2×C22⋊C411yescharacteristic
102C2×C4×C43—24no—
103C2×C4×C43—24no—
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—42no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43#10012yes—
121C2×C4×C43C2×M1612yes—
122C2×Dic43—24no—
123C2×Dic43—24no—
124C2×Dic43—44no—
125C2×Dic43—44no—
126C2×Dic43—48no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129C2×Dic43—42no—
130C2×Dic43—42no—
131Dic86—48no—
132Dic86—44no—
133Dic86—44no—
134C8×C43—82no—
135C43⋊C8—82no—
136#11506—431nomaximal, Sylow
137C22×C43—24no—
138C22×C43—24no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#35412yes—
146C22×C43#35612yes—
147C22×C43#40711yescharacteristic
148C22×C43C2×#9911yescharacteristic
149C22×C43C2×#10011yescharacteristic
150C4×C43—22no—
151C4×C43—22no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43—41no—
156Dic43—44no—
157Dic43—44no—
158C2×#391—431no—
159#1463—431no—
160#1463D4311yescharacteristic
161#1319—434no—
162C2×C43—21no—
163C2×C43—22no—
164C2×C43—22no—
165C2×C43—21no—
166C2×C43#146211yescharacteristic
167C2×C43C2×#35411yescharacteristic
168C2×C43C2×#35611yescharacteristic
169C23×Q8—431no—
170C22×C4⋊C4C2×D4311yescharacteristic
171C22×C42—431no—
172#407—21no—
173#407—861no—
174#391—432no—
175#391—432no—
176#391—861no—
177#391—861no—
178C2×#95—861no—
179C2×#95—861no—
180#324—21no—
181#324—432no—
182#324—861no—
183#324C2×D4312yes—
184C43#1150611yescharacteristic, complemented, Sylow
185C22×Q8—432no—
186C22×Q8—864no—
187C22×Q8—861no—
188C22×Q8—1722no—
189C22×Q8—1721no—
190C22×Q8—1721no—
191C23×C4—861no—
192C23×C4—861no—
193C23×C4C4×D4311yescharacteristic
194C23×C4D17211yescharacteristic
195C23×C4C22⋊D4311yescharacteristic
196C2×M16—41no—
197C2×M16—1721no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4C4×D4311yescharacteristic
201C2×C4⋊C4D17211yescharacteristic
202C2×C4⋊C4C22⋊D4311yescharacteristic
203C2×C4⋊C4C22×D4311yescharacteristic
204C2×C42—432no—
205C2×C42—861no—
206C2×C42—1722no—
207C22⋊C8—22no—
208C22⋊C8—41no—
209C22⋊C8—862no—
210C22⋊C8—1721no—
211#95—862no—
212#95—862no—
213#95—862no—
214#95—862no—
215C24(C2×D43)⋊C411yescharacteristic
216C2×Q8—434no—
217C2×Q8—864no—
218C2×Q8—862no—
219C2×Q8—1728no—
220C2×Q8—1728no—
221C2×Q8—1722no—
222C2×Q8—1722no—
223C2×Q8—1722no—
224C2×Q8—1722no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—864no—
236C22×C4—864no—
237C22×C4—862no—
238C22×C4—862no—
239C22×C4—1722no—
240C22×C4—1722no—
241C22×C4—1722no—
242C22×C4—1721no—
243C22×C4—1721no—
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4C2×D17211yescharacteristic
249C22×C4C2×C22⋊D4311yescharacteristic
250M16—82no—
251M16—3442no—
252C2×C8—42no—
253C2×C8—1722no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C42—1722no—
259C42—1722no—
260C23—21no—
261C23—21no—
262C23—22no—
263C23—22no—
264C23#1306323911yescharacteristic
265C23#1306323911yescharacteristic
266C23C2×(C2×D43)⋊C411yescharacteristic
267Q8—1724no—
268Q8—1728no—
269Q8—1724no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—864no—
289C2×C4—864no—
290C2×C4—1724no—
291C2×C4—1724no—
292C2×C4—1728no—
293C2×C4—1722no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4#1306324112yes—
298C2×C4M16×D4312yes—
299C8—82no—
300C8—3442no—
301C22—24no—
302C22—24no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22#1458269312yes—
310C22#1458269712yes—
311C22#1458286211yescharacteristic
312C22C2×#1306323911yescharacteristic
313C22C2×#1306324111yescharacteristic
314C4—22no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1724no—
321C4—1724no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—22no—
326C2#1913292111yescharacteristic
327C2C2×#1458269311yescharacteristic
328C2C2×#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#11506
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. #19132528C2semidirect
84. C2×Dic86M16semidirect
184. C43#11506semidirect

Maximal subgroups

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

subgroupindex
C2×#145828042
#191329252
#191325282
C43×#14632
#1150643