Finite Group Databasebeta

← #24990082

Subgroups — #24990082

Order 11008.

450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137079C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic
3#19132452C212yesmaximal, complemented
4#19132450C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7C22×C4×Dic43C411yescharacteristic
8#14582956C2212yes—
9#14582798—21no—
10#14582798—21no—
11#14582774—21no—
12#14582774—21no—
13C4×C4⋊Dic43C411yescharacteristic
14C4×C4⋊Dic43C411yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16C4×C4⋊Dic43C2211yescharacteristic
17#14582625—21no—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#432C2212yes—
21C43×#324—21no—
22C43×#323—21no—
23C23×Dic43—21no—
24#13063284—42no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43—42no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C4⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—22no—
39#13063236—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45#117×C43—22no—
46#117×C43—22no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43C2311yescharacteristic
53C4⋊C8×C43—22no—
54C22⋊C8×C43—22no—
55#97×C43—22no—
56C24×C43C22⋊C411yescharacteristic
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
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—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—42no—
72C22×Dic43—42no—
73C22×Dic43—42no—
74C2×C8×C43—42no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C22⋊C4×C43—22no—
78C22⋊C4×C43—22no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43#4112yes—
82C42×C43#4112yes—
83C22⋊Dic43—42no—
84C4⋊Dic43—42no—
85C4⋊Dic43—42no—
86C4⋊Dic43—42no—
87C4⋊Dic43—42no—
88C4⋊Dic43—42no—
89C4×Dic43—42no—
90C4×Dic43—41no—
91C4×Dic43—41no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43#10012yes—
100C23×C43C2×C22⋊C411yescharacteristic
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—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43#10112yes—
114C2×C4×C43#11711yescharacteristic
115C2×C4×C43#11711yescharacteristic
116C2×C4×C43#12312yes—
117C2×C4×C43#12312yes—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—48no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C8×C43—82no—
132C43⋊C8—82no—
133#8742—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—22no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43#38111yescharacteristic
142C22×C43C2×#10011yescharacteristic
143C22×C43C2×#10111yescharacteristic
144C4×C43—22no—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—22no—
148C4×C43—22no—
149C4×C43—41no—
150C4×C43—41no—
151Dic43—42no—
152Dic43—42no—
153Dic43—81no—
154Dic43—81no—
155#2296—431no—
156#1464—431no—
157#1464D4311yescharacteristic
158#1285—432no—
159#1285—432no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—42no—
163C2×C43#182111yescharacteristic
164C2×C43#182711yescharacteristic
165C2×C43#182711yescharacteristic
166C2×#117—431no—
167C2×#117C2×D4311yescharacteristic
168C22×C42—431no—
169#432—432no—
170#432C2×D4312yes—
171#389—861no—
172#389—861no—
173#385—861no—
174#385—861no—
175C4×C4⋊C4—431no—
176C4×C4⋊C4—431no—
177C4×C4⋊C4—431no—
178C4×C4⋊C4—431no—
179#324—21no—
180#324—861no—
181#323—21no—
182#323—861no—
183C43#874211yescharacteristic, complemented, Sylow
184C23×C4—861no—
185C23×C4C4×D4311yescharacteristic
186#117—22no—
187#117—22no—
188#117—1722no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4D17211yescharacteristic
195C2×C4⋊C4C22⋊D4311yescharacteristic
196C2×C22⋊C4—861no—
197C2×C22⋊C4D17211yescharacteristic
198C2×C22⋊C4C22⋊D4311yescharacteristic
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—861no—
204C2×C42—1722no—
205C2×C42C4×D4311yescharacteristic
206C2×C42C22×D4311yescharacteristic
207C4⋊C8—22no—
208C4⋊C8—862no—
209C22⋊C8—22no—
210C22⋊C8—862no—
211#97—22no—
212#97—862no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217C24(C2×D43)⋊C411yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4—1722no—
227C22×C4—1722no—
228C22×C4—1722no—
229C22×C4(C2×D43)⋊C411yescharacteristic
230C22×C4(C2×D43)⋊C411yescharacteristic
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4C2×C4×D4311yescharacteristic
233C22×C4C2×D17211yescharacteristic
234C22×C4C2×C22⋊D4311yescharacteristic
235C2×C8—42no—
236C2×C8—1722no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—1722no—
240C4⋊C4—1722no—
241C4⋊C4—1722no—
242C4⋊C4—1722no—
243C4⋊C4—1722no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—1722no—
247C42—21no—
248C42—21no—
249C42—1721no—
250C42—1721no—
251C42—1721no—
252C42—1721no—
253C42—1722no—
254C42#1062190012yes—
255C42#1062190012yes—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23#1306324112yes—
261C23C2×(C2×D43)⋊C411yescharacteristic
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—862no—
275C2×C4—862no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1728no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4#1306324312yes—
288C2×C4#1306328111yescharacteristic
289C2×C4#1306328111yescharacteristic
290C2×C4#1306330612yes—
291C2×C4#1306330912yes—
292C8—82no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1458276011yescharacteristic
302C22C2×#1306324111yescharacteristic
303C22C2×#1306324311yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—3441no—
312C4—3441no—
313C4—1722no—
314C4—1722no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1913467311yescharacteristic
319C2#1913469611yescharacteristic
320C2#1913470011yescharacteristic
subgroupG/H
centerC22#14582760
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#381
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#8742
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #19132452C2semidirect
4. #19132450C2semidirect
183. C43#8742semidirect

Maximal subgroups

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

subgroupindex
#191370792
#191329292
#191324522
#191324502
C43×#14642
#874243