Finite Group Databasebeta

← #24994276

Subgroups — #24994276

Order 11008.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#19139587C211yesmaximal, characteristic
2#19133320C212yesmaximal, complemented
3#19132936C211yesmaximal, characteristic
4#19132452C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063312C412yes—
8#14582956C2212yes—
9#14582824—21no—
10#14582824—21no—
11#14582804C412yes—
12#14582759—21no—
13#14582759—21no—
14C4×C4⋊Dic43C2211yescharacteristic
15#14582647—24no—
16#14582623—21no—
17#14582623—21no—
18C2×C4×D4×C43C2211yescharacteristic
19C43×#435—24no—
20C43×#432C2212yes—
21C43×#407—21no—
22C2×C22⋊C8×C43—21no—
23C22×Dic86C2×C412yes—
24#13063325—22no—
25#13063325—22no—
26#13063312—44no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—22no—
32C2×C4×Dic43C2×C412yes—
33C4⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35#13063236—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—21no—
39C22×D4×C43C2×C411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C2×M16×C43—22no—
43C22×C8×C43—22no—
44C4×D4×C43—22no—
45C4×D4×C43—22no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43D411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43D414yes—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54#97×C43—22no—
55C24×C43C22⋊C411yescharacteristic
56C24×C43C22⋊C411yescharacteristic
57C2×D4×C43—22no—
58C2×D4×C43—22no—
59C2×D4×C43—41no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—22no—
72C22×Dic43—22no—
73C2×Dic86—24no—
74C2×Dic86—42no—
75C2×Dic86—42no—
76M16×C43—82no—
77C2×C8×C43—24no—
78C2×C8×C43—82no—
79C4⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C22⋊C4×C43—22no—
82C42×C43C2×D412yes—
83C42×C43#4112yes—
84C22⋊Dic43—44no—
85C22⋊Dic43—44no—
86C4⋊Dic43—42no—
87C4⋊Dic43—41no—
88C4⋊Dic43—42no—
89C4⋊Dic43—41no—
90C4×Dic43—42no—
91C2×C43⋊C8—42no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43#10012yes—
102C23×C43C2×C22⋊C411yescharacteristic
103D4×C43—44no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43C4×D412yes—
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43#12112yes—
119C2×C4×C43#12311yescharacteristic
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126Dic86—84no—
127C8×C43—44no—
128C43⋊C8—82no—
129#9451—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—22no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—81no—
141C22×C43—81no—
142C22×C43#38611yescharacteristic
143C22×C43C2×#10011yescharacteristic
144C22×C43#41311yescharacteristic
145C4×C43—21no—
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43#45512yes—
151Dic43—82no—
152Dic43—82no—
153#2973D4311yescharacteristic
154#2547—431no—
155#1558—432no—
156#1466—431no—
157#1285—432no—
158C2×C43—21no—
159C2×C43—21no—
160C2×C43—42no—
161C2×C43—81no—
162C2×C43#188511yescharacteristic
163C2×C43#190011yescharacteristic
164C2×C43#190911yescharacteristic
165C2×C4⋊Q8—431no—
166C2×#124—432no—
167C2×C4×D4C2×D4311yescharacteristic
168#435—24no—
169#432—432no—
170#432C2×D4312yes—
171#407—21no—
172C2×C22⋊C8—21no—
173#397—861no—
174#397—861no—
175#391—432no—
176#380—861no—
177#380—861no—
178C4×C4⋊C4—431no—
179#333—864no—
180#323—861no—
181#323—861no—
182C43#945111yescharacteristic, complemented, Sylow
183C22×Q8—432no—
184C22×D4C4×D4311yescharacteristic
185C23×C4C22⋊D4311yescharacteristic
186C23×C4C22⋊D4311yescharacteristic
187C2×M16—22no—
188C22×C8—22no—
189C4⋊Q8—862no—
190C4⋊Q8—862no—
191#124—1724no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4C4×D4311yescharacteristic
198C2×C22⋊C4—862no—
199C2×C22⋊C4—862no—
200C2×C22⋊C4D17211yescharacteristic
201C2×C22⋊C4D17211yescharacteristic
202C2×C42—432no—
203C2×C42C22×D4311yescharacteristic
204C4⋊C8—862no—
205C4⋊C8C22⋊D4314yes—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—862no—
210#97—22no—
211#97—862no—
212#95—862no—
213#95—862no—
214#95—861no—
215C24(C2×D43)⋊C411yescharacteristic
216C24(C2×D43)⋊C411yescharacteristic
217C2×Q8—864no—
218C2×Q8—1722no—
219C2×Q8—1722no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—862no—
230C22×C4—862no—
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4C2×C4×D4311yescharacteristic
234C22×C4C2×D17211yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—82no—
239C2×C8—1722no—
240C4⋊C4—22no—
241C4⋊C4—1722no—
242C4⋊C4—1721no—
243C4⋊C4—1722no—
244C4⋊C4—1721no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—1724no—
248C22⋊C4—1724no—
249C42—1722no—
250C42#1062189812yes—
251C42C2×C22⋊D4312yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#1306324112yes—
262C23C2×(C2×D43)⋊C411yescharacteristic
263Q8—3444no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4—1722no—
280C2×C4—1722no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4C4×C22⋊D4312yes—
284C2×C4#1306329411yescharacteristic
285C2×C4#1306329912yes—
286C2×C4#1306330811yescharacteristic
287C8—44no—
288C8—3442no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#1458277811yescharacteristic
302C22C2×#1306324111yescharacteristic
303C22#1458288111yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—3442no—
310C4—3442no—
311C4#1458307712yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#1913498311yescharacteristic
317C2#1913505811yescharacteristic
318C2#1913511711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2973C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#2973D43
hypocenterC43#9451
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19133320C2semidirect
4. #19132452C2semidirect
182. C43#9451semidirect

Maximal subgroups

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

subgroupindex
#191395872
#191333202
#191329362
#191324522
C43×#29732
#945143