Finite Group Databasebeta

← #24994339

Subgroups — #24994339

Order 11008.

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

normal subgroups only

This group has 610 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#19139062C211yesmaximal, characteristic
2#19137198C211yesmaximal, characteristic, complemented
3#19133125C212yesmaximal
4#19132449C212yesmaximal, complemented
5C43×#1821C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063308—21no—
8C2×#13063299C2211yescharacteristic
9#14582834—22no—
10#14582800C412yescomplemented
11#14582785—24no—
12#14582768C412yescomplemented
13#14582762C2212yes—
14#14582759—21no—
15C4×C22⋊Dic43—21no—
16C4×C22⋊Dic43C2211yescharacteristic
17#14582634—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#343—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23#13063308—44no—
24#13063308—44no—
25#13063299—22no—
26#13063299—22no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—22no—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—22no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43—22no—
37C2×C4×Dic43C2×C412yes—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95—21no—
42C43⋊#95D414yes—
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43C2×C412yes—
50C2×C4⋊C4×C43D412yes—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C24×C43C2×D411yescharacteristic
54C23×D43—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×C43—42no—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22⋊C412yes—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D412yes—
67C22×C4×C43#4112yes—
68C2×C22⋊D43—42no—
69C2×C22⋊D43—42no—
70C2×C22⋊D43—41no—
71C2×C22⋊D43—41no—
72C22×Dic43—22no—
73C22×Dic43—21no—
74C22×Dic43—24no—
75C2×D172—22no—
76C2×D172—42no—
77M16×C43—44no—
78C2×C8×C43—42no—
79C4⋊C4×C43—24no—
80C4⋊C4×C43—24no—
81C22⋊Dic43—24no—
82C22⋊Dic43—44no—
83(C2×D43)⋊C4—44no—
84(C2×D43)⋊C4—44no—
85(C2×D43)⋊C4—42no—
86C4⋊Dic43—22no—
87C4⋊Dic43—82no—
88Dic43⋊C4—44no—
89Dic43⋊C4—44no—
90C4×Dic43—42no—
91C4×Dic43—82no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—41no—
95C23×C43C2×C22⋊C411yescharacteristic
96C23×C43#12011yescharacteristic
97C23×C43#12311yescharacteristic
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—42no—
101C22×D43—41no—
102C22×D43—42no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43C4×D412yes—
116C2×C4×C43#12112yes—
117C22⋊D43—82no—
118C22⋊D43—82no—
119C2×Dic43—24no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—44no—
125C2×Dic43—44no—
126C2×Dic43—41no—
127C2×Dic43—44no—
128D172—82no—
129C8×C43—82no—
130#9464—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—44no—
139C22×C43#38611yescharacteristic
140C22×C43#41012yes—
141C22×C43#45312yes—
142C2×D43—82no—
143C2×D43—82no—
144C2×D43—81no—
145C2×D43—81no—
146C2×D43—81no—
147C4×C43—22no—
148C4×C43—22no—
149C4×C43—42no—
150C4×C43—42no—
151Dic43—44no—
152Dic43—84no—
153Dic43—81no—
154#2501—431no—
155#2313—431no—
156#1821D4311yescharacteristic, complemented
157#1510—432no—
158#1284—432no—
159C2×C43—22no—
160C2×C43—22no—
161C2×C43—41no—
162C2×C43#188711yescharacteristic
163C2×C43#189911yescharacteristic
164C2×C43#191211yescharacteristic
165D43—161no—
166C2×#123—861no—
167C2×#123—861no—
168C2×#121—431no—
169C22×C4⋊C4C2×D4311yescharacteristic
170#407C2×D4312yes—
171#399—862no—
172#390—432no—
173#387—864no—
174#384—432no—
175#381—432no—
176#380—861no—
177C4×C22⋊C4—431no—
178C4×C22⋊C4—861no—
179#343—22no—
180#327—864no—
181C43#946411yescharacteristic, complemented, Sylow
182C22×D4—431no—
183C22×D4—861no—
184C23×C4D17211yescharacteristic
185C23×C4D17211yescharacteristic
186C23×C4C22×D4311yescharacteristic
187C2×M16—22no—
188#123—1724no—
189#123—1724no—
190#121—862no—
191#121—862no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—862no—
196C2×C4⋊C4—862no—
197C2×C4⋊C4—862no—
198C2×C4⋊C4C4×D4312yes—
199C2×C4⋊C4C22⋊D4312yes—
200C2×C22⋊C4—861no—
201C2×C22⋊C4—862no—
202C2×C22⋊C4—862no—
203C2×C22⋊C4—862no—
204C2×C22⋊C4—861no—
205C2×C42—432no—
206C2×C42—862no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209#95—434no—
210#95—862no—
211#95—862no—
212#95—862no—
213#95—861no—
214C24—861no—
215C24C2×D17211yescharacteristic
216C2×D4—862no—
217C2×D4—1722no—
218C2×D4—1722no—
219C2×D4—1722no—
220C2×D4—1721no—
221C2×D4—1721no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—862no—
230C22×C4—861no—
231C22×C4—864no—
232C22×C4(C2×D43)⋊C412yes—
233C22×C4(C2×D43)⋊C412yes—
234C22×C4C2×C4×D4311yescharacteristic
235C22×C4D4×D4312yes—
236C22×C4#1062190012yes—
237C22×C4C2×C22⋊D4311yescharacteristic
238M16—44no—
239C2×C8—42no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—862no—
243C4⋊C4—3442no—
244C4⋊C4—1724no—
245C4⋊C4—1724no—
246C22⋊C4—864no—
247C22⋊C4—1724no—
248C22⋊C4—1724no—
249C22⋊C4—1724no—
250C22⋊C4—1722no—
251C42—3442no—
252C42—1722no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—1721no—
257C23—1721no—
258C23—1722no—
259C23—1722no—
260C23—1721no—
261C23C2×(C2×D43)⋊C411yescharacteristic
262C23#1306329511yescharacteristic
263C23#1306330911yescharacteristic
264D4—3442no—
265D4—3442no—
266D4—3442no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—864no—
280C2×C4—1724no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1724no—
284C2×C4—1724no—
285C2×C4—1721no—
286C2×C4—1722no—
287C2×C4—1722no—
288C2×C4(C22⋊D43)⋊C412yes—
289C2×C4#1306329712yes—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—3442no—
300C22—3442no—
301C22—3441no—
302C22—3441no—
303C22—3441no—
304C22#1458277611yescharacteristic
305C22#1458287212yes—
306C22#1458306912yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—42no—
311C4—3444no—
312C4—3441no—
313C4—1724no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—6881no—
318C2#1913499111yescharacteristic
319C2#1913505111yescharacteristic
320C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1821C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1821D43
hypocenterC43#9464
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #19137198C2semidirect
4. #19132449C2semidirect
5. C43×#1821C2semidirect
10. #14582800C4semidirect
12. #14582768C4semidirect
156. #1821D43semidirect
181. C43#9464semidirect

Maximal subgroups

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

subgroupindex
#191390622
#191371982
#191331252
#191324492
C43×#18212
#946443