Finite Group Databasebeta

← #25005704

Subgroups — #25005704

Order 11008.

594 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137185C211yesmaximal, characteristic
2#324×D43C212yesmaximal, complemented
3#19132528C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#1318C211yesmaximal, characteristic, complemented
6C22×#10621900C411yescharacteristic
7C2×#13063282C411yescharacteristic
8C2×C4⋊C4×D43C2211yescharacteristic
9C22⋊C8×D43—22no—
10#14582805C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582802C411yescharacteristic
13#14582775—22no—
14#14582757—22no—
15#14582625C2212yes—
16#14582624—22no—
17C43×#390C2211yescharacteristic
18C43×#324C2212yes—
19C2×#10621900—22no—
20C2×#10621900—42no—
21C2×#10621900—42no—
22C2×#10621900C814yescomplemented
23C22×Dic86C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C23×Dic43—21no—
26C22×C4×D43C2×C411yescharacteristic
27C22×C4×D43D412yes—
28C2×C8×D43—42no—
29#13063282—42no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4D412yes—
33C4⋊C4×D43—42no—
34C2×C22⋊Dic43—22no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C22⋊(C43⋊C8)—22no—
38(C2×D43)⋊C8—42no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C22×D4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C22⋊C4×C43—22no—
44C2×C42×C43C2×C411yescharacteristic
45C22⋊C8×C43—22no—
46C24×C43—21no—
47C23×D43C22⋊C411yescharacteristic
48C2×D4×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43C2×C812yescomplemented
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D412yes—
55C2×C22⋊D43—24no—
56C2×C22⋊D43—42no—
57C2×C22⋊D43—42no—
58C22×Dic43—24no—
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—42no—
62C22×Dic43—42no—
63C22×Dic43C22⋊C411yescharacteristic
64C22×Dic43C22⋊C412yes—
65#10621900—48no—
66#10621900—48no—
67C2×C4×D43—22no—
68C2×C4×D43—22no—
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—82no—
72C2×C4×D43C2×C812yes—
73C2×C4×D43M1612yes—
74C2×Dic86—21no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86C2×C812yescomplemented
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C22⋊C4×C43—82no—
81C42×C43—41no—
82C22⋊Dic43—82no—
83(C2×D43)⋊C4—42no—
84C4⋊Dic43—41no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87C4×Dic43—41no—
88C2×C43⋊C8—42no—
89C8×D43—84no—
90C23×C43—22no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43—41no—
97C22×D43—41no—
98C22×D43C22⋊C812yes—
99C22×D43#9912yes—
100C22×D43#10012yes—
101D4×C43—42no—
102D4×C43—42no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43C22×C811yescharacteristic
111C2×C4×C43C2×M1611yescharacteristic
112C22⋊D43—48no—
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—48no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—42no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43C22⋊C812yes—
125C4×D43—24no—
126C4×D43—24no—
127C4×D43—44no—
128C4×D43—82no—
129Dic86—42no—
130Dic86—42no—
131C8×C43—82no—
132C43⋊C8—82no—
133#11432—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—44no—
137C22×C43—42no—
138C22×C43—82no—
139C22×C43—81no—
140C22×C43—81no—
141C22×C43C2×C22⋊C811yescharacteristic
142C22×C43C2×#9911yescharacteristic
143C22×C43C2×#10011yescharacteristic
144C2×D43—22no—
145C2×D43—22no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43#32314yes—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—42no—
152C4×C43—81no—
153Dic43—22no—
154Dic43—42no—
155Dic43—42no—
156Dic43—81no—
157#2311—431no—
158C2×#324—432no—
159#1319—432no—
160#1318—431no—
161#1318D4311yescharacteristic, complemented
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—82no—
165C2×C43C2×#32311yescharacteristic
166C2×C43#212711yescharacteristic
167C2×C43#213311yescharacteristic
168D43—24no—
169C22×#41—431no—
170C2×#117—431no—
171C22×C4⋊C4—431no—
172C2×C22⋊C8—862no—
173#391—431no—
174#391—431no—
175#390—431no—
176#390C2×D4311yescharacteristic
177#386—862no—
178#380—862no—
179#324—432no—
180#324—862no—
181#324C2×D4312yes—
182C43#1143211yescharacteristic, complemented, Sylow
183C2×#41—434no—
184C2×#41—862no—
185C2×#41—1722no—
186C2×#41—1722no—
187C22×Q8—431no—
188C22×D4—861no—
189C22×D4C4×D4311yescharacteristic
190C23×C4—431no—
191C23×C4—432no—
192C23×C4—861no—
193C22×C8—1722no—
194#117—1722no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—432no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—1722no—
199C2×C4⋊C4C22×D4311yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—862no—
202C2×C22⋊C4—861no—
203C2×C42—431no—
204C2×C42C4×D4311yescharacteristic
205C22⋊C8—22no—
206C22⋊C8—862no—
207C22⋊C8—1722no—
208#95—862no—
209#95—862no—
210C24—21no—
211C24—431no—
212#41—1728no—
213#41—1728no—
214C2×Q8—432no—
215C2×Q8—861no—
216C2×Q8—1721no—
217C2×Q8—1721no—
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—864no—
222C2×D4—1722no—
223C2×D4—1722no—
224C2×D4C8×D4312yescomplemented
225C22×C4—21no—
226C22×C4—431no—
227C22×C4—432no—
228C22×C4—432no—
229C22×C4—432no—
230C22×C4—862no—
231C22×C4—862no—
232C22×C4—862no—
233C22×C4—862no—
234C22×C4—864no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—3442no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4C2×C4×D4311yescharacteristic
241C22×C4D4×D4312yes—
242C2×C8—42no—
243C2×C8—3444no—
244C2×C8—1722no—
245C4⋊C4—41no—
246C4⋊C4—1722no—
247C4⋊C4—1721no—
248C4⋊C4—1722no—
249C22⋊C4—82no—
250C22⋊C4—3442no—
251C22⋊C4—1722no—
252C42—41no—
253C42—1721no—
254C23—22no—
255C23—42no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—432no—
260C23—432no—
261C23—432no—
262C23—1721no—
263C23—1721no—
264C23C22⋊C4×D4311yescharacteristic
265Q8—1722no—
266Q8—1722no—
267D4—42no—
268D4—42no—
269D4—1728no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—432no—
278C2×C4—864no—
279C2×C4—864no—
280C2×C4—861no—
281C2×C4—861no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—3442no—
285C2×C4—1724no—
286C2×C4—1728no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1722no—
293C2×C4C2×C8×D4311yescharacteristic
294C2×C4M16×D4311yescharacteristic
295C8—82no—
296C8—3442no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22—42no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22—434no—
305C22—862no—
306C22—862no—
307C22—1722no—
308C22—1722no—
309C22C22⋊C8×D4311yescharacteristic
310C22#99×D4311yescharacteristic
311C22#100×D4311yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—862no—
317C4—3441no—
318C4—1722no—
319C4—1722no—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—864no—
324C2#323×D4311yescharacteristic
325C2#1913626111yescharacteristic
326C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC22×#10621900C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11432
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #324×D43C2semidirect
3. #19132528C2semidirect
4. #19132527C2semidirect
5. C43×#1318C2semidirect
22. C2×#10621900C8semidirect
51. C2×D4×C43C2×C8semidirect
77. C2×Dic86C2×C8semidirect
161. #1318D43semidirect
182. C43#11432semidirect
224. C2×D4C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191371852
#324×D432
#191325282
#191325272
C43×#13182
#1143243