Finite Group Databasebeta

← #25005864

Subgroups — #25005864

Order 11008.

616 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 89 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#19137159C211yesmaximal, characteristic
2#19132912C212yesmaximal, complemented
3#19132540C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#1318C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×D4×Dic43C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9C2×(C22⋊D43)⋊C4—22no—
10C22⋊C8×D43—22no—
11#14582801C411yescharacteristic
12#14582799—22no—
13#14582768C2211yescharacteristic
14C42×Dic43C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#390C2211yescharacteristic
18C43×#324C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C22⋊D43—22no—
21C23×Dic43—21no—
22C22×C4×D43D412yes—
23C2×C8×D43—42no—
24#13063321—22no—
25#13063321C814yescomplemented
26D4×Dic43—41no—
27D4×Dic43—41no—
28#13063287—41no—
29#13063287—41no—
30(C22⋊D43)⋊C4—48no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—22no—
35C2×(C2×D43)⋊C4D412yes—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C22⋊(C43⋊C8)—22no—
41(C2×D43)⋊C8—42no—
42C22×D4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43C2311yescharacteristic
44C2×C22⋊C4×C43—22no—
45C2×C42×C43C2×C411yescharacteristic
46C22⋊C8×C43—22no—
47C24×C43—21no—
48C23×D43C22⋊C412yes—
49C2×D4×C43—21no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43C2×C812yescomplemented
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C2×C22⋊D43—28no—
57C2×C22⋊D43—44no—
58C2×C22⋊D43—44no—
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—44no—
62C22×Dic43—41no—
63C22×Dic43—41no—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C411yescharacteristic
66C2×D172—41no—
67C2×D172—41no—
68C2×D172C2×C812yes—
69C2×D172M1612yes—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—44no—
73C2×C8×C43—42no—
74C4⋊C4×C43—41no—
75C22⋊C4×C43—44no—
76C42×C43—41no—
77C22⋊Dic43—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—44no—
80C4⋊Dic43—41no—
81Dic43⋊C4—44no—
82C4×Dic43—24no—
83C4×Dic43—21no—
84C4×Dic43—21no—
85C4×Dic43—21no—
86C4×Dic43—42no—
87C4×Dic43C2×C812yescomplemented
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—22no—
97C22×D43—22no—
98C22×D43—42no—
99C22×D43—42no—
100C22×D43C22⋊C814yes—
101D4×C43—42no—
102D4×C43—42no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43C22×C811yescharacteristic
111C2×C4×C43C2×M1611yescharacteristic
112C22⋊D43—416no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—21no—
118C2×Dic43—41no—
119C2×Dic43—42no—
120C2×Dic43—41no—
121C2×Dic43—82no—
122C2×Dic43—82no—
123C2×Dic43#9911yescharacteristic
124C2×Dic43#9911yescharacteristic
125D172—42no—
126D172—42no—
127C4×D43—44no—
128C4×D43—82no—
129C8×C43—82no—
130C43⋊C8—82no—
131#11475—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—44no—
135C22×C43—42no—
136C22×C43—82no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43C2×C22⋊C811yescharacteristic
140C22×C43C2×#9911yescharacteristic
141C22×C43#41311yescharacteristic
142C2×D43—24no—
143C2×D43—42no—
144C2×D43—42no—
145C2×D43—44no—
146C2×D43—82no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—42no—
150C4×C43—42no—
151Dic43—24no—
152Dic43—21no—
153Dic43—41no—
154Dic43—81no—
155Dic43#35312yes—
156C4×#127—431no—
157#1459—432no—
158#1325—432no—
159#1318—431no—
160#1318D4311yescharacteristic, complemented
161C2×C43—21no—
162C2×C43—21no—
163C2×C43—82no—
164C2×C43#145911yescharacteristic
165C2×C43C2×#35311yescharacteristic
166C2×C43#213211yescharacteristic
167D43—44no—
168C2×#127—431no—
169C2×C4×D4—431no—
170C2×C4×D4—431no—
171C2×C4×D4—862no—
172C2×C22⋊C8—862no—
173#390—431no—
174#390—862no—
175#390C2×D4311yescharacteristic
176#384—431no—
177C43—431no—
178#324—432no—
179#324C2×D4312yes—
180#323—862no—
181C43#1147511yescharacteristic, complemented, Sylow
182C22×D4—431no—
183C22×D4—862no—
184C22×D4C4×D4311yescharacteristic
185C23×C4—432no—
186C23×C4—861no—
187C22×C8—1722no—
188#127—434no—
189#127—862no—
190C4×D4—1728no—
191C4×D4—1721no—
192C4×D4—1721no—
193C4×D4—1721no—
194C4×D4—1721no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—862no—
197C2×C4⋊C4C22×D4311yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—432no—
200C2×C22⋊C4—862no—
201C2×C22⋊C4—861no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42—861no—
205C2×C42—861no—
206C2×C42C4×D4311yescharacteristic
207C22⋊C8—22no—
208C22⋊C8—862no—
209C22⋊C8—1722no—
210C24—21no—
211C24—432no—
212C2×D4—21no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—432no—
216C2×D4—432no—
217C2×D4—868no—
218C2×D4—1721no—
219C2×D4—1721no—
220C2×D4—1724no—
221C2×D4—1724no—
222C2×D4C8×D4312yescomplemented
223C22×C4—21no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—862no—
227C22×C4—862no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—1724no—
231C22×C4—1721no—
232C22×C4—1721no—
233C22×C4—1724no—
234C22×C4C2×C4×D4311yescharacteristic
235C22×C4D4×D4312yes—
236C2×C8—42no—
237C2×C8—3444no—
238C2×C8—1722no—
239C4⋊C4—41no—
240C4⋊C4—1721no—
241C4⋊C4—1724no—
242C22⋊C4—44no—
243C22⋊C4—1722no—
244C22⋊C4—1724no—
245C22⋊C4—1722no—
246C42—41no—
247C42—432no—
248C42—861no—
249C42—861no—
250C42—864no—
251C42—861no—
252C42—1722no—
253C23—22no—
254C23—42no—
255C23—42no—
256C23—41no—
257C23—41no—
258C23—434no—
259C23—862no—
260C23—862no—
261C23—1722no—
262C23—1722no—
263C23C22⋊C4×D4311yescharacteristic
264D4—42no—
265D4—42no—
266D4—1722no—
267D4—1722no—
268D4—17216no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—431no—
277C2×C4—431no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—862no—
282C2×C4—861no—
283C2×C4—3442no—
284C2×C4—3442no—
285C2×C4—3442no—
286C2×C4—1724no—
287C2×C4—1722no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4C2×C8×D4311yescharacteristic
291C2×C4M16×D4311yescharacteristic
292C8—82no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22—42no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22—864no—
302C22—3442no—
303C22—1724no—
304C22—1722no—
305C22—1722no—
306C22C22⋊C8×D4311yescharacteristic
307C22#99×D4311yescharacteristic
308C22#1458288011yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4—42no—
313C4—432no—
314C4—864no—
315C4—861no—
316C4—3441no—
317C4—1721no—
318C2—21no—
319C2—21no—
320C2—82no—
321C2—1724no—
322C2#1913291011yescharacteristic
323C2#353×D4311yescharacteristic
324C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC2×#13063321C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11475
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. #19132912C2semidirect
3. #19132540C2semidirect
4. #19132527C2semidirect
5. C43×#1318C2semidirect
25. #13063321C8semidirect
52. C2×D4×C43C2×C8semidirect
87. C4×Dic43C2×C8semidirect
160. #1318D43semidirect
181. C43#11475semidirect
222. C2×D4C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191371592
#191329122
#191325402
#191325272
C43×#13182
#1147543