Finite Group Databasebeta

← #24984916

Subgroups — #24984916

Order 11008.

624 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 119 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#19134710C212yesmaximal, complemented
3#19132416C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×D4×Dic43C411yescharacteristic
8C2×#13063287C411yescharacteristic
9C2×(C22⋊D43)⋊C4—22no—
10C2×Dic43⋊C8—22no—
11#14582801C2211yescharacteristic
12#14582799—22no—
13#14582768C411yescharacteristic
14C42×Dic43C2211yescharacteristic
15#14582654C2212yes—
16#14582653—22no—
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C22⋊D43—22no—
21C23×Dic43—21no—
22C22×C4×D43—21no—
23C22×C43⋊C8—22no—
24#13063321—22no—
25#13063321—22no—
26D4×Dic43—42no—
27#13063287—42no—
28(C22⋊D43)⋊C4—44no—
29(C22⋊D43)⋊C4—44no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43D412yes—
38C2×C4×Dic43D412yes—
39Dic43⋊C8—44no—
40C22×D4×C43C2×C411yescharacteristic
41C22×C8×C43—22no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C22⋊C4×C43—22no—
44C2×C42×C43C2311yescharacteristic
45C24×C43—21no—
46C23×D43—21no—
47C2×D4×C43—21no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C2×D4×C43M1612yes—
51C22×C4×C43—21no—
52C22×C4×C43C22×C411yescharacteristic
53C22×C4×C43C2×D412yes—
54C2×C22⋊D43—28no—
55C2×C22⋊D43—44no—
56C2×C22⋊D43—44no—
57C22×Dic43—21no—
58C22×Dic43—42no—
59C22×Dic43—44no—
60C22×Dic43C22⋊C411yescharacteristic
61C22×Dic43C22⋊C412yes—
62C22×Dic43C22⋊C411yescharacteristic
63C2×D172—21no—
64C2×D172—41no—
65C2×D172—41no—
66C2×D172M1612yes—
67C2×C4×D43—42no—
68C2×C4×D43—44no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—41no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—42no—
75C42×C43—41no—
76C22⋊Dic43—42no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43—41no—
81Dic43⋊C4—44no—
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43—22no—
85C4×Dic43—42no—
86C4×Dic43D814yes—
87C4×Dic43SD1614yes—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C23×C43—22no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43C2×C22⋊C411yescharacteristic
97C22×D43—22no—
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—42no—
101C22×D43—42no—
102D4×C43—42no—
103D4×C43—42no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43C2×M1611yescharacteristic
111C2×C4×C43C2×M1611yescharacteristic
112C2×C4×C43C2×D812yes—
113C2×C4×C43C2×SD1612yes—
114C22⋊D43—416no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—21no—
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—42no—
121C2×Dic43—84no—
122C2×Dic43#10012yes—
123C2×Dic43#10214yes—
124C2×Dic43#10214yes—
125D172—42no—
126D172—42no—
127C4×D43—84no—
128C8×C43—82no—
129C43⋊C8—82no—
130#7651—431nomaximal, Sylow
131C22×C43—42no—
132C22×C43—44no—
133C22×C43—81no—
134C22×C43—81no—
135C22×C43—82no—
136C22×C43#40711yescharacteristic
137C22×C43#41011yescharacteristic
138C22×C43C2×#10011yescharacteristic
139C22×C43C2×#10212yes—
140C22×C43#42112yes—
141C2×D43—42no—
142C2×D43—44no—
143C2×D43—81no—
144C2×D43—81no—
145C2×D43—82no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—81no—
151Dic43—24no—
152Dic43—41no—
153Dic43—81no—
154Dic43#33114yes—
155C4×#127—431no—
156#1831—432no—
157#1270—431no—
158#1270—432no—
159#1270D4311yescharacteristic, complemented
160C2×C43—82no—
161C2×C43#146611yescharacteristic
162C2×C43#148612yes—
163C2×C43#151712yes—
164C2×C43#153611yescharacteristic
165C2×C43C2×#33111yescharacteristic
166D43—82no—
167C2×#127—431no—
168C2×C4×D4—431no—
169C2×C4×D4—431no—
170C2×C4×D4—862no—
171C2×C4⋊C8—862no—
172#390—431no—
173#390—862no—
174#390C2×D4311yescharacteristic
175#384—431no—
176C43—431no—
177#336—432no—
178#336—862no—
179#336C2×D4312yes—
180C43#765111yescharacteristic, complemented, Sylow
181C22×D4—431no—
182C22×D4—862no—
183C22×D4C4×D4311yescharacteristic
184C23×C4—861no—
185C23×C4—861no—
186C22×C8—22no—
187C22×C8—862no—
188#127—862no—
189#127—862no—
190C4×D4—1724no—
191C4×D4—1724no—
192C4×D4—1722no—
193C4×D4—1722no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—862no—
196C2×C4⋊C4C4×D4311yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—861no—
199C2×C22⋊C4—861no—
200C2×C22⋊C4—862no—
201C2×C42—432no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42—432no—
205C2×C42C22×D4311yescharacteristic
206C4⋊C8—1724no—
207C24—21no—
208C24—861no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—432no—
213C2×D4—868no—
214C2×D4—861no—
215C2×D4—1721no—
216C2×D4—1721no—
217C2×D4—1724no—
218C2×D4—1724no—
219C2×D4#1062187212yes—
220C22×C4—21no—
221C22×C4—431no—
222C22×C4—432no—
223C22×C4—431no—
224C22×C4—861no—
225C22×C4—1724no—
226C22×C4—1722no—
227C22×C4—1724no—
228C22×C4—1722no—
229C22×C4C2×C4×D4311yescharacteristic
230C22×C4D4×D4312yes—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—1722no—
235C2×C8—1722no—
236C2×C8—1722no—
237C4⋊C4—41no—
238C4⋊C4—1721no—
239C4⋊C4—1724no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—1722no—
243C22⋊C4—1722no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C42—41no—
247C42—434no—
248C42—434no—
249C42—862no—
250C42—861no—
251C42—861no—
252C42—1722no—
253C23—22no—
254C23—41no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—862no—
259C23—1721no—
260C23—1721no—
261C23—1722no—
262C23—1722no—
263C23C22⋊C4×D4311yescharacteristic
264D4—42no—
265D4—42no—
266D4—1722no—
267D4—1722no—
268D4—17216no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—432no—
276C2×C4—434no—
277C2×C4—434no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—861no—
281C2×C4—862no—
282C2×C4—3444no—
283C2×C4—3444no—
284C2×C4—1721no—
285C2×C4—1722no—
286C2×C4M16×D4311yescharacteristic
287C2×C4C2×#1062187211yescharacteristic
288C2×C4D8×D4312yes—
289C2×C4SD16×D4312yes—
290C8—82no—
291C8—3442no—
292C22—42no—
293C22—44no—
294C22—81no—
295C22—81no—
296C22—82no—
297C22—3441no—
298C22—3441no—
299C22—3442no—
300C22—1722no—
301C22—1724no—
302C22#1458286111yescharacteristic
303C22#1458287111yescharacteristic
304C22#100×D4311yescharacteristic
305C22#102×D4312yes—
306C22#1458291412yes—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—22no—
311C4—81no—
312C4—434no—
313C4—864no—
314C4—3441no—
315C4—1721no—
316C2—82no—
317C2—3442no—
318C2#1913293411yescharacteristic
319C2#1913301812yes—
320C2#1913315312yes—
321C2#1913322811yescharacteristic
322C2#331×D4311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7651
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134710C2semidirect
3. #19132416C2semidirect
4. #19132415C2semidirect
5. C43×#1270C2semidirect
159. #1270D43semidirect
180. C43#7651semidirect

Maximal subgroups

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

subgroupindex
#191371592
#191347102
#191324162
#191324152
C43×#12702
#765143