Finite Group Databasebeta

← #24991252

Subgroups — #24991252

Order 11008.

722 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C4×#13063321C211yesmaximal, characteristic
2#19132985C212yesmaximal, complemented
3#19132916C211yesmaximal, characteristic, complemented
4#19132427C212yesmaximal, complemented
5C43×#2972C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×C4×D172C2211yescharacteristic
8C2×C4×C22⋊D43—22no—
9#14582952C2212yes—
10#14582802C411yescharacteristic
11#14582800C411yescharacteristic
12#14582799—22no—
13#14582768C411yescharacteristic
14C42×Dic43C2211yescharacteristic
15#14582626—24no—
16#14582623—22no—
17C2×C4×D4×C43C2211yescharacteristic
18C8×D4×C43—24no—
19C43×#431C2212yes—
20C2×C22⋊C8×C43—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—22no—
23C22×C4×D43—21no—
24#13063321—22no—
25#13063321C814yescomplemented
26C4×D172—22no—
27C4×D172—22no—
28C4×C22⋊D43—48no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38C4⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8—22no—
41C22×D4×C43C2×C411yescharacteristic
42C23×C4×C43D412yes—
43C22×C8×C43—24no—
44C4×D4×C43—22no—
45C4×D4×C43—22no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43D412yes—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43D414yescomplemented
50C22⋊C8×C43—24no—
51C22⋊C8×C43—22no—
52C4×C8×C43—22no—
53C24×C43C22⋊C412yes—
54C23×D43—21no—
55C2×D4×C43—22no—
56C2×D4×C43—22no—
57C2×D4×C43C2×C812yes—
58C2×D4×C43M1612yes—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—44no—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C2×C22⋊D43—28no—
67C2×C22⋊D43—44no—
68C2×C22⋊D43—44no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×D172—21no—
73C2×D172—22no—
74C2×D172—22no—
75C2×D172C2×C812yescomplemented
76C2×C4×D43—44no—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C8×C43—24no—
80C2×C8×C43—84no—
81C4⋊C4×C43—22no—
82C22⋊C4×C43—24no—
83C42×C43C2×D412yes—
84C42×C43#4112yes—
85C22⋊Dic43—44no—
86(C2×D43)⋊C4—44no—
87(C2×D43)⋊C4—42no—
88C4⋊Dic43—22no—
89Dic43⋊C4—44no—
90C4×Dic43—24no—
91C4×Dic43—21no—
92C4×Dic43—22no—
93C4×Dic43—42no—
94C4×Dic43C2×C812yescomplemented
95C2×C43⋊C8—42no—
96C23×C43—22no—
97C23×C43—22no—
98C23×C43—42no—
99C23×C43—42no—
100C23×C43C22⋊C814yes—
101C23×C43C2×C22⋊C411yescharacteristic
102C22×D43—22no—
103C22×D43—42no—
104C22×D43—42no—
105C22×D43—41no—
106C22×D43—41no—
107D4×C43—24no—
108D4×C43—24no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—41no—
112C2×C4×C43—44no—
113C2×C4×C43—42no—
114C2×C4×C43—82no—
115C2×C4×C43C4×D412yes—
116C2×C4×C43#12011yescharacteristic
117C2×C4×C43#12112yes—
118C2×C4×C43#12311yescharacteristic
119C2×C4×C43C22×C811yescharacteristic
120C2×C4×C43C2×M1611yescharacteristic
121C2×C4×C43#13112yes—
122C22⋊D43—416no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—42no—
130C2×Dic43—41no—
131D172—24no—
132D172—42no—
133C4×D43—82no—
134C4×D43—82no—
135C8×C43—44no—
136C43⋊C8—82no—
137#8959—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—24no—
141C22×C43—44no—
142C22×C43—42no—
143C22×C43—42no—
144C22×C43—82no—
145C22×C43#38611yescharacteristic
146C22×C43C2×C22⋊C811yescharacteristic
147C22×C43#40811yescharacteristic
148C2×D43—44no—
149C2×D43—42no—
150C2×D43—82no—
151C2×D43—81no—
152C2×D43—81no—
153C4×C43—22no—
154C4×C43—21no—
155C4×C43—42no—
156C4×C43C8×D412yes—
157C4×C43#43512yes—
158C4×C43#45312yes—
159Dic43—24no—
160Dic43—42no—
161Dic43—81no—
162#2972D4311yescharacteristic, complemented
163C4×#127—431no—
164#1478—432no—
165#1460—431no—
166#1276—432no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43—44no—
170C2×C43#186911yescharacteristic
171C2×C43#188411yescharacteristic
172C2×C43#188711yescharacteristic
173D43—82no—
174C2×#127—431no—
175C2×C4×D4—431no—
176C2×C4×D4—862no—
177C2×C4×D4C2×D4311yescharacteristic
178C8×D4—24no—
179#431—432no—
180#431C2×D4312yes—
181C2×C22⋊C8—22no—
182#390—431no—
183#390—431no—
184#390—862no—
185#384—431no—
186C43—431no—
187D4⋊C8—864no—
188#323—862no—
189C43#895911yescharacteristic, complemented, Sylow
190C22×D4—431no—
191C22×D4—862no—
192C22×D4C4×D4311yescharacteristic
193C23×C4—861no—
194C23×C4C22⋊D4312yes—
195C22×C8—24no—
196#127—434no—
197#127—862no—
198C4×D4—22no—
199C4×D4—22no—
200C4×D4—862no—
201C4×D4—862no—
202C4×D4—1728no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4C4×D4311yescharacteristic
206C2×C22⋊C4—862no—
207C2×C22⋊C4—862no—
208C2×C22⋊C4—861no—
209C2×C22⋊C4D17212yes—
210C2×C42—431no—
211C2×C42—431no—
212C2×C42—861no—
213C2×C42—861no—
214C2×C42C22×D4311yescharacteristic
215C4⋊C8—862no—
216C4⋊C8C22⋊D4314yescomplemented
217C22⋊C8—24no—
218C22⋊C8—22no—
219C22⋊C8—862no—
220C4×C8—22no—
221C4×C8—862no—
222C24—861no—
223C24(C2×D43)⋊C412yes—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—432no—
227C2×D4—868no—
228C2×D4—862no—
229C2×D4—861no—
230C2×D4—862no—
231C2×D4—1724no—
232C2×D4—1724no—
233C2×D4C8×D4312yes—
234C2×D4#1062187212yes—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—44no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1724no—
242C22×C4—1721no—
243C22×C4—1721no—
244C22×C4(C2×D43)⋊C412yes—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4C2×D17211yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248C2×C8—24no—
249C2×C8—84no—
250C2×C8—1722no—
251C4⋊C4—22no—
252C4⋊C4—862no—
253C4⋊C4—1724no—
254C22⋊C4—24no—
255C22⋊C4—1724no—
256C22⋊C4—1724no—
257C22⋊C4—1722no—
258C42—432no—
259C42—864no—
260C42—861no—
261C42—862no—
262C42—1722no—
263C42#1062189812yes—
264C42C2×C22⋊D4312yes—
265C23—22no—
266C23—22no—
267C23—42no—
268C23—42no—
269C23—862no—
270C23—1722no—
271C23—1722no—
272C23—1721no—
273C23—1721no—
274C23(C2×D43)⋊C814yes—
275C23C2×(C2×D43)⋊C411yescharacteristic
276D4—24no—
277D4—24no—
278D4—864no—
279D4—17216no—
280D4—1722no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—82no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—3442no—
292C2×C4—3442no—
293C2×C4—1722no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4C4×C22⋊D4312yes—
298C2×C4#1306329411yescharacteristic
299C2×C4#1306329912yes—
300C2×C4#1306330811yescharacteristic
301C2×C4C2×C8×D4311yescharacteristic
302C2×C4C2×#1062187211yescharacteristic
303C2×C4#1306333112yes—
304C8—44no—
305C8—3442no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—44no—
310C22—42no—
311C22—42no—
312C22—82no—
313C22—3442no—
314C22—3441no—
315C22—3441no—
316C22—1724no—
317C22—1722no—
318C22#1458277811yescharacteristic
319C22C2×(C2×D43)⋊C811yescharacteristic
320C22#1458286511yescharacteristic
321C4—22no—
322C4—21no—
323C4—42no—
324C4—864no—
325C4—3441no—
326C4—1722no—
327C4C8×C22⋊D4312yes—
328C4#1458297012yes—
329C4#1458306712yes—
330C2—21no—
331C2—21no—
332C2—44no—
333C2—3442no—
334C2#1913488711yescharacteristic
335C2#1913497811yescharacteristic
336C2#1913499311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#2972C2
socleC22×C43#386
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#2972D43
hypocenterC43#8959
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #19132985C2semidirect
3. #19132916C2semidirect
4. #19132427C2semidirect
5. C43×#2972C2semidirect
25. #13063321C8semidirect
49. C4⋊C8×C43D4semidirect
75. C2×D172C2×C8semidirect
94. C4×Dic43C2×C8semidirect
162. #2972D43semidirect
189. C43#8959semidirect
216. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633212
#191329852
#191329162
#191324272
C43×#29722
#895943