Finite Group Databasebeta

← #25005706

Subgroups — #25005706

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#19137186C211yesmaximal, characteristic
2#324×D43C212yesmaximal, complemented
3#19132529C211yesmaximal, characteristic, complemented
4#19132526C212yesmaximal, complemented
5C43×#1319C211yesmaximal, characteristic, complemented
6C22×#10621902C411yescharacteristic
7C2×#13063282C411yescharacteristic
8C2×C4⋊C4×D43C2211yescharacteristic
9C22⋊C8×D43—22no—
10#14582806C411yescharacteristic
11#14582801C411yescharacteristic
12#14582800C2211yescharacteristic
13#14582777—22no—
14#14582758—22no—
15#14582625C2212yes—
16#14582624—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C2×#10621902—22no—
20C2×#10621902—42no—
21C2×#10621902—42no—
22C2×#10621902C814yescomplemented
23C22×D172—21no—
24C22×D172C2×C411yescharacteristic
25C22×C4×D43—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×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—22no—
36C2×(C2×D43)⋊C4—22no—
37C2×C4×Dic43C2×C411yescharacteristic
38C22⋊(C43⋊C8)—22no—
39(C2×D43)⋊C8—42no—
40C43⋊#95—22no—
41C22×Q8×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C22⋊C8×C43—22no—
45#95×C43—22no—
46C23×D43—21no—
47C23×D43C22⋊C411yescharacteristic
48C2×Q8×C43—21no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43C2×C812yescomplemented
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C22×Dic43—21no—
57C22×Dic43C22⋊C411yescharacteristic
58C22×Dic43C22⋊C412yes—
59#10621902—48no—
60#10621902—48no—
61C2×D172—21no—
62C2×D172—24no—
63C2×D172—42no—
64C2×D172—42no—
65C2×D172—41no—
66C2×D172—41no—
67C2×D172C2×C812yescomplemented
68C2×C4×D43—24no—
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—22no—
73C2×C4×D43—42no—
74C2×C4×D43—42no—
75C2×C4×D43—82no—
76C2×C4×D43C2×C812yes—
77C2×C4×D43M1612yes—
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C42×C43—41no—
81(C2×D43)⋊C4—42no—
82(C2×D43)⋊C4—82no—
83(C2×D43)⋊C4—82no—
84C4⋊Dic43—41no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87C4×Dic43—41no—
88C2×C43⋊C8—42no—
89C8×D43—84no—
90C23×C43C2×C22⋊C411yescharacteristic
91C22×D43—22no—
92C22×D43—41no—
93C22×D43—41no—
94C22×D43—42no—
95C22×D43—42no—
96C22×D43—41no—
97C22×D43—41no—
98C22×D43C22⋊C812yes—
99C22×D43#9912yes—
100C22×D43#10012yes—
101Q8×C43—42no—
102Q8×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×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43C22×C811yescharacteristic
114C2×C4×C43C2×M1611yescharacteristic
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—42no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43C22⋊C812yes—
123D172—42no—
124D172—42no—
125D172—48no—
126C4×D43—24no—
127C4×D43—24no—
128C4×D43—48no—
129C4×D43—44no—
130C4×D43—82no—
131C8×C43—82no—
132C43⋊C8—82no—
133#11432—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43C2×C22⋊C811yescharacteristic
137C22×C43C2×#9911yescharacteristic
138C22×C43C2×#10011yescharacteristic
139C2×D43—22no—
140C2×D43—22no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—44no—
144C2×D43—42no—
145C2×D43—82no—
146C2×D43—81no—
147C2×D43—81no—
148C2×D43#32314yes—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—42no—
152C4×C43—42no—
153C4×C43—81no—
154Dic43—22no—
155Dic43—42no—
156Dic43—81no—
157#2311—431no—
158C2×#324—432no—
159#1319—431no—
160#1319D4311yescharacteristic, complemented
161#1318—432no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43C2×#32311yescharacteristic
165C2×C43#212711yescharacteristic
166C2×C43#213311yescharacteristic
167D43—24no—
168D43—82no—
169C22×#41—431no—
170C2×#117—431no—
171C22×C4⋊C4—431no—
172C2×C22⋊C8—862no—
173#391—431no—
174#391C2×D4311yescharacteristic
175#390—431no—
176#390—431no—
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×Q8C4×D4311yescharacteristic
188C22×D4—431no—
189C22×D4—861no—
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—862no—
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—22no—
209#95—862no—
210C24—431no—
211C24—861no—
212#41—1728no—
213#41—1728no—
214C2×Q8—21no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8C8×D4312yescomplemented
218C2×D4—432no—
219C2×D4—864no—
220C2×D4—861no—
221C2×D4—1721no—
222C2×D4—1721no—
223C2×D4—1722no—
224C2×D4—1722no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—431no—
228C22×C4—432no—
229C22×C4—432no—
230C22×C4—432no—
231C22×C4—864no—
232C22×C4—862no—
233C22×C4—862no—
234C22×C4—862no—
235C22×C4—862no—
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—3442no—
250C22⋊C4—3442no—
251C22⋊C4—1722no—
252C42—41no—
253C42—1721no—
254C23—432no—
255C23—432no—
256C23—432no—
257C23—862no—
258C23—1721no—
259C23—1721no—
260C23—1722no—
261C23—1722no—
262C23—1721no—
263C23—1721no—
264C23C22⋊C4×D4311yescharacteristic
265Q8—42no—
266Q8—42no—
267D4—1722no—
268D4—1722no—
269D4—1728no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—432no—
281C2×C4—864no—
282C2×C4—864no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—862no—
286C2×C4—3442no—
287C2×C4—1728no—
288C2×C4—1724no—
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—434no—
300C22—862no—
301C22—862no—
302C22—3442no—
303C22—3441no—
304C22—3441no—
305C22—1722no—
306C22—1722no—
307C22—1724no—
308C22—1722no—
309C22C22⋊C8×D4311yescharacteristic
310C22#99×D4311yescharacteristic
311C22#100×D4311yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—862no—
318C4—3441no—
319C4—1722no—
320C2—21no—
321C2—21no—
322C2—864no—
323C2—3442no—
324C2#323×D4311yescharacteristic
325C2#1913626311yescharacteristic
326C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC22×#10621902C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11432
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
2. #324×D43C2semidirect
3. #19132529C2semidirect
4. #19132526C2semidirect
5. C43×#1319C2semidirect
22. C2×#10621902C8semidirect
51. C2×Q8×C43C2×C8semidirect
67. C2×D172C2×C8semidirect
160. #1319D43semidirect
182. C43#11432semidirect
217. C2×Q8C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191371862
#324×D432
#191325292
#191325262
C43×#13192
#1143243