Finite Group Databasebeta

← #25007724

Subgroups — #25007724

Order 11008.

452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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#19138912C211yesmaximal, characteristic
2#19132916C211yesmaximal, characteristic
3#19132618C214yesmaximal, complemented
4C43×#1799C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic, complemented
6#14582952—21no—
7#14582838C412yescomplemented
8#14582835C2212yes—
9#14582797—21no—
10#14582779—21no—
11#14582771—21no—
12#14582759—21no—
13#14582759C411yescharacteristic, complemented
14#14582623—21no—
15#14582623C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C2×#99×C43—21no—
18C43×#380—21no—
19C43×#342C2212yes—
20C23×Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—41no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43C2×C412yes—
26C2×Dic43⋊C4—22no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29C4⋊(C43⋊C8)—41no—
30C22⋊(C43⋊C8)—22no—
31C4×C43⋊C8—41no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95C2×C412yes—
35C22×D4×C43D411yescharacteristic
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C4×D4×C43—41no—
39C4×D4×C43—41no—
40C2×C4⋊C4×C43—41no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43D411yescharacteristic
44C2×C22⋊C4×C43C2311yescharacteristic
45C2×C42×C43D411yescharacteristic
46#99×C43—42no—
47#95×C43—41no—
48C24×C43C22⋊C411yescharacteristic
49C24×C43C2×D411yescharacteristic
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43SD1612yes—
53C2×D4×C43Q1612yes—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—22no—
67C22×Dic43—22no—
68C22×Dic43—42no—
69C22×Dic43—82no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—82no—
72C22⋊C4×C43—41no—
73C22⋊C4×C43—41no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C42×C43—21no—
77C42×C43—21no—
78C22⋊Dic43—42no—
79C22⋊Dic43—82no—
80C4⋊Dic43—42no—
81C4⋊Dic43—41no—
82C4⋊Dic43—41no—
83C4⋊Dic43—42no—
84Dic43⋊C4—82no—
85C2×C43⋊C8—42no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—41no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43#10312yes—
95C23×C43C2×C22⋊C411yescharacteristic
96C23×C43C2×SD1611yescharacteristic
97C23×C43C2×Q1611yescharacteristic
98D4×C43—42no—
99D4×C43—42no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—82no—
114C2×C4×C43—82no—
115C2×C4×C43—82no—
116C2×C4×C43#9911yescharacteristic
117C2×C4×C43#9911yescharacteristic
118C2×C4×C43#10312yes—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—42no—
125C2×Dic43—84no—
126C43⋊C8—82no—
127#11899—431nomaximal, Sylow
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—22no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—42no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—42no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—81no—
142C22×C43C2×#9911yescharacteristic
143C22×C43C2×#10311yescharacteristic
144C22×C43#42111yescharacteristic
145C4×C43—21no—
146C4×C43—22no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—162no—
151C4×C43#35212yes—
152Dic43—82no—
153Dic43—82no—
154#2487—431no—
155#1799D4311yescharacteristic
156#1460—431no—
157#1352—434no—
158C2×C43—21no—
159C2×C43—21no—
160C2×C43—41no—
161C2×C43—42no—
162C2×C43—41no—
163C2×C43#152011yescharacteristic
164C2×C43C2×#35211yescharacteristic
165C2×C43#212811yescharacteristic
166C2×C4×D4C2×D4311yescharacteristic
167C22×C4⋊C4—431no—
168#431—861no—
169C2×#99—21no—
170#400—432no—
171#399—432no—
172#389—861no—
173#386—861no—
174#385—861no—
175#380—21no—
176#380—431no—
177#380—861no—
178#342C2×D4312yes—
179#323—432no—
180#323—861no—
181C43#1189911yescharacteristic, complemented, Sylow
182C22×D4C22⋊D4311yescharacteristic
183C23×C4—861no—
184C23×C4C4×D4311yescharacteristic
185C23×C4C22⋊D4311yescharacteristic
186C4×D4—41no—
187C4×D4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—432no—
190C2×C4⋊C4—862no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—1721no—
194C2×C4⋊C4—1721no—
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—862no—
198C2×C22⋊C4—861no—
199C2×C22⋊C4D17211yescharacteristic
200C2×C22⋊C4C22×D4311yescharacteristic
201C2×C42D17211yescharacteristic
202C4⋊C8—1721no—
203#99—42no—
204C22⋊C8—862no—
205C4×C8—1721no—
206#95—41no—
207#95—432no—
208#95—862no—
209#95—862no—
210C24(C2×D43)⋊C411yescharacteristic
211C24C2×C22⋊D4311yescharacteristic
212C2×D4—41no—
213C2×D4—41no—
214C2×D4#1062188312yes—
215C2×D4#1062188512yes—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—862no—
224C22×C4—862no—
225C22×C4—3442no—
226C22×C4—1722no—
227C22×C4(C2×D43)⋊C411yescharacteristic
228C22×C4(C2×D43)⋊C411yescharacteristic
229C22×C4(C2×D43)⋊C411yescharacteristic
230C22×C4C2×C4×D4311yescharacteristic
231C22×C4C2×D17211yescharacteristic
232C2×C8—1722no—
233C4⋊C4—41no—
234C4⋊C4—82no—
235C4⋊C4—3442no—
236C4⋊C4—1722no—
237C4⋊C4—1722no—
238C4⋊C4—1721no—
239C4⋊C4—1721no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—3442no—
245C22⋊C4—1722no—
246C42—21no—
247C42—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#1306324812yes—
257C23C2×(C2×D43)⋊C411yescharacteristic
258C23C2×#1062188311yescharacteristic
259C23C2×#1062188511yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—3444no—
279C2×C4—1722no—
280C2×C4—1722no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4—1722no—
284C2×C4—1722no—
285C2×C4#1306323911yescharacteristic
286C2×C4#1306323911yescharacteristic
287C2×C4#1306324812yes—
288C8—3442no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#1306323911yescharacteristic
304C22C2×#1306324811yescharacteristic
305C22#1458291711yescharacteristic
306C4—21no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—162no—
312C4—3442no—
313C4—3442no—
314C4#1458268812yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2#1913316611yescharacteristic
321C2C2×#1458268811yescharacteristic
322C2#1913626611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1799D43
hypocenterC43#11899
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #19132618C2semidirect
5. C22×C4⋊Dic43C4semidirect
7. #14582838C4semidirect
13. #14582759C4semidirect
181. C43#11899semidirect

Maximal subgroups

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

subgroupindex
#191389122
#191329162
#191326182
C43×#17992
#1189943