Finite Group Databasebeta

← #25007312

Subgroups — #25007312

Order 11008.

402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 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#19137863C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic
3#19132618C212yesmaximal
4#19132615C212yesmaximal
5C43×#1820C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic, complemented
7#14582956—21no—
8#14582838C411yescharacteristic, complemented
9#14582835C2211yescharacteristic
10#14582832—21no—
11#14582822—21no—
12#14582819C411yescharacteristic, complemented
13#14582811C2211yescharacteristic
14C4×Dic43⋊C4—21no—
15C4×C4⋊Dic43C411yescharacteristic, complemented
16C4×C22⋊Dic43—21no—
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#381—21no—
21C43×#342—21no—
22C43×#342C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C4×Dic86—41no—
25C4×Dic86—41no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—21no—
35C4⋊(C43⋊C8)—41no—
36C22⋊(C43⋊C8)—22no—
37#13063236—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43C2311yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54#95×C43—41no—
55#95×C43—41no—
56C24×C43C2×D411yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—41no—
61C22×C4×C43—42no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×Dic86—41no—
73C2×Dic86—42no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C22⋊C4×C43—41no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C22⋊Dic43—42no—
85C22⋊Dic43—42no—
86C4⋊Dic43—42no—
87C4⋊Dic43—41no—
88Dic43⋊C4—42no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91C4×Dic43—42no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43C2×C22⋊C411yescharacteristic
100C23×C43#13712yes—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—82no—
117C2×C4×C43—82no—
118C2×C4×C43—82no—
119C2×C4×C43#9911yescharacteristic
120C2×C4×C43#9911yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133Dic86—42no—
134Dic86—42no—
135C43⋊C8—82no—
136#11810—431nomaximal, Sylow
137C22×C43—21no—
138C22×C43—21no—
139C22×C43—22no—
140C22×C43—42no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—81no—
144C22×C43C2×#9911yescharacteristic
145C22×C43#41911yescharacteristic
146C22×C43#42111yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—162no—
155Dic43—42no—
156Dic43—42no—
157Dic43—81no—
158Dic43—81no—
159#2396—431no—
160#1820D4311yescharacteristic
161#1464—431no—
162#1352—432no—
163#1351—432no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—42no—
167C2×C43#151111yescharacteristic
168C2×C43#212011yescharacteristic
169C2×C43#212611yescharacteristic
170C2×C4×Q8—431no—
171C2×#117C2×D4311yescharacteristic
172#432—861no—
173#400—431no—
174#399—431no—
175#398—861no—
176#396—861no—
177#395—431no—
178#393—431no—
179#381—21no—
180C4×C4⋊C4—431no—
181C4×C4⋊C4—861no—
182C4×C22⋊C4—861no—
183#342—21no—
184#342C2×D4312yes—
185#324—861no—
186#323—432no—
187C43#1181011yescharacteristic, complemented, Sylow
188C22×Q8—431no—
189C23×C4C22⋊D4311yescharacteristic
190C4×Q8—1721no—
191C4×Q8—1721no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4C4×D4311yescharacteristic
200C2×C4⋊C4D17211yescharacteristic
201C2×C22⋊C4—22no—
202C2×C22⋊C4—861no—
203C2×C22⋊C4—861no—
204C2×C22⋊C4C22⋊D4311yescharacteristic
205C2×C22⋊C4C22×D4311yescharacteristic
206C2×C42—861no—
207C2×C42—861no—
208C2×C42C4×D4311yescharacteristic
209C2×C42D17211yescharacteristic
210C4⋊C8—1721no—
211C22⋊C8—862no—
212#97—1721no—
213#95—41no—
214#95—41no—
215#95—431no—
216#95—431no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221C24C2×C22⋊D4311yescharacteristic
222C2×Q8—1721no—
223C2×Q8—1722no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—42no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4(C2×D43)⋊C411yescharacteristic
234C22×C4(C2×D43)⋊C411yescharacteristic
235C22×C4(C2×D43)⋊C411yescharacteristic
236C22×C4(C2×D43)⋊C411yescharacteristic
237C22×C4C2×C4×D4311yescharacteristic
238C22×C4C2×D17211yescharacteristic
239C2×C8—1722no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1721no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C4⋊C4—1722no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—1722no—
252C22⋊C4—1722no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—1722no—
258C42—1721no—
259C42—1721no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×(C2×D43)⋊C411yescharacteristic
265C23#1306335512yes—
266Q8—1722no—
267Q8—1722no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4#1306323911yescharacteristic
299C2×C4#1306323911yescharacteristic
300C8—3442no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#1306323911yescharacteristic
309C22#1458290711yescharacteristic
310C22#1458291711yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—162no—
319C4—3441no—
320C4—3441no—
321C4—1722no—
322C4—1722no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1913312711yescharacteristic
327C2#1913623411yescharacteristic
328C2#1913625811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1820C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1820D43
hypocenterC43#11810
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
6. C2×C4×Dic86C4semidirect
8. #14582838C4semidirect
12. #14582819C4semidirect
15. C4×C4⋊Dic43C4semidirect
187. C43#11810semidirect

Maximal subgroups

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

subgroupindex
#191378632
#191329292
#191326182
#191326152
C43×#18202
#1181043