Finite Group Databasebeta

← #24993388

Subgroups — #24993388

Order 11008.

416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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#19144402C211yesmaximal, characteristic
2#19143678C211yesmaximal, characteristic
3#19134611C211yesmaximal, characteristic
4#19133160C211yesmaximal, characteristic
5#19132997C211yesmaximal, characteristic
6#19132455C211yesmaximal, characteristic
7C43×#1301C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583207—22no—
11#14583195C412yescomplemented
12#14583185C412yescomplemented
13#14583029—22no—
14#14583026—22no—
15#14582953—22no—
16#14582952C2211yescharacteristic
17#14582941—21no—
18#14582909—21no—
19C2×#13063250—21no—
20#14582765C2211yescharacteristic
21#14582662—21no—
22#14582637—22no—
23#14582629—22no—
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28#13063325C2×C411yescharacteristic
29#13063325C2×C411yescharacteristic
30#13063317—21no—
31#13063304—21no—
32#13063304—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C4×Dic86C2×C412yes—
38C4×Dic86D412yes—
39#13063284—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×C4×Dic43—21no—
44#13063259—22no—
45#13063257—22no—
46C4⋊(C43⋊C8)—21no—
47Dic43⋊C8—24no—
48#13063250—22no—
49#13063250—22no—
50#13063250—42no—
51C22⋊(C43⋊C8)—21no—
52#13063235—24no—
53C4×C43⋊C8D412yes—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C2×M16×C43—21no—
57C22×C8×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43C2×C412yes—
64C22⋊C8×C43D412yes—
65C4×C8×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—41no—
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×Dic86—21no—
79C2×Dic86C22⋊C412yes—
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—22no—
83C2×C8×C43—22no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C42×C43C22×C411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43C2×D411yescharacteristic
90C42×C43#4111yescharacteristic
91C22⋊Dic43—41no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43C22⋊C412yes—
100Dic43⋊C4—22no—
101Dic43⋊C4—22no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104C4×Dic43—22no—
105C4×Dic43—22no—
106C4×Dic43—41no—
107C2×C43⋊C8—22no—
108C23×C43#12111yescharacteristic
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43C2×C22⋊C411yescharacteristic
112C2×C4×C43C4×D411yescharacteristic
113C2×C4×C43C4×D411yescharacteristic
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12311yescharacteristic
117C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C43#13711yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131Dic86—22no—
132Dic86—22no—
133Dic86—41no—
134Dic86—41no—
135Dic86—42no—
136Dic86—81no—
137C8×C43—42no—
138C8×C43—42no—
139C8×C43—81no—
140C43⋊C8—42no—
141#9308—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43#38611yescharacteristic
145C22×C43#46811yescharacteristic
146C22×C43#47011yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43#41711yescharacteristic
152C4×C43#41911yescharacteristic
153C4×C43#46811yescharacteristic
154C4×C43#47011yescharacteristic
155Dic43—42no—
156Dic43—42no—
157Dic43—81no—
158Dic43—81no—
159Dic43—161no—
160#3078—431no—
161#2983—431no—
162#1805—431no—
163#1518—431no—
164#1481—431no—
165#1301D4311yescharacteristic
166#1286—431no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#188111yescharacteristic
170C2×C43#189411yescharacteristic
171C2×C43#190511yescharacteristic
172#533—431no—
173C2×C4×Q8—431no—
174#479—862no—
175#477—432no—
176#475—432no—
177#446—862no—
178#446—862no—
179#432—862no—
180#431—431no—
181#431C2×D4311yescharacteristic
182#428—861no—
183#423C2×D4311yescharacteristic
184C2×C4⋊C8C2×D4311yescharacteristic
185#419—861no—
186C2×#103—861no—
187#382—431no—
188#340—861no—
189#328—862no—
190Q8⋊C8—862no—
191C43#930811yescharacteristic, complemented, Sylow
192C22×Q8—431no—
193C2×M16—21no—
194C22×C8—21no—
195C4⋊Q8—431no—
196C4⋊Q8—431no—
197#125—861no—
198C22⋊Q8—861no—
199C22⋊Q8—861no—
200C4×Q8—432no—
201C4×Q8—432no—
202C4×Q8—861no—
203C4×Q8—861no—
204C4×Q8—861no—
205C4×Q8—861no—
206#117—861no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C42—861no—
211C2×C42C22×D4311yescharacteristic
212#107—862no—
213#106—862no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—864no—
219C4⋊C8—861no—
220C4⋊C8C4×D4312yes—
221#103—862no—
222#103—862no—
223#103—1722no—
224C22⋊C8—861no—
225C22⋊C8D17212yes—
226#97—864no—
227C4×C8—21no—
228C4×C8—432no—
229#95—861no—
230#95—861no—
231C2×Q8—432no—
232C2×Q8—861no—
233C2×Q8—861no—
234C2×Q8—861no—
235C2×Q8—861no—
236C2×Q8—861no—
237C2×Q8—861no—
238C2×Q8—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1721no—
242C22×C4C2×D17211yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4#1062190211yescharacteristic
245M16—41no—
246M16—41no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—862no—
253C4⋊C4—432no—
254C4⋊C4—862no—
255C4⋊C4—861no—
256C4⋊C4—862no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—1721no—
266C42—862no—
267C42—862no—
268C42—1721no—
269C42C2×C4×D4311yescharacteristic
270C42#1062189811yescharacteristic
271C42D4×D4311yescharacteristic
272C42D4×D4311yescharacteristic
273C23#1306330011yescharacteristic
274Q8—862no—
275Q8—862no—
276Q8—3441no—
277Q8—1722no—
278Q8—1721no—
279Q8—1721no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—3441no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4C22⋊C4×D4311yescharacteristic
293C2×C4#1306328711yescharacteristic
294C2×C4C4×D17211yescharacteristic
295C2×C4#1306329511yescharacteristic
296C2×C4#1306329811yescharacteristic
297C2×C4#1306331011yescharacteristic
298C2×C4#1306334911yescharacteristic
299C2×C4#1306335411yescharacteristic
300C2×C4#1306335411yescharacteristic
301C2×C4#1306335711yescharacteristic
302C8—42no—
303C8—42no—
304C8—81no—
305C8—1722no—
306C22—21no—
307C22—21no—
308C22#1458277711yescharacteristic
309C22#1458314611yescharacteristic
310C22#1458315811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—3441no—
316C4—3441no—
317C4—1722no—
318C4—1722no—
319C4—6881no—
320C4#1458289711yescharacteristic
321C4#1458290611yescharacteristic
322C4#1458314411yescharacteristic
323C4#1458315611yescharacteristic
324C2—21no—
325C2—21no—
326C2#1913495811yescharacteristic
327C2#1913502711yescharacteristic
328C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9308
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
11. #14583195C4semidirect
12. #14583185C4semidirect
191. C43#9308semidirect

Maximal subgroups

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

subgroupindex
#191444022
#191436782
#191346112
#191331602
#191329972
#191324552
C43×#13012
#930843