Finite Group Databasebeta

← #25007338

Subgroups — #25007338

Order 11008.

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

normal subgroups only

This group has 388 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#19132624C212yesmaximal, complemented
4#19132621C212yesmaximal, complemented
5C43×#1822C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic
7#14582956—21no—
8#14582838C2211yescharacteristic
9#14582835C411yescharacteristic
10#14582832—21no—
11#14582822—21no—
12#14582819C2211yescharacteristic
13#14582811C411yescharacteristic
14C4×Dic43⋊C4—21no—
15C4×C4⋊Dic43C411yescharacteristic
16C4×C22⋊Dic43—21no—
17#14582625C2212yes—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
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
45C2×M16×C43—22no—
46#117×C43—41no—
47#117×C43—41no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43C2311yescharacteristic
50C2×C22⋊C4×C43C2×C411yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C22⋊C8×C43—41no—
55C22⋊C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—41no—
72C2×Dic86—42no—
73M16×C43—42no—
74M16×C43—42no—
75C2×C8×C43—42no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—41no—
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—21no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43C2×C22⋊C411yescharacteristic
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—42no—
110C2×C4×C43—42no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43#9911yescharacteristic
116C2×C4×C43#9911yescharacteristic
117C2×C4×C43#13712yes—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130Dic86—42no—
131Dic86—42no—
132C8×C43—82no—
133C43⋊C8—82no—
134#11816—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—42no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—81no—
142C22×C43C2×#9911yescharacteristic
143C22×C43#41911yescharacteristic
144C22×C43#42111yescharacteristic
145C4×C43—22no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152Dic43—42no—
153Dic43—42no—
154Dic43—81no—
155Dic43—81no—
156#2396—431no—
157#1822D4311yescharacteristic
158#1464—431no—
159#1354—432no—
160#1353—432no—
161C2×C43—21no—
162C2×C43—21no—
163C2×C43—81no—
164C2×C43#151111yescharacteristic
165C2×C43#212011yescharacteristic
166C2×C43#213211yescharacteristic
167C2×C4×Q8—431no—
168C2×#117C2×D4311yescharacteristic
169#432—861no—
170#407—21no—
171#400—431no—
172#399—431no—
173#398—861no—
174#396—861no—
175#395—431no—
176#393—431no—
177C4×C4⋊C4—431no—
178C4×C4⋊C4—861no—
179C4×C22⋊C4—861no—
180#343—21no—
181#343C2×D4312yes—
182#324—432no—
183#323—861no—
184C43#1181611yescharacteristic, complemented, Sylow
185C22×Q8—431no—
186C23×C4C22⋊D4311yescharacteristic
187C2×M16—22no—
188C4×Q8—1721no—
189C4×Q8—1721no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C4⋊C4C22×D4311yescharacteristic
199C2×C22⋊C4—861no—
200C2×C22⋊C4—861no—
201C2×C22⋊C4C4×D4311yescharacteristic
202C2×C22⋊C4D17211yescharacteristic
203C2×C42—861no—
204C2×C42—861no—
205C2×C42C4×D4311yescharacteristic
206C2×C42D17211yescharacteristic
207C4⋊C8—1721no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—862no—
211#97—1721no—
212#95—431no—
213#95—431no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218C24(C2×D43)⋊C411yescharacteristic
219C2×Q8—1721no—
220C2×Q8—1722no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4(C2×D43)⋊C411yescharacteristic
230C22×C4(C2×D43)⋊C411yescharacteristic
231C22×C4(C2×D43)⋊C411yescharacteristic
232C22×C4C2×C4×D4311yescharacteristic
233C22×C4C2×D17211yescharacteristic
234C22×C4C2×C22⋊D4311yescharacteristic
235M16—42no—
236M16—42no—
237C2×C8—42no—
238C2×C8—1722no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—1721no—
242C4⋊C4—1722no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—1722no—
249C22⋊C4—1722no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—1722no—
255C42—1721no—
256C42—1721no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×(C2×D43)⋊C411yescharacteristic
263Q8—1722no—
264Q8—1722no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4#1306323911yescharacteristic
292C2×C4#1306323911yescharacteristic
293C2×C4#1306335512yes—
294C8—82no—
295C8—3442no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#1306323911yescharacteristic
304C22#1458290711yescharacteristic
305C22#1458291711yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3441no—
314C4—3441no—
315C4—1722no—
316C4—1722no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1913312711yescharacteristic
321C2#1913623711yescharacteristic
322C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1822C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1822D43
hypocenterC43#11816
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #19132624C2semidirect
4. #19132621C2semidirect
184. C43#11816semidirect

Maximal subgroups

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

subgroupindex
#191378632
#191329292
#191326242
#191326212
C43×#18222
#1181643