Finite Group Databasebeta

← #25007508

Subgroups — #25007508

Order 11008.

396 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 83 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#19138882C211yesmaximal, characteristic
2C2×#14582625C211yesmaximal, characteristic
3#19132621C212yesmaximal, complemented
4#19132600C212yesmaximal, complemented
5C43×#1821C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7C2×C22⋊(C43⋊C8)—21no—
8#14582838C411yescharacteristic
9#14582838C2211yescharacteristic
10#14582829C411yescharacteristic
11#14582829C2211yescharacteristic
12#14582780—21no—
13#14582780—21no—
14#14582772—21no—
15#14582762—21no—
16#14582762C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
23C22×C43⋊C8—41no—
24#13063284—41no—
25#13063284—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C4×Dic43—21no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—41no—
35C43⋊#95—21no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—22no—
48C2×C4⋊C4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43C2311yescharacteristic
54C22⋊C8×C43—41no—
55C22⋊C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77M16×C43—42no—
78M16×C43—42no—
79C2×C8×C43—42no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊Dic43—42no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91C4×Dic43—42no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—82no—
94C23×C43—22no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43#9911yescharacteristic
99C23×C43#9911yescharacteristic
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—21no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—81no—
120C2×C4×C43#13512yes—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—42no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C8×C43—82no—
133C43⋊C8—82no—
134#11850—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—42no—
143C22×C43—42no—
144C22×C43#35212yes—
145C22×C43C2×#9911yescharacteristic
146C22×C43#41611yescharacteristic
147C22×C43#42111yescharacteristic
148C4×C43—22no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—41no—
154Dic43—81no—
155Dic43—81no—
156Dic43—81no—
157Dic43—81no—
158#2484—431no—
159#1821D4311yescharacteristic
160C2×#324—431no—
161#1353—432no—
162#1346—432no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—22no—
166C2×C43—41no—
167C2×C43#151611yescharacteristic
168C2×C43C2×#35211yescharacteristic
169C2×C43#213311yescharacteristic
170C2×#117—431no—
171C22×C4⋊C4C2×D4311yescharacteristic
172#407—21no—
173C2×C22⋊C8—861no—
174#400—431no—
175#400—431no—
176#398—431no—
177#398—431no—
178#387—861no—
179#387—861no—
180#385—861no—
181#381—431no—
182#381—861no—
183#343—21no—
184#343C2×D4312yes—
185#324—432no—
186#324—861no—
187C43#1185011yescharacteristic, complemented, Sylow
188C23×C4C4×D4311yescharacteristic
189C23×C4D17211yescharacteristic
190C23×C4C22⋊D4311yescharacteristic
191C2×M16—22no—
192C22×C8—1721no—
193#117—1721no—
194#117—1721no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4C4×D4311yescharacteristic
202C2×C4⋊C4D17211yescharacteristic
203C2×C4⋊C4C22⋊D4311yescharacteristic
204C2×C4⋊C4C22×D4311yescharacteristic
205C2×C22⋊C4—861no—
206C2×C22⋊C4—861no—
207C2×C42—861no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—862no—
211C22⋊C8—1721no—
212#95—431no—
213#95—431no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221C24(C2×D43)⋊C411yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4(C2×D43)⋊C411yescharacteristic
237C22×C4(C2×D43)⋊C411yescharacteristic
238C22×C4(C2×D43)⋊C411yescharacteristic
239C22×C4C2×C4×D4311yescharacteristic
240C22×C4C2×D17211yescharacteristic
241C22×C4C2×C22⋊D4311yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—42no—
245C2×C8—3442no—
246C2×C8—1722no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—1721no—
252C4⋊C4—1721no—
253C4⋊C4—1722no—
254C4⋊C4—1722no—
255C22⋊C4—1722no—
256C22⋊C4—1721no—
257C22⋊C4—1721no—
258C42—1722no—
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23#1306323911yescharacteristic
264C23#1306323911yescharacteristic
265C23C2×(C2×D43)⋊C411yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1722no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4#1306334512yes—
297C8—82no—
298C8—3442no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1458269012yes—
309C22C2×#1306323911yescharacteristic
310C22#1458289311yescharacteristic
311C22#1458291711yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3441no—
319C4—3441no—
320C4—3441no—
321C4—3441no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#1913314911yescharacteristic
327C2C2×#1458269011yescharacteristic
328C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1821C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1821D43
hypocenterC43#11850
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #19132621C2semidirect
4. #19132600C2semidirect
187. C43#11850semidirect

Maximal subgroups

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

subgroupindex
#191388822
C2×#145826252
#191326212
#191326002
C43×#18212
#1185043