Finite Group Databasebeta

← #25006156

Subgroups — #25006156

Order 11008.

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

normal subgroups only

This group has 408 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#19139053C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic, complemented
3#19132538C212yesmaximal, complemented
4#19132526C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic, complemented
6C2×#13063299C411yescharacteristic
7#14582956—21no—
8#14582814—21no—
9#14582814—21no—
10#14582800C411yescharacteristic
11#14582800C2211yescharacteristic
12#14582790—21no—
13#14582790—21no—
14#14582768C411yescharacteristic
15#14582764C2211yescharacteristic
16C4×C22⋊Dic43C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25#13063299—41no—
26#13063299—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38C4⋊(C43⋊C8)—41no—
39C22⋊(C43⋊C8)—22no—
40#13063236—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C4⋊C4×C43C2311yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55C4×C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C23×D43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C2×C22⋊D43—42no—
69C2×C22⋊D43—81no—
70C2×C22⋊D43—81no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C2×D172—22no—
75C2×D172—41no—
76C2×D172—41no—
77C2×C8×C43—42no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—42no—
87(C2×D43)⋊C4—42no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4—81no—
92(C2×D43)⋊C4—81no—
93C4⋊Dic43—41no—
94Dic43⋊C4—81no—
95Dic43⋊C4—81no—
96C4×Dic43—22no—
97C4×Dic43—41no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#13112yes—
129C22⋊D43—84no—
130C2×Dic43—22no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139D172—82no—
140C8×C43—82no—
141C43⋊C8—82no—
142#11550—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43#40811yescharacteristic
151C22×C43C2×#9911yescharacteristic
152C22×C43#41311yescharacteristic
153C2×D43—81no—
154C2×D43—81no—
155C2×D43—81no—
156C2×D43—81no—
157C2×D43—81no—
158C2×D43—81no—
159C2×D43—81no—
160C4×C43—22no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167Dic43—42no—
168Dic43—81no—
169Dic43—81no—
170#2500—431no—
171#1464—431no—
172#1458D4311yescharacteristic, complemented
173#1324—432no—
174#1318—432no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—81no—
178C2×C43#146811yescharacteristic
179C2×C43#212611yescharacteristic
180C2×C43#213411yescharacteristic
181D43—161no—
182C2×#121—431no—
183C2×#117C2×D4311yescharacteristic
184#432—861no—
185#431—21no—
186#394—861no—
187#394—861no—
188#390—431no—
189#390—431no—
190#388—861no—
191#388—861no—
192#384—431no—
193#382—431no—
194C4×C22⋊C4—431no—
195#324—432no—
196#324C2×D4312yes—
197#323—21no—
198#323—861no—
199C43#1155011yescharacteristic, complemented, Sylow
200C22×D4—431no—
201C22×D4—861no—
202C23×C4C4×D4311yescharacteristic
203#121—1721no—
204#121—1721no—
205#117—41no—
206#117—41no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4C4×D4311yescharacteristic
211C2×C4⋊C4C22×D4311yescharacteristic
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4D17211yescharacteristic
219C2×C22⋊C4C22⋊D4311yescharacteristic
220C2×C42—431no—
221C2×C42—431no—
222C2×C42D17211yescharacteristic
223C2×C42C22⋊D4311yescharacteristic
224C4⋊C8—41no—
225C4⋊C8—1721no—
226C22⋊C8—22no—
227C22⋊C8—862no—
228#97—1721no—
229C4×C8—41no—
230#95—861no—
231#95—861no—
232#95—861no—
233C24—861no—
234C24(C2×D43)⋊C411yescharacteristic
235C2×D4—862no—
236C2×D4—3441no—
237C2×D4—3441no—
238C2×D4—1721no—
239C2×D4—1721no—
240C2×D4—1722no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4C2×D17211yescharacteristic
253C22×C4C2×C22⋊D4311yescharacteristic
254C2×C8—42no—
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—3441no—
259C4⋊C4—3441no—
260C4⋊C4—1721no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—3441no—
264C22⋊C4—3441no—
265C22⋊C4—1722no—
266C22⋊C4—1722no—
267C22⋊C4—1722no—
268C22⋊C4—1721no—
269C22⋊C4—1721no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—862no—
275C42—1721no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—1721no—
282C23—1721no—
283C23—1721no—
284C23—1721no—
285C23—1721no—
286C23—1721no—
287C23—1721no—
288C23C2×(C2×D43)⋊C411yescharacteristic
289D4—3442no—
290D4—3444no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—862no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4#1306323911yescharacteristic
315C2×C4#1306323911yescharacteristic
316C2×C4#1306333112yes—
317C8—82no—
318C8—3442no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—3441no—
327C22—3441no—
328C22—3441no—
329C22—3441no—
330C22—3441no—
331C22—3441no—
332C22—3441no—
333C22#1458286511yescharacteristic
334C22C2×#1306323911yescharacteristic
335C22#1458288111yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3441no—
344C4—3441no—
345C4—1722no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—6881no—
350C2#1913294111yescharacteristic
351C2#1913625811yescharacteristic
352C2#1913628611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1458C2
socleC22×C43C2×#99
prime radicalC2×#13063299C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1458D43
hypocenterC43#11550
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19132929C2semidirect
3. #19132538C2semidirect
4. #19132526C2semidirect
5. C43×#1458C2semidirect
172. #1458D43semidirect
199. C43#11550semidirect

Maximal subgroups

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

subgroupindex
#191390532
#191329292
#191325382
#191325262
C43×#14582
#1155043