Finite Group Databasebeta

← #25007403

Subgroups — #25007403

Order 11008.

416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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#19134591C211yesmaximal, characteristic, complemented
2#19132939C211yesmaximal, characteristic, complemented
3#19132622C212yesmaximal, complemented
4#19132598C212yesmaximal
5C43×#2398C211yesmaximal, characteristic
6#14582956—21no—
7#14582923—21no—
8C2×#13063244—21no—
9#14582668C2212yes—
10#14582625—21no—
11#14582625C2212yes—
12C2×C4×Q8×C43C2211yescharacteristic
13C2×C4×D4×C43C411yescharacteristic
14C43×#400C411yescharacteristic
15C43×#400C2211yescharacteristic
16C43×#397—21no—
17C43×#394C411yescharacteristic
18C43×#394C2211yescharacteristic
19C43×#393—21no—
20C4×C22⋊C4×C43—21no—
21C4×C22⋊C4×C43—21no—
22C43×#376C411yescharacteristic
23C2×#10621877—22no—
24C4⋊(C43⋊C8)—41no—
25C4⋊(C43⋊C8)—41no—
26C4⋊(C43⋊C8)—41no—
27#13063244—42no—
28C22⋊(C43⋊C8)—22no—
29#13063236—41no—
30C22×Q8×C43D411yescharacteristic
31C22×D4×C43C2×C411yescharacteristic
32C23×C4×C43—21no—
33C4×Q8×C43—41no—
34C4×Q8×C43—41no—
35C4×D4×C43—41no—
36C4×D4×C43—41no—
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C42×C43—21no—
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43C2×C411yescharacteristic
56#95×C43C2×C411yescharacteristic
57C24×C43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×D4×C43—42no—
63C2×D4×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—42no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—42no—
95#10621877—42no—
96#10621877—42no—
97C2×C43⋊C8—42no—
98C2×C43⋊C8—42no—
99C23×C43—22no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107Q8×C43—42no—
108Q8×C43—42no—
109D4×C43—42no—
110D4×C43—42no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—22no—
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—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—82no—
136C2×C4×C43—82no—
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#9911yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C43⋊C8—82no—
142C43⋊C8—82no—
143#11829—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43C2×#9911yescharacteristic
154C22×C43#41711yescharacteristic
155C22×C43#42111yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43#35512yes—
168#2398D4311yescharacteristic
169#1801—431no—
170#1467—431no—
171#1353—432no—
172#1345—432no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43—82no—
176C2×C43#151311yescharacteristic
177C2×C43#212011yescharacteristic
178C2×C43C2×#35511yescharacteristic
179C2×C4×Q8C2×D4311yescharacteristic
180C2×C4×D4Dic4311yescharacteristic
181#432—861no—
182#423—861no—
183C2×#101—861no—
184#400Dic4311yescharacteristic
185#400C2×D4311yescharacteristic
186#397—21no—
187#394Dic4311yescharacteristic
188#394C2×D4311yescharacteristic
189#393—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192#376Dic4311yescharacteristic
193#343—432no—
194#324—432no—
195#324—861no—
196C43#1182911yescharacteristic, complemented, Sylow
197C22×Q8C22⋊D4311yescharacteristic
198C22×D4C2×Dic4311yescharacteristic
199C23×C4—21no—
200C2×M16—862no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4C2×Dic4311yescharacteristic
206C2×C4⋊C4C2×Dic4311yescharacteristic
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C4⋊C4C22×D4311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42—21no—
215C2×C42C2×Dic4311yescharacteristic
216C2×C42C22⋊D4311yescharacteristic
217C2×C42C22⋊D4311yescharacteristic
218C4⋊C8—1721no—
219C4⋊C8—1721no—
220C4⋊C8—1721no—
221#101—1722no—
222C22⋊C8—862no—
223#97—1721no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×Dic4311yescharacteristic
230#95C2×Dic4311yescharacteristic
231C24—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—41no—
237C2×D4—42no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊Dic4311yescharacteristic
246C22×C4C22⋊Dic4311yescharacteristic
247C22×C4C22⋊Dic4311yescharacteristic
248C22×C4C22⋊Dic4311yescharacteristic
249C22×C4C22×Dic4311yescharacteristic
250C22×C4C2×C22⋊D4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—1722no—
253M16—1722no—
254C2×C8—1722no—
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—42no—
273C23—22no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊Dic4311yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4#1306324011yescharacteristic
312C2×C4#1306324011yescharacteristic
313C2×C4#1306335011yescharacteristic
314C2×C4#1306335511yescharacteristic
315C8—3442no—
316C8—3442no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×#1306324011yescharacteristic
327C22#1458290011yescharacteristic
328C22#1458291611yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4#1458269612yes—
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1913313811yescharacteristic
345C2#1913623611yescharacteristic
346C2C2×#1458269611yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2398C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2398D43
hypocenterC43#11829
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #19134591C2semidirect
2. #19132939C2semidirect
3. #19132622C2semidirect
196. C43#11829semidirect

Maximal subgroups

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

subgroupindex
#191345912
#191329392
#191326222
#191325982
C43×#23982
#1182943