Finite Group Databasebeta

← #25007168

Subgroups — #25007168

Order 11008.

652 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139541C211yesmaximal, characteristic
2C4×#13063240C211yesmaximal, characteristic, complemented
3#19132593C214yesmaximal, complemented
4C43×#1465C211yesmaximal, characteristic, complemented
5C2×#13063322C411yescharacteristic, complemented
6C2×#13063321—21no—
7C2×#13063299—21no—
8C2×#13063299—21no—
9C2×#13063240—21no—
10#14582808C412yescomplemented
11#14582808C2212yes—
12#14582800—21no—
13C4×C4⋊Dic43C411yescharacteristic, complemented
14C4×C22⋊Dic43—21no—
15#14582666C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324—21no—
19C43×#323C2212yes—
20C22×D172—21no—
21C22×D172—21no—
22C22×D172C2×C412yes—
23C22×C22⋊D43—22no—
24C22×C22⋊D43—22no—
25#13063322—41no—
26#13063322—41no—
27#13063321—44no—
28#13063299—44no—
29#13063299—44no—
30C2×C4⋊Dic43—21no—
31C2×C22⋊Dic43—22no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—41no—
36#13063240—24no—
37C43⋊#95—41no—
38C43⋊#95C2×C412yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C2×M16×C43—41no—
43C4×D4×C43—41no—
44C4×D4×C43—41no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43C2311yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49C22⋊C8×C43—22no—
50C22⋊C8×C43—41no—
51C24×C43C22⋊C411yescharacteristic
52C24×C43C2×D411yescharacteristic
53C23×D43—22no—
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43—41no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C2×C22⋊D43—44no—
69C2×C22⋊D43—44no—
70C2×C22⋊D43—44no—
71C2×C22⋊D43—44no—
72C2×C22⋊D43—82no—
73C2×C22⋊D43—82no—
74C22×Dic43—22no—
75C22×Dic43—42no—
76C2×D172—42no—
77C2×D172—42no—
78C2×D172—42no—
79C2×D172—42no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—42no—
83C2×D172—42no—
84C2×D172—82no—
85M16×C43—82no—
86C2×C8×C43—42no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C42×C43—21no—
91C42×C43—21no—
92C22⋊Dic43—24no—
93C22⋊Dic43—42no—
94(C2×D43)⋊C4—44no—
95(C2×D43)⋊C4—44no—
96C4⋊Dic43—24no—
97C4×Dic43—42no—
98C4×Dic43—82no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43C2×C22⋊C411yescharacteristic
109C23×C43AGL(1,ℤ/8)12yes—
110C22×D43—42no—
111C22×D43—42no—
112C22×D43—42no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—42no—
117D4×C43—44no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#9911yescharacteristic
132C2×C4×C43#9911yescharacteristic
133C2×C4×C43#10412yes—
134C22⋊D43—88no—
135C22⋊D43—88no—
136C2×Dic43—24no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43—44no—
140C2×Dic43—82no—
141C2×Dic43—82no—
142D172—82no—
143D172—84no—
144D172—84no—
145D172—82no—
146C8×C43—82no—
147#11776—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—22no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43C2×#9911yescharacteristic
161C22×C43#41811yescharacteristic
162C22×C43C2×#10411yescharacteristic
163C2×D43—82no—
164C2×D43—82no—
165C2×D43—82no—
166C2×D43—82no—
167C2×D43—82no—
168C2×D43—82no—
169C2×D43—82no—
170C4×C43—21no—
171C4×C43—22no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43#35312yes—
176Dic43—44no—
177Dic43—84no—
178#2541—431no—
179C4×#99—431no—
180#1465D4311yescharacteristic, complemented
181#1343—434no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—42no—
185C2×C43—81no—
186C2×C43#150711yescharacteristic
187C2×C43#212211yescharacteristic
188C2×C43C2×#35311yescharacteristic
189D43—162no—
190C2×#127—431no—
191C2×#127—861no—
192C2×#121—861no—
193C2×#121—861no—
194C2×C4×D4C2×D4311yescharacteristic
195C2×#99—861no—
196#407—21no—
197#392—432no—
198#392—432no—
199#390—861no—
200C4×C4⋊C4—431no—
201C4×C22⋊C4—861no—
202#342—432no—
203#324—21no—
204#323C2×D4312yes—
205C43#1177611yescharacteristic, complemented, Sylow
206C22×D4—432no—
207C22×D4—862no—
208C22×D4—862no—
209C22×D4—861no—
210C22×D4—861no—
211C22×D4D17211yescharacteristic
212C23×C4D17211yescharacteristic
213C23×C4C22⋊D4311yescharacteristic
214C2×M16—41no—
215#127—1721no—
216#127—1721no—
217#127—1724no—
218#121—1724no—
219#121—1724no—
220C4×D4—41no—
221C4×D4—41no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C22⋊C4—862no—
225C2×C22⋊C4—862no—
226C2×C22⋊C4—862no—
227C2×C22⋊C4C4×D4311yescharacteristic
228C2×C22⋊C4C22×D4311yescharacteristic
229C2×C42—861no—
230C2×C42—1721no—
231C2×C42C4×D4311yescharacteristic
232#99—864no—
233C22⋊C8—22no—
234C22⋊C8—41no—
235#95—432no—
236#95—1721no—
237C24—862no—
238C24(C2×D43)⋊C411yescharacteristic
239C24C2×D17211yescharacteristic
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—3442no—
244C2×D4—3442no—
245C2×D4—3442no—
246C2×D4—1722no—
247C2×D4—1722no—
248C2×D4—1722no—
249C2×D4—1722no—
250C2×D4—1722no—
251C2×D4—1724no—
252C2×D4—1724no—
253C2×D4—1724no—
254C2×D4—1724no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1722no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—862no—
265C22×C4—1722no—
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4C2×C4×D4311yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271M16—82no—
272C2×C8—42no—
273C4⋊C4—41no—
274C4⋊C4—864no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—864no—
278C22⋊C4—1724no—
279C22⋊C4—1724no—
280C22⋊C4—1722no—
281C42—21no—
282C42—21no—
283C42—3442no—
284C42—1722no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—1722no—
295C23—1722no—
296C23—1722no—
297C23—1722no—
298C23—1722no—
299C23—1722no—
300C23—1722no—
301C23C2×(C2×D43)⋊C411yescharacteristic
302C23#1306335312yes—
303D4—44no—
304D4—3444no—
305D4—3442no—
306D4—3444no—
307D4—3448no—
308D4—3448no—
309D4—3442no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—864no—
324C2×C4—3442no—
325C2×C4—3442no—
326C2×C4—1724no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4#1306323911yescharacteristic
330C2×C4#1306323911yescharacteristic
331C2×C4#1306325112yes—
332C8—82no—
333C22—21no—
334C22—21no—
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—3442no—
346C22—3442no—
347C22—3442no—
348C22—3442no—
349C22—3442no—
350C22—3442no—
351C22—3442no—
352C22C2×#1306323911yescharacteristic
353C22#1458290511yescharacteristic
354C22C2×#1306325111yescharacteristic
355C4—22no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3444no—
361C4—1724no—
362C4#1458269112yes—
363C2—21no—
364C2—21no—
365C2—42no—
366C2—81no—
367C2—6882no—
368C2#1913311211yescharacteristic
369C2#1913624611yescharacteristic
370C2C2×#1458269111yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radical#19139541C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11776
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. C4×#13063240C2semidirect
3. #19132593C2semidirect
4. C43×#1465C2semidirect
5. C2×#13063322C4semidirect
10. #14582808C4semidirect
13. C4×C4⋊Dic43C4semidirect
180. #1465D43semidirect
205. C43#11776semidirect

Maximal subgroups

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

subgroupindex
#191395412
C4×#130632402
#191325932
C43×#14652
#1177643