Finite Group Databasebeta

← #24991611

Subgroups — #24991611

Order 11008.

928 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#14582816C211yesmaximal, characteristic
2#19134525C212yesmaximal
3C2×#14582625C211yesmaximal, characteristic, complemented
4#19132473C212yesmaximal, complemented
5C43×#2313C211yesmaximal, characteristic, complemented
6C23×D172C2211yescharacteristic
7C22×(C2×D43)⋊C4—21no—
8C22×(C2×D43)⋊C4—21no—
9C2×#13063245—24no—
10C2×C22⋊(C43⋊C8)C2212yes—
11#14582816—22no—
12#14582816C414yescomplemented
13C2×C43⋊#95C2211yescharacteristic
14#14582625—22no—
15C22×C4⋊C4×C43C2211yescharacteristic
16C43×#387—24no—
17C43×#381—21no—
18C43×#380C2212yes—
19C4×C22⋊C4×C43—21no—
20C24×D43—21no—
21C22×D172—22no—
22C22×D172—22no—
23C22×D172—21no—
24C22×D172—44no—
25C22×D172C2×C412yes—
26C23×Dic43—21no—
27C22×C43⋊C8—22no—
28C2×(C2×D43)⋊C4—24no—
29C2×(C2×D43)⋊C4—24no—
30C2×(C2×D43)⋊C4—44no—
31C2×(C2×D43)⋊C4—44no—
32#13063245—48no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35C43⋊#95—21no—
36C43⋊#95C2×C412yes—
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C23×C4×C43C2311yescharacteristic
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43C2×C412yes—
43C2×C4⋊C4×C43D412yes—
44C2×C4⋊C4×C43D414yes—
45C2×C22⋊C4×C43—22no—
46C2×C42×C43—22no—
47#95×C43—22no—
48#95×C43—24no—
49#95×C43—22no—
50C24×C43C2×D411yescharacteristic
51C23×D43—24no—
52C23×D43—22no—
53C23×D43—42no—
54C23×D43—42no—
55C23×D43—42no—
56C23×D43—41no—
57C23×D43—41no—
58C23×D43—42no—
59C23×D43—42no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—24no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43C22⋊C412yes—
70C22×C4×C43C22⋊C412yes—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D412yes—
74C22×C4×C43#4112yes—
75C22×Dic43—22no—
76C22×Dic43—42no—
77C22×Dic43—42no—
78C22×Dic43—42no—
79C2×D172—28no—
80C2×D172—24no—
81C2×D172—44no—
82C2×D172—44no—
83C2×D172—48no—
84C2×D172—44no—
85C2×D172—42no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43—24no—
88C4⋊C4×C43—44no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—42no—
91C42×C43—82no—
92(C2×D43)⋊C4—48no—
93(C2×D43)⋊C4—48no—
94C2×C43⋊C8—44no—
95C2×C43⋊C8—42no—
96C23×C43—22no—
97C23×C43—22no—
98C23×C43C2×C22⋊C411yescharacteristic
99C23×C43#12011yescharacteristic
100C23×C43#12311yescharacteristic
101C23×C43#13512yes—
102C23×C43AGL(1,ℤ/8)12yes—
103C22×D43—24no—
104C22×D43—42no—
105C22×D43—44no—
106C22×D43—48no—
107C22×D43—48no—
108C22×D43—42no—
109C22×D43—42no—
110C22×D43—42no—
111C22×D43—42no—
112C22×D43—42no—
113C22×D43—44no—
114C22×D43—84no—
115C22×D43—84no—
116C22×D43—82no—
117C22×D43—82no—
118C22×D43—82no—
119C22×D43—82no—
120C2×C4×C43—24no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—44no—
133C2×C4×C43—44no—
134C2×C4×C43—44no—
135C2×C4×C43—81no—
136C2×C4×C43C4×D412yes—
137C2×C4×C43#12112yes—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—84no—
142D172—28no—
143D172—48no—
144D172—44no—
145C43⋊C8—82no—
146#9018—431nomaximal, Sylow
147C22×C43—24no—
148C22×C43—24no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43#38611yescharacteristic
154C22×C43#41611yescharacteristic
155C22×C43#41811yescharacteristic
156C22×C43#44912yes—
157C22×C43#45412yes—
158C22×C43B(4,𝔽2)12yes—
159C22×C43#48212yes—
160C2×D43—44no—
161C2×D43—44no—
162C2×D43—44no—
163C2×D43—82no—
164C2×D43—82no—
165C2×D43—88no—
166C2×D43—88no—
167C2×D43—82no—
168C2×D43—82no—
169C4×C43—22no—
170C4×C43—22no—
171C4×C43—42no—
172C4×C43—42no—
173C4×C43—84no—
174Dic43—82no—
175C2×#394—431no—
176#2313D4311yescharacteristic, complemented
177#1786—432no—
178C2×#324—431no—
179#1294—432no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—22no—
183C2×C43#159714yes—
184C2×C43#187511yescharacteristic
185C2×C43#188811yescharacteristic
186C2×C43#188911yescharacteristic
187D43—84no—
188C23×D4—431no—
189C22×C4⋊C4C2×D4311yescharacteristic
190C22×C22⋊C4—861no—
191C22×C22⋊C4—861no—
192C2×#102—864no—
193C2×C22⋊C8—432no—
194#394—434no—
195#394—862no—
196#387—24no—
197#381—21no—
198#380C2×D4312yes—
199C4×C22⋊C4—21no—
200C2×#95—431no—
201#324—862no—
202C43#901811yescharacteristic, complemented, Sylow
203C25—861no—
204C22×D4—432no—
205C22×D4—861no—
206C22×D4—862no—
207C22×D4—862no—
208C22×D4—1724no—
209C23×C4—861no—
210C23×C4C22⋊D4311yescharacteristic
211C23×C4C22⋊D4311yescharacteristic
212C23×C4C22×D4311yescharacteristic
213C22×C8—862no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4C4×D4312yes—
217C2×C4⋊C4D17212yes—
218C2×C4⋊C4C22⋊D4314yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—864no—
221C2×C22⋊C4—864no—
222C2×C22⋊C4—1724no—
223C2×C22⋊C4—1724no—
224C2×C42—22no—
225#102—1728no—
226C22⋊C8—862no—
227C22⋊C8—862no—
228#95—22no—
229#95—24no—
230#95—22no—
231#95—432no—
232#95—861no—
233C24—864no—
234C24—862no—
235C24—1722no—
236C24—1722no—
237C24—1722no—
238C24—1721no—
239C24—1721no—
240C24—1722no—
241C24—1722no—
242C24C2×C22⋊D4311yescharacteristic
243C2×D4—868no—
244C2×D4—864no—
245C2×D4—1724no—
246C2×D4—1724no—
247C2×D4—1728no—
248C2×D4—1724no—
249C2×D4—1722no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—862no—
260C22×C4—1722no—
261C22×C4—1722no—
262C22×C4—1722no—
263C22×C4(C2×D43)⋊C412yes—
264C22×C4(C2×D43)⋊C412yes—
265C22×C4C2×C4×D4311yescharacteristic
266C22×C4C2×D17211yescharacteristic
267C22×C4#1062189812yes—
268C22×C4C2×C22⋊D4312yes—
269C2×C8—1724no—
270C2×C8—1722no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—44no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—1728no—
277C22⋊C4—1728no—
278C42—82no—
279C23—22no—
280C23—22no—
281C23—864no—
282C23—3442no—
283C23—3444no—
284C23—3444no—
285C23—3442no—
286C23—3442no—
287C23—3442no—
288C23—1722no—
289C23—1724no—
290C23—1722no—
291C23—1722no—
292C23—1728no—
293C23—1728no—
294C23—1724no—
295C23—1722no—
296C23—1722no—
297C23—1722no—
298C23C2×(C2×D43)⋊C411yescharacteristic
299C23#1306329411yescharacteristic
300C23#1306330811yescharacteristic
301C23#1306334512yes—
302C23#1306335012yes—
303D4—868no—
304D4—1728no—
305D4—1724no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—81no—
322C2×C4—3444no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1722no—
326C2×C4C4×C22⋊D4312yes—
327C2×C4#1306329912yes—
328C8—3442no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—24no—
334C22—24no—
335C22—3442no—
336C22—3448no—
337C22—3442no—
338C22—3442no—
339C22—3448no—
340C22—3442no—
341C22—1724no—
342C22—1724no—
343C22—1724no—
344C22#1458277811yescharacteristic
345C22#1458289311yescharacteristic
346C22#1458290311yescharacteristic
347C22#1458304412yes—
348C22#1458307212yes—
349C22#1458308612yes—
350C22#1458322312yes—
351C4—22no—
352C4—22no—
353C4—42no—
354C4—42no—
355C4—84no—
356C4—3442no—
357C2—21no—
358C2—22no—
359C2—21no—
360C2—3444no—
361C2#1913352414yes—
362C2#1913491711yescharacteristic
363C2#1913499811yescharacteristic
364C2#1913500311yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2313C2
socleC23×C43#120
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenter#2313D43
hypocenterC43#9018
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. C2×#14582625C2semidirect
4. #19132473C2semidirect
5. C43×#2313C2semidirect
12. #14582816C4semidirect
176. #2313D43semidirect
202. C43#9018semidirect

Maximal subgroups

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

subgroupindex
C2×#145828162
#191345252
C2×#145826252
#191324732
C43×#23132
#901843