Finite Group Databasebeta

← #24985665

Subgroups — #24985665

Order 11008.

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

normal subgroups only

This group has 420 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#19141556C211yesmaximal, characteristic
2#19136124C211yesmaximal, characteristic
3#19136067C211yesmaximal, characteristic, complemented
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2084C211yesmaximal, characteristic, complemented
8C2×#13063320—21no—
9C2×#13063258—21no—
10C2×#13063258—21no—
11C2×#13063245—21no—
12#14582836—21no—
13#14582821—21no—
14#14582816—21no—
15#14582801C2211yescharacteristic
16#14582798—21no—
17#14582797C2211yescharacteristic
18#14582791—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#106×C43—21no—
23C43×#389C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30#13063320—42no—
31#13063320—42no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45#13063258—42no—
46#13063258—42no—
47#13063245—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×C8×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#106×C43—42no—
59#95×C43—21no—
60C23×D43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—41no—
73C2×D172—41no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43D812yes—
88C42×C43—41no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—81no—
96(C2×D43)⋊C4—81no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—42no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—81no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C4×Dic43—42no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43#12011yescharacteristic
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150D172—42no—
151D172—81no—
152C8×C43—42no—
153C43⋊C8—42no—
154C43⋊C8—42no—
155#7793—431nomaximal, Sylow
156C22×C43#44711yescharacteristic
157C22×C43#44911yescharacteristic
158C22×C43#45211yescharacteristic
159C22×C43#45311yescharacteristic
160C22×C43#45611yescharacteristic
161C22×C43#45611yescharacteristic
162C22×C43#45811yescharacteristic
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—42no—
177C4×C43—81no—
178C4×C43—161no—
179Dic43—81no—
180Dic43—81no—
181Dic43—81no—
182#2727—431no—
183#2093—431no—
184#2084D4311yescharacteristic, complemented
185#2083—431no—
186#1271—431no—
187#1271—431no—
188#1270—431no—
189C2×C43#160911yescharacteristic
190C2×C43#161011yescharacteristic
191C2×C43#161811yescharacteristic
192C2×C43#162111yescharacteristic
193C2×C43#164711yescharacteristic
194C2×C43#165211yescharacteristic
195C2×C43#166011yescharacteristic
196D43—161no—
197C2×#126—861no—
198C2×#107—861no—
199C2×#107—861no—
200C2×#106—21no—
201C2×#102—861no—
202#399—861no—
203#396—861no—
204#394—861no—
205#390—431no—
206#389—431no—
207#389—861no—
208#389C2×D4311yescharacteristic
209#388—861no—
210#384C2×D4311yescharacteristic
211#340—21no—
212#340—861no—
213#336—431no—
214#336—431no—
215#336C2×D4311yescharacteristic
216C43#779311yescharacteristic, complemented, Sylow
217C22×D4—431no—
218C22×C8—21no—
219C22×C8—861no—
220C22×C8—861no—
221#126—1722no—
222#126—1722no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4C22⋊D4311yescharacteristic
234C2×C4⋊C4C22⋊D4311yescharacteristic
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C42—861no—
242C2×C42C22×D4311yescharacteristic
243#107—1722no—
244#107—1722no—
245#106—42no—
246#102—1722no—
247#95—21no—
248#95—861no—
249#95—861no—
250C24—861no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—1721no—
254C2×D4—1721no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4D4×D4311yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4C2×C22⋊D4311yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—862no—
268C2×C8—862no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8—1721no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—3441no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1722no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4#1062188212yes—
292C22⋊C4—3441no—
293C22⋊C4—3441no—
294C22⋊C4—1722no—
295C22⋊C4—1722no—
296C22⋊C4—1721no—
297C22⋊C4—1721no—
298C22⋊C4—1721no—
299C22⋊C4—1721no—
300C42—41no—
301C42—1722no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23#1306329311yescharacteristic
310D4—3441no—
311D4—1722no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4C2×#1062188211yescharacteristic
337C2×C4#1306334611yescharacteristic
338C2×C4#1306334611yescharacteristic
339C2×C4#1306335011yescharacteristic
340C2×C4#1306335211yescharacteristic
341C2×C4#1306335411yescharacteristic
342C8—42no—
343C8—1722no—
344C8—1722no—
345C22—3441no—
346C22—3441no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22—3441no—
351C22—3441no—
352C22#1458303211yescharacteristic
353C22#1458304311yescharacteristic
354C22#1458305811yescharacteristic
355C22#1458306511yescharacteristic
356C22#1458308011yescharacteristic
357C22#1458308111yescharacteristic
358C22#1458308811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—161no—
368C4—3441no—
369C4—3441no—
370C4—3441no—
371C2—6881no—
372C2#1913359111yescharacteristic
373C2#1913359711yescharacteristic
374C2#1913364011yescharacteristic
375C2#1913365811yescharacteristic
376C2#1913382811yescharacteristic
377C2#1913386211yescharacteristic
378C2#1913390511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2084C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2084D43
hypocenterC43#7793
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
3. #19136067C2semidirect
4. #19132419C2semidirect
5. #19132418C2semidirect
7. C43×#2084C2semidirect
184. #2084D43semidirect
216. C43#7793semidirect

Maximal subgroups

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

subgroupindex
#191415562
#191361242
#191360672
#191324192
#191324182
#191324152
C43×#20842
#779343