Finite Group Databasebeta

← #24985671

Subgroups — #24985671

Order 11008.

420 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 81 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#19141554C211yesmaximal, characteristic
2#19136123C211yesmaximal, characteristic
3#19136073C211yesmaximal, characteristic, complemented
4#19136068C211yesmaximal, characteristic, complemented
5#19132419C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic
8C2×#13063318—21no—
9C2×#13063259—21no—
10C2×#13063258—21no—
11C2×#13063257—21no—
12C2×#13063246—21no—
13#14582835—21no—
14#14582822—21no—
15#14582813—21no—
16#14582797C2211yescharacteristic
17#14582797C2211yescharacteristic
18#14582794—21no—
19#14582792—21no—
20#14582769C2211yescharacteristic
21#14582662—21no—
22#14582662—21no—
23#14582654C2211yescharacteristic
24C43×#390C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28#13063318—42no—
29#13063318—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C4×Dic43—21no—
46#13063259—42no—
47#13063258—42no—
48#13063257—42no—
49#13063246—42no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×D4×C43D411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C24×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—41no—
74C2×C8×C43—22no—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C42×C43—41no—
86C22⋊Dic43—42no—
87C22⋊Dic43—42no—
88C22⋊Dic43—81no—
89C22⋊Dic43—81no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C4⋊Dic43D812yes—
102Dic43⋊C4—42no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—81no—
108C4×Dic43—42no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43#12011yescharacteristic
120D4×C43—42no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C2×Dic43—22no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
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—81no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C8×C43—42no—
153C8×C43—42no—
154C43⋊C8—42no—
155#7793—431nomaximal, Sylow
156C22×C43—81no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43—81no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43#44711yescharacteristic
164C22×C43#44911yescharacteristic
165C22×C43#45211yescharacteristic
166C22×C43#45311yescharacteristic
167C22×C43#45611yescharacteristic
168C22×C43#45611yescharacteristic
169C22×C43#45811yescharacteristic
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—81no—
177Dic43—42no—
178Dic43—81no—
179Dic43—81no—
180Dic43—81no—
181Dic43—161no—
182#2727—431no—
183#2093—431no—
184#2084—431no—
185#2083—431no—
186#1271—431no—
187#1271—431no—
188#1270D4311yescharacteristic
189C2×C43—161no—
190C2×C43#160911yescharacteristic
191C2×C43#161011yescharacteristic
192C2×C43#161811yescharacteristic
193C2×C43#162111yescharacteristic
194C2×C43#164711yescharacteristic
195C2×C43#165211yescharacteristic
196C2×C43#166011yescharacteristic
197C2×#126—861no—
198C2×#107—861no—
199C2×#107—861no—
200C2×#106—861no—
201C2×#102—861no—
202#399—861no—
203#396—861no—
204#394—861no—
205#390C2×D4311yescharacteristic
206#389—431no—
207#389—431no—
208#389—861no—
209#388—861no—
210#384—431no—
211#340—861no—
212#340—861no—
213#336—431no—
214#336C2×D4311yescharacteristic
215#336C2×D4311yescharacteristic
216C43#779311yescharacteristic, complemented, Sylow
217C22×D4D17211yescharacteristic
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—861no—
221#126—1722no—
222#126—1722no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4D17211yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
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—1722no—
246#102—1722no—
247#95—861no—
248#95—861no—
249#95—861no—
250C24—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—1721no—
261C22×C4C2×D17211yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—862no—
271C2×C8—1721no—
272C2×C8—1721no—
273C4⋊C4—41no—
274C4⋊C4—432no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—3441no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1722no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—3441no—
297C22⋊C4—3441no—
298C22⋊C4—1722no—
299C22⋊C4—1722no—
300C42—41no—
301C42—1722no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1306329511yescharacteristic
310D4—42no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—862no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—1721no—
326C2×C4—1721no—
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×C4D8×D4311yescharacteristic
337C2×C4#1306334611yescharacteristic
338C2×C4#1306334711yescharacteristic
339C2×C4#1306334911yescharacteristic
340C2×C4#1306335211yescharacteristic
341C2×C4#1306335811yescharacteristic
342C8—42no—
343C8—42no—
344C8—1722no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#1458303411yescharacteristic
353C22#1458304511yescharacteristic
354C22#1458306311yescharacteristic
355C22#1458306911yescharacteristic
356C22#1458308311yescharacteristic
357C22#1458308311yescharacteristic
358C22#1458309011yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—3441no—
367C4—3441no—
368C4—3441no—
369C4—1722no—
370C4—6881no—
371C2—161no—
372C2#1913359311yescharacteristic
373C2#1913359911yescharacteristic
374C2#1913364511yescharacteristic
375C2#1913366111yescharacteristic
376C2#1913383311yescharacteristic
377C2#1913386811yescharacteristic
378C2#1913390711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7793
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
3. #19136073C2semidirect
4. #19136068C2semidirect
5. #19132419C2semidirect
6. #19132417C2semidirect
216. C43#7793semidirect

Maximal subgroups

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

subgroupindex
#191415542
#191361232
#191360732
#191360682
#191324192
#191324172
C43×#12702
#779343