Finite Group Databasebeta

← #24985658

Subgroups — #24985658

Order 11008.

374 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 85 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#19141547C211yesmaximal, characteristic
2#19136152C211yesmaximal, characteristic
3#19136067C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132418C211yesmaximal, characteristic
7C43×#2083C211yesmaximal, characteristic
8C2×#13063315—21no—
9C2×#13063258—21no—
10#14582831—21no—
11#14582829—21no—
12#14582829—21no—
13#14582798—21no—
14#14582797C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582784—21no—
17#14582661—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#107×C43—21no—
23C43×#389C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063315—42no—
30#13063315—42no—
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×C4×Dic43—21no—
42#13063258—42no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×C8×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C42×C43C2311yescharacteristic
56#107×C43—42no—
57#95×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—41no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68C2×C8×C43—22no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—42no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43D812yes—
81C42×C43—41no—
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—42no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—81no—
89C4⋊Dic43Q1612yes—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—42no—
97C2×C43⋊C8—22no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—22no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—81no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43C2×D811yescharacteristic
120C2×C4×C43C2×Q1611yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C8×C43—42no—
138C43⋊C8—42no—
139C43⋊C8—81no—
140#7792—431nomaximal, Sylow
141C22×C43#44711yescharacteristic
142C22×C43#44911yescharacteristic
143C22×C43#45111yescharacteristic
144C22×C43#45411yescharacteristic
145C22×C43#45611yescharacteristic
146C22×C43#45611yescharacteristic
147C22×C43#45811yescharacteristic
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—42no—
155C4×C43—81no—
156C4×C43—161no—
157Dic43—42no—
158Dic43—81no—
159Dic43—81no—
160Dic43—81no—
161#2726—431no—
162#2099—431no—
163#2083—431no—
164#2083D4311yescharacteristic
165#1271—431no—
166#1271—431no—
167#1271—431no—
168C2×C43#160911yescharacteristic
169C2×C43#161011yescharacteristic
170C2×C43#161711yescharacteristic
171C2×C43#162511yescharacteristic
172C2×C43#164811yescharacteristic
173C2×C43#164911yescharacteristic
174C2×C43#166311yescharacteristic
175C2×#125—861no—
176C2×#107—21no—
177C2×#107—861no—
178#398—861no—
179#398—861no—
180#398—861no—
181#389—431no—
182#389—431no—
183#389—861no—
184#389C2×D4311yescharacteristic
185#387—861no—
186#384C2×D4311yescharacteristic
187#340—21no—
188#340—861no—
189#340—861no—
190#340—861no—
191#336—431no—
192#336—431no—
193#336C2×D4311yescharacteristic
194C43#779211yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—861no—
197C22×C8—861no—
198#125—1722no—
199#125—1722no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4C22⋊D4311yescharacteristic
215C2×C4⋊C4C22⋊D4311yescharacteristic
216C2×C42—861no—
217C2×C42C22×D4311yescharacteristic
218#107—42no—
219#107—1722no—
220#95—21no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4D4×D4311yescharacteristic
234C22×C4D4×D4311yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—862no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—432no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1722no—
262C4⋊C4—1722no—
263C4⋊C4—1722no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4#1062188212yes—
269C42—41no—
270C42—1722no—
271C23#1306329311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—862no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4C2×#1062188211yescharacteristic
300C2×C4Q16×D4311yescharacteristic
301C2×C4#1306334411yescharacteristic
302C2×C4#1306334911yescharacteristic
303C2×C4#1306335011yescharacteristic
304C2×C4#1306335711yescharacteristic
305C8—42no—
306C8—3441no—
307C8—1722no—
308C22#1458303211yescharacteristic
309C22#1458304111yescharacteristic
310C22#1458305311yescharacteristic
311C22#1458307011yescharacteristic
312C22#1458308011yescharacteristic
313C22#1458308111yescharacteristic
314C22#1458308811yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—161no—
324C4—3441no—
325C4—3441no—
326C4—3441no—
327C4—1722no—
328C2#1913358911yescharacteristic
329C2#1913359711yescharacteristic
330C2#1913363511yescharacteristic
331C2#1913368211yescharacteristic
332C2#1913383411yescharacteristic
333C2#1913384211yescharacteristic
334C2#1913392211yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2083C2
socle, prime radicalC23×C43#120
hypercenter#2083D43
hypocenterC43#7792
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
194. C43#7792semidirect

Maximal subgroups

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

subgroupindex
#191415472
#191361522
#191360672
#191324192
#191324182
C43×#20832
#779243