Finite Group Databasebeta

← #24985703

Subgroups — #24985703

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#19141546C211yesmaximal, characteristic
2#19136154C211yesmaximal, characteristic
3#19136073C211yesmaximal, characteristic
4#19136066C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132419C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C2×#13063316—21no—
9C2×#13063258—21no—
10C2×#13063257—21no—
11#14582832—21no—
12#14582832—21no—
13#14582831—21no—
14#14582797C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582796—21no—
17#14582785—21no—
18#14582769C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28#13063316—42no—
29#13063316—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×C4×Dic43—21no—
44#13063258—42no—
45#13063257—42no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#95×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—41no—
68C2×C8×C43—22no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43SD1612yes—
79C42×C43—41no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—42no—
84C4⋊Dic43—42no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43D812yes—
93Dic43⋊C4—42no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99C4×Dic43—42no—
100C2×C43⋊C8—22no—
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×C43C2×D811yescharacteristic
117C2×C4×C43C2×SD1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
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—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C8×C43—42no—
138C8×C43—81no—
139C43⋊C8—42no—
140#7798—431nomaximal, Sylow
141C22×C43#44711yescharacteristic
142C22×C43#44811yescharacteristic
143C22×C43#45211yescharacteristic
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—
156Dic43—42no—
157Dic43—81no—
158Dic43—81no—
159Dic43—81no—
160Dic43—161no—
161#2726—431no—
162#2099—431no—
163#2084—431no—
164#2083—431no—
165#1271—431no—
166#1271—431no—
167#1271D4311yescharacteristic
168C2×C43#161011yescharacteristic
169C2×C43#161111yescharacteristic
170C2×C43#161511yescharacteristic
171C2×C43#162711yescharacteristic
172C2×C43#164711yescharacteristic
173C2×C43#165311yescharacteristic
174C2×C43#166311yescharacteristic
175C2×#125—861no—
176C2×#107—861no—
177C2×#106—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#384—431no—
187#340—861no—
188#340—861no—
189#340—861no—
190#340—861no—
191#336—431no—
192#336C2×D4311yescharacteristic
193#336C2×D4311yescharacteristic
194C43#779811yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—861no—
198#125—1722no—
199#125—1722no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
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⋊C4D17211yescharacteristic
215C2×C4⋊C4D17211yescharacteristic
216C2×C42—861no—
217C2×C42C22×D4311yescharacteristic
218#107—1722no—
219#106—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—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—1721no—
233C22×C4C2×D17211yescharacteristic
234C22×C4D4×D4311yescharacteristic
235C22×C4D4×D4311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—862no—
243C2×C8—1721no—
244C2×C8—1721no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—432no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—3441no—
254C4⋊C4—1722no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C4⋊C4—1722no—
258C4⋊C4—1722no—
259C4⋊C4—1722no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4#1062187312yes—
269C42—41no—
270C42—1722no—
271C23#1306329511yescharacteristic
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—862no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
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×C4D8×D4311yescharacteristic
300C2×C4C2×#1062187311yescharacteristic
301C2×C4#1306334611yescharacteristic
302C2×C4#1306335211yescharacteristic
303C2×C4#1306335711yescharacteristic
304C2×C4#1306335811yescharacteristic
305C8—42no—
306C8—81no—
307C8—1722no—
308C22#1458303411yescharacteristic
309C22#1458304011yescharacteristic
310C22#1458306411yescharacteristic
311C22#1458307311yescharacteristic
312C22#1458308311yescharacteristic
313C22#1458308411yescharacteristic
314C22#1458309011yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—3441no—
324C4—3441no—
325C4—3441no—
326C4—1722no—
327C4—6881no—
328C2#1913359911yescharacteristic
329C2#1913360511yescharacteristic
330C2#1913362911yescharacteristic
331C2#1913370111yescharacteristic
332C2#1913383111yescharacteristic
333C2#1913387411yescharacteristic
334C2#1913392511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43#120
hypercenter#1271D43
hypocenterC43#7798
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
194. C43#7798semidirect

Maximal subgroups

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

subgroupindex
#191415462
#191361542
#191360732
#191360662
#191324192
C43×#12712
#779843