Finite Group Databasebeta

← #24985678

Subgroups — #24985678

Order 11008.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#19141626C211yesmaximal, characteristic
2#19136153C211yesmaximal, characteristic
3#19136068C211yesmaximal, characteristic
4#19136005C211yesmaximal, characteristic
5#19132420C211yesmaximal, characteristic
6#19132419C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C2×#13063324—21no—
9C2×#13063259—21no—
10C2×#13063250—21no—
11#14582832—21no—
12#14582820—21no—
13#14582819—21no—
14#14582805C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582785—21no—
17#14582782—21no—
18#14582769C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582661—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86D411yescharacteristic
29C22×C43⋊C8—21no—
30#13063324—42no—
31#13063324—42no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C4×Dic43—21no—
43#13063259—42no—
44#13063250—42no—
45C43⋊#95—21no—
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×Dic86—21no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71C2×Dic86—42no—
72C2×Dic86—81no—
73C2×Dic86—81no—
74C2×Dic86D812yes—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43Q1612yes—
86C42×C43—41no—
87C4⋊Dic43—21no—
88C4⋊Dic43—42no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43SD1612yes—
97Dic43⋊C4—42no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—81no—
101C4×Dic43—42no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43#12011yescharacteristic
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43C2×D811yescharacteristic
119C2×C4×C43C2×SD1611yescharacteristic
120C2×C4×C43C2×Q1611yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
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—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139Dic86—42no—
140Dic86—81no—
141Dic86—84no—
142C8×C43—42no—
143C8×C43—81no—
144C43⋊C8—81no—
145#7794—431nomaximal, Sylow
146C22×C43#44711yescharacteristic
147C22×C43#44811yescharacteristic
148C22×C43#45111yescharacteristic
149C22×C43#45411yescharacteristic
150C22×C43#45511yescharacteristic
151C22×C43#45611yescharacteristic
152C22×C43#45811yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—81no—
161Dic43—42no—
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165Dic43—161no—
166#2734—431no—
167#2099—431no—
168#2083—431no—
169#2072—431no—
170#1272—431no—
171#1271—431no—
172#1271D4311yescharacteristic
173C2×C43#160711yescharacteristic
174C2×C43#161111yescharacteristic
175C2×C43#161711yescharacteristic
176C2×C43#162711yescharacteristic
177C2×C43#164511yescharacteristic
178C2×C43#164911yescharacteristic
179C2×C43#166411yescharacteristic
180C2×C4⋊Q8—861no—
181C2×#107—861no—
182C2×#103—861no—
183#398—861no—
184#395—861no—
185#395—861no—
186#391—431no—
187#389—431no—
188#389C2×D4311yescharacteristic
189#387—861no—
190#387—861no—
191#384—431no—
192#340—861no—
193#340—861no—
194#340—861no—
195#340—861no—
196#336—431no—
197#336C2×D4311yescharacteristic
198#336C2×D4311yescharacteristic
199C43#779411yescharacteristic, complemented, Sylow
200C22×Q8—431no—
201C22×Q8—861no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—861no—
205C4⋊Q8—1722no—
206C4⋊Q8—1722no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4D17211yescharacteristic
219C2×C4⋊C4D17211yescharacteristic
220C2×C42—861no—
221C2×C42C22×D4311yescharacteristic
222#107—1722no—
223#103—1722no—
224#95—21no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231C2×Q8—432no—
232C2×Q8—861no—
233C2×Q8—3441no—
234C2×Q8—3441no—
235C2×Q8—1721no—
236C2×Q8—1721no—
237C2×Q8—1722no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—1721no—
245C22×C4C2×D17211yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—1721no—
255C2×C8—1721no—
256C2×C8—1721no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—432no—
262C4⋊C4—861no—
263C4⋊C4—3441no—
264C4⋊C4—1722no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1722no—
268C4⋊C4—1722no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4Dic17212yes—
276C42—41no—
277C42—1722no—
278C23#1306329511yescharacteristic
279Q8—3441no—
280Q8—3444no—
281Q8—1722no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—3441no—
297C2×C4—3441no—
298C2×C4—3441no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4D8×D4311yescharacteristic
310C2×C4SD16×D4311yescharacteristic
311C2×C4C2×Dic17211yescharacteristic
312C2×C4#1306335211yescharacteristic
313C2×C4#1306335711yescharacteristic
314C2×C4#1306335811yescharacteristic
315C8—42no—
316C8—81no—
317C8—3441no—
318C22#1458303411yescharacteristic
319C22#1458303911yescharacteristic
320C22#1458305711yescharacteristic
321C22#1458307411yescharacteristic
322C22#1458307811yescharacteristic
323C22#1458308311yescharacteristic
324C22#1458309011yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—3441no—
334C4—3441no—
335C4—1722no—
336C4—1722no—
337C4—6881no—
338C2#1913358211yescharacteristic
339C2#1913360411yescharacteristic
340C2#1913363911yescharacteristic
341C2#1913369911yescharacteristic
342C2#1913381911yescharacteristic
343C2#1913384711yescharacteristic
344C2#1913393011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43#120
hypercenter#1271D43
hypocenterC43#7794
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
199. C43#7794semidirect

Maximal subgroups

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

subgroupindex
#191416262
#191361532
#191360682
#191360052
#191324202
#191324192
C43×#12712
#779443