Finite Group Databasebeta

← #25010295

Subgroups — #25010295

Order 11008.

312 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 67 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#19147464C211yesmaximal, characteristic, complemented
2#19136820C211yesmaximal, characteristic, complemented
3#19136631C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132555C211yesmaximal, characteristic, complemented
7C43×#1365C211yesmaximal, characteristic, complemented
8#14583610—21no—
9C2×D688—21no—
10#14583300—21no—
11#14583276C2211yescharacteristic
12#14583202—22no—
13#14583186—21no—
14#14583100—21no—
15C8×Dic86C2211yescharacteristic
16C4×D344C2211yescharacteristic
17#14582981—21no—
18#14582701—21no—
19#14582699—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582642—21no—
22C43×#500C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621873—41no—
26C2×D344—21no—
27C2×D344—21no—
28C2×D344D411yescharacteristic
29#13063322—21no—
30#13063316—22no—
31#13063305—41no—
32#13063301—42no—
33C4×Dic86D411yescharacteristic
34C4×D172—21no—
35#13063287—22no—
36C4⋊C4×D43—41no—
37D688—42no—
38C2×C43⋊C16—21no—
39#13063259D411yescharacteristic
40#13063256—22no—
41C4⋊(C43⋊C8)D411yescharacteristic
42Dic43⋊C8—21no—
43#13063247—21no—
44#13063247—41no—
45#13063245—22no—
46C8×Dic43—21no—
47C4⋊Q8×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43D412yes—
51C4⋊C8×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—41no—
54C2×D172—21no—
55C2×D172—41no—
56C2×D172—41no—
57C2×D172—41no—
58C2×C4×D43—41no—
59C2×C4×D43—42no—
60C2×Dic86D811yescharacteristic
61C2×C8×C43—41no—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—22no—
65C4⋊C4×C43—41no—
66C42×C43C2×D411yescharacteristic
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—41no—
69C4⋊Dic43—21no—
70C4⋊Dic43—42no—
71C4⋊Dic43D811yescharacteristic
72Dic43⋊C4—21no—
73Dic43⋊C4—42no—
74C4×Dic43—21no—
75C2×C43⋊C8—21no—
76D344—21no—
77D344—42no—
78D344—41no—
79D344—41no—
80D344SD1612yescomplemented
81#10621873—82no—
82C16×C43—41no—
83C43⋊C16—41no—
84C22×D43—41no—
85C22×D43—81no—
86Q8×C43—161no—
87C2×C4×C43—42no—
88C2×C4×C43#12011yescharacteristic
89C2×C4×C43C2×D811yescharacteristic
90C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—41no—
94D172—22no—
95D172—41no—
96D172—81no—
97D172—81no—
98D172—81no—
99D172—81no—
100D172—161no—
101C4×D43—81no—
102C4×D43—81no—
103C4×D43—162no—
104Dic86—21no—
105Dic86—21no—
106C8×C43—21no—
107C8×C43—81no—
108C8×C43C2×SD1611yescharacteristic
109C8×C43#13711yescharacteristic
110C43⋊C8—41no—
111#12355—431nomaximal, Sylow
112C22×C43#44711yescharacteristic
113C2×D43—42no—
114C2×D43—81no—
115C2×D43—81no—
116C2×D43—161no—
117C2×D43—161no—
118C2×D43—161no—
119C4×C43—21no—
120C4×C43—82no—
121C4×C43#44811yescharacteristic
122C4×C43#45411yescharacteristic
123C4×C43#50811yescharacteristic
124C4×C43#50911yescharacteristic
125Dic43—41no—
126Dic43—41no—
127Dic43—81no—
128#3380—431no—
129#2240—431no—
130#2206—431no—
131#1668—431no—
132#1365D4311yescharacteristic, complemented
133Q8⋊C16—431no—
134#1331—431no—
135C2×C43#162711yescharacteristic
136C2×C43#218611yescharacteristic
137C2×C43#219211yescharacteristic
138D43—82no—
139D43—321no—
140#554—861no—
141C2×D16—861no—
142#500C2×D4311yescharacteristic
143#499—861no—
144#493—431no—
145#478—862no—
146#476—861no—
147#460—861no—
148C8×Q8—431no—
149C4×D8—431no—
150C4×D8—861no—
151C4⋊C16C2×D4311yescharacteristic
152#357—861no—
153#357—862no—
154C4×C16—431no—
155#335C2×D4311yescharacteristic
156#331—861no—
157C43#1235511yescharacteristic, complemented, Sylow
158C2×SD16—1721no—
159C2×D8—431no—
160C2×D8—861no—
161C2×D8—861no—
162C4⋊Q8—21no—
163#127—861no—
164#125—862no—
165C22⋊Q8—1721no—
166C22⋊Q8—1722no—
167C4×Q8—431no—
168C4×D4—862no—
169C4×D4—861no—
170C2×C4⋊C4—1721no—
171D16—1722no—
172C2×C16—21no—
173C2×C16—861no—
174#107—21no—
175#107—431no—
176#107D17212yes—
177#106—862no—
178C4⋊C8—21no—
179C4⋊C8—431no—
180C4⋊C8—861no—
181#102—862no—
182#102—861no—
183#102—1721no—
184C4×C8—861no—
185C4×C8C22×D4311yescharacteristic
186C2×Q8—41no—
187C2×Q8—431no—
188C2×D4—861no—
189C2×D4—1721no—
190C2×D4—1721no—
191C2×D4—1721no—
192C22×C4—1722no—
193C22×C4—1721no—
194SD16—3442no—
195D8—432no—
196D8—861no—
197D8—1722no—
198D8—1721no—
199D8—1721no—
200C2×C8—41no—
201C2×C8—861no—
202C2×C8C2×D17211yescharacteristic
203C2×C8D4×D4311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—431no—
207C4⋊C4—861no—
208C4⋊C4—861no—
209C4⋊C4—1722no—
210C4⋊C4—1722no—
211C22⋊C4—1722no—
212C22⋊C4—1721no—
213C42—861no—
214C42D4×D4311yescharacteristic
215C16—41no—
216C16—1721no—
217C23—3441no—
218C23—1721no—
219Q8—161no—
220Q8—861no—
221Q8—861no—
222D4—862no—
223D4—3441no—
224D4—3441no—
225D4—3441no—
226D4—3441no—
227D4—1721no—
228D4—6881no—
229C2×C4—42no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—3441no—
233C2×C4—3441no—
234C2×C4—1721no—
235C2×C4—6882no—
236C2×C4#1306329511yescharacteristic
237C2×C4D8×D4311yescharacteristic
238C2×C4#1306335211yescharacteristic
239C8—21no—
240C8—81no—
241C8—1721no—
242C8SD16×D4311yescharacteristic
243C8#1306335711yescharacteristic
244C22—3441no—
245C22—3441no—
246C22—1722no—
247C22—6881no—
248C22—6881no—
249C22—6881no—
250C22#1458303411yescharacteristic
251C4—21no—
252C4—82no—
253C4—3441no—
254C4—1721no—
255C4—1721no—
256C4#1458303911yescharacteristic
257C4#1458307411yescharacteristic
258C4#1458333211yescharacteristic
259C4#1458333611yescharacteristic
260C2—3442no—
261C2—13761no—
262C2#1913369911yescharacteristic
263C2#1913652111yescharacteristic
264C2#1913655511yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1365C2
socleC22×C43#447
prime radical#19136631C2
hypercenter#1365D43
hypocenterC43#12355
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #19147464C2semidirect
2. #19136820C2semidirect
4. #19133956C2semidirect
5. #19132573C2semidirect
6. #19132555C2semidirect
7. C43×#1365C2semidirect
80. D344SD16semidirect
132. #1365D43semidirect
157. C43#12355semidirect

Maximal subgroups

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

subgroupindex
#191474642
#191368202
#191366312
#191339562
#191325732
#191325552
C43×#13652
#1235543