Finite Group Databasebeta

← #33000405

Subgroups — #33000405

Order 18688.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C16×D292C211yesmaximal, characteristic, complemented
2#22609327C211yesmaximal, characteristic, complemented
3#22609283C211yesmaximal, characteristic
4#22608005C211yesmaximal, characteristic, complemented
5#22607989C211yesmaximal, characteristic, complemented
6#22607977C211yesmaximal, characteristic, complemented
7C73×#2240C211yesmaximal, characteristic, complemented
8C2×C16×D73—21no—
9#17988874—21no—
10#17988779—21no—
11C8×D292C2211yescharacteristic
12C4⋊#11924003C2211yescharacteristic
13#17988366—21no—
14#17988340C2211yescharacteristic
15#17988340C2211yescharacteristic
16#17988336—21no—
17#17988331—21no—
18#500×C73C2211yescharacteristic
19#493×C73C2211yescharacteristic
20#357×C73—21no—
21#357×C73—21no—
22C4×C16×C73C2211yescharacteristic
23C2×#11924013—41no—
24C2×C8×D73—21no—
25C4×D292D411yescharacteristic
26C2×#11924003—21no—
27C16×D73—42no—
28#14556522—41no—
29C4⋊#10596831—21no—
30C4⋊#10596831—21no—
31C4⋊#10596831D411yescharacteristic
32#14556512—41no—
33#14556511—41no—
34#14556503—21no—
35C2×D8×C73—21no—
36C2×D8×C73—21no—
37C4⋊Q8×C73—21no—
38#127×C73—21no—
39C2×C16×C73D411yescharacteristic
40C2×C16×C73D411yescharacteristic
41#107×C73—21no—
42#107×C73—21no—
43C4×C8×C73C2311yescharacteristic
44C2×D292D811yescharacteristic
45C2×C4×D73—21no—
46#11924013—82no—
47C2×#10596831—21no—
48C2×#10596831—41no—
49C2×#10596831—41no—
50C8×D73—41no—
51C8×D73—41no—
52C4⋊Dic73D811yescharacteristic
53#11924005—21no—
54#11924003—41no—
55C2×Q8×C73—41no—
56C2×D4×C73—41no—
57C2×D4×C73—41no—
58C2×D4×C73—41no—
59D8×C73—41no—
60D8×C73—41no—
61D8×C73—81no—
62C2×C8×C73C2×D411yescharacteristic
63C2×C8×C73#4111yescharacteristic
64C4⋊C4×C73—41no—
65C4⋊C4×C73—41no—
66C42×C73C2×D411yescharacteristic
67C16×C73—21no—
68C16×C73—21no—
69C23×C73—81no—
70C22×D73—21no—
71Q8×C73—161no—
72D4×C73—81no—
73D4×C73—81no—
74D4×C73—81no—
75D4×C73—81no—
76D4×C73—161no—
77C2×C4×C73—81no—
78C2×C4×C73#12111yescharacteristic
79C2×C4×C73C2×D811yescharacteristic
80C2×C4×C73#13511yescharacteristic
81C2×Dic73—21no—
82D292—21no—
83D292SD3212yes—
84C4×D73—41no—
85C4×D73—41no—
86C8×C73—21no—
87C8×C73#13511yescharacteristic
88C8×C73AGL(1,ℤ/8)11yescharacteristic
89#10596831—41no—
90#10596831—81no—
91#10596831—81no—
92C22×C73—161no—
93C22×C73—161no—
94C22×C73—161no—
95C22×C73#46611yescharacteristic
96C2×D73—22no—
97C2×D73—41no—
98C2×D73—41no—
99C4×C73—21no—
100C4×C73—161no—
101C4×C73#46311yescharacteristic
102C4×C73#47111yescharacteristic
103C4×C73C2×SD3211yescharacteristic
104C4×C73#50811yescharacteristic
105Dic73—41no—
106#12468—731nomaximal, Sylow
107C2×C73—321no—
108C2×C73#168111yescharacteristic
109C2×C73#221711yescharacteristic
110C2×C73#222111yescharacteristic
111D73—42no—
112#2240D7311yescharacteristic, complemented
113D4×C16—731no—
114#1675—731no—
115#1667—731no—
116#1372—731no—
117#1365—731no—
118#1361—731no—
119C73#1246811yescharacteristic, complemented, Sylow
120C22×C16—1461no—
121#500C2×D7311yescharacteristic
122#493C2×D7311yescharacteristic
123#476—1461no—
124#459—1461no—
125C8×D4—731no—
126C4⋊C16—731no—
127#357—21no—
128#357—21no—
129C22⋊C16—1461no—
130C4×C16C2×D7311yescharacteristic
131#335—731no—
132#335—731no—
133#333—1461no—
134#331—1461no—
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—2921no—
138C22×C8—1461no—
139C4⋊Q8—21no—
140#127—21no—
141C4×D4—731no—
142C2×C16—2922no—
143C2×C16—1461no—
144C2×C16C22⋊D7311yescharacteristic
145C2×C16C22⋊D7311yescharacteristic
146#107—21no—
147#107—21no—
148#106—2921no—
149C4⋊C8—731no—
150C4⋊C8—1461no—
151C4⋊C8—1461no—
152#102—2921no—
153#102—2921no—
154C22⋊C8—1461no—
155C4×C8C22×D7311yescharacteristic
156C2×Q8—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—731no—
161C22×C4—1461no—
162D8—41no—
163D8—41no—
164D8—81no—
165D8—5842no—
166C2×C8—2921no—
167C2×C8—2921no—
168C2×C8—2921no—
169C2×C8—2921no—
170C2×C8—1461no—
171C2×C8C2×C22⋊D7311yescharacteristic
172C2×C8#1192402711yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—731no—
176C22⋊C4—1461no—
177C42D4×D7311yescharacteristic
178C16—21no—
179C16—21no—
180C16—2921no—
181C23—81no—
182C23—1461no—
183Q8—161no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—161no—
189D4—732no—
190D4—1461no—
191C2×C4—81no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—1461no—
195C2×C4#1455656211yescharacteristic
196C2×C4D8×D7311yescharacteristic
197C2×C4#1455661011yescharacteristic
198C8—21no—
199C8—2921no—
200C8—5841no—
201C8—5841no—
202C8#1455661111yescharacteristic
203C8#1455661611yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—2921no—
208C22—2921no—
209C22—1462no—
210C22#1798882011yescharacteristic
211C4—21no—
212C4—161no—
213C4—2921no—
214C4#1798879911yescharacteristic
215C4#1798884711yescharacteristic
216C4SD32×D7311yescharacteristic
217C4#1798901811yescharacteristic
218C2—321no—
219C2—2922no—
220C2#2260936511yescharacteristic
221C2#2261202411yescharacteristic
222C2#2261204811yescharacteristic
subgroupG/H
centerC22#17988820
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2240C2
socleC22×C73#466
prime radical#22609283C2
hypercenter#2240D73
hypocenterC73#12468
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. C16×D292C2semidirect
2. #22609327C2semidirect
4. #22608005C2semidirect
5. #22607989C2semidirect
6. #22607977C2semidirect
7. C73×#2240C2semidirect
112. #2240D73semidirect
119. C73#12468semidirect

Maximal subgroups

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

subgroupindex
C16×D2922
#226093272
#226092832
#226080052
#226079892
#226079772
C73×#22402
#1246873