Finite Group Databasebeta

← #33000407

Subgroups — #33000407

Order 18688.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#22612154C211yesmaximal, characteristic, complemented
2#22611750C211yesmaximal, characteristic, complemented
3#22609331C211yesmaximal, characteristic, complemented
4#22609283C211yesmaximal, characteristic
5#22608004C211yesmaximal, characteristic, complemented
6#22607988C211yesmaximal, characteristic, complemented
7C73×#1361C211yesmaximal, characteristic, complemented
8C2×C16×D73—21no—
9#17988992C2211yescharacteristic
10#17988878—21no—
11#17988779—21no—
12C8×D292C2211yescharacteristic
13#17988388—21no—
14#17988388—21no—
15#17988366—21no—
16C4×#11924003C2211yescharacteristic
17#17988340C2211yescharacteristic
18#17988335—21no—
19#17988331—21no—
20#493×C73C2211yescharacteristic
21C4⋊C16×C73C2211yescharacteristic
22#335×C73C2211yescharacteristic
23C2×#11924013—41no—
24C2×C8×D73—21no—
25#14556591—21no—
26C4×D292D411yescharacteristic
27C2×#11924003D411yescharacteristic
28C2×#11924003D411yescharacteristic
29C16×D73—42no—
30#14556525—21no—
31#14556525—21no—
32#14556523—41no—
33C4⋊#10596831—21no—
34C4⋊#10596831D411yescharacteristic
35#14556513—41no—
36#14556512—41no—
37#14556503—21no—
38C2×D8×C73—21no—
39C2×D8×C73—21no—
40#127×C73—21no—
41C2×C16×C73—21no—
42C4⋊C8×C73—21no—
43C4×C8×C73C2311yescharacteristic
44C2×Dic146—41no—
45C2×D292D811yescharacteristic
46C2×C4×D73—21no—
47#11924013—82no—
48C2×#10596831—21no—
49C2×#10596831—41no—
50C8×D73—41no—
51C8×D73—41no—
52C4⋊Dic73—41no—
53C4⋊Dic73—41no—
54C4⋊Dic73D811yescharacteristic
55#11924005—21no—
56#11924003—21no—
57#11924003—21no—
58C2×D4×C73—41no—
59C2×D4×C73—41no—
60C2×D4×C73—41no—
61D8×C73—41no—
62D8×C73—41no—
63D8×C73—81no—
64C2×C8×C73—41no—
65C2×C8×C73C2×D411yescharacteristic
66C2×C8×C73#4111yescharacteristic
67C42×C73C2×D411yescharacteristic
68C16×C73—41no—
69C23×C73—81no—
70C22×D73—21no—
71D4×C73—81no—
72D4×C73—81no—
73D4×C73—81no—
74D4×C73—81no—
75D4×C73—161no—
76C2×C4×C73#12111yescharacteristic
77C2×C4×C73C2×D811yescharacteristic
78C2×C4×C73#13511yescharacteristic
79C2×Dic73—21no—
80C2×Dic73—81no—
81D292—21no—
82D292SD3212yes—
83C4×D73—41no—
84C4×D73—41no—
85Dic146—161no—
86C8×C73—21no—
87C8×C73—81no—
88C8×C73#13511yescharacteristic
89C8×C73AGL(1,ℤ/8)11yescharacteristic
90#10596831—41no—
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#46311yescharacteristic
101C4×C73#47111yescharacteristic
102C4×C73C2×SD3211yescharacteristic
103C4×C73#50811yescharacteristic
104Dic73—41no—
105Dic73—161no—
106#12468—731nomaximal, Sylow
107C2×C73—321no—
108C2×C73#168111yescharacteristic
109C2×C73#221711yescharacteristic
110C2×C73#222111yescharacteristic
111D73—42no—
112#2240—731no—
113D4×C16—731no—
114#1675—731no—
115#1667—731no—
116#1372—731no—
117#1365—731no—
118#1361D7311yescharacteristic, complemented
119C73#1246811yescharacteristic, complemented, Sylow
120C22×C16—1461no—
121#500—731no—
122#493C2×D7311yescharacteristic
123#476—1461no—
124#459—1461no—
125C8×D4—731no—
126C4⋊C16C2×D7311yescharacteristic
127#357—1461no—
128#357—1461no—
129C22⋊C16—1461no—
130C4×C16—731no—
131#335—731no—
132#335C2×D7311yescharacteristic
133#333—1461no—
134#331—1461no—
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—2921no—
138C22×C8—1461no—
139C4⋊Q8—1461no—
140#127—21no—
141C4×D4—731no—
142C2×C16—21no—
143C2×C16—2922no—
144C2×C16—731no—
145C2×C16—731no—
146#107—1461no—
147#107—1461no—
148#106—2921no—
149C4⋊C8—21no—
150C4⋊C8—731no—
151C4⋊C8—1461no—
152#102—2921no—
153#102—2921no—
154C22⋊C8—1461no—
155C4×C8C22×D7311yescharacteristic
156C2×Q8—2921no—
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—41no—
167C2×C8—2921no—
168C2×C8—2921no—
169C2×C8—2921no—
170C2×C8—1461no—
171C2×C8D4×D7311yescharacteristic
172C2×C8#1192402811yescharacteristic
173C4⋊C4—2921no—
174C4⋊C4—2921no—
175C4⋊C4—731no—
176C22⋊C4—1461no—
177C42D4×D7311yescharacteristic
178C16—41no—
179C16—1461no—
180C16—1461no—
181C23—81no—
182C23—1461no—
183Q8—11681no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—161no—
189D4—732no—
190D4—1461no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—5841no—
194C2×C4—1461no—
195C2×C4#1455656411yescharacteristic
196C2×C4D8×D7311yescharacteristic
197C2×C4#1455661211yescharacteristic
198C8—21no—
199C8—81no—
200C8—2921no—
201C8—5841no—
202C8#1455661211yescharacteristic
203C8#1455661511yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—2921no—
208C22—2921no—
209C22—1462no—
210C22#1798882211yescharacteristic
211C4—21no—
212C4—2921no—
213C4—11681no—
214C4#1798880111yescharacteristic
215C4#1798884911yescharacteristic
216C4SD32×D7311yescharacteristic
217C4#1798901611yescharacteristic
218C2—321no—
219C2—2922no—
220C2#2260936711yescharacteristic
221C2#2261202611yescharacteristic
222C2#2261205011yescharacteristic
subgroupG/H
centerC22#17988822
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1361C2
socleC22×C73#466
prime radical#22609283C2
hypercenter#1361D73
hypocenterC73#12468
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #22612154C2semidirect
2. #22611750C2semidirect
3. #22609331C2semidirect
5. #22608004C2semidirect
6. #22607988C2semidirect
7. C73×#1361C2semidirect
118. #1361D73semidirect
119. C73#12468semidirect

Maximal subgroups

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

subgroupindex
#226121542
#226117502
#226093312
#226092832
#226080042
#226079882
C73×#13612
#1246873