Finite Group Databasebeta

← #33000211

Subgroups — #33000211

Order 18688.

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

normal subgroups only

This group has 230 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#22612183C211yesmaximal, characteristic, complemented
2#22611762C211yesmaximal, characteristic
3#22609297C211yesmaximal, characteristic
4#22609293C211yesmaximal, characteristic
5#22608004C211yesmaximal, characteristic, complemented
6#22607981C211yesmaximal, characteristic, complemented
7C73×#1362C211yesmaximal, characteristic, complemented
8C2×#14556537—21no—
9C2×#14556537—21no—
10C2×#14556530—21no—
11#17988967C2211yescharacteristic
12#17988868—21no—
13#17988864—21no—
14C8×D292C2211yescharacteristic
15#17988366—21no—
16C4×#11924003C2211yescharacteristic
17#17988340C2211yescharacteristic
18#17988333—21no—
19#17988332—21no—
20#494×C73C2211yescharacteristic
21C4⋊C16×C73C2211yescharacteristic
22#335×C73C2211yescharacteristic
23C2×Dic292—21no—
24C2×Dic292—21no—
25C2×C8×D73—21no—
26#14556591—21no—
27C4×D292D411yescharacteristic
28#14556537—42no—
29#14556537—42no—
30#14556530—42no—
31C2×#11924003D411yescharacteristic
32C2×#11924003D411yescharacteristic
33#14556525—41no—
34#14556524—41no—
35C4⋊#10596831—21no—
36C4⋊#10596831D411yescharacteristic
37#14556513—41no—
38#14556511—41no—
39#14556503—21no—
40C2×Q16×C73—21no—
41C2×Q16×C73—21no—
42C4⋊Q8×C73—21no—
43C2×C16×C73—21no—
44C4⋊C8×C73—21no—
45C4×C8×C73C2311yescharacteristic
46C2×Dic146—41no—
47C2×D292D811yescharacteristic
48C2×C4×D73—21no—
49Dic292—41no—
50Dic292—41no—
51Dic292—81no—
52C2×#10596831—21no—
53C2×#10596831—41no—
54C8×D73—41no—
55C8×D73—41no—
56C4⋊Dic73—41no—
57C4⋊Dic73—41no—
58C4⋊Dic73D811yescharacteristic
59#11924005—21no—
60#11924003—21no—
61#11924003D812yes—
62C2×Q8×C73—41no—
63Q16×C73—41no—
64Q16×C73—41no—
65Q16×C73—81no—
66C2×C8×C73—41no—
67C2×C8×C73C2×D411yescharacteristic
68C2×C8×C73#4111yescharacteristic
69C4⋊C4×C73—41no—
70C4⋊C4×C73—41no—
71C42×C73C2×D411yescharacteristic
72C16×C73—41no—
73C22×D73—21no—
74Q8×C73—81no—
75Q8×C73—81no—
76C2×C4×C73—81no—
77C2×C4×C73#12111yescharacteristic
78C2×C4×C73C2×D811yescharacteristic
79C2×C4×C73#13511yescharacteristic
80C2×Dic73—21no—
81C2×Dic73—81no—
82D292—21no—
83D292—21no—
84C4×D73—41no—
85C4×D73—41no—
86Dic146—81no—
87Dic146—81no—
88C8×C73—21no—
89C8×C73—81no—
90C8×C73C2×D811yescharacteristic
91C8×C73AGL(1,ℤ/8)11yescharacteristic
92#10596831—41no—
93#10596831—81no—
94C22×C73#46611yescharacteristic
95C2×D73—41no—
96C2×D73—41no—
97C2×D73—41no—
98C4×C73—21no—
99C4×C73—161no—
100C4×C73#45911yescharacteristic
101C4×C73#47211yescharacteristic
102C4×C73#51011yescharacteristic
103C4×C73#51011yescharacteristic
104Dic73—41no—
105Dic73—161no—
106#12434—731nomaximal, Sylow
107C2×C73#166711yescharacteristic
108C2×C73#221911yescharacteristic
109C2×C73#222211yescharacteristic
110D73—81no—
111#2247—731no—
112#2169—731no—
113#1669—731no—
114#1669—731no—
115#1372—731no—
116#1362—731no—
117#1362D7311yescharacteristic, complemented
118C73#1243411yescharacteristic, complemented, Sylow
119C2×Q32—1461no—
120C2×Q32—1461no—
121C2×M32—1461no—
122#494—731no—
123#494C2×D7311yescharacteristic
124#474—1461no—
125#474—1461no—
126C8×D4—731no—
127C4⋊C16C2×D7311yescharacteristic
128C22⋊C16—1461no—
129C4×C16—731no—
130#335—731no—
131#335C2×D7311yescharacteristic
132#332—1461no—
133#332—1461no—
134C2×Q16—21no—
135C2×Q16—21no—
136C2×Q16—1461no—
137C2×Q16—1461no—
138C22×C8—1461no—
139C4⋊Q8—21no—
140C4⋊Q8—1461no—
141C4×D4—731no—
142Q32—2922no—
143Q32—2922no—
144M32—2922no—
145C2×C16—21no—
146C2×C16—731no—
147C2×C16—731no—
148#107—2921no—
149#107—2921no—
150C4⋊C8—21no—
151C4⋊C8—731no—
152C4⋊C8—1461no—
153#102—2921no—
154#102—2921no—
155C22⋊C8—1461no—
156C4×C8C22×D7311yescharacteristic
157C2×Q8—41no—
158C2×Q8—2921no—
159C2×D4—731no—
160C22×C4—1461no—
161Q16—41no—
162Q16—41no—
163Q16—81no—
164Q16—2921no—
165Q16—2921no—
166Q16—5841no—
167C2×C8—41no—
168C2×C8—2921no—
169C2×C8—2921no—
170C2×C8—2921no—
171C2×C8—1461no—
172C2×C8D4×D7311yescharacteristic
173C2×C8#1192402811yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—2921no—
177C4⋊C4—2921no—
178C4⋊C4—731no—
179C22⋊C4—1461no—
180C42D4×D7311yescharacteristic
181C16—41no—
182C16—732no—
183C16—1461no—
184C23—1461no—
185Q8—81no—
186Q8—81no—
187Q8—5841no—
188Q8—5841no—
189D4—1461no—
190D4—1461no—
191C2×C4—81no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—5841no—
195C2×C4—1461no—
196C2×C4#1455656411yescharacteristic
197C2×C4D8×D7311yescharacteristic
198C2×C4#1455661211yescharacteristic
199C8—21no—
200C8—81no—
201C8—2921no—
202C8—5841no—
203C8D8×D7311yescharacteristic
204C8#1455661811yescharacteristic
205C22—2921no—
206C22—2921no—
207C22—2921no—
208C22#1798882211yescharacteristic
209C4—21no—
210C4—161no—
211C4—2921no—
212C4—11681no—
213C4#1798878111yescharacteristic
214C4#1798885611yescharacteristic
215C4#1798902611yescharacteristic
216C4#1798902911yescharacteristic
217C2—5841no—
218C2#2260928511yescharacteristic
219C2#2261203811yescharacteristic
220C2#2261205511yescharacteristic
subgroupG/H
centerC22#17988822
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1362C2
socleC22×C73#466
prime radicalC2×D292D8
hypercenter#1362D73
hypocenterC73#12434
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #22612183C2semidirect
5. #22608004C2semidirect
6. #22607981C2semidirect
7. C73×#1362C2semidirect
117. #1362D73semidirect
118. C73#12434semidirect

Maximal subgroups

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

subgroupindex
#226121832
#226117622
#226092972
#226092932
#226080042
#226079812
C73×#13622
#1243473