Finite Group Databasebeta

← #33000398

Subgroups — #33000398

Order 18688.

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

normal subgroups only

This group has 240 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#22609317C211yesmaximal, characteristic, complemented
3#22609283C211yesmaximal, characteristic
4#22608003C211yesmaximal, characteristic, complemented
5#22607986C211yesmaximal, characteristic, complemented
6#22607977C211yesmaximal, characteristic, complemented
7C73×#2240C211yesmaximal, characteristic, complemented
8C2×C16×D73—21no—
9#17988789—21no—
10#17988779—21no—
11C8×D292C2211yescharacteristic
12C4⋊#11924003C2211yescharacteristic
13#17988366—21no—
14#17988340C2211yescharacteristic
15#17988340C2211yescharacteristic
16#17988333—21no—
17#17988331—21no—
18#500×C73C2211yescharacteristic
19#493×C73C2211yescharacteristic
20#357×C73—21no—
21#357×C73—21no—
22C4×C16×C73C2211yescharacteristic
23C2×#11924015—41no—
24C2×#11924013—41no—
25C2×C8×D73—21no—
26C4×D292D411yescharacteristic
27C2×#11924003—21no—
28C16×D73—42no—
29C4⋊#10596831—21no—
30C4⋊#10596831—21no—
31C4⋊#10596831D411yescharacteristic
32#14556515—41no—
33#14556512—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#11924015—82no—
47#11924013—82no—
48C2×#10596831—21no—
49C2×#10596831—41no—
50C2×#10596831—41no—
51C8×D73—41no—
52C8×D73—41no—
53C4⋊Dic73D811yescharacteristic
54#11924005—21no—
55#11924003—41no—
56C2×Q8×C73—41no—
57C2×D4×C73—41no—
58C2×D4×C73—41no—
59C2×D4×C73—41no—
60D8×C73—41no—
61D8×C73—41no—
62D8×C73—81no—
63C2×C8×C73C2×D411yescharacteristic
64C2×C8×C73#4111yescharacteristic
65C4⋊C4×C73—41no—
66C4⋊C4×C73—41no—
67C42×C73C2×D411yescharacteristic
68C16×C73—21no—
69C16×C73—21no—
70C23×C73—81no—
71C22×D73—21no—
72Q8×C73—81no—
73Q8×C73—81no—
74D4×C73—81no—
75D4×C73—81no—
76D4×C73—81no—
77D4×C73—81no—
78D4×C73—161no—
79C2×C4×C73—81no—
80C2×C4×C73#12111yescharacteristic
81C2×C4×C73C2×D811yescharacteristic
82C2×C4×C73#13511yescharacteristic
83C2×Dic73—21no—
84D292—21no—
85D292D1612yes—
86C4×D73—41no—
87C4×D73—41no—
88C8×C73—21no—
89C8×C73#13511yescharacteristic
90C8×C73AGL(1,ℤ/8)11yescharacteristic
91#10596831—41no—
92#10596831—81no—
93#10596831—81no—
94C22×C73—161no—
95C22×C73—161no—
96C22×C73—161no—
97C22×C73#46611yescharacteristic
98C2×D73—22no—
99C2×D73—41no—
100C2×D73—41no—
101C4×C73—21no—
102C4×C73—161no—
103C4×C73#46311yescharacteristic
104C4×C73#47111yescharacteristic
105C4×C73C2×D1611yescharacteristic
106C4×C73#50811yescharacteristic
107Dic73—41no—
108#12467—731nomaximal, Sylow
109C2×C73—321no—
110C2×C73#168111yescharacteristic
111C2×C73#221511yescharacteristic
112C2×C73#222311yescharacteristic
113D73—42no—
114#2240D7311yescharacteristic, complemented
115D4×C16—731no—
116#1673—731no—
117#1667—731no—
118#1371—731no—
119#1364—731no—
120#1361—731no—
121C73#1246711yescharacteristic, complemented, Sylow
122C22×C16—1461no—
123#500C2×D7311yescharacteristic
124#493C2×D7311yescharacteristic
125#461—1461no—
126#459—1461no—
127C8×D4—731no—
128C4⋊C16—731no—
129#357—21no—
130#357—21no—
131C22⋊C16—1461no—
132C4×C16C2×D7311yescharacteristic
133#335—731no—
134#335—731no—
135#332—1461no—
136#331—1461no—
137C2×SD16—2921no—
138C2×D8—21no—
139C2×D8—21no—
140C2×D8—2921no—
141C22×C8—1461no—
142C4⋊Q8—21no—
143#127—21no—
144C4×D4—731no—
145C2×C16—2922no—
146C2×C16—1461no—
147C2×C16C22⋊D7311yescharacteristic
148C2×C16C22⋊D7311yescharacteristic
149#107—21no—
150#107—21no—
151C4⋊C8—731no—
152C4⋊C8—1461no—
153C4⋊C8—1461no—
154#103—2921no—
155#102—2921no—
156C22⋊C8—1461no—
157C4×C8C22×D7311yescharacteristic
158C2×Q8—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—731no—
163C22×C4—1461no—
164SD16—5842no—
165D8—41no—
166D8—41no—
167D8—81no—
168D8—5842no—
169C2×C8—2921no—
170C2×C8—2921no—
171C2×C8—2921no—
172C2×C8—2921no—
173C2×C8—1461no—
174C2×C8C2×C22⋊D7311yescharacteristic
175C2×C8#1192402711yescharacteristic
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—731no—
179C22⋊C4—1461no—
180C42D4×D7311yescharacteristic
181C16—21no—
182C16—21no—
183C16—2921no—
184C23—81no—
185C23—1461no—
186Q8—81no—
187Q8—81no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192D4—161no—
193D4—732no—
194D4—1461no—
195C2×C4—81no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—1461no—
199C2×C4#1455656211yescharacteristic
200C2×C4D8×D7311yescharacteristic
201C2×C4#1455661011yescharacteristic
202C8—21no—
203C8—2921no—
204C8—5841no—
205C8—5841no—
206C8#1455661111yescharacteristic
207C8#1455661611yescharacteristic
208C22—161no—
209C22—161no—
210C22—161no—
211C22—2921no—
212C22—2921no—
213C22—1462no—
214C22#1798882011yescharacteristic
215C4—21no—
216C4—161no—
217C4—2921no—
218C4#1798879911yescharacteristic
219C4#1798884711yescharacteristic
220C4D16×D7311yescharacteristic
221C4#1798901611yescharacteristic
222C2—321no—
223C2—2922no—
224C2#2260936511yescharacteristic
225C2#2261201411yescharacteristic
226C2#2261205811yescharacteristic
subgroupG/H
centerC22#17988820
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2240C2
socleC22×C73#466
prime radical#22609283C2
hypercenter#2240D73
hypocenterC73#12467
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. #22609317C2semidirect
4. #22608003C2semidirect
5. #22607986C2semidirect
6. #22607977C2semidirect
7. C73×#2240C2semidirect
114. #2240D73semidirect
121. C73#12467semidirect

Maximal subgroups

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

subgroupindex
C16×D2922
#226093172
#226092832
#226080032
#226079862
#226079772
C73×#22402
#1246773