Finite Group Databasebeta

← #34000858

Subgroups — #34000858

Order 18688.

202 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 40 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#22624861C211yesmaximal, characteristic
2#22624751C211yesmaximal, characteristic
3#22610146C211yesmaximal, characteristic
4#17989453—21no—
5#17989432—21no—
6#17988630—21no—
7C2×#14556510C411yescharacteristic
8#17988494C2211yescharacteristic
9#17988346—21no—
10#519×C73C411yescharacteristic
11C22×#10596833—41no—
12C22⋊#10596833—41no—
13C2×#11924012—21no—
14C2×C4⋊Dic73D411yescharacteristic
15C2×C4×Dic73D411yescharacteristic
16#14556524—41no—
17#14556522—41no—
18#14556510—21no—
19#14556510C812yescomplemented
20#14556498—41no—
21C22×Q8×C73C2×C411yescharacteristic
22C4×Q8×C73—41no—
23C4×Q8×C73—41no—
24#117×C73—21no—
25#117×C73—41no—
26C2×#10596833—42no—
27C2×#10596833—81no—
28C2×#10596833—81no—
29C2×#10596833—81no—
30C22×Dic73—21no—
31C22×Dic73—21no—
32#11924012—22no—
33#11924012—41no—
34C2×#10596831—41no—
35C4⋊Dic73—41no—
36C4×Dic73—41no—
37C2×Q8×C73—21no—
38C2×Q8×C73—41no—
39C2×Q8×C73—41no—
40C2×Q8×C73C2×C811yescharacteristic
41C2×Q8×C73M1611yescharacteristic
42C22×C4×C73—21no—
43C22×C4×C73C22⋊C411yescharacteristic
44C4⋊C4×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—41no—
47C4⋊C4×C73—41no—
48C22⋊C4×C73—41no—
49C42×C73—41no—
50C42×C73—42no—
51C23×C73#9911yescharacteristic
52Q8×C73—41no—
53Q8×C73—41no—
54Q8×C73—42no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—41no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73C22⋊C811yescharacteristic
64C2×C4×C73#10111yescharacteristic
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—81no—
71#10596833—82no—
72#10596833—161no—
73#10596831—42no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73#32411yescharacteristic
77C22×C73AΣL(1,𝔽16)11yescharacteristic
78C22×C73#35211yescharacteristic
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73—81no—
84C4×C73—81no—
85Dic73—41no—
86Dic73—41no—
87Dic73—81no—
88#7376—731nomaximal, Sylow
89C2×C73—21no—
90C2×C73—21no—
91C2×C73#132611yescharacteristic
92C2×C73#140411yescharacteristic
93C2×C73#140511yescharacteristic
94#1857—731no—
95#1319—731no—
96#1272—731no—
97C73#737611yescharacteristic, complemented, Sylow
98#519#6440811yescharacteristic
99#428—1461no—
100C2×#101—731no—
101#391—731no—
102#339—1461no—
103#336—1461no—
104#324—1461no—
105C22×Q8C2×#6440811yescharacteristic
106C2×M16—1461no—
107C22×C8—2921no—
108C4×Q8—41no—
109C4×Q8—41no—
110#117—21no—
111#117—41no—
112C2×C4⋊C4—731no—
113C2×C42—731no—
114#107—2921no—
115#106—2921no—
116#101—732no—
117#101—1461no—
118C22⋊C8—2921no—
119#95—2921no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8#1192403611yescharacteristic
124C2×Q8#1192403811yescharacteristic
125C22×C4—21no—
126C22×C4—1461no—
127C22×C4—1461no—
128C22×C4C22⋊#6440811yescharacteristic
129M16—2921no—
130M16—1462no—
131C2×C8—2921no—
132C2×C8—2922no—
133C2×C8—5841no—
134C2×C8—5841no—
135C2×C8—5841no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—2921no—
141C22⋊C4—41no—
142C42—41no—
143C42—42no—
144C42—2921no—
145C23#1455664911yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—2921no—
158C2×C4—2921no—
159C2×C4—2921no—
160C2×C4—5841no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4#1455664811yescharacteristic
164C2×C4#1455665211yescharacteristic
165C8—2922no—
166C8—5842no—
167C8—11681no—
168C22—21no—
169C22—21no—
170C22#1798943311yescharacteristic
171C22#1798948711yescharacteristic
172C22#1798948911yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—81no—
179C4—2921no—
180C4—2921no—
181C4—5841no—
182C2—21no—
183C2—21no—
184C2#2262487611yescharacteristic
185C2#2262505411yescharacteristic
186C2#2262505611yescharacteristic
subgroupG/H
centerC22#17989487
commutatorC2×Q8×C73C2×C8
FrattiniC22×Q8C2×#64408
Fitting#519×C73C4
socleC22×C73AΣL(1,𝔽16)
prime radicalC23×C73#99
cosocle#17988494C22
hypercenter#519#64408
hypocenterC73#7376
LCSG ▷ C2×Q8×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ #519

Complements

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

NH ≅ G/Ntype
19. #14556510C8semidirect
97. C73#7376semidirect

Maximal subgroups

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

subgroupindex
#226248612
#226247512
#226101462
#737673