Finite Group Databasebeta

← #32973409

Subgroups — #32973409

Order 18688.

228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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#22610140C211yesmaximal, characteristic
2#22607752C211yesmaximal, characteristic
3C73×#1318C211yesmaximal, characteristic
4#17989062C411yescharacteristic
5#17988627—21no—
6C2×#14556508C411yescharacteristic
7#17988347—21no—
8#17988342—21no—
9#390×C73C2211yescharacteristic
10#324×C73—21no—
11C2×#11924012—21no—
12C22×#10596831—41no—
13D4×Dic73—41no—
14D4×Dic73—41no—
15#14556550—21no—
16C2×C22⋊Dic73—41no—
17#14556524—41no—
18#14556522—41no—
19#14556508—21no—
20#14556508C812yescomplemented
21C22×D4×C73C2×C411yescharacteristic
22C2×C4⋊C4×C73D411yescharacteristic
23C2×C22⋊C4×C73—41no—
24C2×C42×C73D411yescharacteristic
25C22⋊C8×C73—41no—
26C22×Dic73—41no—
27C22×Dic73—41no—
28#11924012—22no—
29#11924012—41no—
30C2×#10596831—41no—
31C2×#10596831—42no—
32C2×#10596831—81no—
33C2×#10596831—81no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C22⋊Dic73—42no—
37C22⋊Dic73—41no—
38C4×Dic73—41no—
39C24×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—41no—
42C2×D4×C73—41no—
43C2×D4×C73C2×C811yescharacteristic
44C2×D4×C73M1611yescharacteristic
45C22×C4×C73—21no—
46C22×C4×C73—21no—
47C22×C4×C73C22⋊C411yescharacteristic
48C2×C8×C73—81no—
49C4⋊C4×C73—41no—
50C22⋊C4×C73—81no—
51C22⋊C4×C73—81no—
52C42×C73—41no—
53C23×C73—21no—
54C23×C73—21no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73—81no—
58C23×C73—81no—
59C23×C73#9911yescharacteristic
60D4×C73—41no—
61D4×C73—41no—
62D4×C73—42no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73—81no—
71C2×C4×C73C22⋊C811yescharacteristic
72C2×C4×C73#10111yescharacteristic
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—161no—
76C2×Dic73—161no—
77C8×C73—161no—
78#10596831—42no—
79#10596831—82no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73—81no—
85C22×C73—81no—
86C22×C73—81no—
87C22×C73—81no—
88C22×C73—161no—
89C22×C73#32411yescharacteristic
90C22×C73AΣL(1,𝔽16)11yescharacteristic
91C22×C73#35211yescharacteristic
92C4×C73—21no—
93C4×C73—21no—
94C4×C73—41no—
95C4×C73—41no—
96C4×C73—81no—
97Dic73—81no—
98Dic73—81no—
99#7375—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—21no—
102C2×C73—81no—
103C2×C73—81no—
104C2×C73#132611yescharacteristic
105C2×C73#140211yescharacteristic
106C2×C73#140311yescharacteristic
107#1856—731no—
108#1318D7311yescharacteristic
109#1270—731no—
110C73#737511yescharacteristic, complemented, Sylow
111#518—731no—
112#428—1461no—
113C2×#100—731no—
114#390C2×D7311yescharacteristic
115#339—1461no—
116#336—1461no—
117#324—21no—
118C22×D4C4×D7311yescharacteristic
119C2×M16—1461no—
120C22×C8—2921no—
121C4×D4—2921no—
122C4×D4—2921no—
123#117—1461no—
124C2×C4⋊C4C22⋊D7311yescharacteristic
125C2×C22⋊C4—41no—
126C2×C22⋊C4—2921no—
127C2×C42D29211yescharacteristic
128#107—2921no—
129#106—2921no—
130#100—732no—
131#100—1461no—
132C22⋊C8—41no—
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4C8×D7311yescharacteristic
138C2×D4#1192401111yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—2921no—
142C22×C4—2921no—
143C22×C4#1192400511yescharacteristic
144M16—2921no—
145M16—1462no—
146C2×C8—81no—
147C2×C8—2921no—
148C2×C8—2922no—
149C2×C8—5841no—
150C2×C8—5841no—
151C4⋊C4—41no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C22⋊C4—81no—
155C22⋊C4—81no—
156C22⋊C4—2922no—
157C22⋊C4—2921no—
158C42—41no—
159C42—2921no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1455650511yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—2921no—
179C2×C4—2921no—
180C2×C4—11681no—
181C2×C4—11681no—
182C2×C4#1455650311yescharacteristic
183C2×C4#1455650911yescharacteristic
184C8—161no—
185C8—2922no—
186C8—5842no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1798831211yescharacteristic
197C22#1798837311yescharacteristic
198C22#1798837811yescharacteristic
199C4—21no—
200C4—21no—
201C4—41no—
202C4—41no—
203C4—81no—
204C4—5841no—
205C4—5841no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#2260787811yescharacteristic
211C2#2260807511yescharacteristic
212C2#2260807811yescharacteristic
subgroupG/H
centerC22#17988373
commutatorC2×D4×C73C2×C8
Frattini#390C2×D73
FittingC73×#1318C2
socleC22×C73AΣL(1,𝔽16)
prime radicalC22×D4×C73C2×C4
cosocle#390×C73C22
hypercenter#1318D73
hypocenterC73#7375
LCSG ▷ C2×D4×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
20. #14556508C8semidirect
110. C73#7375semidirect

Maximal subgroups

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

subgroupindex
#226101402
#226077522
C73×#13182
#737573