Finite Group Databasebeta

← #34000454

Subgroups — #34000454

Order 18688.

248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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#22626162C211yesmaximal, characteristic
2#22625814C211yesmaximal, characteristic
3#22609980C211yesmaximal, characteristic
4C2×#14556666C411yescharacteristic, complemented
5C2×#14556664C411yescharacteristic, complemented
6#17989597—21no—
7#17989566—21no—
8#17989482—21no—
9C22⋊#11924031—21no—
10#17989455C412yes—
11C2×#14556599C2211yescharacteristic
12C2×#14556526—21no—
13#17988569—21no—
14#17988345C411yescharacteristic, complemented
15#338×C73C411yescharacteristic, complemented
16#14556670—22no—
17#14556666—41no—
18#14556664—41no—
19C2×#11924031—21no—
20C2×#11924031—21no—
21#14556660—41no—
22#14556659—41no—
23#14556650—41no—
24#14556649—41no—
25C2×#11924028D411yescharacteristic
26#14556599—41no—
27#14556599—41no—
28C2×#11924012—21no—
29C2×#11924011C2×C411yescharacteristic
30C2×#11924011Q811yescharacteristic
31C22×#10596831D411yescharacteristic
32C2×C8×D73C2×C411yescharacteristic
33C2×C8×D73D411yescharacteristic
34#14556526—41no—
35#14556526—41no—
36#14556509—41no—
37#14556507—41no—
38C2×M16×C73—21no—
39C2×M16×C73C2×C411yescharacteristic
40C4⋊#64408—42no—
41C22⋊#64408—42no—
42C4×#64408—42no—
43#11924031—41no—
44#11924031—41no—
45#11924028—41no—
46#11924028—41no—
47C2×Dic146SD1611yescharacteristic
48C2×D292D811yescharacteristic
49C2×C22⋊D73SD1611yescharacteristic
50C2×C22⋊D73Q1611yescharacteristic
51C2×C4×D73C22⋊C411yescharacteristic
52C2×C4×D73C4⋊C411yescharacteristic
53#11924012—41no—
54#11924012—41no—
55#11924011—41no—
56#11924011—41no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C2×#10596831—41no—
60C2×#10596831C22⋊C411yescharacteristic
61C2×#10596831C4⋊C411yescharacteristic
62C8×D73—21no—
63C8×D73—21no—
64C8×D73—21no—
65C8×D73—21no—
66C22×C4×C73C22⋊C411yescharacteristic
67M16×C73—41no—
68M16×C73—41no—
69M16×C73—41no—
70C2×C8×C73—41no—
71C2×C8×C73C4211yescharacteristic
72C2×C8×C73C4⋊C411yescharacteristic
73C23×C73#10311yescharacteristic
74C22×D73#10211yescharacteristic
75C22×D73#10711yescharacteristic
76C2×#64408—82no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73#9511yescharacteristic
80C2×C4×C73#10211yescharacteristic
81C22⋊D73—41no—
82C22⋊D73—41no—
83C2×Dic73#10311yescharacteristic
84C2×Dic73#10611yescharacteristic
85D292—41no—
86C4×D73—21no—
87C4×D73—21no—
88C4×D73—21no—
89C4×D73—21no—
90Dic146—41no—
91C8×C73—21no—
92C8×C73—21no—
93C8×C73—81no—
94#10596831—21no—
95#10596831—81no—
96#10596831#9911yescharacteristic
97#10596831#9911yescharacteristic
98C22×C73—21no—
99C22×C73—41no—
100C22×C73#34011yescharacteristic
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—41no—
104C2×D73—41no—
105#64408—162no—
106C4×C73—21no—
107C4×C73H(3,ℤ/4)11yescharacteristic
108C4×C73#34211yescharacteristic
109Dic73—21no—
110Dic73—21no—
111#7227—731nomaximal, Sylow
112C2×C73—21no—
113C2×C73—41no—
114C2×C73#128911yescharacteristic
115D73—41no—
116D73—41no—
117#2113—731no—
118#1813—731no—
119#1812—731no—
120C73#722711yescharacteristic, complemented, Sylow
121C2×#131—731no—
122C2×M32—731no—
123C22×C16—731no—
124C2×#108—1461no—
125#427—1461no—
126#413—1461no—
127#410—1461no—
128C22⋊C16—1461no—
129C22⋊C16—1461no—
130#338—731no—
131#338#6440811yescharacteristic, complemented
132H(3,ℤ/4)—732no—
133C2×#41—731no—
134#131—2921no—
135#131—2921no—
136C2×M16—21no—
137C2×M16—731no—
138C2×M16—731no—
139C2×M16—1461no—
140C2×M16C2×#6440811yescharacteristic
141C22×C8—731no—
142C22×C8—731no—
143C22×C8—731no—
144#117—1462no—
145M32—2921no—
146C2×C16—2921no—
147C2×C16—1461no—
148C2×C16—1461no—
149#108—2921no—
150#108—2921no—
151#107—2921no—
152#106—2921no—
153#101—2921no—
154#100—2921no—
155#99—2921no—
156#99—2921no—
157#41—2921no—
158#41—2921no—
159C2×Q8—731no—
160C2×D4—731no—
161C2×D4—731no—
162C2×D4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4C22⋊#6440811yescharacteristic
166M16—41no—
167M16—41no—
168M16—41no—
169M16—2921no—
170M16—2921no—
171M16—2921no—
172M16—2921no—
173C2×C8—41no—
174C2×C8—2921no—
175C2×C8—731no—
176C2×C8—731no—
177C2×C8—1461no—
178C2×C8—1461no—
179C2×C8—1461no—
180C2×C8—1461no—
181C2×C8—1461no—
182C2×C8—1461no—
183C2×C8C4×#6440811yescharacteristic
184C2×C8C4⋊#6440811yescharacteristic
185C4⋊C4—2922no—
186C22⋊C4—2922no—
187C42—2922no—
188C16—2921no—
189C16—2921no—
190C23—731no—
191C23—731no—
192C23#1455665411yescharacteristic
193Q8—2921no—
194D4—2921no—
195D4—2921no—
196D4—2921no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—5842no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4(C2×#64408)⋊C411yescharacteristic
207C2×C4#1455665311yescharacteristic
208C8—21no—
209C8—21no—
210C8—81no—
211C8—5841no—
212C8—731no—
213C8—731no—
214C8—1461no—
215C22—21no—
216C22—41no—
217C22—2921no—
218C22—2921no—
219C22—1461no—
220C22—1461no—
221C22#1798946011yescharacteristic
222C4—21no—
223C4—11682no—
224C4—1461no—
225C4—1461no—
226C4#1798945411yescharacteristic
227C4#1798946411yescharacteristic
228C2—21no—
229C2—41no—
230C2—2921no—
231C2—2921no—
232C2#2262479311yescharacteristic
subgroupG/H
centerC4#17989454
commutatorC2×C8×C73C42
FrattiniC2×M16C2×#64408
Fitting#338×C73C4
socleC2×C73#1289
prime radicalC2×#11924028D4
cosocleC2×#14556599C22
hypercenter#338#64408
hypocenterC73#7227
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ #338

Complements

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

NH ≅ G/Ntype
4. C2×#14556666C4semidirect
5. C2×#14556664C4semidirect
14. #17988345C4semidirect
15. #338×C73C4semidirect
120. C73#7227semidirect
131. #338#64408semidirect

Maximal subgroups

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

subgroupindex
#226261622
#226258142
#226099802
#722773