Finite Group Databasebeta

← #32997941

Subgroups — #32997941

Order 18688.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#22611808C211yesmaximal, characteristic
2#22608844C211yesmaximal, characteristic, complemented
3#22608754C211yesmaximal, characteristic, complemented
4#22607897C211yesmaximal, characteristic, complemented
5#22607897C211yesmaximal, characteristic, complemented
6#22607853C211yesmaximal, characteristic, complemented
7C73×#1368C211yesmaximal, characteristic, complemented
8C2×D1168C411yescharacteristic
9C4×D584C2211yescharacteristic
10C4×D584C2211yescharacteristic
11#17988664—21no—
12#17988652—21no—
13#17988415C411yescharacteristic
14#17988389C411yescharacteristic
15#17988389C411yescharacteristic
16#17988363C2211yescharacteristic
17#17988314—21no—
18#17988314—21no—
19#17988308C2211yescharacteristic
20#346×C73C2211yescharacteristic
21#334×C73C2211yescharacteristic
22#334×C73C2211yescharacteristic
23C2×D584C2×C411yescharacteristic
24C2×D584C2×C411yescharacteristic
25C2×#11924011—41no—
26C2×C8×D73—41no—
27C4×D292—21no—
28C4×D292—21no—
29D1168—22no—
30C2×#11924003—21no—
31#14556525C2×C411yescharacteristic
32#14556525C2×C411yescharacteristic
33#14556513—21no—
34#14556513—21no—
35#14556503—41no—
36#14556503—41no—
37C4×#10596831D411yescharacteristic
38C4×#10596831D411yescharacteristic
39C2×C16×C73C2×C411yescharacteristic
40C2×C16×C73C2×C411yescharacteristic
41C4⋊C8×C73—21no—
42C4⋊C8×C73—21no—
43C4×C8×C73C2311yescharacteristic
44C2×D292—21no—
45C2×D292—21no—
46C2×C4×D73—41no—
47C2×C4×D73—41no—
48D584—21no—
49D584—21no—
50D584—21no—
51D584M1612yescomplemented
52#11924011—82no—
53C2×#10596831—21no—
54C2×#10596831—21no—
55C8×D73—82no—
56C4⋊Dic73—21no—
57C4⋊Dic73—21no—
58#11924005—41no—
59#11924005—41no—
60#11924003—22no—
61C2×C8×C73—41no—
62C2×C8×C73—41no—
63C2×C8×C73C22×C411yescharacteristic
64C2×C8×C73#4111yescharacteristic
65C42×C73C2×D411yescharacteristic
66C16×C73—21no—
67C16×C73—21no—
68C22×D73—41no—
69C22×D73—41no—
70C2×C4×C73C4×D411yescharacteristic
71C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
72C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
73C2×Dic73—41no—
74C2×Dic73—41no—
75D292—22no—
76D292—41no—
77D292—41no—
78D292—41no—
79C4×D73—81no—
80C4×D73—81no—
81C4×D73—81no—
82C4×D73—81no—
83C8×C73—21no—
84C8×C73—81no—
85C8×C73—81no—
86C8×C73C2×M1611yescharacteristic
87C8×C73#13111yescharacteristic
88#10596831—41no—
89#10596831—41no—
90C22×C73#44211yescharacteristic
91C2×D73—42no—
92C2×D73—81no—
93C2×D73—81no—
94C2×D73—81no—
95C2×D73—81no—
96C2×D73—81no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73#43511yescharacteristic
100C4×C73#44311yescharacteristic
101Dic73—81no—
102Dic73—81no—
103#12078—731nomaximal, Sylow
104C2×C73#158611yescharacteristic
105C2×C73AGL(1,ℤ/16)11yescharacteristic
106C2×C73AGL(1,ℤ/16)11yescharacteristic
107D73—82no—
108D73—161no—
109#2177—731no—
110#1594—731no—
111#1580—731no—
112#1368D7311yescharacteristic, complemented
113#1333—731no—
114#1333—731no—
115#1313—731no—
116C73#1207811yescharacteristic, complemented, Sylow
117C2×D16—731no—
118C4×D8—731no—
119C4×D8—731no—
120#436—1461no—
121C8×D4—1461no—
122#367—731no—
123#357—731no—
124#357—731no—
125#346—731no—
126#346C2×D7311yescharacteristic
127#334C2×D7311yescharacteristic
128#334C2×D7311yescharacteristic
129D4⋊C8—1461no—
130D4⋊C8—1461no—
131#322—731no—
132C2×D8—731no—
133C2×D8—731no—
134C2×M16—2921no—
135C22×C8—2921no—
136C4×D4—1461no—
137C4×D4—1461no—
138D16—1462no—
139C2×C16—1461no—
140C2×C16C4×D7311yescharacteristic
141C2×C16C4×D7311yescharacteristic
142#107—731no—
143#107—731no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146#102—1461no—
147#102—1461no—
148C22⋊C8—2921no—
149C22⋊C8—2921no—
150C4×C8—731no—
151C4×C8—731no—
152C4×C8C22×D7311yescharacteristic
153C2×D4—1461no—
154C2×D4—1461no—
155C22×C4—2921no—
156C22×C4—2921no—
157D8—732no—
158D8—1461no—
159D8—1461no—
160D8—1461no—
161M16—5842no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—5842no—
165C2×C8—1461no—
166C2×C8—1461no—
167C2×C8C2×C4×D7311yescharacteristic
168C2×C8#1192402911yescharacteristic
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C22⋊C4—2921no—
172C22⋊C4—2921no—
173C42D4×D7311yescharacteristic
174C16—21no—
175C16—21no—
176C16—1462no—
177C23—2921no—
178C23—2921no—
179D4—2921no—
180D4—2921no—
181D4—2921no—
182D4—1462no—
183C2×C4—2921no—
184C2×C4—2921no—
185C2×C4—5841no—
186C2×C4—5841no—
187C2×C4—5841no—
188C2×C4—5841no—
189C2×C4#1455655311yescharacteristic
190C2×C4#1455661811yescharacteristic
191C2×C4#1455661811yescharacteristic
192C8—21no—
193C8—81no—
194C8—81no—
195C8—2921no—
196C8—2921no—
197C8M16×D7311yescharacteristic
198C8#1455659711yescharacteristic
199C22—2922no—
200C22—5841no—
201C22—5841no—
202C22—5841no—
203C22—5841no—
204C22—5841no—
205C22#1798869811yescharacteristic
206C4—21no—
207C4—21no—
208C4—5841no—
209C4—5841no—
210C4#1798865711yescharacteristic
211C4#1798870311yescharacteristic
212C2—5842no—
213C2—11681no—
214C2#2260879411yescharacteristic
215C2#2261182811yescharacteristic
216C2#2261182811yescharacteristic
subgroupG/H
centerC22#17988698
commutatorC2×C8×C73C22×C4
FrattiniC4×C8C22×D73
FittingC73×#1368C2
socleC22×C73#442
prime radicalC2×D1168C4
cosocleC4×C8×C73C23
hypercenter#1368D73
hypocenterC73#12078
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1368

Complements

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

NH ≅ G/Ntype
2. #22608844C2semidirect
3. #22608754C2semidirect
4. #22607897C2semidirect
5. #22607897C2semidirect
6. #22607853C2semidirect
7. C73×#1368C2semidirect
51. D584M16semidirect
112. #1368D73semidirect
116. C73#12078semidirect

Maximal subgroups

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

subgroupindex
#226118082
#226088442
#226087542
#226078972
#226078532
C73×#13682
#1207873