Finite Group Databasebeta

← #34014547

Subgroups — #34014547

Order 18688.

182 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 50 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#22626335C211yesmaximal, characteristic
2#22626328C211yesmaximal, characteristic, complemented
3#22625097C211yesmaximal, characteristic, complemented
4#22625087C211yesmaximal, characteristic, complemented
5#22625084C211yesmaximal, characteristic
6#22625040C211yesmaximal, characteristic, complemented
7#22612247C211yesmaximal, characteristic
8#17989629—21no—
9Q16×#64408—21no—
10#17989520C2211yescharacteristic
11#17989516C2211yescharacteristic
12#17989514C2211yescharacteristic
13#17989501—21no—
14#17989500—21no—
15#17989474C2211yescharacteristic
16#17989016C2211yescharacteristic
17Q32×D73C2211yescharacteristic
18Dic1168C411yescharacteristic, complemented
19#17988427C411yescharacteristic, complemented
20#17988425C411yescharacteristic, complemented
21#17988420C2211yescharacteristic
22SD64×C73C411yescharacteristic, complemented
23#14556678—41no—
24Q8×#64408—41no—
25#14556664D411yescharacteristic
26#14556662—21no—
27#14556660—21no—
28#14556655—41no—
29#14556654—41no—
30C8×#64408D411yescharacteristic
31#14556641—21no—
32#14556610—21no—
33Q16×D73—21no—
34Dic584C2×C411yescharacteristic
35Dic584C2×C411yescharacteristic
36#14556537—21no—
37#14556535—21no—
38C16×D73C2311yescharacteristic
39#14556497C2×C411yescharacteristic
40Q32×C73C2×C411yescharacteristic
41D16×C73C2×C411yescharacteristic
42C32×C73C2×C411yescharacteristic
43#11924038—41no—
44#11924037—81no—
45#11924036D811yescharacteristic
46C2×#10596833—81no—
47C4⋊#64408—41no—
48C4⋊#64408—81no—
49C4×#64408—81no—
50C4×#64408D811yescharacteristic
51#11924031—21no—
52#11924027—41no—
53Q8×D73—41no—
54Dic292—21no—
55Dic292—21no—
56#11924018—41no—
57#11924016—41no—
58C8×D73C2×D411yescharacteristic
59#11924003#4111yescharacteristic
60Q16×C73—21no—
61D8×C73—21no—
62C16×C73C22×C411yescharacteristic
63C2×#64408—21no—
64C2×#64408—81no—
65Q8×C73—41no—
66D4×C73—41no—
67C22⋊D73—81no—
68C2×Dic73—81no—
69C4×D73—81no—
70C4×D73C2×D811yescharacteristic
71Dic146—41no—
72Dic146—41no—
73Dic146—81no—
74#10596833—21no—
75#10596833—81no—
76C8×C73C4×D411yescharacteristic
77#10596831#13511yescharacteristic
78C22×C73—81no—
79C2×D73#50911yescharacteristic
80#64408—41no—
81#64408—161no—
82C4×C73—81no—
83C4×C73C4×D811yescharacteristic
84Dic73—81no—
85Dic73—81no—
86Dic73#50911yescharacteristic
87#13657—731nomaximal, Sylow
88C2×C73—161no—
89C2×C73#217711yescharacteristic
90D73—21no—
91#2264—731no—
92#2179—731no—
93#2176—731no—
94#1426—731no—
95#1420—731no—
96#1418—731no—
97#1398—731no—
98C73#1365711yescharacteristic, complemented, Sylow
99#508—731no—
100C2×Q32—731no—
101#443—1461no—
102C4×Q16—1461no—
103Q64—731no—
104Q64—731no—
105SD64—731no—
106SD64#6440811yescharacteristic, complemented
107M64—731no—
108M64—731no—
109#368—731no—
110#367—731no—
111#359—1461no—
112#358—1461no—
113#346—731no—
114#135—1461no—
115C2×Q16—1461no—
116#131—2921no—
117C4×Q8—2921no—
118Q32—731no—
119Q32—731no—
120Q32—1461no—
121Q32C2×#6440811yescharacteristic
122SD32—1461no—
123D16C2×#6440811yescharacteristic
124C2×C16—731no—
125C2×C16—731no—
126#108—1461no—
127#107—1461no—
128#104—2921no—
129#103—2921no—
130C4×C8—731no—
131C32—731no—
132C32—1461no—
133C32C2×#6440811yescharacteristic
134#41—2921no—
135C2×Q8—2921no—
136Q16—21no—
137Q16—2921no—
138Q16—1461no—
139Q16—1461no—
140SD16—2921no—
141D8—21no—
142M16—2921no—
143M16—5841no—
144C2×C8—5841no—
145C2×C8—731no—
146C2×C8—731no—
147C4⋊C4—2921no—
148C4⋊C4—5841no—
149C42—5841no—
150C42—731no—
151C16—731no—
152C16—1461no—
153C16C22×#6440811yescharacteristic
154Q8—41no—
155Q8—2921no—
156Q8—2921no—
157Q8—5841no—
158D4—41no—
159D4—5841no—
160C2×C4—5841no—
161C2×C4—5841no—
162C2×C4—5841no—
163C2×C4—731no—
164C2×C4—1461no—
165C8—5841no—
166C8—731no—
167C8—1461no—
168C8D4×#6440811yescharacteristic
169C22—81no—
170C22—731no—
171C4—81no—
172C4—2921no—
173C4—5841no—
174C4—5841no—
175C4—731no—
176C4—11681no—
177C4D8×#6440811yescharacteristic
178C2—161no—
179C2—1461no—
180C2#2262632911yescharacteristic
subgroupG/H
centerC2#22626329
commutatorC16×C73C22×C4
FrattiniC16C22×#64408
FittingSD64×C73C4
socleC2×C73#2177
prime radical#17989016C22
cosocleC16×D73C23
hypercenterSD64#64408
hypocenterC73#13657
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
2. #22626328C2semidirect
3. #22625097C2semidirect
4. #22625087C2semidirect
6. #22625040C2semidirect
18. Dic1168C4semidirect
19. #17988427C4semidirect
20. #17988425C4semidirect
22. SD64×C73C4semidirect
98. C73#13657semidirect
106. SD64#64408semidirect

Maximal subgroups

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

subgroupindex
#226263352
#226263282
#226250972
#226250872
#226250842
#226250402
#226122472
#1365773