Finite Group Databasebeta

← #34032839

Subgroups — #34032839

Order 18688.

202 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 45 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#22627008C211yesmaximal, characteristic
2#22626935C211yesmaximal, characteristic
3#22626037C211yesmaximal, characteristic
4#17989706—21no—
5#17989700—21no—
6C2×#14556660C411yescharacteristic
7C2×#14556645C2211yescharacteristic
8#17989538—21no—
9#17989460—21no—
10#106×D73C411yescharacteristic
11#14556688—41no—
12#14556687—22no—
13#14556686—41no—
14C4⋊#10596842—41no—
15C22⋊#10596842—41no—
16C4×#10596842—22no—
17C2×#11924036D411yescharacteristic
18C2×C4⋊#64408—21no—
19C2×C4⋊#64408—41no—
20C2×C4×#64408D411yescharacteristic
21#14556660—41no—
22#14556645—41no—
23(C2×#64408)⋊C4—41no—
24C2×C8×D73C2×C411yescharacteristic
25C4⋊C4×D73—21no—
26#14556523C811yescharacteristic, complemented
27#14556522—21no—
28#106×C73C811yescharacteristic, complemented
29C2×#10596842—42no—
30#11924040—42no—
31C22×#64408—41no—
32C22×#64408D811yescharacteristic
33C22×#64408SD1611yescharacteristic
34#11924036—21no—
35#11924036SD1611yescharacteristic
36#11924036Q1611yescharacteristic
37C2×#10596833—21no—
38C4⋊#64408—41no—
39C4⋊#64408—41no—
40C4⋊#64408—82no—
41C4×#64408—21no—
42C4×#64408—21no—
43C2×C4×D73—41no—
44C2×C4×D73C22⋊C411yescharacteristic
45C2×#10596831M1611yescharacteristic
46C8×D73—21no—
47C8×D73—21no—
48C4⋊Dic73—21no—
49#11924007—41no—
50C2×C8×C73C2×C811yescharacteristic
51C4⋊C4×C73—21no—
52C22×D73#10211yescharacteristic
53C2×#64408—21no—
54C2×#64408—21no—
55C2×#64408—41no—
56C2×#64408—41no—
57C2×#64408—81no—
58C2×#64408—81no—
59C2×#64408—81no—
60#10596842—82no—
61C2×C4×C73—41no—
62C2×C4×C73C22⋊C811yescharacteristic
63C2×Dic73—41no—
64C2×Dic73#10411yescharacteristic
65C4×D73—81no—
66C4×D73—81no—
67C4×D73#9911yescharacteristic
68C4×D73#10111yescharacteristic
69C4×D73#10311yescharacteristic
70C4×D73#10411yescharacteristic
71#10596833—21no—
72#10596833—21no—
73C8×C73—21no—
74#10596831—21no—
75C22×C73D4⋊C811yescharacteristic
76C2×D73—21no—
77C2×D73—21no—
78C2×D73#32711yescharacteristic
79C2×D73#33211yescharacteristic
80#64408—41no—
81#64408—41no—
82#64408—161no—
83C4×C73—81no—
84C4×C73#32411yescharacteristic
85C4×C73Q8⋊C811yescharacteristic
86Dic73—81no—
87Dic73#32811yescharacteristic
88Dic73#33011yescharacteristic
89#7126—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73#127111yescharacteristic
92D73—21no—
93D73#134011yescharacteristic
94D73#134111yescharacteristic
95#1944—731no—
96#1377—731no—
97#1275—731no—
98C73#712611yescharacteristic, complemented, Sylow
99C2×M32—1461no—
100#431—1461no—
101C2×#107—731no—
102C2×#106—731no—
103C2×#97—731no—
104#389—1461no—
105#340—1461no—
106C22×C8—731no—
107C22×C8—731no—
108C2×C4⋊C4—2921no—
109C2×C4⋊C4—1461no—
110C2×C4⋊C4—1461no—
111C2×C42—731no—
112M32—2921no—
113M32—1462no—
114C2×C16—2921no—
115#107—2921no—
116#106—731no—
117#106—1461no—
118#106#1059684211yescharacteristic, complemented
119C4⋊C8—2921no—
120C22⋊C8—2921no—
121#97—2921no—
122C4×C8—1462no—
123#95—2921no—
124C22×C4—2921no—
125C22×C4—2921no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—731no—
129C2×C8—2922no—
130C2×C8—731no—
131C2×C8—731no—
132C2×C8—731no—
133C2×C8—1461no—
134C2×C8—1461no—
135C2×C8—1461no—
136C2×C8—1461no—
137C2×C8C2×#1059684211yescharacteristic
138C4⋊C4—21no—
139C4⋊C4—2921no—
140C4⋊C4—2921no—
141C4⋊C4—2921no—
142C4⋊C4—5842no—
143C4⋊C4—1461no—
144C42—1461no—
145C42—1461no—
146C16—2922no—
147C23—731no—
148C2×C4—41no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—5841no—
153C2×C4—5841no—
154C2×C4—5841no—
155C2×C4—5841no—
156C2×C4—5841no—
157C2×C4—731no—
158C2×C4—731no—
159C2×C4—731no—
160C2×C4—731no—
161C2×C4—731no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4C22⋊#1059684211yescharacteristic
165C8—21no—
166C8—5842no—
167C8—1461no—
168C8—1461no—
169C8—1461no—
170C22—731no—
171C22—731no—
172C22—1461no—
173C22—1461no—
174C22D4⋊#1059684211yescharacteristic
175C4—81no—
176C4—2921no—
177C4—2921no—
178C4—5841no—
179C4—731no—
180C4—731no—
181C4—11681no—
182C4#1798967311yescharacteristic
183C4Q8⋊#1059684211yescharacteristic
184C2—21no—
185C2—731no—
186C2—731no—
187C2—1461no—
188C2#2262693111yescharacteristic
subgroupG/H
centerC2#22626931
commutatorC2×C8×C73C2×C8
FrattiniC2×C8C2×#10596842
Fitting#106×C73C8
socleC2×C73#1271
prime radicalC22×D73#102
cosocleC2×#14556645C22
hypercenter#106#10596842
hypocenterC73#7126
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
26. #14556523C8semidirect
28. #106×C73C8semidirect
98. C73#7126semidirect
118. #106#10596842semidirect

Maximal subgroups

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

subgroupindex
#226270082
#226269352
#226260372
#712673