Finite Group Databasebeta

← #33006646

Subgroups — #33006646

Order 18688.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×Q32×D73C211yesmaximal, characteristic
2C2×Dic1168C211yesmaximal, characteristic, complemented
3C2×#17988427C211yesmaximal, characteristic, complemented
4#22612023C211yesmaximal, characteristic
5#22608111C211yesmaximal, characteristic, complemented
6#22608068C211yesmaximal, characteristic
7C73×#1416C211yesmaximal, characteristic, complemented
8C2×Q16×D73—21no—
9C2×Dic584C2211yescharacteristic
10C2×Dic584C2211yescharacteristic
11C2×#14556537—21no—
12Q32×D73—22no—
13Q32×D73—22no—
14C2×C16×D73C2211yescharacteristic
15#17988829—21no—
16Dic1168—22no—
17#17988427—22no—
18C2×#14556497C2211yescharacteristic
19#17988390—21no—
20C2×Q32×C73C2211yescharacteristic
21C2×C32×C73C2211yescharacteristic
22#366×C73C2211yescharacteristic
23C2×Q8×D73—41no—
24C2×Dic292—21no—
25C2×Dic292—21no—
26C2×#11924018—41no—
27Q16×D73—24no—
28Q16×D73—42no—
29C2×C8×D73D411yescharacteristic
30#14556571—41no—
31Dic584—21no—
32Dic584—21no—
33Dic584—21no—
34Dic584D412yes—
35#14556537—24no—
36C2×#11924003D411yescharacteristic
37C16×D73—21no—
38C16×D73—21no—
39#14556514—41no—
40#14556497—21no—
41C2×Q16×C73—21no—
42Q32×C73—21no—
43Q32×C73D412yes—
44C2×C16×C73C2311yescharacteristic
45#107×C73—21no—
46C32×C73—21no—
47C2×Dic146—41no—
48C2×Dic146—41no—
49C2×Dic146—81no—
50Q8×D73—44no—
51Q8×D73—82no—
52C2×C4×D73—81no—
53C2×C4×D73D811yescharacteristic
54Dic292—22no—
55Dic292—41no—
56Dic292—41no—
57Dic292—41no—
58#11924018—44no—
59C2×#10596831D811yescharacteristic
60C8×D73—21no—
61C8×D73—21no—
62C4⋊Dic73—81no—
63#11924005—81no—
64#11924003—21no—
65C2×Q8×C73—41no—
66Q16×C73—22no—
67Q16×C73—41no—
68C2×C8×C73C2×D411yescharacteristic
69C4⋊C4×C73—41no—
70C16×C73C2×D411yescharacteristic
71C16×C73C2×D411yescharacteristic
72C22×D73D1611yescharacteristic
73Q8×C73—42no—
74Q8×C73—81no—
75C2×C4×C73—81no—
76C2×C4×C73—81no—
77C2×C4×C73C2×D811yescharacteristic
78C2×Dic73—81no—
79C2×Dic73—81no—
80C2×Dic73D1611yescharacteristic
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—84no—
84Dic146—42no—
85Dic146—84no—
86Dic146—81no—
87Dic146—81no—
88Dic146—81no—
89C8×C73#12011yescharacteristic
90C8×C73AGL(1,ℤ/8)11yescharacteristic
91#10596831—21no—
92C22×C73C2×D1611yescharacteristic
93C2×D73—21no—
94C2×D73—21no—
95C2×D73Q6412yescomplemented
96C4×C73—82no—
97C4×C73—161no—
98C4×C73#44711yescharacteristic
99C4×C73#50911yescharacteristic
100Dic73—21no—
101Dic73—82no—
102Dic73—161no—
103#13665—731nomaximal, Sylow
104C2×C73#218411yescharacteristic
105C2×C73C2×Q6411yescharacteristic
106C2×C73#226411yescharacteristic
107D73—22no—
108C22×Q32—731no—
109C2×Q64—731no—
110C2×Q64—731no—
111#2216—731no—
112#1416—731no—
113#1416D7311yescharacteristic, complemented
114C22⋊C32—731no—
115C73#1366511yescharacteristic, complemented, Sylow
116C22×Q16—1461no—
117C2×Q32—731no—
118C2×Q32—731no—
119C2×Q32—1461no—
120C2×Q32—1462no—
121C2×Q32—1462no—
122C2×Q32C2×D7311yescharacteristic
123C22×C16—731no—
124#467—1461no—
125Q64—1462no—
126Q64—1462no—
127C2×C32—731no—
128C2×C32C2×D7311yescharacteristic
129#366C2×D7311yescharacteristic
130#358—1461no—
131C22×Q8—2921no—
132C2×Q16—21no—
133C2×Q16—2921no—
134C2×Q16—2922no—
135C2×Q16—1464no—
136C2×Q16—1461no—
137C2×Q16—1461no—
138C22×C8—731no—
139C22⋊Q8—2921no—
140Q32—21no—
141Q32—732no—
142Q32—1464no—
143Q32—1461no—
144Q32—1461no—
145Q32—1461no—
146Q32D29212yes—
147C2×C16—731no—
148C2×C16—1461no—
149C2×C16—1461no—
150C2×C16C22×D7311yescharacteristic
151#107—21no—
152#103—2921no—
153C32—21no—
154C32—1461no—
155C2×Q8—41no—
156C2×Q8—2924no—
157C2×Q8—2921no—
158C2×Q8—2921no—
159C2×Q8—5841no—
160C2×Q8—5842no—
161C22×C4—5841no—
162C22×C4—731no—
163Q16—22no—
164Q16—41no—
165Q16—2924no—
166Q16—2921no—
167Q16—2921no—
168Q16—2921no—
169Q16—1462no—
170C2×C8—731no—
171C2×C8—1461no—
172C2×C8—1461no—
173C2×C8D4×D7311yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—5841no—
176C22⋊C4—5841no—
177C16—1461no—
178C16D4×D7311yescharacteristic
179C16C2×D29211yescharacteristic
180C23—731no—
181Q8—42no—
182Q8—81no—
183Q8—2922no—
184Q8—5844no—
185Q8—5841no—
186Q8—5841no—
187Q8—5841no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—5844no—
191C2×C4—5841no—
192C2×C4—5841no—
193C2×C4—731no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4D8×D7311yescharacteristic
197C8—1461no—
198C8#1455656111yescharacteristic
199C8#1455661811yescharacteristic
200C22—732no—
201C22—1461no—
202C22—1461no—
203C22D16×D7311yescharacteristic
204C4—82no—
205C4—161no—
206C4—5842no—
207C4—11681no—
208C4—1461no—
209C4#1798872211yescharacteristic
210C4#1798902411yescharacteristic
211C2—1462no—
212C2#2261184411yescharacteristic
213C2Q64×D7311yescharacteristic
214C2#2261224711yescharacteristic
subgroupG/H
centerC22D16×D73
commutator, cosocleC2×C16×C73C23
FrattiniC2×C16C22×D73
FittingC73×#1416C2
socleC22×C73C2×D16
prime radicalC22×D73D16
hypercenter#1416D73
hypocenterC73#13665
LCSG ▷ C2×C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
2. C2×Dic1168C2semidirect
3. C2×#17988427C2semidirect
5. #22608111C2semidirect
7. C73×#1416C2semidirect
95. C2×D73Q64semidirect
113. #1416D73semidirect
115. C73#13665semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×D732
C2×Dic11682
C2×#179884272
#226120232
#226081112
#226080682
C73×#14162
#1366573