Finite Group Databasebeta

← #16948893

Subgroups — #16948893

Order 4352.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#14530921C211yesmaximal, characteristic
2#14528378C211yesmaximal, characteristic, complemented
3#14527669C211yesmaximal, characteristic
4#14526853C211yesmaximal, characteristic, complemented
5#14526838C211yesmaximal, characteristic, complemented
6#14526833C211yesmaximal, characteristic, complemented
7C17×#2208C211yesmaximal, characteristic
8#11763214C2211yescharacteristic
9#11763205—21no—
10#11763161—21no—
11#11762887—21no—
12#11762634—21no—
13C4⋊#63214C2211yescharacteristic
14#11762610—21no—
15#11762562C2211yescharacteristic
16D4⋊#3622—21no—
17C8×#3622C2211yescharacteristic
18C2×C17×SD32—21no—
19C17×#494C2211yescharacteristic
20C4×D8×C17C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#358—21no—
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C2×D8×C17D411yescharacteristic
26C17×C4⋊Q8—21no—
27C4×D4×C17—21no—
28C2×#63223—41no—
29#10587555—21no—
30C17×SD32—42no—
31C2×C16×C17—21no—
32C17×#107D411yescharacteristic
33C17×#102—21no—
34C4×C8×C17C2311yescharacteristic
35C22⋊#3622—41no—
36#10587489—21no—
37#10587489—21no—
38C2×#63214—21no—
39#10587481—41no—
40#10587481—41no—
41#10587479—42no—
42C4⋊#3622—21no—
43C4×#3622D411yescharacteristic
44C4×#3622D411yescharacteristic
45C2×Q8×C17—41no—
46C2×D4×C17—21no—
47C22×C4×C17—41no—
48C2×Dic34—41no—
49Q16×C17—41no—
50Q16×C17—41no—
51Q16×C17—81no—
52D8×C17—21no—
53D8×C17—21no—
54C2×C8×C17C2×D411yescharacteristic
55C2×C8×C17#4111yescharacteristic
56C4⋊C4×C17—21no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—41no—
59C22⋊C4×C17—41no—
60C42×C17C2×D411yescharacteristic
61C4⋊Dic17—41no—
62C4⋊Dic17—41no—
63#63223—82no—
64C2×#3622—21no—
65C2×#3622—41no—
66C2×#3622D811yescharacteristic
67C2×#3622D811yescharacteristic
68C16×C17—41no—
69#63214—41no—
70#12489—171nomaximal, Sylow
71C23×C17—41no—
72Q8×C17—81no—
73Q8×C17—81no—
74D4×C17—41no—
75D4×C17—41no—
76C2×C4×C17—41no—
77C2×C4×C17—81no—
78C2×C4×C17—81no—
79C2×C4×C17—81no—
80C2×C4×C17#12111yescharacteristic
81C2×C4×C17C2×D811yescharacteristic
82C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
83C2×Dic17—81no—
84Dic34—81no—
85Dic34—81no—
86C8×C17—21no—
87C8×C17AGL(1,ℤ/8)11yescharacteristic
88C8×C17#13711yescharacteristic
89#3622—22no—
90#3622—21no—
91#3622—21no—
92#3622—81no—
93#2224—171no—
94#2208D1711yescharacteristic
95#1707—171no—
96#1589—171no—
97#1370—171no—
98#1364—171no—
99#1362—171no—
100C22×C17—81no—
101C22×C17—81no—
102C22×C17—81no—
103C22×C17#45911yescharacteristic
104C4×C17—21no—
105C4×C17—81no—
106C4×C17—161no—
107C4×C17#46811yescharacteristic
108C4×C17#47111yescharacteristic
109C4×C17#50811yescharacteristic
110C4×C17#50911yescharacteristic
111Dic17—161no—
112C2×SD32—21no—
113#500—171no—
114#498—341no—
115#494C2×D1711yescharacteristic
116#487—341no—
117C4×D8C2×D1711yescharacteristic
118#436—341no—
119#366—341no—
120C4⋊C16—171no—
121C4⋊C16C2×D1711yescharacteristic
122#358—21no—
123#357—341no—
124#335—171no—
125D4⋊C8—341no—
126C82—171no—
127C2×C17—161no—
128C2×C17#168511yescharacteristic
129C2×C17#221011yescharacteristic
130C2×C17#221411yescharacteristic
131C2×Q16—21no—
132C2×Q16—21no—
133C2×D8C22⋊D1711yescharacteristic
134C2×M16—681no—
135C4⋊Q8—21no—
136C4⋊Q8—341no—
137C4×D4—21no—
138SD32—42no—
139C2×C16—21no—
140C2×C16—341no—
141#107—341no—
142#107—341no—
143#107C22⋊D1711yescharacteristic
144#106—682no—
145C4⋊C8—341no—
146#103—681no—
147#103—681no—
148#102—21no—
149C22⋊C8—681no—
150C4×C8—171no—
151C4×C8—171no—
152C4×C8C22×D1711yescharacteristic
153C17#1248911yescharacteristic, complemented, Sylow
154C2×Q8—41no—
155C2×Q8—681no—
156C2×D4—21no—
157C22×C4—41no—
158Q16—41no—
159Q16—41no—
160Q16—81no—
161D8—21no—
162D8—21no—
163M16—1362no—
164C2×C8—171no—
165C2×C8—171no—
166C2×C8—341no—
167C2×C8—681no—
168C2×C8#6325411yescharacteristic
169C2×C8C2×C22⋊D1711yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—681no—
174C4⋊C4—681no—
175C22⋊C4—41no—
176C42D4×D1711yescharacteristic
177C16—41no—
178C16—681no—
179C23—41no—
180Q8—81no—
181Q8—81no—
182Q8—1361no—
183Q8—1361no—
184D4—41no—
185D4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—1361no—
191C2×C4D8×D1711yescharacteristic
192C2×C4#1058759711yescharacteristic
193C2×C4#1058762511yescharacteristic
194C8—21no—
195C8—342no—
196C8—341no—
197C8—341no—
198C8—1361no—
199C8#1058761811yescharacteristic
200C8#1058763711yescharacteristic
201C22—81no—
202C22—81no—
203C22—81no—
204C22#1176300211yescharacteristic
205C4—21no—
206C4—81no—
207C4—161no—
208C4—2721no—
209C4#1176305311yescharacteristic
210C4#1176307011yescharacteristic
211C4#1176324011yescharacteristic
212C4#1176324611yescharacteristic
213C2—161no—
214C2#1452824711yescharacteristic
215C2#1453084111yescharacteristic
216C2#1453086311yescharacteristic
subgroupG/H
centerC22#11763002
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#2208C2
socleC22×C17#459
prime radicalC2×D8×C17D4
hypercenter#2208D17
hypocenterC17#12489
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #14528378C2semidirect
4. #14526853C2semidirect
5. #14526838C2semidirect
6. #14526833C2semidirect
153. C17#12489semidirect

Maximal subgroups

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

subgroupindex
#145309212
#145283782
#145276692
#145268532
#145268382
#145268332
C17×#22082
#1248917