Finite Group Databasebeta

← #16943759

Subgroups — #16943759

Order 4352.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#14537421C211yesmaximal, characteristic
2#14530593C212yesmaximal, complemented
3#14526735C211yesmaximal, characteristic, complemented
4#14526719C212yesmaximal
5C17×#1327C211yesmaximal, characteristic, complemented
6C2×#10587558C411yescharacteristic
7#11762869—22no—
8#11762869—22no—
9#11762833C411yescharacteristic
10#11762772C411yescharacteristic
11#11762772C2211yescharacteristic
12M16×Dic17C411yescharacteristic
13M16×Dic17C2211yescharacteristic
14#11762629—22no—
15#11762591C2212yes—
16#11762586—22no—
17C17×#423C2211yescharacteristic
18C17×#349C2212yes—
19C22×C4×D17C2×C411yescharacteristic
20C2×M16×C17C2×C411yescharacteristic
21C2×M16×C17C2311yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23C2×#63227—21no—
24C2×#63225—21no—
25C2×C4×Dic17C2×C411yescharacteristic
26C2×#63223C2×C411yescharacteristic
27C2×#63223C2×C411yescharacteristic
28#10587558—21no—
29#10587558—21no—
30#10587558—22no—
31C17×M32—22no—
32C17×C4⋊C8—22no—
33#10587491—22no—
34#10587491—22no—
35#10587486—21no—
36#10587486D412yes—
37C8×Dic17—21no—
38C8×Dic17D412yes—
39#10587483—22no—
40C4⋊#3622—22no—
41C23×D17M1611yescharacteristic
42C22×C4×C17—21no—
43C22×C4×C17C22×C411yescharacteristic
44C22×Dic17—21no—
45C22×Dic17M1611yescharacteristic
46C2×C4×D17—21no—
47C2×C4×D17—21no—
48C2×C4×D17—41no—
49C2×C4×D17—41no—
50M16×C17—41no—
51M16×C17—41no—
52C2×C8×C17—21no—
53C2×C8×C17C2×D412yes—
54C42×C17—21no—
55C42×C17M1612yes—
56#63227—22no—
57#63227—22no—
58#63225—22no—
59#63225—22no—
60C4×Dic17—21no—
61C4×Dic17C22⋊C411yescharacteristic
62C4×Dic17C22⋊C411yescharacteristic
63#63223—41no—
64#63223—41no—
65C2×#3622—21no—
66C2×#3622C22⋊C412yes—
67C16×C17—42no—
68#63214—42no—
69#11522—171nomaximal, Sylow
70C23×C17C2×M1611yescharacteristic
71C22×D17—21no—
72C22×D17—41no—
73C22×D17—81no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—22no—
77C2×C4×C17—81no—
78C2×C4×C17C2×C22⋊C411yescharacteristic
79C2×C4×C17C2×M1611yescharacteristic
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—41no—
84C2×Dic17—81no—
85C4×D17—42no—
86C4×D17—41no—
87C4×D17—41no—
88C8×C17—22no—
89C8×C17—41no—
90#3622—22no—
91#3622—41no—
92#2921—171no—
93#2165—172no—
94#1327—171no—
95#1327D1711yescharacteristic, complemented
96#1320—172no—
97C22×C17—21no—
98C22×C17—41no—
99C22×C17#40711yescharacteristic
100C2×D17—42no—
101C2×D17—41no—
102C2×D17—82no—
103C4×C17—21no—
104C4×C17—42no—
105C4×C17#41011yescharacteristic
106C4×C17#41311yescharacteristic
107Dic17—41no—
108Dic17—41no—
109Dic17—41no—
110C2×#117—171no—
111#433—342no—
112#433—342no—
113#423—171no—
114#423C2×D1711yescharacteristic
115#407—171no—
116#407—171no—
117C4×M16—171no—
118C4×M16—171no—
119#364—342no—
120#349—172no—
121#349C2×D1712yes—
122#347—342no—
123C2×C17—21no—
124C2×C17—41no—
125C2×C17#146411yescharacteristic
126D17—81no—
127C23×C4—171no—
128C2×M16—171no—
129C2×M16—171no—
130C2×M16C4×D1711yescharacteristic
131C2×M16C22×D1711yescharacteristic
132#117—341no—
133#117—341no—
134#117—342no—
135C2×C4⋊C4—341no—
136C2×C22⋊C4—341no—
137C2×C42—171no—
138C2×C42C4×D1711yescharacteristic
139M32—22no—
140M32—342no—
141C4⋊C8—22no—
142C4⋊C8—342no—
143C22⋊C8—342no—
144C22⋊C8—342no—
145#97—172no—
146#97—341no—
147C4×C8—172no—
148C4×C8—341no—
149C17#1152211yescharacteristic, complemented, Sylow
150C24—171no—
151C22×C4—21no—
152C22×C4—171no—
153C22×C4—341no—
154C22×C4—341no—
155C22×C4—341no—
156C22×C4—681no—
157C22×C4—681no—
158C22×C4C2×C4×D1711yescharacteristic
159M16—41no—
160M16—41no—
161M16—681no—
162M16—681no—
163C2×C8—21no—
164C2×C8—172no—
165C2×C8—341no—
166C2×C8D4×D1712yes—
167C4⋊C4—342no—
168C4⋊C4—342no—
169C22⋊C4—342no—
170C22⋊C4—342no—
171C42—21no—
172C42—171no—
173C42—171no—
174C42—341no—
175C42#6321812yes—
176C16—42no—
177C16—682no—
178C23—341no—
179C23—681no—
180C23—1361no—
181C23M16×D1711yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—341no—
187C2×C4—341no—
188C2×C4—341no—
189C2×C4—682no—
190C2×C4—681no—
191C2×C4—681no—
192C2×C4—681no—
193C2×C4—1361no—
194C2×C4C22⋊C4×D1711yescharacteristic
195C2×C4C2×#6321811yescharacteristic
196C8—22no—
197C8—41no—
198C8—342no—
199C8—681no—
200C22—21no—
201C22—41no—
202C22—682no—
203C22—681no—
204C22—1362no—
205C22#1176277111yescharacteristic
206C4—21no—
207C4—42no—
208C4—681no—
209C4—681no—
210C4—681no—
211C4#1176278111yescharacteristic
212C4#1176279211yescharacteristic
213C2—21no—
214C2—41no—
215C2—1361no—
216C2#1452711711yescharacteristic
subgroupG/H
centerC4#11762781
commutatorC22×C4×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#1327C2
socleC2×C17#1464
prime radicalC23×D17M16
cosocleC2×M16×C17C23
hypercenter#1327D17
hypocenterC17#11522
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #14530593C2semidirect
3. #14526735C2semidirect
5. C17×#1327C2semidirect
95. #1327D17semidirect
149. C17#11522semidirect

Maximal subgroups

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

subgroupindex
#145374212
#145305932
#145267352
#145267192
C17×#13272
#1152217