Finite Group Databasebeta

← #17982710

Subgroups — #17982710

Order 4352.

334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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#14545974C211yesmaximal, characteristic
2#14545940C211yesmaximal, characteristic
3#14545864C214yesmaximal
4#14545573C211yesmaximal, characteristic
5C2×#10587666C2212yes—
6C2×#10587665C2212yes—
7#11763912—21no—
8#11763912—21no—
9#11763903—21no—
10#11763903—21no—
11#11763860—21no—
12#11763859—21no—
13#11763858—21no—
14Q8×#3624—21no—
15#11763816C412yes—
16#11763813C411yescharacteristic
17#11763774C2212yes—
18C4×#63242C2211yescharacteristic
19#11763364C411yescharacteristic
20C2×#63243C2×C412yes—
21C2×#63242C2×C411yescharacteristic
22C2×#63242C2311yescharacteristic
23C2×#63241—22no—
24C2×#63241—22no—
25#10587666—24no—
26#10587665—22no—
27#10587665Q814yescomplemented
28C17×C4⋊Q8C811yescharacteristic
29#10587632—21no—
30Q8×Dic17—21no—
31#10587583—21no—
32#10587578C2×C412yes—
33#10587576C812yes—
34#10587573—21no—
35C42×D17C2×C411yescharacteristic
36#10587555C811yescharacteristic
37#10587544—22no—
38#10587542—22no—
39C4⋊#3624—21no—
40C4⋊#3624—21no—
41C4⋊#3624—22no—
42C4×#3624—22no—
43C4×#3624D411yescharacteristic
44C4×#3624D411yescharacteristic
45C4×#3624D411yescharacteristic
46C4×#3624D411yescharacteristic
47C2×Q8×C17—21no—
48C2×C4×D17M1611yescharacteristic
49C2×C4×D17M1611yescharacteristic
50C2×C4×D17C22×C411yescharacteristic
51C2×Dic34—21no—
52C2×#3624—22no—
53C2×#3624C22⋊C411yescharacteristic
54C2×#3624C22⋊C411yescharacteristic
55C2×#3624C2×D411yescharacteristic
56C2×#3624C2×D411yescharacteristic
57#63243—24no—
58#63242—22no—
59#63242C2×Q812yes—
60#63242#4112yes—
61#63241—24no—
62#63241—42no—
63C4⋊C4×C17—21no—
64C4⋊C4×C17C2×C812yes—
65C42×C17C2×C811yescharacteristic
66#63227—22no—
67C4⋊Dic17—21no—
68C4⋊Dic17—22no—
69C4⋊Dic17C2×C812yes—
70#63225—22no—
71C4×Dic17—22no—
72C4×Dic17C22⋊C411yescharacteristic
73C4×Dic17C22⋊C411yescharacteristic
74C4×Dic17C2×C811yescharacteristic
75#13267—171nomaximal, Sylow
76C22×D17C2×M1611yescharacteristic
77Q8×C17—42no—
78C2×C4×C17—22no—
79C2×C4×C17C22⋊C811yescharacteristic
80C2×C4×C17C22⋊C811yescharacteristic
81C2×C4×C17C22×C811yescharacteristic
82C2×Dic17—22no—
83C2×Dic17C22⋊C811yescharacteristic
84C2×Dic17C22⋊C811yescharacteristic
85C2×Dic17C2×C22⋊C411yescharacteristic
86C4×D17—41no—
87C4×D17—41no—
88C4×D17C4×Q812yes—
89C4×D17#13112yes—
90Dic34—42no—
91#3624—21no—
92#3624—21no—
93#3624—42no—
94#3624C22⋊Q812yes—
95#3624#12411yescharacteristic
96#3624C4⋊Q811yescharacteristic
97#2960—171no—
98#2150—171no—
99C2×#346—171no—
100#1379—174no—
101C22×C17C2×C22⋊C811yescharacteristic
102C2×D17—21no—
103C2×D17—21no—
104C2×D17#44612yes—
105C4×C17—21no—
106C4×C17—21no—
107C4×C17—42no—
108C4×C17C8×Q812yes—
109Dic17—21no—
110Dic17—21no—
111Dic17—42no—
112Dic17#39111yescharacteristic
113Dic17#40811yescharacteristic
114#533—171no—
115C2×M32—172no—
116C22×C16—172no—
117#446—341no—
118#446—341no—
119C8×Q8—341no—
120C8×Q8—341no—
121#424—172no—
122#423—171no—
123#405—172no—
124C2×C4×C8—171no—
125C4⋊C16—341no—
126C4⋊C16—341no—
127#346—341no—
128#346—341no—
129C2×C17#198411yescharacteristic
130C2×C17#211711yescharacteristic
131C2×C17#211711yescharacteristic
132D17—22no—
133C2×M16—172no—
134C22×C8—171no—
135C22×C8—171no—
136C4⋊Q8—171no—
137C4⋊Q8#363311yescharacteristic
138#125—172no—
139C22⋊Q8—341no—
140C22⋊Q8—341no—
141C4×Q8—341no—
142C4×Q8—341no—
143#117—172no—
144C2×C42—171no—
145M32—344no—
146C2×C16—174no—
147C2×C16—342no—
148C2×C16—342no—
149C2×C16—342no—
150C4⋊C8—341no—
151C4⋊C8—341no—
152C4⋊C8—342no—
153C4⋊C8—342no—
154#97—342no—
155C4×C8—171no—
156C4×C8—171no—
157C4×C8—171no—
158C4×C8—171no—
159C4×C8—342no—
160C17#1326711yescharacteristic, complemented, Sylow
161C2×Q8—21no—
162C2×Q8—341no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—171no—
166M16—344no—
167C2×C8—172no—
168C2×C8—172no—
169C2×C8—171no—
170C2×C8—171no—
171C2×C8—171no—
172C2×C8—171no—
173C2×C8—342no—
174C2×C8—342no—
175C4⋊C4—21no—
176C4⋊C4—172no—
177C4⋊C4—342no—
178C4⋊C4—342no—
179C4⋊C4—341no—
180C4⋊C4C2×#363312yes—
181C22⋊C4—342no—
182C42—171no—
183C42—171no—
184C42—171no—
185C42—342no—
186C42C2×#363311yescharacteristic
187C16—344no—
188C16—682no—
189C23—171no—
190Q8—42no—
191Q8—682no—
192C2×C4—22no—
193C2×C4—171no—
194C2×C4—172no—
195C2×C4—172no—
196C2×C4—171no—
197C2×C4—171no—
198C2×C4—342no—
199C2×C4—681no—
200C2×C4—681no—
201C2×C4C22⋊#363311yescharacteristic
202C2×C4C22⋊#363311yescharacteristic
203C2×C4C22×#363311yescharacteristic
204C8—172no—
205C8—171no—
206C8—171no—
207C8—341no—
208C8—341no—
209C8—682no—
210C22—172no—
211C22—341no—
212C22—341no—
213C22C2×C22⋊#363311yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—171no—
218C4—171no—
219C4—341no—
220C4—341no—
221C4—682no—
222C4Q8×#363312yes—
223C2—342no—
224C2(C2×#3633)⋊Q811yescharacteristic
225C2#1454596611yescharacteristic
226C2#1454596811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC2×C4×C17C22×C8
FrattiniC2×C4C22×#3633
FittingC17×C4⋊Q8C8
socleC22×C17C2×C22⋊C8
prime radicalC22×D17C2×M16
cosocleC2×#63242C23
hypercenterC4⋊Q8#3633
hypocenterC17#13267
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
27. #10587665Q8semidirect
160. C17#13267semidirect

Maximal subgroups

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

subgroupindex
#145459742
#145459402
#145458642
#145455732
#1326717