Finite Group Databasebeta

← #17948713

Subgroups — #17948713

Order 4352.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#10587545C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14529719C211yesmaximal, characteristic
4#11763826—21no—
5C2×#10587545C412yes—
6C4×#63247—21no—
7#11763689—21no—
8#11763655—21no—
9#11763654C412yes—
10C2×C4×Dic34C2211yescharacteristic
11C2×C4×#3622C411yescharacteristic
12#11762563—21no—
13#11762563—21no—
14C2×C17×C4⋊C8C411yescharacteristic
15C22×Dic34C2×C411yescharacteristic
16C2×#63247—22no—
17C22×C8×C17—21no—
18C2×C42×C17C2×C411yescharacteristic
19C2×C4⋊Dic17C2×C411yescharacteristic
20C2×#63225D411yescharacteristic
21C2×#63225Q811yescharacteristic
22C2×C4×Dic17D411yescharacteristic
23C2×C4×Dic17D411yescharacteristic
24C22×#3622—21no—
25C4×Dic34—41no—
26C4×Dic34—41no—
27C22⋊#3624—22no—
28#10587545—22no—
29#10587545C814yescomplemented
30#10587544—41no—
31#10587542—41no—
32C4×#3624—41no—
33C4×#3624—41no—
34C17×C4⋊C8—41no—
35C4×#3622—41no—
36C22×C4×C17C4211yescharacteristic
37C22×C4×C17C22⋊C411yescharacteristic
38C22×C4×C17C4⋊C411yescharacteristic
39C22×Dic17C22⋊C411yescharacteristic
40C22×Dic17C22⋊C411yescharacteristic
41C22×Dic17C4⋊C411yescharacteristic
42C22×Dic17C4⋊C411yescharacteristic
43C2×Dic34—41no—
44C2×Dic34—41no—
45C2×Dic34C2×C812yes—
46C2×Dic34M1612yes—
47#63247—24no—
48#63247—42no—
49C2×#3624—42no—
50C2×#3624—42no—
51C2×C8×C17—42no—
52C2×C8×C17—41no—
53C42×C17—21no—
54C42×C17—21no—
55C4⋊Dic17—41no—
56#63225—41no—
57#63225—41no—
58C4×Dic17—21no—
59C4×Dic17—21no—
60C4×Dic17—21no—
61C4×Dic17—21no—
62C2×#3622—22no—
63C2×#3622—41no—
64C2×#3622—41no—
65#7206—171nomaximal, Sylow
66C23×C17#9511yescharacteristic
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—41no—
73C2×C4×C17C4×C811yescharacteristic
74C2×C4×C17#9711yescharacteristic
75C2×C4×C17#9911yescharacteristic
76C2×C4×C17#9911yescharacteristic
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—41no—
84C2×Dic17—41no—
85C2×Dic17C22⋊C812yes—
86C2×Dic17C4⋊C812yes—
87Dic34—42no—
88Dic34—42no—
89#3624—44no—
90#3624—82no—
91C8×C17—81no—
92#3622—42no—
93#1984—171no—
94C4×#101—171no—
95#1461—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17#33611yescharacteristic
99C22×C17#34211yescharacteristic
100C22×C17#34411yescharacteristic
101C4×C17—21no—
102C4×C17—21no—
103C4×C17—21no—
104C4×C17—41no—
105C4×C17#35511yescharacteristic
106C4×C17#35611yescharacteristic
107Dic17—22no—
108Dic17—22no—
109Dic17—41no—
110Dic17—41no—
111C2×C4×Q8—171no—
112#431—341no—
113C2×C4⋊C8#59511yescharacteristic
114C2×#101—172no—
115C4×M16—341no—
116C2×C4×C8—171no—
117#343—341no—
118#336—341no—
119#336—341no—
120#324—172no—
121#324—341no—
122C2×C17—21no—
123C2×C17—21no—
124C2×C17#128211yescharacteristic
125C2×C17#139411yescharacteristic
126C2×C17#139511yescharacteristic
127C22×Q8—171no—
128C2×M16—342no—
129C22×C8—21no—
130C22×C8—341no—
131C4×Q8—681no—
132C4×Q8—681no—
133C2×C4⋊C4—171no—
134C2×C4⋊C4—171no—
135C2×C4⋊C4—171no—
136C2×C42—171no—
137C2×C42—171no—
138C2×C42C2×#59511yescharacteristic
139C4⋊C8—41no—
140C4⋊C8—681no—
141#101—174no—
142#101—342no—
143C22⋊C8—342no—
144#97—681no—
145C4×C8—681no—
146C4×C8—681no—
147C4×C8—681no—
148C17#720611yescharacteristic, complemented, Sylow
149C2×Q8—172no—
150C2×Q8—172no—
151C2×Q8—681no—
152C2×Q8—681no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4C4×#59511yescharacteristic
158C22×C4C4⋊#59511yescharacteristic
159C22×C4C22⋊#59511yescharacteristic
160M16—344no—
161M16—682no—
162C2×C8—42no—
163C2×C8—41no—
164C2×C8—342no—
165C2×C8—681no—
166C2×C8—682no—
167C2×C8—681no—
168C2×C8—682no—
169C4⋊C4—681no—
170C4⋊C4—681no—
171C4⋊C4—681no—
172C42—21no—
173C42—21no—
174C42—341no—
175C42—341no—
176C42—341no—
177C42—341no—
178C23(C2×#595)⋊C411yescharacteristic
179Q8—682no—
180Q8—682no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—172no—
188C2×C4—172no—
189C2×C4—341no—
190C2×C4—341no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—341no—
195C2×C4—681no—
196C2×C4—681no—
197C2×C4C8×#59511yescharacteristic
198C2×C4#1058753211yescharacteristic
199C2×C4#1058753911yescharacteristic
200C2×C4#1058755111yescharacteristic
201C8—81no—
202C8—682no—
203C8—684no—
204C8—1362no—
205C22—21no—
206C22—21no—
207C22#1176367411yescharacteristic
208C22#1176368711yescharacteristic
209C22#1176369111yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—342no—
215C4—342no—
216C4—681no—
217C4—681no—
218C4#1176371711yescharacteristic
219C4#1176371911yescharacteristic
220C2—21no—
221C2—21no—
222C2#1454362611yescharacteristic
223C2#1454388211yescharacteristic
224C2#1454388511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC2×C4×C17C4×C8
FrattiniC2×C42C2×#595
FittingC2×C17×C4⋊C8C4
socleC22×C17#342
prime radicalC23×C17#95
cosocleC2×C4×Dic34C22
hypercenterC2×C4⋊C8#595
hypocenterC17#7206
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
29. #10587545C8semidirect
148. C17#7206semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440262
#145297192
#720617