Finite Group Databasebeta

← #13245149

Subgroups — #13245149

Order 1792.

810 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#6433C211yesmaximal, characteristic
2C7×#1817C211yesmaximal, characteristic
3#11729285C211yesmaximal, characteristic
4C2×#89264C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C22×C4⋊Dic7C411yescharacteristic
7C22×C4⋊Dic7C411yescharacteristic
8C22×Dic7⋊C4C412yes—
9C22×Dic7⋊C4C2212yes—
10C2×#6433—22no—
11C2×#6433—22no—
12C2×#6433—28no—
13C2×C7×C22⋊C8C2212yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15C7×#336—22no—
16#89319—22no—
17#89264—28no—
18#8306—71nomaximal, Sylow
19C23×C4×C7C2×C411yescharacteristic
20C23×C4×C7C2×C411yescharacteristic
21C23×C4×C7C2311yescharacteristic
22C23×Dic7C2×C412yes—
23C23×Dic7C2×C412yes—
24C22×C7×C8—22no—
25C2×C42×C7—24no—
26C2×C42×C7D412yes—
27C2×C42×C7D412yes—
28C2×C4⋊Dic7—22no—
29C2×C4⋊Dic7—22no—
30C2×C4⋊Dic7—24no—
31C2×C4⋊Dic7—24no—
32C2×Dic7⋊C4—24no—
33C2×Dic7⋊C4—22no—
34C2×Dic7⋊C4—24no—
35C2×Dic7⋊C4—22no—
36C2×Dic7⋊C4—24no—
37C2×Dic7⋊C4—24no—
38C2×Dic7⋊C4D418yes—
39C22×C7⋊C8—22no—
40#6433—216no—
41#6433—216no—
42C7×C22⋊C8—24no—
43C22⋊(C7⋊C8)—24no—
44C22×#125—71no—
45#1817—71no—
46#1817D711yescharacteristic
47C2×#324—74no—
48C24×C7C22×C411yescharacteristic
49C22×C4×C7—22no—
50C22×C4×C7—24no—
51C22×C4×C7—22no—
52C22×C4×C7—22no—
53C22×C4×C7—22no—
54C22×C4×C7—42no—
55C22×C4×C7C22⋊C412yes—
56C22×C4×C7C22⋊C412yes—
57C22×C4×C7C2×D411yescharacteristic
58C22×C4×C7C2×D411yescharacteristic
59C22×C4×C7C2×D414yes—
60C22×Dic7—22no—
61C22×Dic7—22no—
62C22×Dic7—22no—
63C22×Dic7—22no—
64C22×Dic7—24no—
65C22×Dic7—24no—
66C22×Dic7—44no—
67C22×Dic7C22⋊C414yes—
68C22×Dic7C22⋊C414yes—
69C2×C7×C8—44no—
70C2×C7×C8—42no—
71C42×C7—24no—
72C42×C7—24no—
73C4⋊Dic7—28no—
74C4⋊Dic7—28no—
75Dic7⋊C4—216no—
76Dic7⋊C4—28no—
77Dic7⋊C4—28no—
78C2×C7⋊C8—44no—
79C2×C7⋊C8—42no—
80C2×#125—148no—
81C2×#125—142no—
82C2×#125—142no—
83C22×C4⋊C4—72no—
84C22×C4⋊C4—72no—
85C22×C4⋊C4—71no—
86C22×C4⋊C4—71no—
87C22×C42C2×D711yescharacteristic
88C2×C22⋊C8—72no—
89C2×C22⋊C8C2×D712yes—
90#336—22no—
91#336—142no—
92#324—148no—
93C23×C7—22no—
94C23×C7—22no—
95C23×C7C2×C22⋊C412yes—
96C23×C7C2×C22⋊C411yescharacteristic
97C23×C7#13112yes—
98C23×C7#13112yes—
99C2×C4×C7—28no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—22no—
103C2×C4×C7—22no—
104C2×C4×C7—22no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—44no—
108C2×C4×C7—44no—
109C2×C4×C7#10114yes—
110C2×C4×C7#12012yes—
111C2×C4×C7#12012yes—
112C2×Dic7—24no—
113C2×Dic7—24no—
114C2×Dic7—28no—
115C2×Dic7—44no—
116C2×Dic7—42no—
117C2×Dic7—42no—
118C2×Dic7—44no—
119C2×Dic7—44no—
120C2×Dic7—44no—
121C7×C8—82no—
122C7⋊C8—82no—
123C23×C4—72no—
124C23×C4—72no—
125C23×C4C4×D711yescharacteristic
126C23×C4C4×D711yescharacteristic
127C23×C4C22×D711yescharacteristic
128C22×C8—22no—
129C22×C8—142no—
130#125—1416no—
131#125—1416no—
132C2×C4⋊C4—78no—
133C2×C4⋊C4—144no—
134C2×C4⋊C4—144no—
135C2×C4⋊C4—144no—
136C2×C4⋊C4—144no—
137C2×C4⋊C4—144no—
138C2×C4⋊C4—142no—
139C2×C4⋊C4—142no—
140C2×C4⋊C4—142no—
141C2×C4⋊C4—144no—
142C2×C4⋊C4—142no—
143C2×C42—24no—
144C2×C42D2812yes—
145C2×C42C22⋊D712yes—
146C22⋊C8—24no—
147C22⋊C8—144no—
148C22×C7—24no—
149C22×C7—24no—
150C22×C7—22no—
151C22×C7—22no—
152C22×C7#37911yescharacteristic
153C22×C7#40811yescharacteristic
154C22×C7#40811yescharacteristic
155C22×C7#40814yes—
156C22×C7#41012yes—
157C22×C7C2×#10112yes—
158C4×C7—22no—
159C4×C7—22no—
160C4×C7—24no—
161C4×C7—42no—
162Dic7—44no—
163Dic7—44no—
164C24C2×C4×D711yescharacteristic
165C22×C4—22no—
166C22×C4—24no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—74no—
172C22×C4—74no—
173C22×C4—142no—
174C22×C4—142no—
175C22×C4—144no—
176C22×C4—144no—
177C22×C4—142no—
178C22×C4—142no—
179C22×C4—284no—
180C22×C4(C2×D7)⋊C412yes—
181C22×C4(C2×D7)⋊C412yes—
182C22×C4C2×D2811yescharacteristic
183C22×C4D4×D714yes—
184C22×C4C2×C22⋊D711yescharacteristic
185C2×C8—44no—
186C2×C8—42no—
187C2×C8—284no—
188C2×C8—282no—
189C4⋊C4—1416no—
190C4⋊C4—148no—
191C4⋊C4—148no—
192C4⋊C4—148no—
193C4⋊C4—148no—
194C42—24no—
195C42—24no—
196C2×C7—24no—
197C2×C7#147012yes—
198C2×C7#147012yes—
199C2×C7#178011yescharacteristic
200C2×C7#178211yescharacteristic
201C2×C7#178411yescharacteristic
202C23—22no—
203C23—22no—
204C23D7×C22⋊C412yes—
205C23#646412yes—
206C23#647012yes—
207C23C2×(C2×D7)⋊C411yescharacteristic
208C2×C4—28no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—44no—
217C2×C4—44no—
218C2×C4—144no—
219C2×C4—144no—
220C2×C4—148no—
221C2×C4—284no—
222C2×C4—282no—
223C2×C4—282no—
224C2×C4—284no—
225C2×C4—284no—
226C2×C4—284no—
227C2×C4#639814yes—
228C2×C4#644512yes—
229C2×C4#650012yes—
230C8—82no—
231C8—562no—
232C7#830611yescharacteristic, complemented, Sylow
233C22—22no—
234C22—24no—
235C22—22no—
236C22—24no—
237C22#8949914yes—
238C22#8972711yescharacteristic
239C22#8977812yes—
240C22#8988211yescharacteristic
241C22#8990111yescharacteristic
242C22C2×#639812yes—
243C4—24no—
244C4—22no—
245C4—22no—
246C4—42no—
247C4—284no—
248C4—284no—
249C2—24no—
250C2#1172729111yescharacteristic
251C2#1172771011yescharacteristic
252C2#1172774411yescharacteristic
253C2#1172854112yes—
254C2#1172858512yes—
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1817C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenter#1817D7
hypocenterC7#8306
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
232. C7#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#64332
C7×#18172
#117292852
C2×#892642
#83067