Finite Group Databasebeta

← #13264443

Subgroups — #13264443

Order 1792.

378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739924C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725302C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C2×C7×#101—21no—
8C4×C7×M16—21no—
9#90002—21no—
10#89758C412yes—
11#89758C2212yes—
12#89749—21no—
13C4×C4⋊Dic7C411yescharacteristic
14#89701—21no—
15#89701—21no—
16#89698—21no—
17C7×#343C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11794—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×Dic14—21no—
23C2×C7×M16—22no—
24C4×C7×Q8—41no—
25C4×C7×Q8—41no—
26C2×C7×C4⋊C4C2×C411yescharacteristic
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7C2×C412yes—
35C2×C4×Dic7—21no—
36#6432—41no—
37#6432—41no—
38C7×#101—24no—
39C7×#97—41no—
40C4×C7×C8—41no—
41C7⋊#95—22no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C7⋊#95—22no—
45C7⋊#95C2×C412yes—
46C22⋊(C7⋊C8)—22no—
47C4⋊(C7⋊C8)—41no—
48#6377—41no—
49#2568—71no—
50C4×#101D711yescharacteristic
51#1467—71no—
52#1353—74no—
53C2×C7×Q8—22no—
54C2×C7×Q8—22no—
55C2×C7×Q8—41no—
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22×C411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×Dic7—22no—
64C22×Dic7—22no—
65C2×Dic14—44no—
66C2×Dic14—41no—
67C2×Dic14—41no—
68C7×M16—24no—
69C7×M16—42no—
70C2×C7×C8—42no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—41no—
74C42×C7—21no—
75C42×C7—21no—
76C42×C7—21no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C4⋊Dic7—42no—
81C4⋊Dic7—42no—
82C4⋊Dic7—42no—
83C4×Dic7—42no—
84C2×C7⋊C8—42no—
85C2×C4⋊Q8—71no—
86C2×C4×Q8C2×D711yescharacteristic
87#432—141no—
88C2×#101—21no—
89C4×M16—21no—
90#400—72no—
91#400—72no—
92#391—141no—
93#391—141no—
94#391—141no—
95#382—141no—
96C4×C4⋊C4—71no—
97#343C2×D712yes—
98#324—72no—
99#324—141no—
100C23×C7C2×C22⋊C411yescharacteristic
101C7×Q8—44no—
102C2×C4×C7—21no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—22no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7—41no—
116C2×C4×C7#9911yescharacteristic
117C2×C4×C7#9911yescharacteristic
118C2×C4×C7#10412yes—
119C2×C4×C7#13712yes—
120C2×Dic7—42no—
121C2×Dic7—44no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125Dic14—82no—
126Dic14—82no—
127C7×C8—44no—
128C7⋊C8—82no—
129C22×Q8—141no—
130C22×Q8C22⋊D711yescharacteristic
131C2×M16—22no—
132C4⋊Q8—281no—
133C4⋊Q8—281no—
134C4×Q8—41no—
135C4×Q8—41no—
136C2×C4⋊C4—72no—
137C2×C4⋊C4—141no—
138C2×C4⋊C4—141no—
139C2×C4⋊C4C4×D711yescharacteristic
140C2×C4⋊C4D2811yescharacteristic
141C2×C4⋊C4C22×D711yescharacteristic
142C2×C42—141no—
143C2×C42C4×D711yescharacteristic
144C2×C42D2811yescharacteristic
145C2×C42C22⋊D711yescharacteristic
146C4⋊C8—281no—
147#101—24no—
148C22⋊C8—142no—
149#97—41no—
150#97—281no—
151C4×C8—41no—
152#95—72no—
153#95—142no—
154#95—142no—
155#95—142no—
156#95—142no—
157C22×C7—21no—
158C22×C7—21no—
159C22×C7C2×#9911yescharacteristic
160C22×C7#41911yescharacteristic
161C22×C7C2×#10411yescharacteristic
162C4×C7—21no—
163C4×C7—22no—
164C4×C7—22no—
165C4×C7—41no—
166C4×C7—41no—
167C4×C7—41no—
168C4×C7—41no—
169C4×C7#35512yes—
170Dic7—82no—
171Dic7—82no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—284no—
176C2×Q8—281no—
177C2×Q8—281no—
178C22×C4—142no—
179C22×C4—142no—
180C22×C4(C2×D7)⋊C411yescharacteristic
181C22×C4(C2×D7)⋊C411yescharacteristic
182C22×C4(C2×D7)⋊C411yescharacteristic
183C22×C4(C2×D7)⋊C411yescharacteristic
184C22×C4C2×C4×D711yescharacteristic
185C22×C4C2×D2811yescharacteristic
186C22×C4C2×C22⋊D711yescharacteristic
187M16—24no—
188M16—42no—
189C2×C8—42no—
190C2×C8—282no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—282no—
195C4⋊C4—282no—
196C4⋊C4—282no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—282no—
204C2×C7—21no—
205C2×C7—21no—
206C2×C7#150811yescharacteristic
207C2×C7#212311yescharacteristic
208C2×C7C2×#35511yescharacteristic
209C23C2×(C2×D7)⋊C411yescharacteristic
210Q8—44no—
211Q8—562no—
212Q8—562no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—282no—
228C2×C4—282no—
229C2×C4—284no—
230C2×C4—282no—
231C2×C4—282no—
232C2×C4#637912yes—
233C2×C4#638011yescharacteristic
234C2×C4#638011yescharacteristic
235C2×C4#651412yes—
236C8—44no—
237C8—562no—
238C7#1179411yescharacteristic, complemented, Sylow
239C22—21no—
240C22—21no—
241C22C2×#637911yescharacteristic
242C22C2×#638011yescharacteristic
243C22#8977611yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—562no—
252C4—562no—
253C4#8927212yes—
254C2—21no—
255C2—21no—
256C2#1172719911yescharacteristic
257C2C2×#8927211yescharacteristic
258C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#101D7
hypocenterC7#11794
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
238. C7#11794semidirect

Maximal subgroups

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

subgroupindex
#117399242
C4×C7×#1012
#117293792
#117253022
#117947