Finite Group Databasebeta

← #13246441

Subgroups — #13246441

Order 1792.

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

normal subgroups only

This group has 778 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×C7×#125C211yesmaximal, characteristic
2#11729316C212yesmaximal
3#11729306C212yesmaximal
4#11729306C212yesmaximal
5C2×C7×#125—24no—
6C2×C7×#125—24no—
7C2×C7×#125—24no—
8C22×C7×C4⋊C4C411yescharacteristic
9C22×C7×C4⋊C4C411yescharacteristic
10C22×C7×C4⋊C4C411yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C411yescharacteristic
15#89979C2214yes—
16#89325—24no—
17#89323—24no—
18#89323—24no—
19#8554—71nomaximal, Sylow
20C23×C4×C7C2×C411yescharacteristic
21C23×C4×C7C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2×C411yescharacteristic
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C7×#125—232no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4—22no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4—22no—
35C2×C7×C4⋊C4—22no—
36C2×C7×C4⋊C4—22no—
37C2×C7×C4⋊C4—22no—
38C2×C7×C4⋊C4—22no—
39C2×C7×C4⋊C4—22no—
40C2×C7×C4⋊C4—22no—
41C2×C7×C4⋊C4—22no—
42C2×C7×C4⋊C4—22no—
43C2×C7×C4⋊C4D414yes—
44C2×C7×C4⋊C4D414yes—
45C2×C7×C4⋊C4D414yes—
46C2×C42×C7—22no—
47C2×C42×C7—22no—
48C2×C42×C7—22no—
49C2×#1136—24no—
50C22⋊(C7⋊C8)—24no—
51C22⋊(C7⋊C8)—24no—
52C22×#125D711yescharacteristic
53#1821—72no—
54#1463—72no—
55#1463—72no—
56C24×C7C22×C411yescharacteristic
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—24no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—42no—
71C22×C4×C7—42no—
72C22×C4×C7—42no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7—42no—
76C22×C4×C7C22⋊C412yes—
77C22×C4×C7C22⋊C412yes—
78C22×C4×C7C22⋊C412yes—
79C22×C4×C7C22⋊C412yes—
80C22×C4×C7C22⋊C412yes—
81C22×C4×C7C22⋊C412yes—
82C22×C4×C7C2×D412yes—
83C22×C4×C7C2×D412yes—
84C22×C4×C7C2×D412yes—
85C7×C4⋊C4—28no—
86C7×C4⋊C4—28no—
87C7×C4⋊C4—28no—
88C7×C4⋊C4—28no—
89C7×C4⋊C4—28no—
90C7×C4⋊C4—28no—
91C42×C7—28no—
92#1136—48no—
93C2×C7⋊C8—44no—
94C2×#125—24no—
95C2×#125—24no—
96C2×#125—24no—
97C22×C4⋊C4Dic711yescharacteristic
98C22×C4⋊C4Dic711yescharacteristic
99C22×C4⋊C4Dic711yescharacteristic
100C22×C4⋊C4C2×D711yescharacteristic
101C22×C4⋊C4C2×D711yescharacteristic
102C22×C4⋊C4C2×D711yescharacteristic
103C22×C42Dic711yescharacteristic
104#407—74no—
105#343—144no—
106#324—144no—
107#324—144no—
108C23×C7—22no—
109C23×C7—22no—
110C23×C7—22no—
111C23×C7C2×C22⋊C411yescharacteristic
112C23×C7C2×C22⋊C411yescharacteristic
113C23×C7C2×C22⋊C411yescharacteristic
114C2×C4×C7—24no—
115C2×C4×C7—24no—
116C2×C4×C7—22no—
117C2×C4×C7—24no—
118C2×C4×C7—22no—
119C2×C4×C7—22no—
120C2×C4×C7—22no—
121C2×C4×C7—22no—
122C2×C4×C7—22no—
123C2×C4×C7—22no—
124C2×C4×C7—24no—
125C2×C4×C7—42no—
126C2×C4×C7—42no—
127C2×C4×C7—42no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—42no—
134C2×C4×C7—42no—
135C2×C4×C7—42no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7#10114yes—
142C2×C4×C7#12014yes—
143C7⋊C8—84no—
144C23×C4C2×Dic711yescharacteristic
145C23×C4C2×Dic711yescharacteristic
146C23×C4C2×Dic711yescharacteristic
147C23×C4C2×Dic711yescharacteristic
148C23×C4C2×Dic711yescharacteristic
149C23×C4C2×Dic711yescharacteristic
150C23×C4C22×D711yescharacteristic
151C2×M16—144no—
152#125—232no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C22⋊D714yes—
169C2×C4⋊C4C22⋊D714yes—
170C2×C4⋊C4C22⋊D714yes—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—22no—
174C22⋊C8—144no—
175C22⋊C8—144no—
176C22×C7—28no—
177C22×C7—21no—
178C22×C7—21no—
179C22×C7—21no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7—21no—
183C22×C7#37911yescharacteristic
184C22×C7#41012yes—
185C22×C7C2×#10112yes—
186C22×C7#41312yes—
187C4×C7—24no—
188C4×C7—24no—
189C4×C7—42no—
190C4×C7—42no—
191C4×C7—42no—
192C4×C7—42no—
193C4×C7—42no—
194C24C22×Dic711yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—24no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4C22⋊Dic712yes—
215C22×C4C22⋊Dic712yes—
216C22×C4C22⋊Dic712yes—
217C22×C4C22⋊Dic712yes—
218C22×C4C22⋊Dic712yes—
219C22×C4C22⋊Dic712yes—
220C22×C4C2×C22⋊D712yes—
221C22×C4C2×C22⋊D712yes—
222C22×C4C2×C22⋊D712yes—
223M16—288no—
224C2×C8—284no—
225C4⋊C4—28no—
226C4⋊C4—28no—
227C4⋊C4—28no—
228C4⋊C4—28no—
229C4⋊C4—28no—
230C4⋊C4—28no—
231C42—28no—
232C2×C7—22no—
233C2×C7—22no—
234C2×C7—22no—
235C2×C7#178211yescharacteristic
236C2×C7#178411yescharacteristic
237C2×C7#178511yescharacteristic
238C23—22no—
239C23—22no—
240C23—22no—
241C23C2×C22⋊Dic711yescharacteristic
242C23C2×C22⋊Dic711yescharacteristic
243C23C2×C22⋊Dic711yescharacteristic
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4#641014yes—
272C2×C4#651614yes—
273C8—564no—
274C7#855411yescharacteristic, complemented, Sylow
275C22—28no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22C2×#641012yes—
283C22#9000912yes—
284C22#9001212yes—
285C22#9001911yescharacteristic
286C4—24no—
287C4—24no—
288C4—42no—
289C4—42no—
290C4—42no—
291C4—42no—
292C4—42no—
293C2—22no—
294C2—22no—
295C2—22no—
296C2#1172988711yescharacteristic
297C2#1172989111yescharacteristic
298C2#1172989311yescharacteristic
subgroupG/H
centerC22#90019
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC22×C7×#125C2
socleC22×C7#379
cosocleC23×C4×C7C23
hypercenterC22×#125D7
hypocenterC7#8554
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
274. C7#8554semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1252
#117293162
#117293062
#85547