Finite Group Databasebeta

← #13242307

Subgroups — #13242307

Order 1792.

390 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2863C211yesmaximal, characteristic
2#11727143C211yesmaximal, characteristic
3#11727142C211yesmaximal, characteristic
4#11725448C212yesmaximal
5#11725444C212yesmaximal
6C7×#391C411yescharacteristic
7C7×#391C411yescharacteristic
8C7×#391C2211yescharacteristic
9C7×#389C411yescharacteristic
10C7×#389C411yescharacteristic
11C7×#389C2211yescharacteristic
12C7×#387—21no—
13C7×#387—21no—
14C7×#387—21no—
15C7×#383—21no—
16C43×C7C2211yescharacteristic
17C2×#6377—21no—
18C2×C4×C7⋊C8—21no—
19#89319—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7693—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C2×C7×C4⋊C4—21no—
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C42×C7C2311yescharacteristic
38C22×C7⋊C8—22no—
39C22×C7⋊C8—22no—
40C7×#95—21no—
41C7×#95—21no—
42C7×#95—21no—
43C7×#95—21no—
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49#6377—24no—
50C4×C7⋊C8—24no—
51#2863D711yescharacteristic
52#1745—71no—
53#1744—71no—
54#1272—72no—
55#1271—72no—
56C2×C7×Q8—22no—
57C2×C7×Q8—41no—
58C2×C7×Q8—41no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22×C411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C7×C4⋊C4—22no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—42no—
74C7×C4⋊C4—42no—
75C7×C4⋊C4—42no—
76C42×C7—22no—
77C42×C7—22no—
78C42×C7—22no—
79C42×C7—22no—
80C42×C7—22no—
81C42×C7—41no—
82C42×C7—41no—
83C2×C7⋊C8—24no—
84C2×C7⋊C8—24no—
85C2×C7⋊C8—42no—
86C2×C7⋊C8—42no—
87C2×C7⋊C8—42no—
88C2×C7⋊C8—42no—
89C2×#97—141no—
90C2×C4×C8—141no—
91#391Dic711yescharacteristic
92#391Dic711yescharacteristic
93#391C2×D711yescharacteristic
94#389Dic711yescharacteristic
95#389Dic711yescharacteristic
96#389C2×D711yescharacteristic
97#387—21no—
98#387—21no—
99#387—21no—
100#383—21no—
101C43C2×D711yescharacteristic
102#336—72no—
103#336—72no—
104#336—141no—
105#336—141no—
106C23×C7C2×C22⋊C411yescharacteristic
107C7×Q8—82no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7#10412yes—
137C2×C4×C7#10412yes—
138C2×C4×C7#13112yes—
139C2×C4×C7#13512yes—
140C2×C4×C7#13712yes—
141C7⋊C8—44no—
142C7⋊C8—44no—
143C22×Q8C2×Dic711yescharacteristic
144C22×C8—142no—
145C22×C8—142no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4C2×Dic711yescharacteristic
150C2×C4⋊C4C2×Dic711yescharacteristic
151C2×C4⋊C4C2×Dic711yescharacteristic
152C2×C42C2×Dic711yescharacteristic
153C2×C42C2×Dic711yescharacteristic
154C2×C42C22⋊D711yescharacteristic
155C2×C42C22⋊D711yescharacteristic
156C2×C42C22⋊D711yescharacteristic
157C2×C42C22⋊D711yescharacteristic
158C2×C42C22×D711yescharacteristic
159#97—144no—
160C4×C8—144no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—21no—
170C22×C7#40811yescharacteristic
171C22×C7#41011yescharacteristic
172C22×C7#41311yescharacteristic
173C22×C7#41611yescharacteristic
174C22×C7#41911yescharacteristic
175C22×C7C2×#10411yescharacteristic
176C22×C7C2×#10411yescharacteristic
177C4×C7—22no—
178C4×C7—22no—
179C4×C7—22no—
180C4×C7—22no—
181C4×C7—22no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—81no—
185C4×C7—81no—
186C4×C7—81no—
187C4×C7—81no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—41no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4C22⋊Dic711yescharacteristic
196C22×C4C22⋊Dic711yescharacteristic
197C22×C4C22⋊Dic711yescharacteristic
198C22×C4C22⋊Dic711yescharacteristic
199C22×C4C22×Dic711yescharacteristic
200C22×C4C2×C22⋊D711yescharacteristic
201C22×C4C2×C22⋊D711yescharacteristic
202C2×C8—144no—
203C2×C8—144no—
204C2×C8—282no—
205C2×C8—282no—
206C2×C8—282no—
207C2×C8—282no—
208C4⋊C4—22no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C42—22no—
215C42—22no—
216C42—22no—
217C42—22no—
218C42—22no—
219C42—41no—
220C42—41no—
221C2×C7#147311yescharacteristic
222C2×C7#148511yescharacteristic
223C2×C7#149411yescharacteristic
224C2×C7#150011yescharacteristic
225C2×C7#150611yescharacteristic
226C2×C7#152411yescharacteristic
227C2×C7#155411yescharacteristic
228C23C2×C22⋊Dic711yescharacteristic
229Q8—82no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4#641112yes—
259C2×C4#641112yes—
260C2×C4#650512yes—
261C2×C4#651112yes—
262C2×C4#651312yes—
263C8—284no—
264C8—284no—
265C7#769311yescharacteristic, complemented, Sylow
266C22#8999711yescharacteristic
267C22#9000511yescharacteristic
268C22#9000611yescharacteristic
269C22C2×#641111yescharacteristic
270C22C2×#641111yescharacteristic
271C22#9000911yescharacteristic
272C22#9001211yescharacteristic
273C4—22no—
274C4—22no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—41no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—81no—
283C4—81no—
284C2#1172949911yescharacteristic
285C2#1172950011yescharacteristic
286C2#1172950611yescharacteristic
287C2#1172950811yescharacteristic
288C2#1172957911yescharacteristic
289C2#1172958611yescharacteristic
290C2#1172959011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2863C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2863D7
hypocenterC7#7693
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2863

Complements

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

NH ≅ G/Ntype
265. C7#7693semidirect

Maximal subgroups

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

subgroupindex
C7×#28632
#117271432
#117271422
#117254482
#117254442
#76937