Finite Group Databasebeta

← #13242379

Subgroups — #13242379

Order 1792.

372 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2863C211yesmaximal, characteristic
2#11727146C211yesmaximal, characteristic
3#11727143C211yesmaximal, 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×C4⋊(C7⋊C8)—21no—
18C2×#6377—21no—
19#89319—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7709—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—
49C4⋊(C7⋊C8)—42no—
50#6377—24no—
51#2863D711yescharacteristic
52#1831—71no—
53#1745—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—41no—
76C7×C4⋊C4—41no—
77C42×C7—22no—
78C42×C7—22no—
79C42×C7—21no—
80C42×C7—22no—
81C42×C7—21no—
82C42×C7—41no—
83C42×C7—41no—
84C42×C7—41no—
85C2×C7⋊C8—24no—
86C2×C7⋊C8—42no—
87C2×C7⋊C8—42no—
88C2×C7⋊C8—42no—
89C2×C7⋊C8—42no—
90C2×C7⋊C8—42no—
91C2×C4⋊C8—141no—
92C2×#97—141no—
93#391Dic711yescharacteristic
94#391Dic711yescharacteristic
95#391C2×D711yescharacteristic
96#389Dic711yescharacteristic
97#389Dic711yescharacteristic
98#389C2×D711yescharacteristic
99#387—21no—
100#387—21no—
101#387—21no—
102#383—21no—
103C43C2×D711yescharacteristic
104#336—72no—
105#336—72no—
106#336—141no—
107#336—141no—
108C23×C7C2×C22⋊C411yescharacteristic
109C7×Q8—82no—
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—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
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—41no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7#10412yes—
140C2×C4×C7#13112yes—
141C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C7#13712yes—
143C2×C4×C7#13711yescharacteristic
144C7⋊C8—44no—
145C7⋊C8—82no—
146C22×Q8C2×Dic711yescharacteristic
147C22×C8—142no—
148C22×C8—142no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4C2×Dic711yescharacteristic
153C2×C4⋊C4C2×Dic711yescharacteristic
154C2×C4⋊C4C2×Dic711yescharacteristic
155C2×C42C2×Dic711yescharacteristic
156C2×C42C2×Dic711yescharacteristic
157C2×C42C22⋊D711yescharacteristic
158C2×C42C22⋊D711yescharacteristic
159C2×C42C22⋊D711yescharacteristic
160C2×C42C22⋊D711yescharacteristic
161C2×C42C22×D711yescharacteristic
162C4⋊C8—282no—
163#97—144no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—21no—
172#95—21no—
173C22×C7#40811yescharacteristic
174C22×C7#41011yescharacteristic
175C22×C7#41311yescharacteristic
176C22×C7#41711yescharacteristic
177C22×C7#41911yescharacteristic
178C22×C7C2×#10411yescharacteristic
179C22×C7#42111yescharacteristic
180C4×C7—22no—
181C4×C7—22no—
182C4×C7—22no—
183C4×C7—21no—
184C4×C7—21no—
185C4×C7—41no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—81no—
189C4×C7—81no—
190C4×C7—81no—
191C4×C7—81no—
192C2×Q8—22no—
193C2×Q8—41no—
194C2×Q8—41no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4C22⋊Dic711yescharacteristic
200C22×C4C22⋊Dic711yescharacteristic
201C22×C4C22⋊Dic711yescharacteristic
202C22×C4C22⋊Dic711yescharacteristic
203C22×C4C22×Dic711yescharacteristic
204C22×C4C2×C22⋊D711yescharacteristic
205C22×C4C2×C22⋊D711yescharacteristic
206C2×C8—144no—
207C2×C8—282no—
208C2×C8—282no—
209C2×C8—282no—
210C2×C8—282no—
211C2×C8—282no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C42—22no—
220C42—22no—
221C42—22no—
222C42—21no—
223C42—21no—
224C42—41no—
225C42—41no—
226C42—41no—
227C2×C7#147311yescharacteristic
228C2×C7#148311yescharacteristic
229C2×C7#149711yescharacteristic
230C2×C7#150611yescharacteristic
231C2×C7#151211yescharacteristic
232C2×C7#152911yescharacteristic
233C2×C7#155911yescharacteristic
234C23C2×C22⋊Dic711yescharacteristic
235Q8—82no—
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—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#641112yes—
266C2×C4#650512yes—
267C2×C4#651112yes—
268C2×C4#651211yescharacteristic
269C2×C4#651411yescharacteristic
270C8—284no—
271C8—562no—
272C7#770911yescharacteristic, complemented, Sylow
273C22#8999711yescharacteristic
274C22#9000411yescharacteristic
275C22#9000611yescharacteristic
276C22C2×#641111yescharacteristic
277C22#9000811yescharacteristic
278C22#9000911yescharacteristic
279C22#9001211yescharacteristic
280C4—22no—
281C4—22no—
282C4—21no—
283C4—21no—
284C4—22no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—81no—
291C4—81no—
292C2#1172949911yescharacteristic
293C2#1172950111yescharacteristic
294C2#1172950511yescharacteristic
295C2#1172951011yescharacteristic
296C2#1172958111yescharacteristic
297C2#1172958711yescharacteristic
298C2#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#7709
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
272. C7#7709semidirect

Maximal subgroups

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

subgroupindex
C7×#28632
#117271462
#117271432
#117254482
#117254442
#77097