Finite Group Databasebeta

← #13251490

Subgroups — #13251490

Order 1792.

448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C7×#2983C211yesmaximal, characteristic
2#11739923C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11728576C212yesmaximal
5#11725556C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6432C2211yescharacteristic
8C7×#446—24no—
9C7×#432—21no—
10C7×#432C2212yes—
11C7×#431—21no—
12#90002C412yes—
13#89751—21no—
14#89751—21no—
15#89748C412yes—
16C4×C4⋊Dic7C2211yescharacteristic
17#89700—21no—
18#89700—21no—
19#89698C2212yes—
20#89323—21no—
21#89323—21no—
22#89281—24no—
23#9454—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C22×Dic14—21no—
26C4×C7×Q8—22no—
27C4×C7×Q8—22no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7C2311yescharacteristic
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C412yes—
37C2×Dic7⋊C4—22no—
38C2×Dic7⋊C4—22no—
39C2×C4×Dic7C2×C412yes—
40#6432—22no—
41#6432—22no—
42C7×C4⋊C8—22no—
43C7×C4⋊C8—22no—
44C7×C4⋊C8D414yes—
45C7×C22⋊C8—22no—
46C7×#97—22no—
47C7×#97—22no—
48C4×C7×C8—22no—
49C7⋊#95—22no—
50C7⋊#95—22no—
51C7⋊#95—21no—
52C22⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)—22no—
54#6377—22no—
55#2983D711yescharacteristic
56#2567—71no—
57#1556—72no—
58#1467—71no—
59#1285—72no—
60C2×C7×Q8—22no—
61C2×C7×Q8—22no—
62C2×C7×Q8—41no—
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
70C22×Dic7—22no—
71C22×Dic7—22no—
72C2×Dic14—42no—
73C2×Dic14—82no—
74C2×C7×C8—24no—
75C7×C4⋊C4—22no—
76C7×C4⋊C4—22no—
77C7×C4⋊C4—22no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7C2×D412yes—
83C42×C7#4112yes—
84C4⋊Dic7—24no—
85C4⋊Dic7—24no—
86C4⋊Dic7—41no—
87C4⋊Dic7—41no—
88Dic7⋊C4—82no—
89Dic7⋊C4—82no—
90C4×Dic7—42no—
91C2×C7⋊C8—42no—
92C2×C4⋊Q8—71no—
93C2×C4×Q8C2×D711yescharacteristic
94#446—24no—
95#432—21no—
96#432—72no—
97#432C2×D712yes—
98#431—21no—
99#395—141no—
100#395—141no—
101#391—72no—
102#389—141no—
103#389—141no—
104#384—72no—
105C4×C4⋊C4—71no—
106#332—144no—
107#324—141no—
108#324—141no—
109C23×C7C2×C22⋊C411yescharacteristic
110C7×Q8—44no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—22no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7—41no—
124C2×C4×C7#10112yes—
125C2×C4×C7C4×D412yes—
126C2×C4×C7#12011yescharacteristic
127C2×C4×C7#12112yes—
128C2×C4×C7#12311yescharacteristic
129C2×Dic7—24no—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135Dic14—84no—
136C7×C8—44no—
137C7⋊C8—82no—
138C22×Q8—141no—
139C22×Q8C4×D711yescharacteristic
140C4⋊Q8—142no—
141C4⋊Q8—142no—
142C4×Q8—22no—
143C4×Q8—22no—
144C2×C4⋊C4—72no—
145C2×C4⋊C4—141no—
146C2×C4⋊C4—141no—
147C2×C4⋊C4—142no—
148C2×C4⋊C4—142no—
149C2×C4⋊C4C4×D711yescharacteristic
150C2×C4⋊C4D2811yescharacteristic
151C2×C4⋊C4D2811yescharacteristic
152C2×C42—72no—
153C2×C42C22⋊D711yescharacteristic
154C2×C42C22⋊D711yescharacteristic
155C2×C42C22×D711yescharacteristic
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—142no—
159C4⋊C8C22⋊D714yes—
160C22⋊C8—22no—
161C22⋊C8—142no—
162#97—22no—
163#97—22no—
164#97—142no—
165C4×C8—22no—
166#95—142no—
167#95—142no—
168#95—141no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7#38611yescharacteristic
172C22×C7C2×#10111yescharacteristic
173C22×C7#41311yescharacteristic
174C4×C7—21no—
175C4×C7—22no—
176C4×C7—22no—
177C4×C7—22no—
178C4×C7—41no—
179C4×C7—41no—
180C4×C7—41no—
181C4×C7#45612yes—
182Dic7—44no—
183Dic7—82no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—282no—
188C2×Q8—562no—
189C22×C4—142no—
190C22×C4—142no—
191C22×C4(C2×D7)⋊C411yescharacteristic
192C22×C4(C2×D7)⋊C411yescharacteristic
193C22×C4(C2×D7)⋊C411yescharacteristic
194C22×C4(C2×D7)⋊C411yescharacteristic
195C22×C4C2×C4×D711yescharacteristic
196C22×C4C2×D2811yescharacteristic
197C22×C4C2×C22⋊D711yescharacteristic
198C2×C8—24no—
199C2×C8—282no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—144no—
204C4⋊C4—144no—
205C4⋊C4—281no—
206C4⋊C4—281no—
207C4⋊C4—562no—
208C4⋊C4—562no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—282no—
214C42#115712yes—
215C42C2×C22⋊D712yes—
216C2×C7—21no—
217C2×C7—21no—
218C2×C7#188611yescharacteristic
219C2×C7#190111yescharacteristic
220C2×C7#191011yescharacteristic
221C23C2×(C2×D7)⋊C411yescharacteristic
222Q8—44no—
223Q8—564no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—144no—
238C2×C4—282no—
239C2×C4—282no—
240C2×C4—282no—
241C2×C4—282no—
242C2×C4—282no—
243C2×C4#639812yes—
244C2×C4C4×C22⋊D712yes—
245C2×C4#649211yescharacteristic
246C2×C4#649312yes—
247C2×C4#651611yescharacteristic
248C8—44no—
249C8—562no—
250C7#945411yescharacteristic, complemented, Sylow
251C22—21no—
252C22—21no—
253C22#8990411yescharacteristic
254C22C2×#639811yescharacteristic
255C22#8998511yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—284no—
264C4—562no—
265C4#9001812yes—
266C2—21no—
267C2—21no—
268C2#1172941411yescharacteristic
269C2#1172975711yescharacteristic
270C2#1172977911yescharacteristic
subgroupG/H
centerC22#89985
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2983C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2983D7
hypocenterC7#9454
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
250. C7#9454semidirect

Maximal subgroups

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

subgroupindex
C7×#29832
#117399232
#117293792
#117285762
#117255562
#94547