Finite Group Databasebeta

← #13251478

Subgroups — #13251478

Order 1792.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#11739920C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic
3C7×#1467C211yesmaximal, characteristic
4#11728578C212yesmaximal
5#11725555C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6507C412yes—
8C2×#6432C2211yescharacteristic
9C7×#432C2212yes—
10#89796—24no—
11#89755—21no—
12#89755—21no—
13#89746C412yes—
14C4×C4⋊Dic7C2211yescharacteristic
15#89700—21no—
16#89700—21no—
17#89698—21no—
18#89698C2212yes—
19#89697—21no—
20C7×#324—21no—
21C7×#324—21no—
22#89276—24no—
23#9452—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C22×Dic14C2×C412yes—
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
34#6507—44no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×Dic7⋊C4—22no—
39C2×Dic7⋊C4—22no—
40C2×C4×Dic7C2×C412yes—
41#6432—22no—
42#6432—22no—
43C7×C4⋊C8—22no—
44C7×C22⋊C8—22no—
45C7×#97—22no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C7⋊#95—21no—
49C22⋊(C7⋊C8)—22no—
50C4⋊(C7⋊C8)—22no—
51C4⋊(C7⋊C8)—22no—
52C4⋊(C7⋊C8)D414yes—
53#6377—22no—
54#6377—22no—
55C4×C7⋊C8—22no—
56#2983—71no—
57#2546—71no—
58#1558—72no—
59#1467D711yescharacteristic
60#1285—72no—
61C2×C7×Q8—22no—
62C2×C7×Q8—22no—
63C2×C7×Q8—41no—
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×Dic7—22no—
72C22×Dic7—22no—
73C2×Dic14—24no—
74C2×Dic14—42no—
75C2×Dic14—42no—
76C2×C7×C8—42no—
77C7×C4⋊C4—22no—
78C7×C4⋊C4—22no—
79C7×C4⋊C4—22no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7C2×D412yes—
85C42×C7#4112yes—
86C4⋊Dic7—24no—
87C4⋊Dic7—41no—
88C4⋊Dic7—42no—
89C4⋊Dic7—41no—
90Dic7⋊C4—44no—
91Dic7⋊C4—44no—
92C4×Dic7—42no—
93C2×C7⋊C8—24no—
94C2×C4⋊Q8—72no—
95C2×C4⋊Q8—71no—
96C2×C4×Q8C2×D711yescharacteristic
97#446—144no—
98#432—72no—
99#432—141no—
100#432C2×D712yes—
101#431—141no—
102#398—141no—
103#398—141no—
104#391—72no—
105#389—141no—
106#389—141no—
107C4×C4⋊C4—71no—
108#333—144no—
109#324—21no—
110#324—21no—
111C23×C7C2×C22⋊C411yescharacteristic
112C7×Q8—44no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—22no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—41no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7#10012yes—
127C2×C4×C7C4×D412yes—
128C2×C4×C7#12011yescharacteristic
129C2×C4×C7#12112yes—
130C2×C4×C7#12311yescharacteristic
131C2×Dic7—24no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137Dic14—84no—
138C7×C8—82no—
139C7⋊C8—44no—
140C22×Q8—72no—
141C22×Q8C4×D711yescharacteristic
142C4⋊Q8—142no—
143C4⋊Q8—142no—
144C4⋊Q8—284no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—141no—
148C2×C4⋊C4—142no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4—141no—
151C2×C4⋊C4—141no—
152C2×C4⋊C4C4×D711yescharacteristic
153C2×C4⋊C4C22⋊D711yescharacteristic
154C2×C4⋊C4C22⋊D711yescharacteristic
155C2×C42—72no—
156C2×C42D2811yescharacteristic
157C2×C42D2811yescharacteristic
158C2×C42C22×D711yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—74no—
161C4⋊C8—142no—
162C4⋊C8—142no—
163C22⋊C8—22no—
164C22⋊C8—142no—
165#97—22no—
166#97—142no—
167#97—142no—
168C4×C8—142no—
169#95—142no—
170#95—142no—
171#95—141no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7#38611yescharacteristic
175C22×C7C2×#10011yescharacteristic
176C22×C7#41311yescharacteristic
177C4×C7—21no—
178C4×C7—22no—
179C4×C7—22no—
180C4×C7—22no—
181C4×C7—41no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7#45612yes—
185Dic7—44no—
186Dic7—82no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—144no—
191C2×Q8—282no—
192C2×Q8—282no—
193C22×C4—142no—
194C22×C4—142no—
195C22×C4(C2×D7)⋊C411yescharacteristic
196C22×C4(C2×D7)⋊C411yescharacteristic
197C22×C4(C2×D7)⋊C411yescharacteristic
198C22×C4(C2×D7)⋊C411yescharacteristic
199C22×C4C2×C4×D711yescharacteristic
200C22×C4C2×D2811yescharacteristic
201C22×C4C2×C22⋊D711yescharacteristic
202C2×C8—42no—
203C2×C8—144no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—144no—
208C4⋊C4—284no—
209C4⋊C4—281no—
210C4⋊C4—281no—
211C4⋊C4—282no—
212C4⋊C4—284no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—282no—
218C42D4×D712yes—
219C42#115912yes—
220C2×C7—21no—
221C2×C7—21no—
222C2×C7#188611yescharacteristic
223C2×C7#190011yescharacteristic
224C2×C7#190911yescharacteristic
225C23C2×(C2×D7)⋊C411yescharacteristic
226Q8—44no—
227Q8—564no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—144no—
242C2×C4—282no—
243C2×C4—282no—
244C2×C4—282no—
245C2×C4—282no—
246C2×C4—282no—
247C2×C4#639712yes—
248C2×C4(C22⋊D7)⋊C412yes—
249C2×C4#644511yescharacteristic
250C2×C4#644911yescharacteristic
251C2×C4#650212yes—
252C8—82no—
253C8—284no—
254C7#945211yescharacteristic, complemented, Sylow
255C22—21no—
256C22—21no—
257C22#8973011yescharacteristic
258C22C2×#639711yescharacteristic
259C22#8990411yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—284no—
268C4—562no—
269C4#8952412yes—
270C2—21no—
271C2—21no—
272C2#1172773911yescharacteristic
273C2#1172780011yescharacteristic
274C2#1172785711yescharacteristic
subgroupG/H
centerC22#89730
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1467C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1467D7
hypocenterC7#9452
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
254. C7#9452semidirect

Maximal subgroups

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

subgroupindex
#117399202
#117398812
C7×#14672
#117285782
#117255552
#94527