Finite Group Databasebeta

← #13263453

Subgroups — #13263453

Order 1792.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739922C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725259C212yesmaximal
5#11725258C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C7×#432—21no—
9#90002C411yescharacteristic
10#90002C411yescharacteristic
11#89756—21no—
12#89756—21no—
13#89749C2211yescharacteristic
14#89748C2211yescharacteristic
15C4×C4⋊Dic7C411yescharacteristic
16#89705—21no—
17#89705—21no—
18#89697—21no—
19C7×#324—21no—
20C7×#324C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11571—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C4×C7×Q8—41no—
26C4×C7×Q8—41no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4C2311yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×C4×Dic7C2×C411yescharacteristic
41C2×C4×Dic7C2×C411yescharacteristic
42#6433—41no—
43#6433—41no—
44C7×C4⋊C8—41no—
45C7×C22⋊C8—22no—
46C7×#97—41no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C22⋊(C7⋊C8)—22no—
55C4⋊(C7⋊C8)—41no—
56C4×C7⋊C8—41no—
57#2565—71no—
58#1467D711yescharacteristic
59#1461—71no—
60#1325—72no—
61#1324—72no—
62C2×C7×Q8—22no—
63C2×C7×Q8—22no—
64C2×C7×Q8—41no—
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22×C411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×Dic7—21no—
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C2×C7×C8—42no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—41no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C4⋊Dic7—42no—
87C4⋊Dic7—41no—
88C4⋊Dic7—41no—
89Dic7⋊C4—42no—
90Dic7⋊C4—42no—
91Dic7⋊C4—42no—
92Dic7⋊C4—41no—
93Dic7⋊C4—41no—
94C4×Dic7—22no—
95C4×Dic7—22no—
96C2×C7⋊C8—42no—
97C2×#125—71no—
98C2×C4×Q8C2×D711yescharacteristic
99#432—21no—
100#431—141no—
101#398—141no—
102#398—141no—
103#391—71no—
104#391—71no—
105#387—141no—
106#387—141no—
107#384—71no—
108#382—71no—
109C4×C4⋊C4—71no—
110#324—21no—
111#324—72no—
112#324—141no—
113#324C2×D712yes—
114C23×C7C2×C22⋊C411yescharacteristic
115C7×Q8—44no—
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—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7#9911yescharacteristic
132C2×C4×C7#10112yes—
133C2×C4×C7#13112yes—
134C2×Dic7—22no—
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—42no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C7×C8—82no—
146C7⋊C8—82no—
147C22×Q8C4×D711yescharacteristic
148#125—281no—
149#125—281no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—71no—
153C2×C4⋊C4—71no—
154C2×C4⋊C4—141no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4—141no—
158C2×C4⋊C4—141no—
159C2×C4⋊C4D2811yescharacteristic
160C2×C4⋊C4C22⋊D711yescharacteristic
161C2×C4⋊C4C22×D711yescharacteristic
162C2×C42—71no—
163C2×C42—71no—
164C2×C42C4×D711yescharacteristic
165C2×C42D2811yescharacteristic
166C2×C42C22⋊D711yescharacteristic
167C4⋊C8—41no—
168C4⋊C8—281no—
169C22⋊C8—22no—
170C22⋊C8—142no—
171#97—41no—
172C4×C8—281no—
173#95—141no—
174#95—141no—
175#95—141no—
176#95—141no—
177#95—141no—
178#95—141no—
179#95—141no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7#40811yescharacteristic
183C22×C7C2×#9911yescharacteristic
184C22×C7C2×#10111yescharacteristic
185C4×C7—21no—
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—41no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193Dic7—42no—
194Dic7—81no—
195Dic7—81no—
196Dic7—81no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—41no—
200C22×C4—141no—
201C22×C4—141no—
202C22×C4—141no—
203C22×C4—141no—
204C22×C4(C2×D7)⋊C411yescharacteristic
205C22×C4(C2×D7)⋊C411yescharacteristic
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4(C2×D7)⋊C411yescharacteristic
208C22×C4C2×C4×D711yescharacteristic
209C22×C4C2×D2811yescharacteristic
210C22×C4C2×C22⋊D711yescharacteristic
211C2×C8—42no—
212C2×C8—282no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—281no—
217C4⋊C4—281no—
218C4⋊C4—282no—
219C4⋊C4—282no—
220C4⋊C4—282no—
221C4⋊C4—282no—
222C4⋊C4—281no—
223C4⋊C4—281no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—142no—
231C42—142no—
232C2×C7—21no—
233C2×C7—21no—
234C2×C7#147211yescharacteristic
235C2×C7#212611yescharacteristic
236C2×C7#213311yescharacteristic
237C23C2×(C2×D7)⋊C411yescharacteristic
238Q8—44no—
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—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—142no—
254C2×C4—281no—
255C2×C4—281no—
256C2×C4—281no—
257C2×C4—281no—
258C2×C4—281no—
259C2×C4—281no—
260C2×C4—282no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4—281no—
264C2×C4#638011yescharacteristic
265C2×C4#638011yescharacteristic
266C2×C4#639812yes—
267C2×C4#647012yes—
268C8—82no—
269C8—562no—
270C7#1157111yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22C2×#638011yescharacteristic
274C22#8990111yescharacteristic
275C22C2×#639811yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—282no—
285C4—561no—
286C4—561no—
287C4—561no—
288C2—21no—
289C2—21no—
290C2#1172772611yescharacteristic
291C2#1172781411yescharacteristic
292C2#1172788211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1467C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1467D7
hypocenterC7#11571
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
270. C7#11571semidirect

Maximal subgroups

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

subgroupindex
#117399222
C7×#14672
#117293782
#117252592
#117252582
#115717