Finite Group Databasebeta

← #13242305

Subgroups — #13242305

Order 1792.

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

normal subgroups only

This group has 390 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
1#11730754C211yesmaximal, characteristic
2C7×#1744C211yesmaximal, characteristic
3#11727143C211yesmaximal, characteristic
4#11725286C212yesmaximal
5#11725283C212yesmaximal
6C2×C4×C7×C8—21no—
7C43×C7C2211yescharacteristic
8#89709—21no—
9#89705—21no—
10#89705—21no—
11#89705—21no—
12#89701C411yescharacteristic
13#89701C411yescharacteristic
14#89701C2211yescharacteristic
15#89700C411yescharacteristic
16#89700C411yescharacteristic
17#89700C2211yescharacteristic
18C2×#6377—21no—
19C7×#336—21no—
20C7×#336C2212yes—
21#89319—21no—
22#89319C2212yes—
23#7693—71nomaximal, Sylow
24C22×Dic14C2×C411yescharacteristic
25C22×C7×C8—22no—
26C2×C42×C7C2×C411yescharacteristic
27C2×C42×C7C2×C411yescharacteristic
28C2×C42×C7D411yescharacteristic
29C2×C42×C7D411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7C2311yescharacteristic
33C2×C4⋊Dic7C2×C411yescharacteristic
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C22×C7⋊C8—22no—
40C4×C7×C8—24no—
41C7⋊#95—21no—
42C7⋊#95—21no—
43C7⋊#95—21no—
44C7⋊#95—21no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50#6377—24no—
51#2863—71no—
52#1745—71no—
53#1744D711yescharacteristic
54#1272—72no—
55#1271—72no—
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22×C411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×Dic7—21no—
64C22×Dic7—21no—
65C22×Dic7—21no—
66C22×Dic7—21no—
67C2×Dic14—22no—
68C2×Dic14—41no—
69C2×Dic14—41no—
70C2×C7×C8—24no—
71C2×C7×C8—42no—
72C2×C7×C8—42no—
73C42×C7—22no—
74C42×C7—22no—
75C42×C7—22no—
76C42×C7—22no—
77C42×C7—22no—
78C42×C7—41no—
79C42×C7—41no—
80C4⋊Dic7—22no—
81C4⋊Dic7—41no—
82C4⋊Dic7—41no—
83Dic7⋊C4—42no—
84Dic7⋊C4—42no—
85Dic7⋊C4—42no—
86C2×C7⋊C8—24no—
87C2×C7⋊C8—42no—
88C2×C7⋊C8—42no—
89C2×#97—141no—
90C2×C4×C8—21no—
91#391—71no—
92#391—71no—
93#391—71no—
94#389—71no—
95#389—71no—
96#389—71no—
97#387—141no—
98#387—141no—
99#387—141no—
100#383—141no—
101C43C2×D711yescharacteristic
102#336—21no—
103#336—72no—
104#336—141no—
105#336C2×D712yes—
106C23×C7C2×C22⋊C411yescharacteristic
107C2×C4×C7—21no—
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#10412yes—
124C2×C4×C7#10412yes—
125C2×C4×C7#13112yes—
126C2×C4×C7#13512yes—
127C2×C4×C7#13712yes—
128C2×Dic7—41no—
129C2×Dic7—41no—
130C2×Dic7—41no—
131C2×Dic7—41no—
132C2×Dic7—41no—
133C2×Dic7—41no—
134C2×Dic7—41no—
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140Dic14—82no—
141C7×C8—44no—
142C7⋊C8—44no—
143C22×Q8—71no—
144C22×C8—22no—
145C22×C8—142no—
146C2×C4⋊C4—71no—
147C2×C4⋊C4—71no—
148C2×C4⋊C4—71no—
149C2×C4⋊C4—141no—
150C2×C4⋊C4—141no—
151C2×C4⋊C4—141no—
152C2×C42C4×D711yescharacteristic
153C2×C42C4×D711yescharacteristic
154C2×C42D2811yescharacteristic
155C2×C42D2811yescharacteristic
156C2×C42C22⋊D711yescharacteristic
157C2×C42C22⋊D711yescharacteristic
158C2×C42C22×D711yescharacteristic
159#97—144no—
160C4×C8—24no—
161#95—141no—
162#95—141no—
163#95—141no—
164#95—141no—
165#95—141no—
166#95—141no—
167#95—141no—
168#95—141no—
169#95—141no—
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—
184Dic7—81no—
185Dic7—81no—
186Dic7—81no—
187Dic7—81no—
188C2×Q8—142no—
189C2×Q8—281no—
190C2×Q8—281no—
191C22×C4—141no—
192C22×C4—141no—
193C22×C4—141no—
194C22×C4—141no—
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—24no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—144no—
206C2×C8—282no—
207C2×C8—282no—
208C4⋊C4—142no—
209C4⋊C4—281no—
210C4⋊C4—281no—
211C4⋊C4—282no—
212C4⋊C4—282no—
213C4⋊C4—282no—
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×(C2×D7)⋊C411yescharacteristic
229Q8—562no—
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—281no—
247C2×C4—281no—
248C2×C4—281no—
249C2×C4—281no—
250C2×C4—281no—
251C2×C4—281no—
252C2×C4—281no—
253C2×C4—281no—
254C2×C4—281no—
255C2×C4—281no—
256C2×C4—281no—
257C2×C4—281no—
258C2×C4#637912yes—
259C2×C4#639912yes—
260C2×C4#646412yes—
261C2×C4#646712yes—
262C2×C4#651412yes—
263C8—44no—
264C8—284no—
265C7#769311yescharacteristic, complemented, Sylow
266C22C2×#637911yescharacteristic
267C22#8977611yescharacteristic
268C22#8977811yescharacteristic
269C22#8988211yescharacteristic
270C22#8988511yescharacteristic
271C22#8990411yescharacteristic
272C22C2×#639911yescharacteristic
273C4—22no—
274C4—22no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—41no—
279C4—41no—
280C4—561no—
281C4—561no—
282C4—561no—
283C4—561no—
284C2#1172718711yescharacteristic
285C2#1172749011yescharacteristic
286C2#1172755111yescharacteristic
287C2#1172852311yescharacteristic
288C2#1172853511yescharacteristic
289C2#1172853911yescharacteristic
290C2#1172854211yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1744C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1744D7
hypocenterC7#7693
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #1744

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
#117307542
C7×#17442
#117271432
#117252862
#117252832
#76937