Finite Group Databasebeta

← #13264435

Subgroups — #13264435

Order 1792.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2581C211yesmaximal, characteristic
2C4×#6410C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725458C212yesmaximal
5#11725454C212yesmaximal
6C2×C4×C7×Q8C411yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#400C411yescharacteristic
9C7×#400C2211yescharacteristic
10C7×#395C411yescharacteristic
11C7×#395C2211yescharacteristic
12C7×#391—21no—
13C7×#389—21no—
14C7×#387—21no—
15C7×#387—21no—
16C7×#382C411yescharacteristic
17C2×#6410—21no—
18#89698—21no—
19C4×#1136—21no—
20#89325C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11792—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C22×C7×Q8D411yescharacteristic
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C4×C7×Q8—41no—
29C4×C7×Q8—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4C2311yescharacteristic
38C2×C42×C7—21no—
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×#1136—22no—
43C7×#95—21no—
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95C2×C411yescharacteristic
51C7×#95C2×C411yescharacteristic
52#6410—24no—
53C22⋊(C7⋊C8)—22no—
54C4⋊(C7⋊C8)—41no—
55#6377—41no—
56#6377—41no—
57C4×C7⋊C8—41no—
58#2581D711yescharacteristic
59C4×#101—71no—
60#1467—71no—
61#1354—72no—
62#1353—72no—
63C2×C7×Q8—22no—
64C2×C7×Q8—22no—
65C2×C7×Q8—41no—
66C2×C7×Q8—42no—
67C2×C7×Q8—41no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C7×C4⋊C4—41no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—42no—
84C7×C4⋊C4—42no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—42no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7—21no—
94C42×C7—42no—
95#1136—24no—
96#1136—42no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C2×C4×Q8Dic711yescharacteristic
100C2×C4×Q8C2×D711yescharacteristic
101#432—141no—
102C2×#101—141no—
103C4×M16—141no—
104#400Dic711yescharacteristic
105#400C2×D711yescharacteristic
106#395Dic711yescharacteristic
107#395C2×D711yescharacteristic
108#391—21no—
109#389—21no—
110#387—21no—
111#387—21no—
112#382Dic711yescharacteristic
113#343—72no—
114#324—72no—
115#324—141no—
116C23×C7C2×C22⋊C411yescharacteristic
117C7×Q8—44no—
118C7×Q8—42no—
119C7×Q8—42no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—22no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
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—41no—
140C2×C4×C7—41no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7#9911yescharacteristic
146C2×C4×C7#9911yescharacteristic
147C2×C4×C7#10412yes—
148C2×C4×C7#13712yes—
149C7⋊C8—44no—
150C7⋊C8—82no—
151C22×Q8C2×Dic711yescharacteristic
152C22×Q8C22⋊D711yescharacteristic
153C2×M16—142no—
154C4×Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×Dic711yescharacteristic
163C2×C4⋊C4C2×Dic711yescharacteristic
164C2×C4⋊C4C22⋊D711yescharacteristic
165C2×C4⋊C4C22×D711yescharacteristic
166C2×C42—21no—
167C2×C42C2×Dic711yescharacteristic
168C2×C42C22⋊D711yescharacteristic
169C2×C42C22⋊D711yescharacteristic
170C4⋊C8—281no—
171#101—144no—
172C22⋊C8—142no—
173#97—281no—
174#97—281no—
175C4×C8—281no—
176#95—21no—
177#95—21no—
178#95—21no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—21no—
183#95C2×Dic711yescharacteristic
184#95C2×Dic711yescharacteristic
185C22×C7—21no—
186C22×C7—21no—
187C22×C7C2×#9911yescharacteristic
188C22×C7#41911yescharacteristic
189C22×C7C2×#10411yescharacteristic
190C4×C7—21no—
191C4×C7—21no—
192C4×C7—22no—
193C4×C7—22no—
194C4×C7—41no—
195C4×C7—41no—
196C4×C7—42no—
197C4×C7—41no—
198C4×C7—41no—
199C4×C7—81no—
200C4×C7—81no—
201C4×C7—81no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×Q8—42no—
206C2×Q8—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22⋊Dic711yescharacteristic
212C22×C4C22⋊Dic711yescharacteristic
213C22×C4C22⋊Dic711yescharacteristic
214C22×C4C22⋊Dic711yescharacteristic
215C22×C4C22×Dic711yescharacteristic
216C22×C4C2×C22⋊D711yescharacteristic
217C22×C4C2×C22⋊D711yescharacteristic
218M16—144no—
219M16—282no—
220C2×C8—282no—
221C2×C8—282no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—42no—
238C2×C7—21no—
239C2×C7—21no—
240C2×C7#150811yescharacteristic
241C2×C7#212011yescharacteristic
242C2×C7#213311yescharacteristic
243C23C2×C22⋊Dic711yescharacteristic
244Q8—44no—
245Q8—42no—
246Q8—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4#640811yescharacteristic
273C2×C4#640811yescharacteristic
274C2×C4#641112yes—
275C2×C4#650512yes—
276C8—284no—
277C8—562no—
278C7#1179211yescharacteristic, complemented, Sylow
279C22—21no—
280C22—21no—
281C22C2×#640811yescharacteristic
282C22#8999711yescharacteristic
283C22C2×#641111yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2#1172944211yescharacteristic
299C2#1172947011yescharacteristic
300C2#1172962611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2581C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2581D7
hypocenterC7#11792
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
278. C7#11792semidirect

Maximal subgroups

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

subgroupindex
C7×#25812
C4×#64102
#117293792
#117254582
#117254542
#117927