Finite Group Databasebeta

← #13263448

Subgroups — #13263448

Order 1792.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739824C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725259C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6487—21no—
7C2×#6487—21no—
8C2×#6432C411yescharacteristic
9C7×#407—21no—
10#89993C412yes—
11C2×C22⋊(C7⋊C8)—21no—
12#89748C2212yes—
13#89721—21no—
14#89721—21no—
15C4×C4⋊Dic7C411yescharacteristic
16C7×#324C2212yes—
17C7×#323—21no—
18#89323C2212yes—
19#89320—21no—
20#11570—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×Dic14—21no—
25C2×C7×M16—41no—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C7×C22⋊C4D411yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C22⋊Dic7—22no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C412yes—
37#6487—44no—
38#6487—44no—
39C2×Dic7⋊C4—22no—
40C2×Dic7⋊C4—22no—
41C2×C4×Dic7C2×C412yes—
42C22×C7⋊C8—41no—
43#6432—41no—
44#6432—41no—
45C7×C22⋊C8—22no—
46C7×C22⋊C8—41no—
47C7⋊#95—21no—
48C22⋊(C7⋊C8)—22no—
49C22⋊(C7⋊C8)—41no—
50#2542—71no—
51#1465D711yescharacteristic
52#1459—71no—
53#1325—74no—
54C24×C7C22⋊C411yescharacteristic
55C24×C7C22⋊C411yescharacteristic
56C2×C7×D4—22no—
57C2×C7×D4—22no—
58C2×C7×D4—41no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
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—42no—
74C2×Dic14—41no—
75C2×Dic14—41no—
76C7×M16—82no—
77C2×C7×C8—42no—
78C7×C4⋊C4—41no—
79C7×C22⋊C4—41no—
80C7×C22⋊C4—41no—
81C42×C7—21no—
82C42×C7—21no—
83C22⋊Dic7—44no—
84C22⋊Dic7—44no—
85C4⋊Dic7—24no—
86C4⋊Dic7—42no—
87C4⋊Dic7—42no—
88Dic7⋊C4—44no—
89Dic7⋊C4—44no—
90C4×Dic7—24no—
91C2×C7⋊C8—42no—
92C2×C7⋊C8—82no—
93C2×C4⋊Q8—71no—
94C2×C22⋊Q8—141no—
95C2×C22⋊Q8—141no—
96C2×C4×D4C2×D711yescharacteristic
97#407—21no—
98C2×C22⋊C8—141no—
99#399—141no—
100#399—141no—
101#390—72no—
102#384—72no—
103C4×C4⋊C4—71no—
104#324—72no—
105#324C2×D712yes—
106#323—21no—
107#323—141no—
108C23×C7—21no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—41no—
114C23×C7—41no—
115C23×C7—41no—
116C23×C7—41no—
117C23×C7#10112yes—
118C23×C7C2×C22⋊C411yescharacteristic
119C7×D4—44no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—22no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—42no—
127C2×C4×C7—42no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—81no—
132C2×C4×C7—81no—
133C2×C4×C7#9911yescharacteristic
134C2×C4×C7#9911yescharacteristic
135C2×C4×C7#13112yes—
136C2×Dic7—24no—
137C2×Dic7—42no—
138C2×Dic7—42no—
139C2×Dic7—42no—
140C2×Dic7—42no—
141C2×Dic7—42no—
142Dic14—82no—
143Dic14—82no—
144C7×C8—82no—
145C7⋊C8—82no—
146C22×Q8—141no—
147C22×D4C4×D711yescharacteristic
148C23×C4D2811yescharacteristic
149C23×C4C22⋊D711yescharacteristic
150C2×M16—41no—
151C22×C8—281no—
152C4⋊Q8—281no—
153C4⋊Q8—281no—
154C22⋊Q8—284no—
155C22⋊Q8—284no—
156C4×D4—41no—
157C4×D4—41no—
158C2×C4⋊C4—72no—
159C2×C4⋊C4—141no—
160C2×C4⋊C4—141no—
161C2×C4⋊C4—142no—
162C2×C4⋊C4—142no—
163C2×C4⋊C4C22×D711yescharacteristic
164C2×C22⋊C4—142no—
165C2×C22⋊C4—142no—
166C2×C22⋊C4D2811yescharacteristic
167C2×C22⋊C4C22⋊D711yescharacteristic
168C2×C42—72no—
169C2×C42C4×D711yescharacteristic
170C22⋊C8—22no—
171C22⋊C8—41no—
172C22⋊C8—142no—
173C22⋊C8—281no—
174#95—141no—
175C22×C7—21no—
176C22×C7—21no—
177C22×C7—22no—
178C22×C7—42no—
179C22×C7—42no—
180C22×C7—41no—
181C22×C7—41no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7—41no—
185C22×C7—81no—
186C22×C7—81no—
187C22×C7#40811yescharacteristic
188C22×C7C2×#9911yescharacteristic
189C22×C7C2×#10111yescharacteristic
190C4×C7—21no—
191C4×C7—22no—
192C4×C7—41no—
193C4×C7—41no—
194C4×C7—41no—
195C4×C7#35312yes—
196Dic7—44no—
197Dic7—82no—
198C24(C2×D7)⋊C411yescharacteristic
199C24(C2×D7)⋊C411yescharacteristic
200C2×Q8—282no—
201C2×Q8—282no—
202C2×Q8—281no—
203C2×Q8—281no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—142no—
214C22×C4—142no—
215C22×C4(C2×D7)⋊C411yescharacteristic
216C22×C4(C2×D7)⋊C411yescharacteristic
217C22×C4C2×C4×D711yescharacteristic
218C22×C4C2×D2811yescharacteristic
219C22×C4C2×C22⋊D711yescharacteristic
220M16—82no—
221C2×C8—42no—
222C2×C8—282no—
223C2×C8—562no—
224C4⋊C4—41no—
225C4⋊C4—144no—
226C4⋊C4—282no—
227C4⋊C4—282no—
228C4⋊C4—284no—
229C4⋊C4—284no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—284no—
233C22⋊C4—284no—
234C42—21no—
235C42—21no—
236C42—144no—
237C2×C7—21no—
238C2×C7—21no—
239C2×C7—42no—
240C2×C7—81no—
241C2×C7#147211yescharacteristic
242C2×C7C2×#35311yescharacteristic
243C2×C7#213511yescharacteristic
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#639812yes—
254C23C2×(C2×D7)⋊C411yescharacteristic
255Q8—562no—
256Q8—562no—
257D4—44no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—144no—
272C2×C4—282no—
273C2×C4—282no—
274C2×C4—282no—
275C2×C4—282no—
276C2×C4—282no—
277C2×C4#638011yescharacteristic
278C2×C4#638011yescharacteristic
279C2×C4#647012yes—
280C8—82no—
281C8—562no—
282C7#1157011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C2×#638011yescharacteristic
296C22#8990111yescharacteristic
297C22C2×#639811yescharacteristic
298C4—22no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—284no—
304C4—562no—
305C4#8926912yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1172772611yescharacteristic
311C2C2×#8926911yescharacteristic
312C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1465D7
hypocenterC7#11570
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725259C2semidirect
282. C7#11570semidirect

Maximal subgroups

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

subgroupindex
#117398242
C7×#14652
#117293542
#117252592
#115707