Finite Group Databasebeta

← #13263442

Subgroups — #13263442

Order 1792.

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

normal subgroups only

This group has 424 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#11739829C211yesmaximal, characteristic
2C7×#1459C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725258C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C2×C7×C22⋊C8—21no—
8#89993C412yes—
9#89984—21no—
10#89984—21no—
11#89979—21no—
12#89749C2212yes—
13#89719—21no—
14#89719—21no—
15C4×C4⋊Dic7C411yescharacteristic
16C7×#324C2212yes—
17C7×#323—21no—
18#89323C2212yes—
19#89320—21no—
20#11569—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×Dic14—21no—
25C22×C7×C8—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—
37C2×C4×Dic7C2×C412yes—
38C2×#1136—41no—
39#6432—41no—
40#6432—41no—
41C7×C22⋊C8—22no—
42C7×C22⋊C8—41no—
43C7⋊#95—21no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C22⋊(C7⋊C8)—22no—
47C22⋊(C7⋊C8)—41no—
48#2563—71no—
49#1465—71no—
50#1459D711yescharacteristic
51#1324—74no—
52C24×C7C22⋊C411yescharacteristic
53C24×C7C22⋊C411yescharacteristic
54C2×C7×D4—22no—
55C2×C7×D4—22no—
56C2×C7×D4—41no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—42no—
62C22×C4×C7—42no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22×C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×Dic7—22no—
69C22×Dic7—22no—
70C2×Dic14—42no—
71C2×Dic14—82no—
72C2×C7×C8—42no—
73C2×C7×C8—82no—
74C7×C4⋊C4—41no—
75C7×C22⋊C4—41no—
76C7×C22⋊C4—41no—
77C42×C7—21no—
78C42×C7—21no—
79C22⋊Dic7—82no—
80C22⋊Dic7—82no—
81C4⋊Dic7—42no—
82C4⋊Dic7—41no—
83C4⋊Dic7—41no—
84C4⋊Dic7—42no—
85C4×Dic7—24no—
86#1136—82no—
87C2×C7⋊C8—42no—
88C2×C4⋊Q8—71no—
89C2×C4×D4C2×D711yescharacteristic
90#407—141no—
91C2×C22⋊C8—21no—
92#393—141no—
93#393—141no—
94#390—72no—
95#382—72no—
96#380—141no—
97#380—141no—
98C4×C4⋊C4—71no—
99#324—72no—
100#324C2×D712yes—
101#323—21no—
102#323—141no—
103C23×C7—21no—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7—21no—
108C23×C7—41no—
109C23×C7—41no—
110C23×C7—41no—
111C23×C7—41no—
112C23×C7#10112yes—
113C23×C7C2×C22⋊C411yescharacteristic
114C7×D4—44no—
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—42no—
122C2×C4×C7—42no—
123C2×C4×C7—41no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—81no—
127C2×C4×C7—81no—
128C2×C4×C7#9911yescharacteristic
129C2×C4×C7#9911yescharacteristic
130C2×C4×C7#13112yes—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137Dic14—84no—
138C7×C8—82no—
139C7⋊C8—82no—
140C22×Q8—141no—
141C22×D4C4×D711yescharacteristic
142C23×C4D2811yescharacteristic
143C23×C4C22⋊D711yescharacteristic
144C2×M16—281no—
145C22×C8—41no—
146C4⋊Q8—281no—
147C4⋊Q8—281no—
148C4×D4—41no—
149C4×D4—41no—
150C2×C4⋊C4—72no—
151C2×C4⋊C4—141no—
152C2×C4⋊C4—141no—
153C2×C4⋊C4C22×D711yescharacteristic
154C2×C22⋊C4—142no—
155C2×C22⋊C4—142no—
156C2×C22⋊C4D2811yescharacteristic
157C2×C22⋊C4C22⋊D711yescharacteristic
158C2×C42—72no—
159C2×C42C4×D711yescharacteristic
160C22⋊C8—22no—
161C22⋊C8—41no—
162C22⋊C8—142no—
163C22⋊C8—281no—
164#95—141no—
165#95—142no—
166#95—142no—
167C22×C7—21no—
168C22×C7—21no—
169C22×C7—22no—
170C22×C7—42no—
171C22×C7—42no—
172C22×C7—41no—
173C22×C7—41no—
174C22×C7—41no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—81no—
178C22×C7—81no—
179C22×C7#40811yescharacteristic
180C22×C7C2×#9911yescharacteristic
181C22×C7C2×#10111yescharacteristic
182C4×C7—21no—
183C4×C7—22no—
184C4×C7—41no—
185C4×C7—41no—
186C4×C7—41no—
187C4×C7#35412yes—
188Dic7—82no—
189Dic7—82no—
190C24(C2×D7)⋊C411yescharacteristic
191C24(C2×D7)⋊C411yescharacteristic
192C2×Q8—282no—
193C2×Q8—562no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—41no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—142no—
204C22×C4—142no—
205C22×C4(C2×D7)⋊C411yescharacteristic
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4C2×C4×D711yescharacteristic
208C22×C4C2×D2811yescharacteristic
209C22×C4C2×C22⋊D711yescharacteristic
210M16—562no—
211C2×C8—42no—
212C2×C8—82no—
213C2×C8—282no—
214C4⋊C4—41no—
215C4⋊C4—282no—
216C4⋊C4—282no—
217C4⋊C4—281no—
218C4⋊C4—281no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—562no—
222C22⋊C4—562no—
223C42—21no—
224C42—21no—
225C42—144no—
226C2×C7—21no—
227C2×C7—21no—
228C2×C7—42no—
229C2×C7—81no—
230C2×C7#147211yescharacteristic
231C2×C7C2×#35411yescharacteristic
232C2×C7#213411yescharacteristic
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23#639812yes—
243C23C2×(C2×D7)⋊C411yescharacteristic
244Q8—564no—
245D4—44no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—282no—
260C2×C4—282no—
261C2×C4—282no—
262C2×C4—282no—
263C2×C4—282no—
264C2×C4—282no—
265C2×C4#638011yescharacteristic
266C2×C4#638011yescharacteristic
267C2×C4#646412yes—
268C8—82no—
269C8—562no—
270C7#1156911yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C2×#638011yescharacteristic
284C22#8988211yescharacteristic
285C22C2×#639811yescharacteristic
286C4—22no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—562no—
292C4—562no—
293C4#8926812yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1172767711yescharacteristic
299C2C2×#8926811yescharacteristic
300C2#1172790311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1459C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1459D7
hypocenterC7#11569
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #11725258C2semidirect
270. C7#11569semidirect

Maximal subgroups

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

subgroupindex
#117398292
C7×#14592
#117293562
#117252582
#115697