Finite Group Databasebeta

← #13262929

Subgroups — #13262929

Order 1792.

450 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C22×Dic7⋊C8C211yesmaximal, characteristic
2C7×#2112C211yesmaximal, characteristic
3#11729717C211yesmaximal, characteristic
4#11725330C214yesmaximal, complemented
5C23×C7×C8C2211yescharacteristic
6C22×C4×Dic7C411yescharacteristic
7C23×C7⋊C8C411yescharacteristic
8C2×C7×M32—21no—
9C2×Dic7⋊C8—21no—
10C2×Dic7⋊C8—21no—
11C2×Dic7⋊C8—21no—
12C2×Dic7⋊C8—21no—
13C2×Dic7⋊C8C412yes—
14C2×Dic7⋊C8C2212yes—
15C2×#6386—21no—
16C7×C22⋊C16—21no—
17C7×C22⋊C16C2212yes—
18C22⋊(C7⋊C16)—21no—
19C22⋊(C7⋊C16)C2212yes—
20#11440—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×Dic7C811yescharacteristic
23C23×Dic7C811yescharacteristic
24C22×C7×C8—42no—
25C22×C7×C8C2×C411yescharacteristic
26C22×C7×C8D411yescharacteristic
27C22×C7×C8D411yescharacteristic
28C22×C7×C8D411yescharacteristic
29C22×C7×C8D411yescharacteristic
30C22×C7×C8C2311yescharacteristic
31C2×C4×Dic7—21no—
32C2×C4×Dic7—21no—
33C2×C4×Dic7—21no—
34C2×C4×Dic7—21no—
35C2×C4×Dic7C812yes—
36C2×C4×Dic7C2×C412yes—
37C22×C7⋊C8—21no—
38C22×C7⋊C8—21no—
39C22×C7⋊C8—42no—
40C22×C7⋊C8C2×C412yes—
41C7×M32—42no—
42C2×C7×C16—22no—
43Dic7⋊C8—22no—
44Dic7⋊C8—22no—
45Dic7⋊C8—22no—
46Dic7⋊C8—22no—
47#6386—42no—
48C2×C7⋊C16—22no—
49C22×C4⋊C8—71no—
50#2112—71no—
51#2112D711yescharacteristic
52#1322—74no—
53C24×C7C2×C811yescharacteristic
54C22×C4×C7—22no—
55C22×C4×C7—22no—
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C2×C811yescharacteristic
59C22×C4×C7M1611yescharacteristic
60C22×C4×C7M1611yescharacteristic
61C22×C4×C7C22×C411yescharacteristic
62C22×Dic7—21no—
63C22×Dic7—21no—
64C22×Dic7—24no—
65C22×Dic7—21no—
66C22×Dic7—21no—
67C22×Dic7—42no—
68C22×Dic7C2×C812yes—
69C22×Dic7C2×C812yes—
70C2×C7×C8—22no—
71C2×C7×C8—22no—
72C2×C7×C8—41no—
73C2×C7×C8—41no—
74C2×C7×C8—41no—
75C2×C7×C8—41no—
76C2×C7×C8C22⋊C411yescharacteristic
77C2×C7×C8C22⋊C411yescharacteristic
78C2×C7×C8C2×D411yescharacteristic
79C2×C7×C8C2×D411yescharacteristic
80C4×Dic7—22no—
81C4×Dic7—22no—
82C4×Dic7—22no—
83C4×Dic7—22no—
84C2×C7⋊C8—22no—
85C2×C7⋊C8—42no—
86C2×C7⋊C8—42no—
87C2×C7⋊C8—42no—
88C7×C16—42no—
89C7⋊C16—42no—
90C23×C8—71no—
91C23×C8C2×D711yescharacteristic
92C22×C42—71no—
93C2×M32—21no—
94C2×M32—141no—
95C2×C4⋊C8—72no—
96C2×C4⋊C8—72no—
97C2×C4⋊C8—141no—
98C2×C4⋊C8—141no—
99C2×C4⋊C8—141no—
100C2×C4⋊C8—141no—
101C22⋊C16—21no—
102C22⋊C16—72no—
103C22⋊C16—141no—
104C22⋊C16C2×D712yes—
105C23×C7—22no—
106C23×C7—22no—
107C23×C7—22no—
108C23×C7C22⋊C811yescharacteristic
109C23×C7C22⋊C811yescharacteristic
110C23×C7C22×C811yescharacteristic
111C2×C4×C7—22no—
112C2×C4×C7—22no—
113C2×C4×C7—22no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7C22⋊C811yescharacteristic
119C2×C4×C7C22⋊C811yescharacteristic
120C2×C4×C7#9912yes—
121C2×C4×C7#10112yes—
122C2×C4×C7C2×C22⋊C411yescharacteristic
123C2×C4×C7C2×M1611yescharacteristic
124C2×Dic7—24no—
125C2×Dic7—24no—
126C2×Dic7—22no—
127C2×Dic7—22no—
128C2×Dic7—22no—
129C2×Dic7—42no—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7M3214yescomplemented
133C7×C8—21no—
134C7×C8—21no—
135C7×C8—21no—
136C7×C8—21no—
137C7⋊C8—42no—
138C23×C4—71no—
139C23×C4—71no—
140C23×C4C4×D711yescharacteristic
141C22×C8—42no—
142C22×C8—72no—
143C22×C8—141no—
144C22×C8—141no—
145C22×C8—282no—
146C22×C8C4×D711yescharacteristic
147C22×C8D2811yescharacteristic
148C22×C8D2811yescharacteristic
149C22×C8C22⋊D711yescharacteristic
150C22×C8C22⋊D711yescharacteristic
151C22×C8C22×D711yescharacteristic
152C2×C42—72no—
153C2×C42—72no—
154C2×C42—141no—
155C2×C42—141no—
156C2×C42—141no—
157C2×C42—141no—
158M32—42no—
159M32—282no—
160C2×C16—22no—
161C2×C16—142no—
162C4⋊C8—142no—
163C4⋊C8—142no—
164C4⋊C8—142no—
165C4⋊C8—142no—
166C22×C7—28no—
167C22×C7—21no—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7#32412yes—
174C22×C7#34912yes—
175C22×C7C2×C22⋊C811yescharacteristic
176C22×C7C2×M3212yes—
177C4×C7—21no—
178C4×C7—21no—
179C4×C7#32412yes—
180C4×C7C2×#9911yescharacteristic
181C4×C7C2×#10111yescharacteristic
182Dic7—24no—
183Dic7—42no—
184C24C8×D711yescharacteristic
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—72no—
188C22×C4—72no—
189C22×C4—144no—
190C22×C4—141no—
191C22×C4—141no—
192C22×C4—141no—
193C22×C4—141no—
194C22×C4—282no—
195C22×C4C8×D711yescharacteristic
196C22×C4#113111yescharacteristic
197C22×C4#113111yescharacteristic
198C22×C4(C2×D7)⋊C411yescharacteristic
199C22×C4(C2×D7)⋊C411yescharacteristic
200C22×C4C2×C4×D711yescharacteristic
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—142no—
208C2×C8—282no—
209C2×C8—282no—
210C2×C8—282no—
211C2×C8(C2×D7)⋊C411yescharacteristic
212C2×C8(C2×D7)⋊C411yescharacteristic
213C2×C8C2×D2811yescharacteristic
214C2×C8C2×C22⋊D711yescharacteristic
215C42—142no—
216C42—142no—
217C42—142no—
218C42—142no—
219C16—42no—
220C16—282no—
221C2×C7—22no—
222C2×C7—22no—
223C2×C7—22no—
224C2×C7C2×#32411yescharacteristic
225C2×C7#211211yescharacteristic
226C2×C7C2×#34911yescharacteristic
227C23—22no—
228C23—22no—
229C23—22no—
230C23(C2×D7)⋊C811yescharacteristic
231C23(C2×D7)⋊C811yescharacteristic
232C23C2×C8×D711yescharacteristic
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—74no—
241C2×C4—144no—
242C2×C4—144no—
243C2×C4—142no—
244C2×C4—142no—
245C2×C4—142no—
246C2×C4—282no—
247C2×C4—282no—
248C2×C4—282no—
249C2×C4#638012yes—
250C2×C4(C2×D7)⋊C811yescharacteristic
251C2×C4(C2×D7)⋊C811yescharacteristic
252C2×C4#639812yes—
253C2×C4C2×#113111yescharacteristic
254C2×C4C2×(C2×D7)⋊C411yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—282no—
260C7#1144011yescharacteristic, complemented, Sylow
261C22—28no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22#8926412yes—
269C22#8930912yes—
270C22D7×M3212yes—
271C22C2×(C2×D7)⋊C811yescharacteristic
272C4—21no—
273C4—21no—
274C4—144no—
275C4—282no—
276C4#8926412yes—
277C4C2×#638011yescharacteristic
278C4C2×#639811yescharacteristic
279C2—22no—
280C2—22no—
281C2—22no—
282C2C2×#8926411yescharacteristic
283C2#1172918511yescharacteristic
284C2C2×#8930911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D7)⋊C4
commutatorC23×C7C22×C8
FrattiniC22×C8C22×D7
FittingC7×#2112C2
socleC22×C7C2×C22⋊C8
prime radicalC24×C7C2×C8
cosocleC22×C7×C8C23
hypercenter#2112D7
hypocenterC7#11440
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
4. #11725330C2semidirect
132. C2×Dic7M32semidirect
260. C7#11440semidirect

Maximal subgroups

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

subgroupindex
C22×Dic7⋊C82
C7×#21122
#117297172
#117253302
#114407