Finite Group Databasebeta

← #13264390

Subgroups — #13264390

Order 1792.

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

normal subgroups only

This group has 414 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#11739920C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725301C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6507—21no—
7C2×#6432C411yescharacteristic
8C2×C7×#101—21no—
9C4×C7×M16—21no—
10#89755C412yes—
11#89755C2212yes—
12#89746—21no—
13C4×C4⋊Dic7C411yescharacteristic
14#89700—21no—
15#89700—21no—
16#89698—21no—
17C7×#343C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11782—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×Dic14—21no—
23C2×C7×M16—22no—
24C4×C7×Q8—41no—
25C4×C7×Q8—41no—
26C2×C7×C4⋊C4C2×C411yescharacteristic
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32#6507—44no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7C2×C412yes—
36C2×Dic7⋊C4—22no—
37C2×Dic7⋊C4—22no—
38C2×C4×Dic7—21no—
39#6432—41no—
40#6432—41no—
41C7×#101—24no—
42C7×#97—41no—
43C4×C7×C8—41no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95C2×C412yes—
47C22⋊(C7⋊C8)—22no—
48C4⋊(C7⋊C8)—41no—
49#6377—41no—
50#2546—71no—
51C4×#101D711yescharacteristic
52#1467—71no—
53#1346—74no—
54C2×C7×Q8—22no—
55C2×C7×Q8—22no—
56C2×C7×Q8—41no—
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22×C411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×Dic7—22no—
65C22×Dic7—22no—
66C2×Dic14—42no—
67C2×Dic14—42no—
68C2×Dic14—42no—
69C7×M16—24no—
70C7×M16—42no—
71C2×C7×C8—42no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C42×C7—21no—
76C42×C7—21no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C4⋊Dic7—24no—
82C4⋊Dic7—41no—
83C4⋊Dic7—41no—
84C4⋊Dic7—42no—
85Dic7⋊C4—44no—
86Dic7⋊C4—44no—
87C4×Dic7—42no—
88C2×C7⋊C8—42no—
89C2×C4⋊Q8—71no—
90C2×C4⋊Q8—141no—
91C2×C4×Q8C2×D711yescharacteristic
92#432—141no—
93C2×#101—21no—
94C4×M16—21no—
95#398—72no—
96#398—72no—
97#391—141no—
98#389—141no—
99#389—141no—
100C4×C4⋊C4—71no—
101#343C2×D712yes—
102#324—72no—
103#324—141no—
104C23×C7C2×C22⋊C411yescharacteristic
105C7×Q8—44no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—22no—
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—41no—
118C2×C4×C7—41no—
119C2×C4×C7—41no—
120C2×C4×C7#9911yescharacteristic
121C2×C4×C7#9911yescharacteristic
122C2×C4×C7#10412yes—
123C2×C4×C7AGL(1,ℤ/8)12yes—
124C2×Dic7—24no—
125C2×Dic7—42no—
126C2×Dic7—42no—
127C2×Dic7—42no—
128C2×Dic7—42no—
129C2×Dic7—42no—
130Dic14—84no—
131C7×C8—44no—
132C7⋊C8—82no—
133C22×Q8—141no—
134C22×Q8C22⋊D711yescharacteristic
135C2×M16—22no—
136C4⋊Q8—281no—
137C4⋊Q8—281no—
138C4⋊Q8—284no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—72no—
142C2×C4⋊C4—141no—
143C2×C4⋊C4—142no—
144C2×C4⋊C4—141no—
145C2×C4⋊C4—142no—
146C2×C4⋊C4C4×D711yescharacteristic
147C2×C4⋊C4D2811yescharacteristic
148C2×C4⋊C4C22×D711yescharacteristic
149C2×C42—141no—
150C2×C42C4×D711yescharacteristic
151C2×C42D2811yescharacteristic
152C2×C42C22⋊D711yescharacteristic
153C4⋊C8—281no—
154#101—24no—
155C22⋊C8—142no—
156#97—41no—
157#97—281no—
158C4×C8—41no—
159#95—72no—
160#95—142no—
161#95—142no—
162C22×C7—21no—
163C22×C7—21no—
164C22×C7C2×#9911yescharacteristic
165C22×C7#41811yescharacteristic
166C22×C7C2×#10411yescharacteristic
167C4×C7—21no—
168C4×C7—22no—
169C4×C7—22no—
170C4×C7—41no—
171C4×C7—41no—
172C4×C7—41no—
173C4×C7—41no—
174C4×C7#35612yes—
175Dic7—44no—
176Dic7—82no—
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—282no—
181C2×Q8—282no—
182C2×Q8—282no—
183C22×C4—142no—
184C22×C4—142no—
185C22×C4(C2×D7)⋊C411yescharacteristic
186C22×C4(C2×D7)⋊C411yescharacteristic
187C22×C4(C2×D7)⋊C411yescharacteristic
188C22×C4(C2×D7)⋊C411yescharacteristic
189C22×C4C2×C4×D711yescharacteristic
190C22×C4C2×D2811yescharacteristic
191C22×C4C2×C22⋊D711yescharacteristic
192M16—24no—
193M16—42no—
194C2×C8—42no—
195C2×C8—282no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—144no—
200C4⋊C4—282no—
201C4⋊C4—284no—
202C4⋊C4—284no—
203C4⋊C4—281no—
204C4⋊C4—281no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—282no—
212C2×C7—21no—
213C2×C7—21no—
214C2×C7#150711yescharacteristic
215C2×C7#212311yescharacteristic
216C2×C7C2×#35611yescharacteristic
217C23C2×(C2×D7)⋊C411yescharacteristic
218Q8—44no—
219Q8—564no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—144no—
235C2×C4—282no—
236C2×C4—282no—
237C2×C4—282no—
238C2×C4—282no—
239C2×C4—282no—
240C2×C4#637912yes—
241C2×C4#638011yescharacteristic
242C2×C4#638011yescharacteristic
243C2×C4#651212yes—
244C8—44no—
245C8—562no—
246C7#1178211yescharacteristic, complemented, Sylow
247C22—21no—
248C22—21no—
249C22C2×#637911yescharacteristic
250C22C2×#638011yescharacteristic
251C22#8977311yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—284no—
260C4—562no—
261C4#8927312yes—
262C2—21no—
263C2—21no—
264C2#1172719811yescharacteristic
265C2C2×#8927311yescharacteristic
266C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#101D7
hypocenterC7#11782
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
246. C7#11782semidirect

Maximal subgroups

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

subgroupindex
#117399202
C4×C7×#1012
#117293792
#117253012
#117827