Finite Group Databasebeta

← #13263281

Subgroups — #13263281

Order 1792.

424 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 75 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#11733742C211yesmaximal, characteristic
2#11725881C212yesmaximal, complemented
3C7×#1318C211yesmaximal, characteristic
4#11725446C211yesmaximal, characteristic
5#11725259C212yesmaximal, complemented
6C2×#6499C411yescharacteristic
7C2×D4×Dic7C411yescharacteristic
8C2×#6450C2211yescharacteristic
9C7×#390C2211yescharacteristic
10#89748C2211yescharacteristic
11#89718—22no—
12#89717—22no—
13#89704C411yescharacteristic
14#89701C411yescharacteristic
15#89491—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89264—22no—
19#11534—71nomaximal, Sylow
20C22×C7×D4C2×C411yescharacteristic
21C23×Dic7—21no—
22C22×Dic14C2×C411yescharacteristic
23C2×C7×C4⋊C4C2311yescharacteristic
24C2×C7×C22⋊C4—22no—
25C2×C42×C7C2×C411yescharacteristic
26C2×C22⋊Dic7—22no—
27C2×C22⋊Dic7—21no—
28#6499—22no—
29#6499—22no—
30D4×Dic7—42no—
31C2×C4⋊Dic7C2×C411yescharacteristic
32C2×Dic7⋊C4—22no—
33C2×Dic7⋊C4D412yes—
34C2×C4×Dic7C2×C411yescharacteristic
35C2×C4×Dic7C2×C411yescharacteristic
36C2×C4×Dic7D412yes—
37#6450—42no—
38C7×C22⋊C8—22no—
39C7⋊#95—22no—
40C7⋊#95—21no—
41C7⋊#95—21no—
42C22⋊(C7⋊C8)—22no—
43#6389—42no—
44Dic7⋊C8—42no—
45#2326—71no—
46#1467—72no—
47#1325—72no—
48#1318—71no—
49#1318D711yescharacteristic
50C24×C7—21no—
51C2×C7×D4—21no—
52C2×C7×D4—41no—
53C2×C7×D4—41no—
54C2×C7×D4M1612yes—
55C22×C4×C7—21no—
56C22×C4×C7C22×C411yescharacteristic
57C22×C4×C7C2×D412yes—
58C22×Dic7—21no—
59C22×Dic7—21no—
60C22×Dic7—42no—
61C22×Dic7—82no—
62C22×Dic7C22⋊C412yes—
63C22×Dic7C22⋊C411yescharacteristic
64C22×Dic7C22⋊C411yescharacteristic
65C2×Dic14—21no—
66C2×Dic14—21no—
67C2×Dic14—41no—
68C2×Dic14—41no—
69C2×C7×C8—42no—
70C7×C4⋊C4—41no—
71C7×C22⋊C4—82no—
72C42×C7—41no—
73C22⋊Dic7—28no—
74C22⋊Dic7—42no—
75C4⋊Dic7—41no—
76Dic7⋊C4—42no—
77Dic7⋊C4—82no—
78C4×Dic7—21no—
79C4×Dic7—22no—
80C4×Dic7—22no—
81C4×Dic7—22no—
82C4×Dic7M1612yes—
83C2×C7⋊C8—42no—
84C2×#124—71no—
85C2×C4×Q8—71no—
86C2×C4×D4—71no—
87#432—142no—
88#391—71no—
89#390C2×D711yescharacteristic
90#388—142no—
91#385—142no—
92#384—71no—
93#376—71no—
94#324—72no—
95#324—142no—
96#324C2×D712yes—
97C23×C7—22no—
98C23×C7—42no—
99C23×C7—42no—
100C23×C7—41no—
101C23×C7—41no—
102C23×C7C2×C22⋊C411yescharacteristic
103C7×D4—42no—
104C7×D4—42no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7—22no—
108C2×C4×C7—42no—
109C2×C4×C7—41no—
110C2×C4×C7—41no—
111C2×C4×C7—41no—
112C2×C4×C7C2×M1611yescharacteristic
113C2×C4×C7C2×M1611yescharacteristic
114C2×Dic7—22no—
115C2×Dic7—22no—
116C2×Dic7—21no—
117C2×Dic7—22no—
118C2×Dic7—22no—
119C2×Dic7—41no—
120C2×Dic7—41no—
121C2×Dic7—41no—
122C2×Dic7—41no—
123C2×Dic7—42no—
124C2×Dic7—41no—
125C2×Dic7—84no—
126C2×Dic7#9912yes—
127Dic14—42no—
128Dic14—42no—
129C7×C8—82no—
130C7⋊C8—82no—
131C22×Q8—71no—
132C22×D4C4×D711yescharacteristic
133C23×C4—141no—
134#124—142no—
135#124—142no—
136C4×Q8—282no—
137C4×D4—282no—
138C2×C4⋊C4—72no—
139C2×C4⋊C4—71no—
140C2×C4⋊C4—142no—
141C2×C4⋊C4C22×D711yescharacteristic
142C2×C22⋊C4—22no—
143C2×C22⋊C4—142no—
144C2×C22⋊C4—141no—
145C2×C42—71no—
146C2×C42—71no—
147C2×C42—72no—
148C2×C42C4×D711yescharacteristic
149C4⋊C8—282no—
150C22⋊C8—22no—
151C22⋊C8—142no—
152#97—282no—
153#95—141no—
154#95—141no—
155#95—142no—
156C22×C7—21no—
157C22×C7—21no—
158C22×C7—44no—
159C22×C7—42no—
160C22×C7—82no—
161C22×C7—81no—
162C22×C7—81no—
163C22×C7#40711yescharacteristic
164C22×C7C2×#9911yescharacteristic
165C22×C7#41311yescharacteristic
166C4×C7—21no—
167C4×C7—21no—
168C4×C7—42no—
169C4×C7—81no—
170Dic7—22no—
171Dic7—42no—
172Dic7—41no—
173Dic7—42no—
174Dic7—81no—
175C24—21no—
176C2×Q8—141no—
177C2×Q8—141no—
178C2×Q8—281no—
179C2×Q8—281no—
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4#113112yes—
184C22×C4—21no—
185C22×C4—71no—
186C22×C4—72no—
187C22×C4—71no—
188C22×C4—141no—
189C22×C4—141no—
190C22×C4—282no—
191C22×C4—562no—
192C22×C4C2×C4×D711yescharacteristic
193C22×C4D4×D712yes—
194C2×C8—42no—
195C2×C8—282no—
196C4⋊C4—41no—
197C4⋊C4—282no—
198C4⋊C4—281no—
199C4⋊C4—562no—
200C22⋊C4—82no—
201C22⋊C4—148no—
202C22⋊C4—282no—
203C42—41no—
204C42—72no—
205C42—142no—
206C42—142no—
207C42—142no—
208C42—141no—
209C2×C7—21no—
210C2×C7—21no—
211C2×C7—82no—
212C2×C7#146511yescharacteristic
213C2×C7#212811yescharacteristic
214C2×C7#213311yescharacteristic
215C23—22no—
216C23—42no—
217C23—42no—
218C23—41no—
219C23—41no—
220C23D7×C22⋊C411yescharacteristic
221Q8—282no—
222Q8—282no—
223D4—42no—
224D4—42no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—72no—
233C2×C4—142no—
234C2×C4—142no—
235C2×C4—141no—
236C2×C4—142no—
237C2×C4—142no—
238C2×C4—281no—
239C2×C4—281no—
240C2×C4—281no—
241C2×C4—281no—
242C2×C4—282no—
243C2×C4—281no—
244C2×C4—564no—
245C2×C4C2×#113111yescharacteristic
246C2×C4D7×M1611yescharacteristic
247C8—82no—
248C8—562no—
249C7#1153411yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22—44no—
253C22—42no—
254C22—82no—
255C22—81no—
256C22—81no—
257C22#8949811yescharacteristic
258C22D7×#9911yescharacteristic
259C22#8951711yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—81no—
264C4—142no—
265C4—282no—
266C4—282no—
267C4—281no—
268C4—561no—
269C2—21no—
270C2—21no—
271C2—82no—
272C2#1172587511yescharacteristic
273C2#1172690611yescharacteristic
274C2#1172691811yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1318C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1318D7
hypocenterC7#11534
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #11725881C2semidirect
5. #11725259C2semidirect
249. C7#11534semidirect

Maximal subgroups

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

subgroupindex
#117337422
#117258812
C7×#13182
#117254462
#117252592
#115347