Finite Group Databasebeta

← #13281029

Subgroups — #13281029

Order 1792.

1118 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89420C211yesmaximal, characteristic
2C7×#1443C211yesmaximal, characteristic
3#11727172C213yesmaximal
4#11727171C213yesmaximal
5#11727170C211yesmaximal, characteristic
6Dic7⋊#95C213yesmaximal
7Dic7⋊#95C213yesmaximal
8C22×Dic7⋊C4C2211yescharacteristic
9C22×Dic7⋊C4C2213yes—
10C22×C4×Dic7C2213yes—
11C2×C7×#95C2213yes—
12C2×C7×#95C2213yes—
13C2×C7×#95C2211yescharacteristic
14C2×C7⋊#95C2213yes—
15C2×C7⋊#95C2213yes—
16C2×C7⋊#95C2213yes—
17C2×C7⋊#95C2216yes—
18C2×C7⋊#95C2213yes—
19C2×C7⋊#95C2213yes—
20#89420C418yescomplemented
21#14350—71nomaximal, Sylow
22C23×C4×C7C2313yes—
23C23×C4×C7C2311yescharacteristic
24C23×C4×C7C2313yes—
25C23×Dic7C2311yescharacteristic
26C23×Dic7C2313yes—
27C23×Dic7C2313yes—
28C23×Dic7C2311yescharacteristic
29C2×Dic7⋊C4—26no—
30C2×Dic7⋊C4—26no—
31C2×Dic7⋊C4—26no—
32C2×Dic7⋊C4—26no—
33C2×C4×Dic7—26no—
34C2×C4×Dic7—26no—
35C2×C4×Dic7C2×C4112yes—
36C7×#95—43no—
37C7×#95—43no—
38C7×#95C2×C414yes—
39C7⋊#95—46no—
40C7⋊#95—43no—
41C7⋊#95—43no—
42C7⋊#95—43no—
43C7⋊#95—43no—
44C7⋊#95C2×C4112yes—
45C2×#376—71no—
46#1443—71no—
47#1443—73no—
48#1443—73no—
49#1443D711yescharacteristic
50C4⋊#95—73no—
51C4⋊#95—73no—
52C24×C7C2411yescharacteristic
53C22×C4×C7—23no—
54C22×C4×C7—23no—
55C22×C4×C7—23no—
56C22×C4×C7—23no—
57C22×C4×C7—23no—
58C22×C4×C7—23no—
59C22×C4×C7—23no—
60C22×C4×C7—23no—
61C22×C4×C7—23no—
62C22×C4×C7—23no—
63C22×C4×C7—23no—
64C22×C4×C7—23no—
65C22×C4×C7—23no—
66C22×C4×C7—23no—
67C22×C4×C7—21no—
68C22×C4×C7—23no—
69C22×C4×C7C22×C416yes—
70C22×Dic7—23no—
71C22×Dic7—23no—
72C22×Dic7—23no—
73C22×Dic7—23no—
74C22×Dic7—23no—
75C22×Dic7—23no—
76C22×Dic7—23no—
77C22×Dic7—23no—
78C22×Dic7—23no—
79C22×Dic7—23no—
80C22×Dic7—23no—
81C22×Dic7—23no—
82C22×Dic7—23no—
83C22×Dic7—23no—
84C22×Dic7—21no—
85C22×Dic7—23no—
86C22×Dic7C22×C416yes—
87C22×Dic7C22×C412yes—
88C22×Dic7#4116yes—
89C22×Dic7#4116yes—
90Dic7⋊C4—412no—
91Dic7⋊C4—44no—
92C4×Dic7—224no—
93C22×C4⋊C4—71no—
94C22×C4⋊C4—73no—
95C22×C42—73no—
96#376—78no—
97C2×#95—73no—
98C2×#95—73no—
99C2×#95—76no—
100C2×#95—73no—
101C2×#95—73no—
102C2×#95—73no—
103C2×#95C2×D713yes—
104C2×#95C2×D713yes—
105C2×#95C2×D711yescharacteristic
106C23×C7C23×C411yescharacteristic
107C23×C7C2×#4113yes—
108C23×C7C2×#4113yes—
109C23×C7H(5,𝔽2)13yes—
110C23×C7H(5,𝔽2)11yescharacteristic
111C23×C72−1+411yescharacteristic
112C23×C72−1+413yes—
113C2×C4×C7—26no—
114C2×C4×C7—26no—
115C2×C4×C7—26no—
116C2×C4×C7—43no—
117C2×C4×C7—43no—
118C2×C4×C7—43no—
119C2×C4×C7—43no—
120C2×C4×C7—43no—
121C2×C4×C7—41no—
122C2×C4×C7—43no—
123C2×C4×C7—43no—
124C2×C4×C7—43no—
125C2×C4×C7—43no—
126C2×C4×C7—43no—
127C2×C4×C7—43no—
128C2×C4×C7—43no—
129C2×C4×C7—43no—
130C2×Dic7—26no—
131C2×Dic7—26no—
132C2×Dic7—26no—
133C2×Dic7—43no—
134C2×Dic7—43no—
135C2×Dic7—43no—
136C2×Dic7—43no—
137C2×Dic7—43no—
138C2×Dic7—41no—
139C2×Dic7—43no—
140C2×Dic7—43no—
141C2×Dic7—43no—
142C2×Dic7—43no—
143C2×Dic7—43no—
144C2×Dic7—43no—
145C2×Dic7—43no—
146C2×Dic7—43no—
147C2×Dic7#117112yes—
148C2×Dic7#12614yes—
149C2×Dic7#126112yes—
150C23×C4—71no—
151C23×C4—73no—
152C23×C4—71no—
153C23×C4—73no—
154C23×C4C22×D713yes—
155C23×C4C22×D711yescharacteristic
156C23×C4C22×D713yes—
157C2×C4⋊C4—146no—
158C2×C4⋊C4—146no—
159C2×C4⋊C4—146no—
160C2×C4⋊C4—146no—
161C2×C42—712no—
162C2×C42—146no—
163C2×C42—146no—
164#95—43no—
165#95—43no—
166#95—712no—
167#95—283no—
168#95—283no—
169#95—283no—
170#95—283no—
171#95—286no—
172#95C4×D714yes—
173C22×C7C2×#11713yes—
174C22×C7#52013yes—
175C22×C7#52011yescharacteristic
176C22×C7C2×#12611yescharacteristic
177C22×C7C2×#12613yes—
178C22×C7#54013yes—
179C22×C7#54013yes—
180C22×C7#54113yes—
181C22×C7#54113yes—
182C22×C7#54213yes—
183C22×C7#54213yes—
184C22×C7#54213yes—
185C22×C7#54213yes—
186C4×C7—46no—
187C4×C7—83no—
188C4×C7—81no—
189Dic7—46no—
190Dic7—83no—
191Dic7—81no—
192Dic7#38318yes—
193C24C23×D711yescharacteristic
194C22×C4—23no—
195C22×C4—23no—
196C22×C4—23no—
197C22×C4—23no—
198C22×C4—23no—
199C22×C4—23no—
200C22×C4—23no—
201C22×C4—23no—
202C22×C4—23no—
203C22×C4—21no—
204C22×C4—23no—
205C22×C4—23no—
206C22×C4—23no—
207C22×C4—23no—
208C22×C4—23no—
209C22×C4—23no—
210C22×C4—72no—
211C22×C4—76no—
212C22×C4—76no—
213C22×C4—76no—
214C22×C4—143no—
215C22×C4—143no—
216C22×C4—143no—
217C22×C4—143no—
218C22×C4—143no—
219C22×C4—143no—
220C22×C4—143no—
221C22×C4—143no—
222C22×C4—143no—
223C22×C4—141no—
224C22×C4—143no—
225C22×C4—143no—
226C22×C4—143no—
227C22×C4—143no—
228C22×C4—143no—
229C22×C4—143no—
230C22×C4C2×C4×D716yes—
231C4⋊C4—2812no—
232C4⋊C4—284no—
233C42—1424no—
234C2×C7C2×#38311yescharacteristic
235C2×C7#231413yes—
236C2×C7#231413yes—
237C2×C7#264413yes—
238C2×C7#264411yescharacteristic
239C2×C7#264511yescharacteristic
240C2×C7#264513yes—
241C23C22×C4×D711yescharacteristic
242C23#654813yes—
243C23#655111yescharacteristic
244C23D7×#4113yes—
245C23D7×#4113yes—
246C23#655311yescharacteristic
247C23#655413yes—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—43no—
252C2×C4—43no—
253C2×C4—43no—
254C2×C4—43no—
255C2×C4—43no—
256C2×C4—41no—
257C2×C4—43no—
258C2×C4—43no—
259C2×C4—43no—
260C2×C4—43no—
261C2×C4—43no—
262C2×C4—43no—
263C2×C4—43no—
264C2×C4—43no—
265C2×C4—74no—
266C2×C4—712no—
267C2×C4—712no—
268C2×C4—146no—
269C2×C4—146no—
270C2×C4—146no—
271C2×C4—283no—
272C2×C4—283no—
273C2×C4—283no—
274C2×C4—283no—
275C2×C4—283no—
276C2×C4—281no—
277C2×C4—283no—
278C2×C4—283no—
279C2×C4—283no—
280C2×C4—283no—
281C2×C4—283no—
282C2×C4—283no—
283C2×C4—283no—
284C2×C4—283no—
285C7#1435011yescharacteristic, complemented, Sylow
286C22D7×#11713yes—
287C22#9023713yes—
288C22#9026511yescharacteristic
289C22#9030613yes—
290C22#9033113yes—
291C22#9035313yes—
292C22#9035413yes—
293C22#9036013yes—
294C22#9038713yes—
295C22#9039213yes—
296C22D7×#12611yescharacteristic
297C22D7×#12613yes—
298C22#9040113yes—
299C4—46no—
300C4—78no—
301C4—83no—
302C4—81no—
303C4—286no—
304C4—563no—
305C4—561no—
306C2D7×#38311yescharacteristic
307C2#1173238913yes—
308C2#1173290113yes—
309C2#1173478211yescharacteristic
310C2#1173499313yes—
311C2#1173566013yes—
312C2#1173586111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1443C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1443D7
hypocenterC7#14350
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
20. #89420C4semidirect
285. C7#14350semidirect

Maximal subgroups

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

subgroupindex
C2×#894202
C7×#14432
#117271722
#117271712
#117271702
Dic7⋊#952
#143507