Finite Group Databasebeta

← #13253897

Subgroups — #13253897

Order 1792.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2864C211yesmaximal, characteristic
2#11727145C211yesmaximal, characteristic
3C4×#6377C211yesmaximal, characteristic
4#11725436C212yesmaximal
5#11725436C212yesmaximal
6C7×#389C411yescharacteristic
7C7×#389C411yescharacteristic
8C7×#389C411yescharacteristic
9C7×#389C411yescharacteristic
10C7×#387—21no—
11C7×#387—21no—
12C7×#387—21no—
13C7×#387—21no—
14C7×#382C2211yescharacteristic
15C7×#382C2211yescharacteristic
16C43×C7C2211yescharacteristic
17C2×C4⋊(C7⋊C8)—21no—
18C2×#6377—21no—
19C2×#6377C2212yes—
20C2×#6377C2212yes—
21C2×C4×C7⋊C8—21no—
22#89319—21no—
23#9892—71nomaximal, Sylow
24C2×C7×C4⋊C4—21no—
25C2×C7×C4⋊C4—21no—
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7C2311yescharacteristic
39C22×C7⋊C8—22no—
40C22×C7⋊C8—22no—
41C7×#95—21no—
42C7×#95—21no—
43C7×#95—21no—
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C4⋊(C7⋊C8)—24no—
50#6377—24no—
51#6377—22no—
52#6377—24no—
53#6377Q814yes—
54C4×C7⋊C8—24no—
55#2864D711yescharacteristic
56#1767—71no—
57C4×#97—71no—
58#1295—72no—
59#1295—72no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C7×C4⋊C4—41no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—42no—
76C7×C4⋊C4—42no—
77C7×C4⋊C4—42no—
78C7×C4⋊C4—42no—
79C42×C7—22no—
80C42×C7—22no—
81C42×C7—22no—
82C42×C7—41no—
83C42×C7—41no—
84C42×C7—41no—
85C42×C7C2×Q812yes—
86C42×C7#4112yes—
87C2×C7⋊C8—24no—
88C2×C7⋊C8—24no—
89C2×C7⋊C8—24no—
90C2×C7⋊C8—24no—
91C2×C7⋊C8—42no—
92C2×C7⋊C8—42no—
93C2×C4⋊C8—141no—
94C2×#97—72no—
95C2×#97—72no—
96C2×#97—141no—
97C2×C4×C8—141no—
98#389Dic711yescharacteristic
99#389Dic711yescharacteristic
100#389Dic711yescharacteristic
101#389Dic711yescharacteristic
102#387—21no—
103#387—21no—
104#387—21no—
105#387—21no—
106#382C2×D711yescharacteristic
107#382C2×D711yescharacteristic
108C43C2×D711yescharacteristic
109#336—141no—
110C23×C7C2×C22⋊C411yescharacteristic
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—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7#10412yes—
139C2×C4×C7#10412yes—
140C2×C4×C7#10412yes—
141C2×C4×C7C4×Q812yes—
142C2×C4×C7C22⋊Q812yes—
143C2×C4×C7#12411yescharacteristic
144C2×C4×C7C4⋊Q811yescharacteristic
145C7⋊C8—28no—
146C7⋊C8—44no—
147C22×C8—142no—
148C22×C8—142no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic711yescharacteristic
154C2×C4⋊C4C2×Dic711yescharacteristic
155C2×C4⋊C4C2×Dic711yescharacteristic
156C2×C4⋊C4C2×Dic711yescharacteristic
157C2×C42C2×Dic711yescharacteristic
158C2×C42C2×Dic711yescharacteristic
159C2×C42C22⋊D711yescharacteristic
160C2×C42C22⋊D711yescharacteristic
161C2×C42C22⋊D711yescharacteristic
162C2×C42C22⋊D711yescharacteristic
163C2×C42C22×D711yescharacteristic
164C4⋊C8—144no—
165#97—74no—
166#97—144no—
167#97—142no—
168#97—144no—
169C4×C8—144no—
170#95—21no—
171#95—21no—
172#95—21no—
173#95—21no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—21no—
178C22×C7#39111yescharacteristic
179C22×C7#41311yescharacteristic
180C22×C7#41311yescharacteristic
181C22×C7C2×#10411yescharacteristic
182C22×C7C2×#10411yescharacteristic
183C22×C7C2×#10411yescharacteristic
184C22×C7#42111yescharacteristic
185C4×C7—21no—
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—22no—
190C4×C7—22no—
191C4×C7—22no—
192C4×C7—41no—
193C4×C7—81no—
194C4×C7—81no—
195C4×C7—81no—
196C4×C7—81no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4C22⋊Dic711yescharacteristic
202C22×C4C22⋊Dic711yescharacteristic
203C22×C4C22⋊Dic711yescharacteristic
204C22×C4C22⋊Dic711yescharacteristic
205C22×C4C22×Dic711yescharacteristic
206C22×C4C2×C22⋊D711yescharacteristic
207C22×C4C2×C22⋊D711yescharacteristic
208C2×C8—144no—
209C2×C8—144no—
210C2×C8—144no—
211C2×C8—144no—
212C2×C8—282no—
213C2×C8—282no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42Q8×D712yes—
229C42#116112yes—
230C2×C7#152411yescharacteristic
231C2×C7#152411yescharacteristic
232C2×C7#152911yescharacteristic
233C2×C7#153211yescharacteristic
234C2×C7#198611yescharacteristic
235C2×C7#199411yescharacteristic
236C2×C7#199811yescharacteristic
237C23C2×C22⋊Dic711yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#641112yes—
266C2×C4#641112yes—
267C2×C4#641112yes—
268C2×C4#650711yescharacteristic
269C2×C4Q8×Dic712yes—
270C2×C4#650912yes—
271C2×C4#651011yescharacteristic
272C8—148no—
273C8—284no—
274C7#989211yescharacteristic, complemented, Sylow
275C22#9000211yescharacteristic
276C22C2×#641111yescharacteristic
277C22C2×#641111yescharacteristic
278C22C2×#641111yescharacteristic
279C22#9000811yescharacteristic
280C22#9000911yescharacteristic
281C22#9000911yescharacteristic
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—81no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2#1172949611yescharacteristic
295C2#1172950011yescharacteristic
296C2#1172950011yescharacteristic
297C2#1172950111yescharacteristic
298C2#1172950211yescharacteristic
299C2#1172959311yescharacteristic
300C2#1172959511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2864C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2864D7
hypocenterC7#9892
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2864

Complements

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

NH ≅ G/Ntype
274. C7#9892semidirect

Maximal subgroups

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

subgroupindex
C7×#28642
#117271452
C4×#63772
#117254362
#98927