Finite Group Databasebeta

← #13242035

Subgroups — #13242035

Order 1792.

434 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2295C211yesmaximal, characteristic
2#11727145C211yesmaximal, characteristic
3#11727143C211yesmaximal, characteristic
4#11725448C212yesmaximal
5#11725444C212yesmaximal
6C2×C4×C7×Q8C411yescharacteristic
7C7×#391C411yescharacteristic
8C7×#391C2211yescharacteristic
9C7×#389C411yescharacteristic
10C7×#389C2211yescharacteristic
11C7×#387—21no—
12C7×#387—21no—
13C4×C7×C4⋊C4—21no—
14C4×C7×C4⋊C4C411yescharacteristic
15C7×#376—21no—
16C43×C7C2211yescharacteristic
17C2×C4⋊(C7⋊C8)—21no—
18C2×#6377—21no—
19C2×#6377—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7630—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C4×C7×Q8—22no—
26C4×C7×Q8—22no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C42×C7—21no—
34C2×C42×C7—21no—
35C2×C42×C7C2×C411yescharacteristic
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7C2311yescharacteristic
42C22×C7⋊C8—22no—
43C22×C7⋊C8—22no—
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C4⋊(C7⋊C8)—24no—
52#6377—24no—
53#6377—42no—
54#2295D711yescharacteristic
55#1767—71no—
56#1745—71no—
57#1272—72no—
58#1271—72no—
59C2×C7×Q8—21no—
60C2×C7×Q8—41no—
61C2×C7×Q8—41no—
62C2×C7×Q8M1612yes—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C7×C4⋊C4—24no—
75C7×C4⋊C4—21no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—42no—
79C7×C4⋊C4—41no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4M1612yes—
82C42×C7—24no—
83C42×C7—22no—
84C42×C7—22no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—22no—
89C42×C7—21no—
90C42×C7—41no—
91C42×C7—41no—
92C42×C7—42no—
93C2×C7⋊C8—24no—
94C2×C7⋊C8—24no—
95C2×C7⋊C8—42no—
96C2×C7⋊C8—42no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C2×C4×Q8Dic711yescharacteristic
100C2×C4⋊C8—141no—
101C2×#97—141no—
102C2×#97—141no—
103#391Dic711yescharacteristic
104#391C2×D711yescharacteristic
105#389Dic711yescharacteristic
106#389C2×D711yescharacteristic
107#387—21no—
108#387—21no—
109C4×C4⋊C4—21no—
110C4×C4⋊C4Dic711yescharacteristic
111#376—21no—
112C43C2×D711yescharacteristic
113#336—72no—
114#336—72no—
115#336—141no—
116C23×C7C2×C22⋊C411yescharacteristic
117C7×Q8—42no—
118C7×Q8—42no—
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—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—22no—
131C2×C4×C7—22no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7#10412yes—
148C2×C4×C7#10412yes—
149C2×C4×C7C2×M1611yescharacteristic
150C2×C4×C7C2×M1611yescharacteristic
151C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C7#13712yes—
153C2×C4×C7#13711yescharacteristic
154C7⋊C8—44no—
155C7⋊C8—44no—
156C22×Q8C2×Dic711yescharacteristic
157C22×C8—142no—
158C22×C8—142no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×Dic711yescharacteristic
165C2×C4⋊C4C2×Dic711yescharacteristic
166C2×C4⋊C4C2×Dic711yescharacteristic
167C2×C42—21no—
168C2×C42—21no—
169C2×C42C2×Dic711yescharacteristic
170C2×C42C2×Dic711yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C2×C42C22⋊D711yescharacteristic
173C2×C42C22⋊D711yescharacteristic
174C2×C42C22⋊D711yescharacteristic
175C2×C42C22×D711yescharacteristic
176C4⋊C8—144no—
177#97—144no—
178#97—282no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—21no—
183#95—21no—
184#95—21no—
185#95—21no—
186C22×C7#40711yescharacteristic
187C22×C7#41011yescharacteristic
188C22×C7#41311yescharacteristic
189C22×C7#41711yescharacteristic
190C22×C7#41911yescharacteristic
191C22×C7C2×#10411yescharacteristic
192C22×C7C2×#10411yescharacteristic
193C4×C7—21no—
194C4×C7—21no—
195C4×C7—22no—
196C4×C7—22no—
197C4×C7—21no—
198C4×C7—21no—
199C4×C7—22no—
200C4×C7—41no—
201C4×C7—42no—
202C4×C7—41no—
203C4×C7—42no—
204C4×C7—81no—
205C4×C7—81no—
206C2×Q8—21no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8#113612yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C22⋊Dic711yescharacteristic
215C22×C4C22⋊Dic711yescharacteristic
216C22×C4C22⋊Dic711yescharacteristic
217C22×C4C22⋊Dic711yescharacteristic
218C22×C4C22×Dic711yescharacteristic
219C22×C4C2×C22⋊D711yescharacteristic
220C22×C4C2×C22⋊D711yescharacteristic
221C2×C8—144no—
222C2×C8—144no—
223C2×C8—282no—
224C2×C8—282no—
225C2×C8—282no—
226C2×C8—282no—
227C4⋊C4—24no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4#113612yes—
235C42—24no—
236C42—22no—
237C42—22no—
238C42—21no—
239C42—21no—
240C42—22no—
241C42—21no—
242C42—21no—
243C42—41no—
244C42—41no—
245C42—42no—
246C2×C7#146411yescharacteristic
247C2×C7#148911yescharacteristic
248C2×C7#149111yescharacteristic
249C2×C7#150611yescharacteristic
250C2×C7#150911yescharacteristic
251C2×C7#152411yescharacteristic
252C2×C7#155911yescharacteristic
253C23C2×C22⋊Dic711yescharacteristic
254Q8—42no—
255Q8—42no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4#641112yes—
285C2×C4#641112yes—
286C2×C4C2×#113611yescharacteristic
287C2×C4C2×#113611yescharacteristic
288C2×C4#650512yes—
289C2×C4#651211yescharacteristic
290C2×C4#651411yescharacteristic
291C8—284no—
292C8—284no—
293C7#763011yescharacteristic, complemented, Sylow
294C22#8997911yescharacteristic
295C22#8999711yescharacteristic
296C22#9000411yescharacteristic
297C22C2×#641111yescharacteristic
298C22C2×#641111yescharacteristic
299C22#9000911yescharacteristic
300C22#9001211yescharacteristic
301C4—22no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—81no—
314C2#1172932611yescharacteristic
315C2#1172937711yescharacteristic
316C2#1172939511yescharacteristic
317C2#1172950011yescharacteristic
318C2#1172950911yescharacteristic
319C2#1172958711yescharacteristic
320C2#1172959011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2295C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2295D7
hypocenterC7#7630
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
293. C7#7630semidirect

Maximal subgroups

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

subgroupindex
C7×#22952
#117271452
#117271432
#117254482
#117254442
#76307