Finite Group Databasebeta

← #13249810

Subgroups — #13249810

Order 1792.

504 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
1C7×#2628C211yesmaximal, characteristic
2#11739649C211yesmaximal, characteristic
3#11729529C212yesmaximal, complemented
4#11729325C211yesmaximal, characteristic
5#11725437C212yesmaximal, complemented
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C7×#117C2211yescharacteristic
8C22×#1136—21no—
9C7×#400C412yes—
10C7×#399C412yes—
11C7×#395—21no—
12C7×#393—21no—
13C7×#389—21no—
14C7×#382C2211yescharacteristic
15C7×#380—21no—
16#89771—24no—
17#89697C2212yes—
18#89696—21no—
19#89696C2212yes—
20#89342—24no—
21#89323—21no—
22#89320—21no—
23#9193—71nomaximal, Sylow
24C22×C7×Q8—21no—
25C23×C4×C7D411yescharacteristic
26C7×C4⋊Q8—22no—
27C7×C4⋊Q8—22no—
28C7×#117—22no—
29C7×#117—22no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4C2×C411yescharacteristic
38C2×C7×C22⋊C4D411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C2×C42×C7C2311yescharacteristic
41C2×#1136—22no—
42C2×#1136—22no—
43C2×#1136—42no—
44C2×#1136—42no—
45C22×C7⋊C8—22no—
46C7×#95—22no—
47C7×#95—22no—
48C7×#95—21no—
49C7×#95C2×C412yes—
50C22⋊(C7⋊C8)—22no—
51C4⋊(C7⋊C8)—24no—
52C4⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)—22no—
54C4⋊(C7⋊C8)D414yes—
55C4×C7⋊C8—22no—
56#2905—71no—
57#2628D711yescharacteristic
58#1549—72no—
59#1458—71no—
60#1286—72no—
61C24×C7C22⋊C411yescharacteristic
62C2×C7×Q8—42no—
63C2×C7×Q8—82no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7SD1612yes—
74C22×C4×C7Q1612yes—
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C7×C4⋊C4—22no—
79C7×C4⋊C4—22no—
80C7×C4⋊C4—24no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—82no—
86C7×C22⋊C4—22no—
87C7×C22⋊C4—22no—
88C7×C22⋊C4—82no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7C2×D412yes—
92C42×C7#4112yes—
93#1136—44no—
94#1136—42no—
95#1136—42no—
96C2×C7⋊C8—24no—
97C2×C7⋊C8—44no—
98C2×C7⋊C8—42no—
99C22×M16—141no—
100C2×C4⋊Q8C2×D711yescharacteristic
101C2×#117C2×D711yescharacteristic
102#431—72no—
103#424—144no—
104#423—72no—
105#423—141no—
106#400Dic712yes—
107#399Dic712yes—
108#395—21no—
109#393—21no—
110#389—21no—
111#382C2×D711yescharacteristic
112#380—21no—
113#332—144no—
114#324—141no—
115#323—141no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—41no—
119C23×C7—41no—
120C23×C7#10312yes—
121C23×C7C2×C22⋊C411yescharacteristic
122C7×Q8—84no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—22no—
126C2×C4×C7—22no—
127C2×C4×C7—22no—
128C2×C4×C7—22no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—42no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7#10312yes—
142C2×C4×C7C4×D412yes—
143C2×C4×C7#12011yescharacteristic
144C2×C4×C7#12112yes—
145C2×C4×C7#12311yescharacteristic
146C2×C4×C7C2×SD1611yescharacteristic
147C2×C4×C7C2×Q1611yescharacteristic
148C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C7#13711yescharacteristic
150C7⋊C8—44no—
151C7⋊C8—82no—
152C22×Q8—21no—
153C23×C4C22⋊D711yescharacteristic
154C2×M16—142no—
155C2×M16—142no—
156C2×M16—282no—
157C2×M16—282no—
158C22×C8—142no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic712yes—
167C2×C4⋊C4C2×Dic711yescharacteristic
168C2×C4⋊C4C22⋊D711yescharacteristic
169C2×C22⋊C4—22no—
170C2×C22⋊C4C2×Dic711yescharacteristic
171C2×C22⋊C4C22⋊D711yescharacteristic
172C2×C42C22⋊D711yescharacteristic
173C2×C42C22×D711yescharacteristic
174C4⋊C8—74no—
175C4⋊C8—144no—
176C4⋊C8—142no—
177C4⋊C8—142no—
178C22⋊C8—142no—
179C4×C8—142no—
180#95—22no—
181#95—22no—
182#95—21no—
183#95C2×Dic712yes—
184C22×C7—21no—
185C22×C7—21no—
186C22×C7—22no—
187C22×C7—42no—
188C22×C7—41no—
189C22×C7—41no—
190C22×C7—81no—
191C22×C7#38611yescharacteristic
192C22×C7C2×#10311yescharacteristic
193C22×C7#41711yescharacteristic
194C4×C7—22no—
195C4×C7—22no—
196C4×C7—22no—
197C4×C7—41no—
198C4×C7—41no—
199C4×C7—82no—
200C4×C7—82no—
201C4×C7#45011yescharacteristic
202C4×C7#45111yescharacteristic
203C4×C7#48311yescharacteristic
204C4×C7#48411yescharacteristic
205C24C22⋊Dic711yescharacteristic
206C2×Q8—42no—
207C2×Q8—82no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4#114312yes—
215C22×C4#114412yes—
216C22×C4C22⋊Dic711yescharacteristic
217C22×C4C22⋊Dic711yescharacteristic
218C22×C4C22⋊Dic711yescharacteristic
219C22×C4C22×Dic711yescharacteristic
220C22×C4C2×C22⋊D711yescharacteristic
221C22×C4C2×C22⋊D711yescharacteristic
222M16—284no—
223M16—282no—
224M16—282no—
225C2×C8—144no—
226C2×C8—284no—
227C2×C8—282no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—24no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—82no—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—82no—
239C42—21no—
240C42—21no—
241C42D4×D712yes—
242C42#115912yes—
243C2×C7—21no—
244C2×C7—21no—
245C2×C7—42no—
246C2×C7#187211yescharacteristic
247C2×C7#191011yescharacteristic
248C2×C7#191511yescharacteristic
249C23—21no—
250C23—21no—
251C23—41no—
252C23—41no—
253C23#640912yes—
254C23C2×C22⋊Dic711yescharacteristic
255Q8—84no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4#640912yes—
275C2×C4D4×Dic712yes—
276C2×C4#649811yescharacteristic
277C2×C4#650011yescharacteristic
278C2×C4#650212yes—
279C2×C4C2×#114311yescharacteristic
280C2×C4C2×#114411yescharacteristic
281C2×C4#651211yescharacteristic
282C2×C4#651411yescharacteristic
283C8—284no—
284C8—562no—
285C7#919311yescharacteristic, complemented, Sylow
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#8999211yescharacteristic
294C22C2×#640911yescharacteristic
295C22#9000411yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—82no—
302C4—82no—
303C4#8981511yescharacteristic
304C4#8981611yescharacteristic
305C4#8981811yescharacteristic
306C4#8982211yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#1172944611yescharacteristic
311C2#1172960811yescharacteristic
312C2#1172962011yescharacteristic
subgroupG/H
centerC22#89992
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2628C2
socleC22×C7#386
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2628D7
hypocenterC7#9193
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
3. #11729529C2semidirect
5. #11725437C2semidirect
285. C7#9193semidirect

Maximal subgroups

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

subgroupindex
C7×#26282
#117396492
#117295292
#117293252
#117254372
#91937