Finite Group Databasebeta

← #13242288

Subgroups — #13242288

Order 1792.

410 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11730754C211yesmaximal, characteristic
2C7×#1767C211yesmaximal, characteristic
3C4×C4⋊(C7⋊C8)C211yesmaximal, characteristic
4#11725286C212yesmaximal
5#11725283C212yesmaximal
6C2×C7×C4⋊C8—21no—
7C2×C7×#97—21no—
8C43×C7C2211yescharacteristic
9#89709—21no—
10#89705—21no—
11#89705—21no—
12#89705—21no—
13#89701C411yescharacteristic
14#89701C411yescharacteristic
15#89701C2211yescharacteristic
16#89700C411yescharacteristic
17#89700C411yescharacteristic
18#89700C2211yescharacteristic
19C2×C4⋊(C7⋊C8)—21no—
20C2×C4×C7⋊C8—21no—
21C7×#336C2212yes—
22#89319C2212yes—
23#7689—71nomaximal, Sylow
24C22×Dic14C2×C411yescharacteristic
25C22×C7×C8—22no—
26C2×C42×C7C2×C411yescharacteristic
27C2×C42×C7C2×C411yescharacteristic
28C2×C42×C7D411yescharacteristic
29C2×C42×C7D411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7C2311yescharacteristic
33C2×C4⋊Dic7C2×C411yescharacteristic
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C22×C7⋊C8—22no—
40C7×C4⋊C8—24no—
41C7×#97—42no—
42C7⋊#95—21no—
43C7⋊#95—21no—
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—
52C4×C7⋊C8—42no—
53#2863—71no—
54#1767D711yescharacteristic
55C4×C4⋊C8—71no—
56#1272—72no—
57#1271—72no—
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22×C411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×Dic7—21no—
66C22×Dic7—21no—
67C22×Dic7—21no—
68C22×Dic7—21no—
69C2×Dic14—22no—
70C2×Dic14—41no—
71C2×Dic14—41no—
72C2×C7×C8—24no—
73C2×C7×C8—42no—
74C2×C7×C8—42no—
75C42×C7—22no—
76C42×C7—22no—
77C42×C7—22no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—41no—
81C42×C7—41no—
82C42×C7SD1612yes—
83C42×C7Q1612yes—
84C4⋊Dic7—22no—
85C4⋊Dic7—41no—
86C4⋊Dic7—41no—
87Dic7⋊C4—42no—
88Dic7⋊C4—42no—
89Dic7⋊C4—41no—
90Dic7⋊C4—41no—
91C2×C7⋊C8—24no—
92C2×C7⋊C8—42no—
93C2×C7⋊C8—42no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—141no—
96C2×#97—21no—
97C2×C4×C8—141no—
98#391—71no—
99#391—71no—
100#391—71no—
101#389—71no—
102#389—71no—
103#389—71no—
104#387—141no—
105#387—141no—
106#387—141no—
107#383—141no—
108C43C2×D711yescharacteristic
109#336—72no—
110#336C2×D712yes—
111C23×C7C2×C22⋊C411yescharacteristic
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#10312yes—
127C2×C4×C7#10312yes—
128C2×C4×C7#10412yes—
129C2×C4×C7#10412yes—
130C2×C4×C7#13112yes—
131C2×C4×C7C2×SD1611yescharacteristic
132C2×C4×C7C2×Q1611yescharacteristic
133C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C7#13711yescharacteristic
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147Dic14—82no—
148C7×C8—44no—
149C7⋊C8—44no—
150C22×Q8—71no—
151C22×C8—22no—
152C22×C8—142no—
153C2×C4⋊C4—71no—
154C2×C4⋊C4—71no—
155C2×C4⋊C4—71no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4—141no—
158C2×C4⋊C4—141no—
159C2×C42C4×D711yescharacteristic
160C2×C42C4×D711yescharacteristic
161C2×C42D2811yescharacteristic
162C2×C42D2811yescharacteristic
163C2×C42C22⋊D711yescharacteristic
164C2×C42C22⋊D711yescharacteristic
165C2×C42C22×D711yescharacteristic
166C4⋊C8—24no—
167C4⋊C8—144no—
168#97—42no—
169C4×C8—282no—
170#95—141no—
171#95—141no—
172#95—141no—
173#95—141no—
174#95—141no—
175#95—141no—
176#95—141no—
177#95—141no—
178#95—141no—
179C22×C7#40811yescharacteristic
180C22×C7#41011yescharacteristic
181C22×C7#41311yescharacteristic
182C22×C7C2×#10311yescharacteristic
183C22×C7#41711yescharacteristic
184C22×C7C2×#10411yescharacteristic
185C22×C7C2×#10411yescharacteristic
186C4×C7—22no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—22no—
190C4×C7—21no—
191C4×C7—21no—
192C4×C7—21no—
193C4×C7—21no—
194C4×C7—22no—
195Dic7—81no—
196Dic7—81no—
197Dic7—81no—
198Dic7—81no—
199C2×Q8—142no—
200C2×Q8—281no—
201C2×Q8—281no—
202C22×C4—141no—
203C22×C4—141no—
204C22×C4—141no—
205C22×C4—141no—
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4(C2×D7)⋊C411yescharacteristic
208C22×C4(C2×D7)⋊C411yescharacteristic
209C22×C4(C2×D7)⋊C411yescharacteristic
210C22×C4C2×C4×D711yescharacteristic
211C22×C4C2×D2811yescharacteristic
212C22×C4C2×C22⋊D711yescharacteristic
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—144no—
217C2×C8—282no—
218C2×C8—282no—
219C4⋊C4—142no—
220C4⋊C4—281no—
221C4⋊C4—281no—
222C4⋊C4—281no—
223C4⋊C4—281no—
224C4⋊C4—282no—
225C4⋊C4—282no—
226C42—22no—
227C42—21no—
228C42—21no—
229C42—22no—
230C42—22no—
231C42—41no—
232C42—41no—
233C42#114212yes—
234C42#114412yes—
235C2×C7#147311yescharacteristic
236C2×C7#148311yescharacteristic
237C2×C7#149311yescharacteristic
238C2×C7#150311yescharacteristic
239C2×C7#150911yescharacteristic
240C2×C7#152411yescharacteristic
241C2×C7#155011yescharacteristic
242C23C2×(C2×D7)⋊C411yescharacteristic
243Q8—562no—
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—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—281no—
259C2×C4—281no—
260C2×C4—281no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4—281no—
264C2×C4—281no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4#637912yes—
271C2×C4#638412yes—
272C2×C4#638412yes—
273C2×C4#639912yes—
274C2×C4#647012yes—
275C2×C4#647111yescharacteristic
276C2×C4#647211yescharacteristic
277C2×C4C2×#114211yescharacteristic
278C2×C4C2×#114411yescharacteristic
279C8—44no—
280C8—284no—
281C7#768911yescharacteristic, complemented, Sylow
282C22C2×#637911yescharacteristic
283C22C2×#638411yescharacteristic
284C22#8977811yescharacteristic
285C22#8990111yescharacteristic
286C22#8990411yescharacteristic
287C22#8990511yescharacteristic
288C22C2×#639911yescharacteristic
289C4—21no—
290C4—21no—
291C4—22no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—22no—
298C4—561no—
299C4—561no—
300C4—561no—
301C4—561no—
302C2#1172722511yescharacteristic
303C2#1172755111yescharacteristic
304C2#1172760611yescharacteristic
305C2#1172825511yescharacteristic
306C2#1172826311yescharacteristic
307C2#1172858311yescharacteristic
308C2#1172858711yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1767C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1767D7
hypocenterC7#7689
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
281. C7#7689semidirect

Maximal subgroups

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

subgroupindex
#117307542
C7×#17672
C4×C4⋊(C7⋊C8)2
#117252862
#117252832
#76897