Finite Group Databasebeta

← #13253856

Subgroups — #13253856

Order 1792.

600 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89700C211yesmaximal, characteristic
2C7×#1797C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4#11725480C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C22×C4⋊Dic7C411yescharacteristic
7C22×C4⋊Dic7C411yescharacteristic
8C22×Dic7⋊C4C412yes—
9C2×C7×C4⋊C8—21no—
10C2×C7×C22⋊C8C2212yes—
11C2×C7⋊#95C2212yes—
12C2×C22⋊(C7⋊C8)C2212yes—
13#89700—21no—
14#89700—21no—
15#89700—21no—
16#89700—21no—
17C2×#6377—21no—
18C7×#336—21no—
19#89319—21no—
20#9883—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2311yescharacteristic
24C23×Dic7C2×C412yes—
25C23×Dic7C2×C412yes—
26C22×C7×C8—22no—
27C2×C42×C7—42no—
28C2×C42×C7D411yescharacteristic
29C2×C42×C7D411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—24no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—42no—
38C2×Dic7⋊C4—22no—
39C2×Dic7⋊C4—22no—
40C2×Dic7⋊C4—44no—
41C22×C7⋊C8—22no—
42C7×C4⋊C8—42no—
43C7×C22⋊C8—24no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C22⋊(C7⋊C8)—22no—
47C22⋊(C7⋊C8)Q814yes—
48#6377—42no—
49C2×#389—71no—
50#1797D711yescharacteristic
51#1749—71no—
52#1280—74no—
53C24×C7C22×C411yescharacteristic
54C22×C4×C7—22no—
55C22×C4×C7—22no—
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—41no—
60C22×C4×C7—41no—
61C22×C4×C7—41no—
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×Q812yes—
69C22×C4×C7#4112yes—
70C22×Dic7—22no—
71C22×Dic7—22no—
72C22×Dic7—22no—
73C22×Dic7—24no—
74C22×Dic7—42no—
75C22×Dic7—42no—
76C22×Dic7—42no—
77C22×Dic7—42no—
78C22×Dic7M1614yes—
79C2×C7×C8—42no—
80C2×C7×C8—42no—
81C2×C7×C8—42no—
82C42×C7—22no—
83C42×C7—22no—
84C42×C7—41no—
85C42×C7—41no—
86C4⋊Dic7—24no—
87C4⋊Dic7—24no—
88C4⋊Dic7—42no—
89C4⋊Dic7—42no—
90Dic7⋊C4—44no—
91Dic7⋊C4—44no—
92C2×C7⋊C8—24no—
93C2×C7⋊C8—42no—
94C2×C7⋊C8—42no—
95C22×C4⋊C4—71no—
96C22×C4⋊C4—72no—
97C22×C4⋊C4—71no—
98C22×C42C2×D711yescharacteristic
99C2×C4⋊C8—21no—
100C2×C22⋊C8—72no—
101C2×C22⋊C8C2×D712yes—
102C2×#97—141no—
103#389—141no—
104#389—141no—
105#389—141no—
106#389—141no—
107C2×#95—72no—
108#336—21no—
109#336—141no—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—21no—
114C23×C7C2×C22⋊C411yescharacteristic
115C23×C7C4×Q812yes—
116C23×C7C2×M1612yes—
117C23×C7#13112yes—
118C2×C4×C7—28no—
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—21no—
131C2×C4×C7—21no—
132C2×C4×C7—42no—
133C2×C4×C7—42no—
134C2×C4×C7—44no—
135C2×C4×C7#9912yes—
136C2×C4×C7#10012yes—
137C2×C4×C7#10112yes—
138C2×C4×C7C22⋊Q812yes—
139C2×C4×C7#12411yescharacteristic
140C2×C4×C7C4⋊Q811yescharacteristic
141C2×Dic7—24no—
142C2×Dic7—44no—
143C2×Dic7—42no—
144C2×Dic7—42no—
145C2×Dic7—44no—
146C2×Dic7—42no—
147C2×Dic7—42no—
148C2×Dic7—42no—
149C2×Dic7—84no—
150C7×C8—82no—
151C7⋊C8—44no—
152C23×C4—72no—
153C23×C4—72no—
154C23×C4C4×D711yescharacteristic
155C23×C4C4×D711yescharacteristic
156C23×C4C22×D711yescharacteristic
157C22×C8—22no—
158C22×C8—142no—
159C2×C4⋊C4—144no—
160C2×C4⋊C4—141no—
161C2×C4⋊C4—141no—
162C2×C4⋊C4—142no—
163C2×C4⋊C4—142no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4—284no—
167C2×C4⋊C4—282no—
168C2×C42—42no—
169C2×C42D2811yescharacteristic
170C2×C42D2811yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C2×C42C22⋊D711yescharacteristic
173C4⋊C8—42no—
174C22⋊C8—24no—
175C22⋊C8—74no—
176C22⋊C8—142no—
177#97—282no—
178#95—142no—
179#95—142no—
180C22×C7—22no—
181C22×C7—22no—
182C22×C7—22no—
183C22×C7—22no—
184C22×C7—22no—
185C22×C7—22no—
186C22×C7#39111yescharacteristic
187C22×C7#40711yescharacteristic
188C22×C7#40811yescharacteristic
189C22×C7C2×#9911yescharacteristic
190C22×C7#41011yescharacteristic
191C22×C7C2×#10011yescharacteristic
192C22×C7C2×#10111yescharacteristic
193C22×C7#44614yes—
194C4×C7—22no—
195C4×C7—22no—
196C4×C7—22no—
197C4×C7—22no—
198C4×C7—21no—
199C4×C7—21no—
200C4×C7—41no—
201Dic7—44no—
202Dic7—82no—
203C24C2×C4×D711yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—74no—
213C22×C4—142no—
214C22×C4—142no—
215C22×C4—142no—
216C22×C4—144no—
217C22×C4—282no—
218C22×C4—282no—
219C22×C4—282no—
220C22×C4—282no—
221C22×C4(C2×D7)⋊C411yescharacteristic
222C22×C4(C2×D7)⋊C411yescharacteristic
223C22×C4(C2×D7)⋊C411yescharacteristic
224C22×C4(C2×D7)⋊C411yescharacteristic
225C22×C4C2×D2811yescharacteristic
226C22×C4#115912yes—
227C22×C4Q8×D712yes—
228C22×C4C2×C22⋊D711yescharacteristic
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—144no—
233C2×C8—282no—
234C2×C8—282no—
235C4⋊C4—144no—
236C4⋊C4—144no—
237C4⋊C4—284no—
238C4⋊C4—282no—
239C4⋊C4—282no—
240C4⋊C4—284no—
241C42—22no—
242C42—22no—
243C42—41no—
244C42—41no—
245C2×C7—24no—
246C2×C7#146311yescharacteristic
247C2×C7#146611yescharacteristic
248C2×C7#147011yescharacteristic
249C2×C7#147111yescharacteristic
250C2×C7#198511yescharacteristic
251C2×C7#199611yescharacteristic
252C2×C7#199711yescharacteristic
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#645012yes—
258C23#646412yes—
259C23D7×M1612yes—
260C23C2×(C2×D7)⋊C411yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—144no—
279C2×C4—284no—
280C2×C4—282no—
281C2×C4—282no—
282C2×C4—284no—
283C2×C4—282no—
284C2×C4—282no—
285C2×C4—282no—
286C2×C4—564no—
287C2×C4#638012yes—
288C2×C4#639712yes—
289C2×C4#639812yes—
290C2×C4#646012yes—
291C2×C4#649911yescharacteristic
292C2×C4#650711yescharacteristic
293C8—82no—
294C8—284no—
295C7#988311yescharacteristic, complemented, Sylow
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22#8960014yes—
303C22C2×#638011yescharacteristic
304C22#8974611yescharacteristic
305C22#8977811yescharacteristic
306C22#8988211yescharacteristic
307C22#8989811yescharacteristic
308C22C2×#639711yescharacteristic
309C22C2×#639811yescharacteristic
310C4—22no—
311C4—22no—
312C4—22no—
313C4—21no—
314C4—22no—
315C4—21no—
316C4—41no—
317C4—284no—
318C4—562no—
319C2—24no—
320C2#1172728311yescharacteristic
321C2#1172767511yescharacteristic
322C2#1172772511yescharacteristic
323C2#1172822711yescharacteristic
324C2#1172827811yescharacteristic
325C2#1172854111yescharacteristic
326C2#1172858111yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenter#1797D7
hypocenterC7#9883
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
295. C7#9883semidirect

Maximal subgroups

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

subgroupindex
C2×#897002
C7×#17972
#117292832
#117254802
#98837