Finite Group Databasebeta

← #13253858

Subgroups — #13253858

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×C7×#389C211yesmaximal, characteristic
2#11729284C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4#11725419C214yesmaximal
5C22×C7×C4⋊C4C411yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C22×C7×C4⋊C4C412yes—
8C22×C42×C7C2211yescharacteristic
9C7×#389—21no—
10C7×#389—21no—
11C7×#389—21no—
12C7×#389—21no—
13C2×C7×#95C2212yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15C2×C22⋊(C7⋊C8)C2212yes—
16C2×C4⋊(C7⋊C8)—21no—
17C2×#6377—21no—
18#89319—21no—
19#89319—21no—
20#9883—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2×C412yes—
24C23×C4×C7C2×C412yes—
25C23×C4×C7C2311yescharacteristic
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—24no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—42no—
34C2×C7×C4⋊C4—44no—
35C2×C42×C7—42no—
36C2×C42×C7D411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C22×C7⋊C8—22no—
41C22×C7⋊C8—22no—
42C7×#95—22no—
43C7×#95—22no—
44C22⋊(C7⋊C8)—22no—
45C22⋊(C7⋊C8)—24no—
46C22⋊(C7⋊C8)Q814yes—
47C4⋊(C7⋊C8)—42no—
48#6377—42no—
49C2×#389D711yescharacteristic
50#1797—71no—
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—22no—
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7—24no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7—41no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7M1614yes—
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×Q812yes—
78C22×C4×C7#4112yes—
79C7×C4⋊C4—24no—
80C7×C4⋊C4—24no—
81C7×C4⋊C4—42no—
82C7×C4⋊C4—44no—
83C7×C4⋊C4—42no—
84C7×C4⋊C4—44no—
85C42×C7—22no—
86C42×C7—22no—
87C42×C7—41no—
88C42×C7—41no—
89C2×C7⋊C8—24no—
90C2×C7⋊C8—42no—
91C2×C7⋊C8—42no—
92C2×C7⋊C8—42no—
93C2×C7⋊C8—42no—
94C2×C7⋊C8—42no—
95C22×C4⋊C4Dic711yescharacteristic
96C22×C4⋊C4Dic711yescharacteristic
97C22×C4⋊C4Dic712yes—
98C22×C42C2×D711yescharacteristic
99C2×C4⋊C8—141no—
100C2×C22⋊C8—72no—
101C2×C22⋊C8—72no—
102C2×#97—141no—
103#389—21no—
104#389—21no—
105#389—21no—
106#389—21no—
107C2×#95C2×D712yes—
108#336—141no—
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—24no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—42no—
134C2×C4×C7—42no—
135C2×C4×C7—44no—
136C2×C4×C7—44no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—44no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—84no—
144C2×C4×C7#9912yes—
145C2×C4×C7#10012yes—
146C2×C4×C7#10112yes—
147C2×C4×C7C22⋊Q812yes—
148C2×C4×C7#12411yescharacteristic
149C2×C4×C7C4⋊Q811yescharacteristic
150C7⋊C8—44no—
151C7⋊C8—82no—
152C23×C4C2×Dic711yescharacteristic
153C23×C4C2×Dic711yescharacteristic
154C23×C4C2×Dic712yes—
155C23×C4C2×Dic712yes—
156C23×C4C22×D711yescharacteristic
157C22×C8—142no—
158C22×C8—142no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—42no—
168C2×C42—42no—
169C2×C42C22⋊D711yescharacteristic
170C2×C42C22⋊D711yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C2×C42C22⋊D711yescharacteristic
173C4⋊C8—282no—
174C22⋊C8—74no—
175C22⋊C8—142no—
176C22⋊C8—144no—
177#97—282no—
178#95—22no—
179#95—22no—
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—44no—
201C4×C7—41no—
202C4×C7—82no—
203C24C22×Dic711yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4#113614yes—
221C22×C4C22⋊Dic711yescharacteristic
222C22×C4C22⋊Dic711yescharacteristic
223C22×C4C22⋊Dic711yescharacteristic
224C22×C4C22⋊Dic711yescharacteristic
225C22×C4Q8×D712yes—
226C22×C4#116112yes—
227C22×C4C2×C22⋊D711yescharacteristic
228C22×C4C2×C22⋊D711yescharacteristic
229C2×C8—144no—
230C2×C8—282no—
231C2×C8—282no—
232C2×C8—282no—
233C2×C8—282no—
234C2×C8—282no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—42no—
238C4⋊C4—44no—
239C4⋊C4—44no—
240C4⋊C4—42no—
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—
257C23C2×#113612yes—
258C23Q8×Dic712yes—
259C23#651112yes—
260C23C2×C22⋊Dic711yescharacteristic
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—24no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—84no—
287C2×C4#640712yes—
288C2×C4#640812yes—
289C2×C4#641012yes—
290C2×C4#650711yescharacteristic
291C2×C4#650912yes—
292C2×C4#651011yescharacteristic
293C8—284no—
294C8—562no—
295C7#988311yescharacteristic, complemented, Sylow
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22#8979614yes—
303C22#8997911yescharacteristic
304C22C2×#640711yescharacteristic
305C22C2×#640811yescharacteristic
306C22C2×#641011yescharacteristic
307C22#9000211yescharacteristic
308C22#9000611yescharacteristic
309C22#9001211yescharacteristic
310C4—22no—
311C4—22no—
312C4—21no—
313C4—21no—
314C4—22no—
315C4—22no—
316C4—41no—
317C4—44no—
318C4—82no—
319C2—24no—
320C2#1172930611yescharacteristic
321C2#1172935711yescharacteristic
322C2#1172938911yescharacteristic
323C2#1172943011yescharacteristic
324C2#1172945511yescharacteristic
325C2#1172949111yescharacteristic
326C2#1172954411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#389C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenterC2×#389D7
hypocenterC7#9883
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

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×C7×#3892
#117292842
#117292832
#117254192
#98837