Finite Group Databasebeta

← #13252643

Subgroups — #13252643

Order 1792.

640 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89323C214yesmaximal
3#11729284C211yesmaximal, characteristic
4#11729283C211yesmaximal, characteristic
5C22×C7×C4⋊C4C411yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C22×C7×C4⋊C4C2212yes—
8C22×C42×C7C2211yescharacteristic
9C7×#389—21no—
10C7×#389—21no—
11C7×#389—21no—
12C7×#389—21no—
13C2×C7×#95C412yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15C2×C22⋊(C7⋊C8)C2212yes—
16C2×C4⋊(C7⋊C8)—21no—
17C2×#6377—21no—
18#89323—28no—
19#89319—21no—
20#89319—21no—
21#9654—71nomaximal, Sylow
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2×C412yes—
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7C2×C412yes—
26C23×C4×C7C2311yescharacteristic
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—24no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4—24no—
35C2×C7×C4⋊C4—24no—
36C2×C7×C4⋊C4—42no—
37C2×C42×C7—42no—
38C2×C42×C7D411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C22×C7⋊C8—22no—
43C22×C7⋊C8—22no—
44C7×#95—22no—
45C7×#95—22no—
46C22⋊(C7⋊C8)—22no—
47C22⋊(C7⋊C8)—24no—
48C22⋊(C7⋊C8)D414yes—
49C4⋊(C7⋊C8)—42no—
50#6377—42no—
51C2×#389D711yescharacteristic
52#1797—71no—
53#1749—71no—
54C2×#324—74no—
55C24×C7C22×C411yescharacteristic
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—24no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—24no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—24no—
67C22×C4×C7—41no—
68C22×C4×C7—41no—
69C22×C4×C7—41no—
70C22×C4×C7—42no—
71C22×C4×C7—42no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7M1614yes—
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D412yes—
80C22×C4×C7#4112yes—
81C7×C4⋊C4—24no—
82C7×C4⋊C4—24no—
83C7×C4⋊C4—42no—
84C7×C4⋊C4—42no—
85C7×C4⋊C4—44no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—42no—
88C42×C7—22no—
89C42×C7—22no—
90C42×C7—41no—
91C42×C7—41no—
92C2×C7⋊C8—24no—
93C2×C7⋊C8—42no—
94C2×C7⋊C8—42no—
95C2×C7⋊C8—42no—
96C2×C7⋊C8—42no—
97C2×C7⋊C8—42no—
98C22×C4⋊C4Dic711yescharacteristic
99C22×C4⋊C4Dic711yescharacteristic
100C22×C4⋊C4C2×D712yes—
101C22×C42C2×D711yescharacteristic
102C2×C4⋊C8—141no—
103C2×C22⋊C8—72no—
104C2×C22⋊C8—72no—
105C2×#97—141no—
106#389—21no—
107#389—21no—
108#389—21no—
109#389—21no—
110C2×#95Dic712yes—
111#336—141no—
112#336—141no—
113#324—148no—
114C23×C7—21no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7C2×C22⋊C411yescharacteristic
119C23×C7C4×D412yes—
120C23×C7C2×M1612yes—
121C23×C7#13112yes—
122C2×C4×C7—28no—
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—21no—
133C2×C4×C7—24no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—28no—
138C2×C4×C7—42no—
139C2×C4×C7—42no—
140C2×C4×C7—44no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—44no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—84no—
148C2×C4×C7#9912yes—
149C2×C4×C7#10112yes—
150C2×C4×C7#10112yes—
151C2×C4×C7#12112yes—
152C2×C4×C7#12411yescharacteristic
153C2×C4×C7#12711yescharacteristic
154C7⋊C8—44no—
155C7⋊C8—82no—
156C23×C4C2×Dic712yes—
157C23×C4C2×Dic711yescharacteristic
158C23×C4C2×Dic711yescharacteristic
159C23×C4C2×Dic712yes—
160C23×C4C22×D711yescharacteristic
161C22×C8—142no—
162C22×C8—142no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—42no—
173C2×C42—42no—
174C2×C42C22⋊D711yescharacteristic
175C2×C42C22⋊D711yescharacteristic
176C2×C42C22⋊D711yescharacteristic
177C2×C42C22⋊D711yescharacteristic
178C4⋊C8—282no—
179C22⋊C8—74no—
180C22⋊C8—142no—
181C22⋊C8—144no—
182#97—282no—
183#95—22no—
184#95—22no—
185C22×C7—22no—
186C22×C7—22no—
187C22×C7—22no—
188C22×C7—22no—
189C22×C7—22no—
190C22×C7—22no—
191C22×C7#39011yescharacteristic
192C22×C7#40711yescharacteristic
193C22×C7#40811yescharacteristic
194C22×C7C2×#9911yescharacteristic
195C22×C7#41011yescharacteristic
196C22×C7C2×#10111yescharacteristic
197C22×C7C2×#10111yescharacteristic
198C22×C7#43514yes—
199C4×C7—22no—
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—22no—
203C4×C7—22no—
204C4×C7—22no—
205C4×C7—44no—
206C4×C7—41no—
207C4×C7—82no—
208C24C22×Dic711yescharacteristic
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4#113614yes—
226C22×C4C22⋊Dic711yescharacteristic
227C22×C4C22⋊Dic711yescharacteristic
228C22×C4C22⋊Dic711yescharacteristic
229C22×C4C22⋊Dic711yescharacteristic
230C22×C4D4×D712yes—
231C22×C4#115912yes—
232C22×C4C2×C22⋊D711yescharacteristic
233C22×C4C2×C22⋊D711yescharacteristic
234C2×C8—144no—
235C2×C8—282no—
236C2×C8—282no—
237C2×C8—282no—
238C2×C8—282no—
239C2×C8—282no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—44no—
246C4⋊C4—42no—
247C42—22no—
248C42—22no—
249C42—41no—
250C42—41no—
251C2×C7—24no—
252C2×C7#146311yescharacteristic
253C2×C7#146711yescharacteristic
254C2×C7#147011yescharacteristic
255C2×C7#147211yescharacteristic
256C2×C7#195511yescharacteristic
257C2×C7#196411yescharacteristic
258C2×C7#196611yescharacteristic
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23C2×#113612yes—
264C23D4×Dic712yes—
265C23#651112yes—
266C23C2×C22⋊Dic711yescharacteristic
267C2×C4—28no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—28no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4#640812yes—
294C2×C4#641012yes—
295C2×C4#641012yes—
296C2×C4#649911yescharacteristic
297C2×C4#650112yes—
298C2×C4#650311yescharacteristic
299C8—284no—
300C8—562no—
301C7#965411yescharacteristic, complemented, Sylow
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#8978314yes—
309C22#8997911yescharacteristic
310C22C2×#640811yescharacteristic
311C22#8999311yescharacteristic
312C22C2×#641011yescharacteristic
313C22C2×#641011yescharacteristic
314C22#9000611yescharacteristic
315C22#9001211yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—44no—
324C4—82no—
325C2—24no—
326C2#1172930611yescharacteristic
327C2#1172936911yescharacteristic
328C2#1172937911yescharacteristic
329C2#1172944011yescharacteristic
330C2#1172944511yescharacteristic
331C2#1172949111yescharacteristic
332C2#1172954311yescharacteristic
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#9654
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
301. C7#9654semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#893232
#117292842
#117292832
#96547