Finite Group Databasebeta

← #13253968

Subgroups — #13253968

Order 1792.

684 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C7×#1797C211yesmaximal, characteristic
3C4×C7⋊#95C211yesmaximal, characteristic
4#11725481C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C2×#6487—21no—
7C22×C4×Dic7—21no—
8C2×#6432C411yescharacteristic, complemented
9C2×C7×C4⋊C8—21no—
10C2×C7×C22⋊C8C2212yes—
11#89984—21no—
12#89984C2212yes—
13C2×C7⋊#95—21no—
14C2×C7⋊#95C2212yes—
15#89707C411yescharacteristic, complemented
16#89701—21no—
17#89700—21no—
18#89700C412yescomplemented
19C7×#336—21no—
20#9909—71nomaximal, Sylow
21C23×C4×C7D411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7C2311yescharacteristic
24C23×Dic7—22no—
25C22×Dic14—21no—
26C22×C7×C8—22no—
27C2×C42×C7—42no—
28C2×C42×C7C2×C411yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C412yes—
37C2×C4⋊Dic7C2×C412yes—
38#6487—42no—
39#6487—42no—
40C2×Dic7⋊C4—22no—
41C2×C4×Dic7—24no—
42C2×C4×Dic7—42no—
43C2×C4×Dic7—42no—
44#6432—42no—
45C7×C4⋊C8—42no—
46C7×C22⋊C8—24no—
47C7⋊#95—24no—
48C7⋊#95—22no—
49C7⋊#95—22no—
50C7⋊#95—22no—
51C7⋊#95Q814yescomplemented
52#2857—71no—
53#1797D711yescharacteristic
54C4×#95—71no—
55#1294—74no—
56C24×C7C2×D411yescharacteristic
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—22no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7—41no—
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7D812yes—
69C22×C4×C7SD1612yes—
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×Q812yes—
73C22×C4×C7#4112yes—
74C22×Dic7—24no—
75C22×Dic7—24no—
76C22×Dic7—24no—
77C22×Dic7—22no—
78C22×Dic7—22no—
79C22×Dic7—42no—
80C22×Dic7—42no—
81C22×Dic7—42no—
82C22×Dic7—42no—
83C2×Dic14—42no—
84C2×Dic14—42no—
85C2×Dic14—42no—
86C2×C7×C8—42no—
87C2×C7×C8—42no—
88C2×C7×C8—42no—
89C42×C7—22no—
90C42×C7—22no—
91C42×C7—41no—
92C42×C7—41no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C4⋊Dic7—42no—
96C4⋊Dic7—42no—
97C4⋊Dic7—42no—
98C4⋊Dic7—42no—
99C4⋊Dic7—42no—
100Dic7⋊C4—44no—
101C4×Dic7—48no—
102C2×C4⋊Q8—71no—
103C2×C22⋊Q8—141no—
104C22×C42—141no—
105C22×C42C2×D711yescharacteristic
106C2×C4⋊C8—21no—
107C2×C22⋊C8C2×D712yes—
108#391—141no—
109#389—72no—
110#389—141no—
111#384—71no—
112#380—72no—
113#380—141no—
114C2×#95—72no—
115C2×#95—141no—
116#336—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7C2×C22⋊C411yescharacteristic
122C23×C7C22⋊Q812yes—
123C23×C7C2×D811yescharacteristic
124C23×C7C2×SD1611yescharacteristic
125C23×C7#13712yes—
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—21no—
134C2×C4×C7—24no—
135C2×C4×C7—24no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7—44no—
142C2×C4×C7#9912yes—
143C2×C4×C7#10212yes—
144C2×C4×C7#10212yes—
145C2×C4×C7#10412yes—
146C2×C4×C7#10412yes—
147C2×C4×C7C4×Q812yes—
148C2×C4×C7#12411yescharacteristic
149C2×C4×C7C4⋊Q811yescharacteristic
150C2×Dic7—28no—
151C2×Dic7—44no—
152C2×Dic7—44no—
153C2×Dic7—44no—
154C2×Dic7—44no—
155C2×Dic7—44no—
156C2×Dic7—44no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7—42no—
160C2×Dic7—42no—
161C2×Dic7—42no—
162C2×Dic7—42no—
163Dic14—84no—
164C7×C8—82no—
165C22×Q8—141no—
166C23×C4—142no—
167C23×C4D2811yescharacteristic
168C23×C4D2811yescharacteristic
169C23×C4C22×D711yescharacteristic
170C22×C8—22no—
171C4⋊Q8—282no—
172C22⋊Q8—282no—
173C22⋊Q8—282no—
174C2×C4⋊C4—72no—
175C2×C4⋊C4—72no—
176C2×C4⋊C4—142no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C22⋊C4—142no—
181C2×C42—42no—
182C2×C42—144no—
183C2×C42—282no—
184C2×C42—282no—
185C2×C42C4×D711yescharacteristic
186C2×C42C4×D711yescharacteristic
187C2×C42C22⋊D711yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189C4⋊C8—42no—
190C22⋊C8—24no—
191#95—74no—
192#95—144no—
193#95—142no—
194#95—142no—
195#95—142no—
196C22×C7—22no—
197C22×C7—22no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—22no—
203C22×C7—22no—
204C22×C7#39111yescharacteristic
205C22×C7C2×#9911yescharacteristic
206C22×C7#41011yescharacteristic
207C22×C7C2×#10211yescharacteristic
208C22×C7#41911yescharacteristic
209C22×C7C2×#10411yescharacteristic
210C22×C7C2×#10411yescharacteristic
211C22×C7#47412yes—
212C22×C7#47512yes—
213C4×C7—21no—
214C4×C7—22no—
215C4×C7—21no—
216C4×C7—22no—
217C4×C7—22no—
218C4×C7—41no—
219C4×C7#32714yes—
220Dic7—48no—
221Dic7—82no—
222Dic7—82no—
223C24C2×D2811yescharacteristic
224C2×Q8—282no—
225C2×Q8—282no—
226C2×Q8—282no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—144no—
235C22×C4—144no—
236C22×C4—144no—
237C22×C4—142no—
238C22×C4—142no—
239C22×C4—282no—
240C22×C4—282no—
241C22×C4—282no—
242C22×C4—282no—
243C22×C4#113212yes—
244C22×C4D5612yes—
245C22×C4(C2×D7)⋊C411yescharacteristic
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4(C2×D7)⋊C411yescharacteristic
249C22×C4C2×C4×D711yescharacteristic
250C22×C4#115912yes—
251C22×C4Q8×D712yes—
252C22×C4C2×C22⋊D711yescharacteristic
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C4⋊C4—282no—
257C4⋊C4—282no—
258C4⋊C4—282no—
259C4⋊C4—284no—
260C4⋊C4—282no—
261C4⋊C4—282no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C42—22no—
265C42—22no—
266C42—41no—
267C42—41no—
268C42—288no—
269C2×C7—22no—
270C2×C7—22no—
271C2×C7C2×#32711yescharacteristic
272C2×C7#150211yescharacteristic
273C2×C7#150611yescharacteristic
274C2×C7#150811yescharacteristic
275C2×C7#198811yescharacteristic
276C2×C7#199411yescharacteristic
277C2×C7#199611yescharacteristic
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#646012yes—
283C23C2×#113211yescharacteristic
284C23C2×D5611yescharacteristic
285C23#647212yes—
286C23C2×(C2×D7)⋊C411yescharacteristic
287Q8—564no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—148no—
305C2×C4—284no—
306C2×C4—284no—
307C2×C4—284no—
308C2×C4—284no—
309C2×C4—284no—
310C2×C4—284no—
311C2×C4—282no—
312C2×C4—282no—
313C2×C4—282no—
314C2×C4—282no—
315C2×C4—282no—
316C2×C4—282no—
317C2×C4#638012yes—
318C2×C4#639512yes—
319C2×C4#639512yes—
320C2×C4#639912yes—
321C2×C4#639912yes—
322C2×C4#645012yes—
323C2×C4#649911yescharacteristic
324C2×C4#650711yescharacteristic
325C8—82no—
326C7#990911yescharacteristic, complemented, Sylow
327C22—21no—
328C22—21no—
329C22—22no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22#8961812yes—
336C22#8962312yes—
337C22C2×#638011yescharacteristic
338C22#8974611yescharacteristic
339C22#8977811yescharacteristic
340C22C2×#639511yescharacteristic
341C22#8989211yescharacteristic
342C22C2×#639911yescharacteristic
343C22C2×#639911yescharacteristic
344C4—22no—
345C4—22no—
346C4—21no—
347C4—22no—
348C4—21no—
349C4—41no—
350C4—288no—
351C4—562no—
352C4—562no—
353C4#8926514yes—
354C2—22no—
355C2—22no—
356C2#1172728311yescharacteristic
357C2C2×#8926511yescharacteristic
358C2#1172773411yescharacteristic
359C2#1172821411yescharacteristic
360C2#1172826811yescharacteristic
361C2#1172854311yescharacteristic
362C2#1172859011yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1797D7
hypocenterC7#9909
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
8. C2×#6432C4semidirect
15. #89707C4semidirect
18. #89700C4semidirect
51. C7⋊#95Q8semidirect
326. C7#9909semidirect

Maximal subgroups

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

subgroupindex
#117395212
C7×#17972
C4×C7⋊#952
#117254812
#99097