Finite Group Databasebeta

← #13263470

Subgroups — #13263470

Order 1792.

554 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739794C211yesmaximal, characteristic
2C7×#1466C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725253C214yesmaximal, complemented
5C23×Dic14C411yescharacteristic
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487—21no—
8C7×#432—21no—
9#89992C412yes—
10#89984C411yescharacteristic
11C2×C22⋊(C7⋊C8)—21no—
12#89751—21no—
13#89719—21no—
14#89718C2212yes—
15#89701—21no—
16C7×#323—21no—
17C7×#323C2212yes—
18#89323—21no—
19#89320C2212yes—
20#11575—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×Dic7C2×C412yes—
25C22×Dic14—21no—
26C22×Dic14—21no—
27C22×Dic14—44no—
28C22×Dic14—41no—
29C22×Dic14—41no—
30C4×C7×D4—41no—
31C4×C7×D4—41no—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C7×C22⋊C4C2311yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C22⋊Dic7—22no—
37C2×C22⋊Dic7C2×C412yes—
38C2×C4⋊Dic7—21no—
39#6487—44no—
40C2×Dic7⋊C4—22no—
41C22×C7⋊C8—41no—
42C7×C4⋊C8—41no—
43C7×C22⋊C8—22no—
44C7×#97—41no—
45C7⋊#95—22no—
46C7⋊#95—21no—
47C7⋊#95—22no—
48C22⋊(C7⋊C8)—22no—
49C22⋊(C7⋊C8)—41no—
50#2409—71no—
51#1466D711yescharacteristic
52#1459—71no—
53#1326—74no—
54C24×C7C22⋊C411yescharacteristic
55C24×C7C22×C411yescharacteristic
56C2×C7×D4—22no—
57C2×C7×D4—22no—
58C2×C7×D4—41no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×Dic7—22no—
71C22×Dic7—22no—
72C22×Dic7—44no—
73C22×Dic7—42no—
74C2×Dic14—24no—
75C2×Dic14—44no—
76C2×Dic14—42no—
77C2×Dic14—42no—
78C2×Dic14—48no—
79C2×Dic14—44no—
80C2×Dic14—41no—
81C2×Dic14—41no—
82C2×Dic14—44no—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C22⋊C4—41no—
86C7×C22⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C22⋊Dic7—24no—
90C22⋊Dic7—44no—
91C4⋊Dic7—42no—
92Dic7⋊C4—44no—
93C2×C7⋊C8—42no—
94C2×C7⋊C8—82no—
95C23×Q8—71no—
96C2×C22⋊Q8—141no—
97C2×C4×D4C2×D711yescharacteristic
98#432—21no—
99C2×C22⋊C8—141no—
100#395—141no—
101#393—141no—
102#391—141no—
103#386—72no—
104#385—72no—
105#380—71no—
106#324—141no—
107#323—21no—
108#323—72no—
109#323C2×D712yes—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—21no—
114C23×C7—41no—
115C23×C7—41no—
116C23×C7—41no—
117C23×C7—41no—
118C23×C7#10112yes—
119C23×C7C2×C22⋊C411yescharacteristic
120C23×C7#13112yes—
121C7×D4—44no—
122C2×C4×C7—22no—
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—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—81no—
136C2×C4×C7#9911yescharacteristic
137C2×C4×C7#9911yescharacteristic
138C2×Dic7—24no—
139C2×Dic7—42no—
140C2×Dic7—44no—
141C2×Dic7—42no—
142C2×Dic7—44no—
143C2×Dic7—42no—
144C2×Dic7—42no—
145C2×Dic7—42no—
146Dic14—44no—
147Dic14—48no—
148Dic14—44no—
149C7×C8—82no—
150C7⋊C8—82no—
151C22×Q8—141no—
152C22×Q8—141no—
153C22×Q8—281no—
154C22×Q8—281no—
155C22×Q8—284no—
156C22×D4C4×D711yescharacteristic
157C23×C4—72no—
158C23×C4C4×D711yescharacteristic
159C23×C4D2811yescharacteristic
160C22×C8—281no—
161C22⋊Q8—284no—
162C4×D4—41no—
163C4×D4—41no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—142no—
166C2×C4⋊C4D2811yescharacteristic
167C2×C22⋊C4—72no—
168C2×C22⋊C4—142no—
169C2×C22⋊C4C22⋊D711yescharacteristic
170C2×C22⋊C4C22×D711yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C4⋊C8—41no—
173C22⋊C8—22no—
174C22⋊C8—142no—
175C22⋊C8—281no—
176#97—41no—
177#95—141no—
178#95—142no—
179#95—142no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7—22no—
183C22×C7—22no—
184C22×C7—42no—
185C22×C7—42no—
186C22×C7—42no—
187C22×C7—41no—
188C22×C7—41no—
189C22×C7—41no—
190C22×C7—41no—
191C22×C7—81no—
192C22×C7#40811yescharacteristic
193C22×C7C2×#9911yescharacteristic
194C22×C7C2×#10111yescharacteristic
195C4×C7—21no—
196C4×C7—41no—
197C4×C7—41no—
198C4×C7—41no—
199C4×C7—41no—
200C4×C7AΣL(1,𝔽16)12yes—
201Dic7—44no—
202Dic7—82no—
203C24(C2×D7)⋊C411yescharacteristic
204C24C2×C4×D711yescharacteristic
205C2×Q8—144no—
206C2×Q8—282no—
207C2×Q8—282no—
208C2×Q8—284no—
209C2×Q8—284no—
210C2×Q8—288no—
211C2×Q8—284no—
212C2×Q8—281no—
213C2×Q8—281no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—142no—
224C22×C4—142no—
225C22×C4—284no—
226C22×C4—282no—
227C22×C4(C2×D7)⋊C411yescharacteristic
228C22×C4(C2×D7)⋊C411yescharacteristic
229C22×C4(C2×D7)⋊C411yescharacteristic
230C22×C4C2×D2811yescharacteristic
231C22×C4C2×C22⋊D711yescharacteristic
232C2×C8—42no—
233C2×C8—282no—
234C2×C8—562no—
235C4⋊C4—41no—
236C4⋊C4—282no—
237C4⋊C4—284no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—144no—
241C22⋊C4—284no—
242C42—21no—
243C42—21no—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7—42no—
247C2×C7—42no—
248C2×C7#147211yescharacteristic
249C2×C7C2×AΣL(1,𝔽16)11yescharacteristic
250C2×C7#212311yescharacteristic
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23#639812yes—
260C23#647012yes—
261C23C2×(C2×D7)⋊C411yescharacteristic
262Q8—284no—
263Q8—288no—
264Q8—284no—
265D4—44no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—81no—
280C2×C4—144no—
281C2×C4—282no—
282C2×C4—284no—
283C2×C4—282no—
284C2×C4—284no—
285C2×C4—282no—
286C2×C4—282no—
287C2×C4—282no—
288C2×C4#638011yescharacteristic
289C2×C4#638011yescharacteristic
290C8—82no—
291C8—562no—
292C7#1157511yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C2×#638011yescharacteristic
306C22#8990111yescharacteristic
307C22C2×#639811yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—284no—
314C4—562no—
315C4#8927012yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2#1172772611yescharacteristic
321C2#1172781211yescharacteristic
322C2C2×#8927011yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1466C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#1466D7
hypocenterC7#11575
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
4. #11725253C2semidirect
292. C7#11575semidirect

Maximal subgroups

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

subgroupindex
#117397942
C7×#14662
#117293542
#117252532
#115757