Finite Group Databasebeta

← #13263189

Subgroups — #13263189

Order 1792.

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

normal subgroups only

This group has 510 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#11739675C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic
3#11729326C211yesmaximal, characteristic
4#11725261C214yesmaximal, complemented
5C23×Dic14C411yescharacteristic
6C2×C7×#117C2211yescharacteristic
7C2×#6489C411yescharacteristic
8C7×#432—21no—
9#89746C412yes—
10#89746C2212yes—
11#89715—21no—
12#89715—21no—
13#89701—21no—
14#89701—21no—
15#89698—21no—
16C7×#324C2212yes—
17C7×#323—21no—
18#89323C2212yes—
19#89320—21no—
20#11510—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×Dic7—21no—
23C22×Dic14—21no—
24C22×Dic14—24no—
25C22×Dic14—42no—
26C22×Dic14—41no—
27C22×Dic14—41no—
28C22×Dic14C2×C412yes—
29C7×#117—41no—
30C7×#117—41no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C7×C22⋊C4D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C22⋊Dic7—21no—
38#6489—42no—
39C2×C4⋊Dic7—21no—
40C2×C4×Dic7C2×C412yes—
41C7×C4⋊C8—41no—
42C7×C22⋊C8—22no—
43C7×#97—41no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C22⋊(C7⋊C8)—22no—
49C4⋊(C7⋊C8)—41no—
50#6377—41no—
51#2310—71no—
52#1464—71no—
53#1464D711yescharacteristic
54#1319—74no—
55C24×C7C22⋊C411yescharacteristic
56C22×C4×C7—22no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—22no—
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×Dic7—24no—
67C22×Dic7—22no—
68C22×Dic7—22no—
69C22×Dic7—42no—
70C22×Dic7—42no—
71C2×Dic14—24no—
72C2×Dic14—22no—
73C2×Dic14—42no—
74C2×Dic14—48no—
75C2×Dic14—48no—
76C2×Dic14—41no—
77C2×Dic14—41no—
78C2×Dic14—42no—
79C2×Dic14—42no—
80C2×Dic14M1614yes—
81C2×C7×C8—42no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C22⋊C4—41no—
85C7×C22⋊C4—41no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C22⋊Dic7—42no—
91C4⋊Dic7—42no—
92C4×Dic7—42no—
93C2×C7⋊C8—42no—
94C23×Q8—71no—
95C2×#117—71no—
96C2×#117C2×D711yescharacteristic
97#432—21no—
98#432—141no—
99#391—72no—
100#391—72no—
101#391—141no—
102#391—141no—
103#381—141no—
104#381—141no—
105#324—72no—
106#324C2×D712yes—
107#323—21no—
108#323—141no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—41no—
112C23×C7—41no—
113C23×C7#10012yes—
114C23×C7C2×C22⋊C411yescharacteristic
115C2×C4×C7—24no—
116C2×C4×C7—24no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
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—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7#9911yescharacteristic
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7C2×M1612yes—
132C2×Dic7—24no—
133C2×Dic7—48no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137C2×Dic7—42no—
138C2×Dic7—42no—
139Dic14—44no—
140Dic14—44no—
141Dic14—44no—
142Dic14—44no—
143C7×C8—82no—
144C7⋊C8—82no—
145C22×Q8—72no—
146C22×Q8—144no—
147C22×Q8—141no—
148C22×Q8—281no—
149C22×Q8—281no—
150C22×Q8—282no—
151C23×C4—141no—
152C23×C4C4×D711yescharacteristic
153#117—41no—
154#117—41no—
155#117—282no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4C4×D711yescharacteristic
158C2×C4⋊C4C22×D711yescharacteristic
159C2×C22⋊C4—141no—
160C2×C22⋊C4D2811yescharacteristic
161C2×C22⋊C4C22⋊D711yescharacteristic
162C2×C42—72no—
163C2×C42D2811yescharacteristic
164C2×C42C22⋊D711yescharacteristic
165C4⋊C8—41no—
166C4⋊C8—281no—
167C22⋊C8—22no—
168C22⋊C8—142no—
169#97—41no—
170#97—281no—
171#95—142no—
172#95—142no—
173#95—142no—
174#95—142no—
175C22×C7—21no—
176C22×C7—21no—
177C22×C7—22no—
178C22×C7—42no—
179C22×C7—42no—
180C22×C7—41no—
181C22×C7—41no—
182C22×C7#40711yescharacteristic
183C22×C7C2×#9911yescharacteristic
184C22×C7C2×#10011yescharacteristic
185C4×C7—21no—
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—41no—
189C4×C7—41no—
190C4×C7—41no—
191C4×C7—41no—
192Dic7—44no—
193Dic7—82no—
194C24(C2×D7)⋊C411yescharacteristic
195C2×Q8—74no—
196C2×Q8—144no—
197C2×Q8—142no—
198C2×Q8—288no—
199C2×Q8—288no—
200C2×Q8—282no—
201C2×Q8—282no—
202C2×Q8—282no—
203C2×Q8—281no—
204C2×Q8—281no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—144no—
210C22×C4—142no—
211C22×C4—142no—
212C22×C4—282no—
213C22×C4—282no—
214C22×C4(C2×D7)⋊C411yescharacteristic
215C22×C4(C2×D7)⋊C411yescharacteristic
216C22×C4(C2×D7)⋊C411yescharacteristic
217C22×C4C2×C4×D711yescharacteristic
218C22×C4C2×D2811yescharacteristic
219C22×C4C2×C22⋊D711yescharacteristic
220C2×C8—42no—
221C2×C8—282no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—282no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—282no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—282no—
233C2×C7—21no—
234C2×C7—21no—
235C2×C7—42no—
236C2×C7#146211yescharacteristic
237C2×C7#212911yescharacteristic
238C2×C7#213511yescharacteristic
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23#639712yes—
244C23C2×(C2×D7)⋊C411yescharacteristic
245Q8—284no—
246Q8—284no—
247Q8—284no—
248Q8—284no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—144no—
264C2×C4—288no—
265C2×C4—282no—
266C2×C4—282no—
267C2×C4—282no—
268C2×C4—282no—
269C2×C4—282no—
270C2×C4#638011yescharacteristic
271C2×C4#638011yescharacteristic
272C2×C4D7×M1612yes—
273C8—82no—
274C8—562no—
275C7#1151011yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22C2×#638011yescharacteristic
284C22#8989811yescharacteristic
285C22C2×#639711yescharacteristic
286C4—22no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—284no—
294C4—562no—
295C2—21no—
296C2—21no—
297C2—42no—
298C2#1172772111yescharacteristic
299C2#1172781311yescharacteristic
300C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1464D7
hypocenterC7#11510
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
4. #11725261C2semidirect
275. C7#11510semidirect

Maximal subgroups

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

subgroupindex
#117396752
C7×#14642
#117293262
#117252612
#115107