Finite Group Databasebeta

← #13247205

Subgroups — #13247205

Order 1792.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#11731593C211yesmaximal, characteristic
2#11727561C212yesmaximal
3C7×#1295C211yesmaximal, characteristic, complemented
4#11725465C212yesmaximal, complemented
5#11725436C211yesmaximal, characteristic, complemented
6C2×#6455C411yescharacteristic
7C2×#6455C411yescharacteristic
8C2×C42×D7C2211yescharacteristic
9C2×C7×#97C2212yes—
10C7×#382C2211yescharacteristic
11C2×(C2×D7)⋊C8—22no—
12#89748C411yescharacteristic
13#89748C411yescharacteristic
14#89708C2211yescharacteristic
15C2×#6377C2212yes—
16#89439—22no—
17#89421—22no—
18#89345—22no—
19#8721—71nomaximal, Sylow
20C22×C4×D7C2×C411yescharacteristic
21C22×C4×D7D412yes—
22C22×C7×C8—22no—
23C2×C7×C4⋊C4C2×C411yescharacteristic
24C2×C7×C4⋊C4C2×C411yescharacteristic
25C2×C42×C7C2311yescharacteristic
26C2×(C2×D7)⋊C4—21no—
27C2×(C2×D7)⋊C4—21no—
28C2×C4⋊Dic7C2×C411yescharacteristic
29C2×C4⋊Dic7C2×C411yescharacteristic
30C2×Dic7⋊C4—22no—
31C2×Dic7⋊C4—22no—
32C2×C4×Dic7—21no—
33C2×C4×Dic7—21no—
34C2×C4×Dic7C2×C411yescharacteristic
35C2×C4×Dic7D412yes—
36C22×C7⋊C8—22no—
37#6455—42no—
38#6455—42no—
39C42×D7—22no—
40C42×D7—21no—
41C42×D7—21no—
42C7×#97—22no—
43C7×#97—22no—
44C7×#95—22no—
45C7⋊#95—22no—
46(C2×D7)⋊C8—28no—
47#6377—22no—
48#6377—22no—
49#2285—71no—
50#1749—72no—
51#1295—72no—
52#1295—71no—
53#1295D711yescharacteristic, complemented
54C23×D7C22⋊C411yescharacteristic
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7C22×C411yescharacteristic
58C22×C4×C7C2×D412yes—
59C22×Dic7—21no—
60C22×Dic7—21no—
61C22×Dic7C22⋊C411yescharacteristic
62C22×Dic7C22⋊C412yes—
63C2×C4×D7—22no—
64C2×C4×D7—21no—
65C2×C4×D7—21no—
66C2×C4×D7—22no—
67C2×C4×D7—22no—
68C2×C4×D7—22no—
69C2×C4×D7—24no—
70C2×C4×D7—42no—
71C2×C7×C8—24no—
72C2×C7×C8—42no—
73C2×C7×C8—42no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—41no—
76C42×C7#4112yes—
77C42×C7#4111yescharacteristic
78C42×C7#4111yescharacteristic
79(C2×D7)⋊C4—42no—
80(C2×D7)⋊C4—42no—
81C4⋊Dic7—41no—
82C4⋊Dic7—41no—
83Dic7⋊C4—44no—
84Dic7⋊C4—44no—
85C4×Dic7—21no—
86C4×Dic7—21no—
87C4×Dic7—22no—
88C4×Dic7—22no—
89C4×Dic7—42no—
90C4×Dic7—42no—
91C2×C7⋊C8—24no—
92C2×C7⋊C8—42no—
93C2×C7⋊C8—42no—
94C2×#117—71no—
95C2×#117—71no—
96C22×C42—71no—
97C2×C22⋊C8—142no—
98C2×#97—72no—
99C2×#97C2×D712yes—
100#384—71no—
101#384—71no—
102#382—71no—
103#382C2×D711yescharacteristic
104#380—142no—
105C4×C4⋊C4—142no—
106#336—142no—
107C23×C7C2×C22⋊C411yescharacteristic
108C22×D7—21no—
109C22×D7—21no—
110C22×D7—22no—
111C22×D7—22no—
112C22×D7#10112yes—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—22no—
116C2×C4×C7—22no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—42no—
120C2×C4×C7—42no—
121C2×C4×C7#11711yescharacteristic
122C2×C4×C7#11711yescharacteristic
123C2×C4×C7#12312yes—
124C2×C4×C7#12312yes—
125C2×Dic7—21no—
126C2×Dic7—22no—
127C2×Dic7—21no—
128C2×Dic7—22no—
129C2×Dic7—41no—
130C2×Dic7—41no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7#10012yes—
134C2×Dic7#10414yes—
135C4×D7—24no—
136C4×D7—24no—
137C4×D7—44no—
138C4×D7—44no—
139C7×C8—44no—
140C7⋊C8—44no—
141C23×C4—71no—
142C23×C4—72no—
143C22×C8—22no—
144C22×C8—142no—
145#117—282no—
146#117—282no—
147C2×C4⋊C4—71no—
148C2×C4⋊C4—71no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4—142no—
151C2×C4⋊C4C4×D711yescharacteristic
152C2×C4⋊C4C4×D711yescharacteristic
153C2×C22⋊C4—141no—
154C2×C22⋊C4—141no—
155C2×C42—71no—
156C2×C42—72no—
157C2×C42—142no—
158C2×C42—141no—
159C2×C42—141no—
160C2×C42—141no—
161C2×C42—141no—
162C2×C42C22×D711yescharacteristic
163C22⋊C8—148no—
164#97—22no—
165#97—22no—
166#97—142no—
167#97—142no—
168#95—22no—
169#95—142no—
170C22×C7#38111yescharacteristic
171C22×C7C2×#10011yescharacteristic
172C22×C7C2×#10111yescharacteristic
173C22×C7C2×#10412yes—
174C22×C7#42112yes—
175C2×D7—22no—
176C2×D7—24no—
177C2×D7—41no—
178C2×D7—42no—
179C2×D7—41no—
180C4×C7—21no—
181C4×C7—21no—
182C4×C7—22no—
183C4×C7—22no—
184C4×C7—81no—
185C4×C7—81no—
186Dic7—22no—
187Dic7—24no—
188Dic7—81no—
189Dic7—81no—
190C24—71no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—71no—
194C22×C4—72no—
195C22×C4—142no—
196C22×C4—144no—
197C22×C4—142no—
198C22×C4—141no—
199C22×C4—141no—
200C22×C4—142no—
201C22×C4—142no—
202C22×C4—141no—
203C22×C4—141no—
204C22×C4—282no—
205C22×C4C2×C4×D711yescharacteristic
206C22×C4D4×D712yes—
207C2×C8—24no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—144no—
211C2×C8—282no—
212C2×C8—282no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—281no—
216C4⋊C4—281no—
217C4⋊C4—284no—
218C4⋊C4—284no—
219C22⋊C4—282no—
220C22⋊C4—282no—
221C42—141no—
222C42—142no—
223C42—141no—
224C42—142no—
225C42—282no—
226C42—282no—
227C42#115712yes—
228C42#115911yescharacteristic
229C42#116111yescharacteristic
230C2×C7#152511yescharacteristic
231C2×C7#153112yes—
232C2×C7#153611yescharacteristic
233C2×C7#182111yescharacteristic
234C2×C7#182612yes—
235D7—42no—
236C23—72no—
237C23—141no—
238C23—141no—
239C23—142no—
240C23—142no—
241C23D7×C22⋊C411yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—72no—
251C2×C4—74no—
252C2×C4—144no—
253C2×C4—144no—
254C2×C4—141no—
255C2×C4—142no—
256C2×C4—141no—
257C2×C4—142no—
258C2×C4—284no—
259C2×C4—284no—
260C2×C4—281no—
261C2×C4—281no—
262C2×C4—282no—
263C2×C4—282no—
264C2×C4#643511yescharacteristic
265C2×C4#644612yes—
266C2×C4#645511yescharacteristic
267C2×C4#645712yes—
268C8—44no—
269C8—284no—
270C7#872111yescharacteristic, complemented, Sylow
271C22—144no—
272C22—142no—
273C22—281no—
274C22—281no—
275C22—282no—
276C22#8943611yescharacteristic
277C22D7×#10011yescharacteristic
278C22D7×#10111yescharacteristic
279C22D7×#10412yes—
280C22#8959312yes—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—81no—
286C4—81no—
287C4—142no—
288C4—144no—
289C4—561no—
290C4—561no—
291C2—282no—
292C2#1172609611yescharacteristic
293C2#1172610311yescharacteristic
294C2#1172611912yes—
295C2#1172650812yes—
296C2#1172674411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1295D7
hypocenterC7#8721
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. C7×#1295C2semidirect
4. #11725465C2semidirect
5. #11725436C2semidirect
53. #1295D7semidirect
270. C7#8721semidirect

Maximal subgroups

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

subgroupindex
#117315932
#117275612
C7×#12952
#117254652
#117254362
#87217