Finite Group Databasebeta

← #13263452

Subgroups — #13263452

Order 1792.

350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C7×#2565C211yesmaximal, characteristic
2#11729379C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725441C212yesmaximal
5#11725438C212yesmaximal
6C2×C7×#125C411yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#398—21no—
9C7×#398—21no—
10C7×#391C411yescharacteristic
11C7×#391C411yescharacteristic
12C7×#387—21no—
13C7×#387—21no—
14C7×#384C2211yescharacteristic
15C7×#382C2211yescharacteristic
16C4×C7×C4⋊C4C411yescharacteristic
17#89698—21no—
18#89697—21no—
19#89323—21no—
20#89323—21no—
21#89323C2212yes—
22#89323C2212yes—
23#11571—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C7×#125—41no—
26C7×#125—41no—
27C4×C7×Q8—41no—
28C4×C7×Q8—41no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C7×C4⋊C4C2311yescharacteristic
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7C2×C411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C22⋊(C7⋊C8)—22no—
52C22⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)—41no—
54C4⋊(C7⋊C8)—41no—
55#6377—41no—
56C4×C7⋊C8—41no—
57#2565D711yescharacteristic
58#1467—71no—
59#1461—71no—
60#1325—72no—
61#1324—72no—
62C2×C7×Q8—22no—
63C2×C7×Q8—22no—
64C2×C7×Q8—41no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—41no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—42no—
82C7×C4⋊C4—42no—
83C7×C4⋊C4—42no—
84C7×C4⋊C4—42no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7—22no—
94C42×C7—22no—
95C2×C7⋊C8—42no—
96C2×C7⋊C8—42no—
97C2×#125Dic711yescharacteristic
98C2×C4×Q8C2×D711yescharacteristic
99#432—141no—
100#431—141no—
101#398—21no—
102#398—21no—
103#391Dic711yescharacteristic
104#391Dic711yescharacteristic
105#387—21no—
106#387—21no—
107#384C2×D711yescharacteristic
108#382C2×D711yescharacteristic
109C4×C4⋊C4Dic711yescharacteristic
110#324—72no—
111#324—72no—
112#324—141no—
113#324—141no—
114C23×C7C2×C22⋊C411yescharacteristic
115C7×Q8—44no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—22no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—42no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7#9911yescharacteristic
142C2×C4×C7#9911yescharacteristic
143C2×C4×C7#10112yes—
144C2×C4×C7#13112yes—
145C7⋊C8—82no—
146C7⋊C8—82no—
147C22×Q8C2×Dic711yescharacteristic
148#125—41no—
149#125—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×Dic711yescharacteristic
158C2×C4⋊C4C2×Dic711yescharacteristic
159C2×C4⋊C4C22⋊D711yescharacteristic
160C2×C4⋊C4C22⋊D711yescharacteristic
161C2×C4⋊C4C22×D711yescharacteristic
162C2×C42C2×Dic711yescharacteristic
163C2×C42C2×Dic711yescharacteristic
164C2×C42C2×Dic711yescharacteristic
165C2×C42C22⋊D711yescharacteristic
166C2×C42C22⋊D711yescharacteristic
167C4⋊C8—281no—
168C4⋊C8—281no—
169C22⋊C8—142no—
170C22⋊C8—142no—
171#97—281no—
172C4×C8—281no—
173#95—21no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—21no—
179#95—21no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7#40811yescharacteristic
183C22×C7C2×#9911yescharacteristic
184C22×C7C2×#10111yescharacteristic
185C4×C7—21no—
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—42no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7—41no—
194C4×C7—81no—
195C4×C7—81no—
196C4×C7—81no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—41no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4C22⋊Dic711yescharacteristic
205C22×C4C22⋊Dic711yescharacteristic
206C22×C4C22⋊Dic711yescharacteristic
207C22×C4C22⋊Dic711yescharacteristic
208C22×C4C22×Dic711yescharacteristic
209C22×C4C2×C22⋊D711yescharacteristic
210C22×C4C2×C22⋊D711yescharacteristic
211C2×C8—282no—
212C2×C8—282no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—22no—
231C42—22no—
232C2×C7—21no—
233C2×C7—21no—
234C2×C7#147211yescharacteristic
235C2×C7#212611yescharacteristic
236C2×C7#213311yescharacteristic
237C23C2×C22⋊Dic711yescharacteristic
238Q8—44no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4#640811yescharacteristic
265C2×C4#640811yescharacteristic
266C2×C4#641012yes—
267C2×C4#651112yes—
268C8—562no—
269C8—562no—
270C7#1157111yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22C2×#640811yescharacteristic
274C22C2×#641011yescharacteristic
275C22#9000611yescharacteristic
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#1172944511yescharacteristic
291C2#1172957311yescharacteristic
292C2#1172962611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2565C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2565D7
hypocenterC7#11571
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2565

Complements

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

NH ≅ G/Ntype
270. C7#11571semidirect

Maximal subgroups

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

subgroupindex
C7×#25652
#117293792
#117293782
#117254412
#117254382
#115717