Finite Group Databasebeta

← #13263328

Subgroups — #13263328

Order 1792.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#11739699C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic
3#11729325C211yesmaximal, characteristic
4#11725253C212yesmaximal
5#11725251C212yesmaximal
6C2×C7×#117C2211yescharacteristic
7C22×Dic7⋊C4C411yescharacteristic
8C7×#432—21no—
9#89983C411yescharacteristic
10#89754—21no—
11#89752—21no—
12#89718C411yescharacteristic
13#89718C2211yescharacteristic
14#89715C411yescharacteristic
15#89715C2211yescharacteristic
16#89705—21no—
17#89705—21no—
18#89697—21no—
19C7×#324—21no—
20C7×#323C2212yes—
21#89323—21no—
22#89320C2212yes—
23#11544—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×Dic7C2×C411yescharacteristic
26C23×Dic7C2×C411yescharacteristic
27C7×#117—41no—
28C7×#117—41no—
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C22⋊C4C2×C411yescharacteristic
32C2×C7×C22⋊C4C2311yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C22⋊Dic7C2×C411yescharacteristic
36C2×C22⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—41no—
42C2×Dic7⋊C4—41no—
43C7×C4⋊C8—41no—
44C7×C22⋊C8—22no—
45C7×#97—41no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C22⋊(C7⋊C8)—22no—
55C4⋊(C7⋊C8)—41no—
56C4×C7⋊C8—41no—
57#2484—71no—
58#1464D711yescharacteristic
59#1458—71no—
60#1326—72no—
61#1317—72no—
62C24×C7C22×C411yescharacteristic
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—22no—
78C22×Dic7—42no—
79C22×Dic7—41no—
80C22×Dic7—41no—
81C22×Dic7—41no—
82C2×C7×C8—42no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C22⋊C4—41no—
86C7×C22⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C22⋊Dic7—22no—
92C22⋊Dic7—41no—
93Dic7⋊C4—42no—
94Dic7⋊C4—42no—
95Dic7⋊C4—42no—
96Dic7⋊C4—41no—
97Dic7⋊C4—41no—
98C2×C7⋊C8—42no—
99C2×#117C2×D711yescharacteristic
100C22×C4⋊C4—71no—
101#432—21no—
102#431—141no—
103#400—141no—
104#398—141no—
105#387—141no—
106#387—141no—
107#385—71no—
108#385—71no—
109#381—71no—
110#381—71no—
111#381—71no—
112#324—21no—
113#324—141no—
114#323—72no—
115#323C2×D712yes—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—41no—
119C23×C7—41no—
120C23×C7C2×C22⋊C411yescharacteristic
121C23×C7#13112yes—
122C2×C4×C7—21no—
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—21no—
130C2×C4×C7—21no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#9911yescharacteristic
139C2×Dic7—22no—
140C2×Dic7—41no—
141C2×Dic7—42no—
142C2×Dic7—41no—
143C2×Dic7—42no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—82no—
154C7×C8—82no—
155C7⋊C8—82no—
156C23×C4—71no—
157C23×C4—71no—
158C23×C4C4×D711yescharacteristic
159#117—41no—
160#117—41no—
161C2×C4⋊C4—141no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—281no—
166C2×C4⋊C4—281no—
167C2×C4⋊C4D2811yescharacteristic
168C2×C4⋊C4C22⋊D711yescharacteristic
169C2×C22⋊C4—71no—
170C2×C22⋊C4—71no—
171C2×C22⋊C4C4×D711yescharacteristic
172C2×C22⋊C4C22×D711yescharacteristic
173C2×C42D2811yescharacteristic
174C2×C42C22⋊D711yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—281no—
177C22⋊C8—22no—
178C22⋊C8—142no—
179#97—41no—
180C4×C8—281no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185#95—141no—
186#95—141no—
187#95—141no—
188#95—141no—
189C22×C7—21no—
190C22×C7—21no—
191C22×C7—22no—
192C22×C7—42no—
193C22×C7—42no—
194C22×C7—41no—
195C22×C7—41no—
196C22×C7#40811yescharacteristic
197C22×C7C2×#9911yescharacteristic
198C22×C7#41311yescharacteristic
199C4×C7—21no—
200C4×C7—21no—
201C4×C7—41no—
202C4×C7—41no—
203C4×C7—41no—
204C4×C7—41no—
205C4×C7—41no—
206Dic7—42no—
207Dic7—81no—
208Dic7—81no—
209Dic7—81no—
210C24C2×C4×D711yescharacteristic
211C22×C4—22no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—141no—
216C22×C4—141no—
217C22×C4—141no—
218C22×C4—141no—
219C22×C4—142no—
220C22×C4—282no—
221C22×C4—281no—
222C22×C4—281no—
223C22×C4—281no—
224C22×C4(C2×D7)⋊C411yescharacteristic
225C22×C4(C2×D7)⋊C411yescharacteristic
226C22×C4(C2×D7)⋊C411yescharacteristic
227C22×C4(C2×D7)⋊C411yescharacteristic
228C22×C4C2×D2811yescharacteristic
229C22×C4C2×C22⋊D711yescharacteristic
230C2×C8—42no—
231C2×C8—282no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—282no—
235C4⋊C4—282no—
236C4⋊C4—282no—
237C4⋊C4—281no—
238C4⋊C4—281no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—142no—
242C22⋊C4—281no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C2×C7—21no—
248C2×C7—21no—
249C2×C7—42no—
250C2×C7#146811yescharacteristic
251C2×C7#212011yescharacteristic
252C2×C7#212311yescharacteristic
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23#647012yes—
258C23C2×(C2×D7)⋊C411yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—142no—
275C2×C4—281no—
276C2×C4—282no—
277C2×C4—281no—
278C2×C4—282no—
279C2×C4—281no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—281no—
284C2×C4—281no—
285C2×C4—281no—
286C2×C4—281no—
287C2×C4—281no—
288C2×C4—562no—
289C2×C4#638011yescharacteristic
290C2×C4#638011yescharacteristic
291C8—82no—
292C8—562no—
293C7#1154411yescharacteristic, complemented, Sylow
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C2×#638011yescharacteristic
302C22#8990111yescharacteristic
303C22#8990411yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—282no—
312C4—561no—
313C4—561no—
314C4—561no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1172772311yescharacteristic
319C2#1172781211yescharacteristic
320C2#1172789911yescharacteristic
subgroupG/H
centerC22C2×#6380
commutator, prime radicalC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
cosocleC2×C7×C22⋊C4C23
hypercenter#1464D7
hypocenterC7#11544
LCSG ▷ C24×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
293. C7#11544semidirect

Maximal subgroups

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

subgroupindex
#117396992
C7×#14642
#117293252
#117252532
#117252512
#115447