Finite Group Databasebeta

← #13247290

Subgroups — #13247290

Order 1792.

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

normal subgroups only

This group has 384 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
1#11739674C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic
3#11729326C211yesmaximal, characteristic
4#11725556C212yesmaximal, complemented
5#11725555C212yesmaximal, complemented
6C2×C7×#117C2211yescharacteristic
7C7×#432C2212yes—
8C4×C22⋊Dic7C411yescharacteristic
9C4×C22⋊Dic7C411yescharacteristic
10#89753—21no—
11#89753—21no—
12#89723—21no—
13#89723—21no—
14C4×C4⋊Dic7C2211yescharacteristic
15C4×C4⋊Dic7C2211yescharacteristic
16#89704C411yescharacteristic
17C42×Dic7C411yescharacteristic
18#89698C2212yes—
19C7×#324—21no—
20C7×#323—21no—
21#89323—21no—
22#89320—21no—
23#8745—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C7×#117—22no—
26C7×#117—22no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C22⋊C4D411yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7C2311yescharacteristic
33C2×C22⋊Dic7—21no—
34C2×C22⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4×Dic7—21no—
38C2×C4×Dic7—21no—
39C2×C4×Dic7C2×C411yescharacteristic
40C2×C4×Dic7C2×C411yescharacteristic
41C2×C4×Dic7C2×C411yescharacteristic
42C2×C4×Dic7C2×C411yescharacteristic
43C7×C4⋊C8—22no—
44C7×C22⋊C8—22no—
45C7×#97—22no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C22⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)—22no—
54#6377—22no—
55#2298—71no—
56#1464—71no—
57#1464D711yescharacteristic
58#1285—72no—
59#1285—72no—
60C24×C7C22⋊C411yescharacteristic
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×Dic7—21no—
72C22×Dic7—21no—
73C22×Dic7—21no—
74C22×Dic7—21no—
75C2×C7×C8—42no—
76C7×C4⋊C4—22no—
77C7×C4⋊C4—22no—
78C7×C22⋊C4—22no—
79C7×C22⋊C4—22no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7#4112yes—
83C42×C7#4112yes—
84C22⋊Dic7—42no—
85C22⋊Dic7—42no—
86C4⋊Dic7—42no—
87C4⋊Dic7—42no—
88C4×Dic7—42no—
89C4×Dic7—42no—
90C4×Dic7—41no—
91C4×Dic7—41no—
92C4×Dic7—41no—
93C4×Dic7—41no—
94C2×C7⋊C8—42no—
95C2×#117C2×D711yescharacteristic
96#432—72no—
97#432C2×D712yes—
98#388—141no—
99#388—141no—
100#387—141no—
101#387—141no—
102C4×C4⋊C4—71no—
103C4×C4⋊C4—71no—
104C4×C22⋊C4—71no—
105C4×C22⋊C4—71no—
106#376—71no—
107C43—71no—
108#324—21no—
109#324—141no—
110#323—21no—
111#323—141no—
112C23×C7—21no—
113C23×C7—21no—
114C23×C7—21no—
115C23×C7—41no—
116C23×C7—41no—
117C23×C7C2×C22⋊C411yescharacteristic
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—42no—
128C2×C4×C7—42no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7#11711yescharacteristic
132C2×C4×C7#11711yescharacteristic
133C2×C4×C7#12312yes—
134C2×C4×C7#12312yes—
135C2×Dic7—22no—
136C2×Dic7—22no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C7×C8—82no—
148C7⋊C8—82no—
149C23×C4C4×D711yescharacteristic
150#117—22no—
151#117—22no—
152C2×C4⋊C4—141no—
153C2×C4⋊C4—141no—
154C2×C4⋊C4D2811yescharacteristic
155C2×C4⋊C4C22⋊D711yescharacteristic
156C2×C22⋊C4—141no—
157C2×C22⋊C4—141no—
158C2×C22⋊C4D2811yescharacteristic
159C2×C22⋊C4C22⋊D711yescharacteristic
160C2×C42—71no—
161C2×C42—71no—
162C2×C42—71no—
163C2×C42—71no—
164C2×C42—141no—
165C2×C42—141no—
166C2×C42C4×D711yescharacteristic
167C2×C42C22×D711yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—142no—
170C22⋊C8—22no—
171C22⋊C8—142no—
172#97—22no—
173#97—142no—
174#95—141no—
175#95—141no—
176#95—141no—
177#95—141no—
178#95—141no—
179#95—141no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7—41no—
185C22×C7—81no—
186C22×C7—81no—
187C22×C7#38111yescharacteristic
188C22×C7#41311yescharacteristic
189C22×C7#41311yescharacteristic
190C4×C7—21no—
191C4×C7—21no—
192C4×C7—22no—
193C4×C7—22no—
194C4×C7—41no—
195C4×C7—41no—
196C4×C7—41no—
197Dic7—42no—
198Dic7—42no—
199Dic7—81no—
200Dic7—81no—
201C24(C2×D7)⋊C411yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—141no—
207C22×C4—141no—
208C22×C4—141no—
209C22×C4—141no—
210C22×C4(C2×D7)⋊C411yescharacteristic
211C22×C4(C2×D7)⋊C411yescharacteristic
212C22×C4(C2×D7)⋊C411yescharacteristic
213C22×C4C2×C4×D711yescharacteristic
214C22×C4C2×D2811yescharacteristic
215C22×C4C2×C22⋊D711yescharacteristic
216C2×C8—42no—
217C2×C8—282no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—282no—
221C4⋊C4—282no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—282no—
225C22⋊C4—282no—
226C42—21no—
227C42—21no—
228C42—281no—
229C42—281no—
230C42—281no—
231C42—281no—
232C42—282no—
233C42—282no—
234C42#115912yes—
235C42#115912yes—
236C2×C7—21no—
237C2×C7—21no—
238C2×C7—81no—
239C2×C7#182211yescharacteristic
240C2×C7#182711yescharacteristic
241C2×C7#182711yescharacteristic
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23C2×(C2×D7)⋊C411yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—142no—
262C2×C4—142no—
263C2×C4—281no—
264C2×C4—281no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4#644011yescharacteristic
274C2×C4#644011yescharacteristic
275C2×C4#644912yes—
276C2×C4#649812yes—
277C8—82no—
278C8—562no—
279C7#874511yescharacteristic, complemented, Sylow
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#8971511yescharacteristic
288C22#8990411yescharacteristic
289C22#8990411yescharacteristic
290C4—22no—
291C4—21no—
292C4—21no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—282no—
298C4—282no—
299C4—561no—
300C4—561no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1172772811yescharacteristic
305C2#1172779311yescharacteristic
306C2#1172788511yescharacteristic
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1464C2
socleC22×C7#381
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1464D7
hypocenterC7#8745
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
4. #11725556C2semidirect
5. #11725555C2semidirect
279. C7#8745semidirect

Maximal subgroups

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

subgroupindex
#117396742
C7×#14642
#117293262
#117255562
#117255552
#87457