Finite Group Databasebeta

← #13264531

Subgroups — #13264531

Order 1792.

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

normal subgroups only

This group has 434 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
1C2×#89758C211yesmaximal, characteristic
2C7×#1463C211yesmaximal, characteristic
3#11729316C211yesmaximal, characteristic
4#11725265C214yesmaximal, complemented
5C22×C7×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic7C411yescharacteristic
7C7×#407—21no—
8C2×C7⋊#95—21no—
9C2×C7⋊#95—21no—
10C2×C7⋊#95C411yescharacteristic
11#89979—21no—
12#89758—21no—
13#89758—21no—
14#89758C412yes—
15#89758C2212yes—
16C7×#324—21no—
17C7×#324C2212yes—
18#89325—21no—
19#89325C2212yes—
20#11814—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×Dic7—21no—
25C23×Dic7—21no—
26C2×C7×M16—41no—
27C2×C7×C4⋊C4—41no—
28C2×C7×C4⋊C4—41no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—41no—
35C2×C4⋊Dic7—41no—
36C2×C4⋊Dic7C2×C412yes—
37C2×#1136—22no—
38C7×C22⋊C8—22no—
39C7×C22⋊C8—41no—
40C7⋊#95—22no—
41C7⋊#95—22no—
42C7⋊#95—21no—
43C7⋊#95—22no—
44C7⋊#95—22no—
45C7⋊#95C2×C412yes—
46C22⋊(C7⋊C8)—41no—
47C22⋊(C7⋊C8)—41no—
48C2×#400—71no—
49#1821—71no—
50#1463D711yescharacteristic
51#1353—74no—
52C24×C7C22⋊C411yescharacteristic
53C22×C4×C7—21no—
54C22×C4×C7—21no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—22no—
60C22×C4×C7—41no—
61C22×C4×C7—42no—
62C22×C4×C7—42no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22×C411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×Dic7—22no—
70C22×Dic7—22no—
71C22×Dic7—42no—
72C22×Dic7—42no—
73C22×Dic7—44no—
74C22×Dic7—42no—
75C22×Dic7—41no—
76C22×Dic7—41no—
77C7×M16—82no—
78C2×C7×C8—42no—
79C7×C4⋊C4—41no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C4⋊Dic7—42no—
84C4⋊Dic7—42no—
85#1136—42no—
86#1136—42no—
87C2×C7⋊C8—42no—
88C22×C4⋊C4—71no—
89C22×C4⋊C4C2×D711yescharacteristic
90#407—21no—
91#407—141no—
92#400—72no—
93#400—72no—
94#400—141no—
95#400—141no—
96C2×#95—71no—
97C2×#95—141no—
98C2×#95—141no—
99#343—72no—
100#343—141no—
101#324—21no—
102#324C2×D712yes—
103C23×C7—22no—
104C23×C7—22no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7#9911yescharacteristic
108C23×C7#9911yescharacteristic
109C23×C7C2×C22⋊C411yescharacteristic
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—42no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—81no—
129C2×C4×C7#13712yes—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—44no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—84no—
136C2×Dic7—82no—
137C2×Dic7—82no—
138C7×C8—82no—
139C7⋊C8—82no—
140C23×C4—141no—
141C23×C4—141no—
142C23×C4C4×D711yescharacteristic
143C23×C4D2811yescharacteristic
144C23×C4C22⋊D711yescharacteristic
145C2×M16—41no—
146C2×M16—142no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—72no—
150C2×C4⋊C4—141no—
151C2×C4⋊C4—281no—
152C2×C4⋊C4—281no—
153C2×C4⋊C4C4×D711yescharacteristic
154C2×C4⋊C4D2811yescharacteristic
155C2×C4⋊C4C22⋊D711yescharacteristic
156C2×C4⋊C4C22×D711yescharacteristic
157C22⋊C8—22no—
158C22⋊C8—41no—
159C22⋊C8—281no—
160C22⋊C8—281no—
161#95—72no—
162#95—141no—
163#95—142no—
164#95—142no—
165#95—142no—
166#95—142no—
167C22×C7—24no—
168C22×C7—24no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7—21no—
175C22×C7#35212yes—
176C22×C7#35512yes—
177C22×C7C2×#9911yescharacteristic
178C22×C7#41911yescharacteristic
179C22×C7#42111yescharacteristic
180C4×C7—22no—
181C4×C7—41no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—41no—
186Dic7—82no—
187Dic7—82no—
188C24(C2×D7)⋊C411yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—142no—
200C22×C4—142no—
201C22×C4—282no—
202C22×C4—282no—
203C22×C4—284no—
204C22×C4—282no—
205C22×C4—281no—
206C22×C4—281no—
207C22×C4(C2×D7)⋊C411yescharacteristic
208C22×C4(C2×D7)⋊C411yescharacteristic
209C22×C4(C2×D7)⋊C411yescharacteristic
210C22×C4C2×C4×D711yescharacteristic
211C22×C4C2×D2811yescharacteristic
212C22×C4C2×C22⋊D711yescharacteristic
213M16—82no—
214M16—282no—
215M16—282no—
216C2×C8—42no—
217C2×C8—282no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—282no—
223C4⋊C4—282no—
224C2×C7—21no—
225C2×C7—22no—
226C2×C7—22no—
227C2×C7—21no—
228C2×C7#151111yescharacteristic
229C2×C7C2×#35211yescharacteristic
230C2×C7C2×#35511yescharacteristic
231C23—21no—
232C23—21no—
233C23—22no—
234C23—22no—
235C23#638011yescharacteristic
236C23#638011yescharacteristic
237C23C2×(C2×D7)⋊C411yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—282no—
258C2×C4—282no—
259C2×C4—284no—
260C2×C4—282no—
261C2×C4—282no—
262C2×C4—564no—
263C2×C4—562no—
264C2×C4—562no—
265C2×C4#647212yes—
266C8—82no—
267C8—562no—
268C7#1181411yescharacteristic, complemented, Sylow
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#8926712yes—
278C22#8927212yes—
279C22C2×#638011yescharacteristic
280C22#8989211yescharacteristic
281C22#8991111yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—562no—
289C4—562no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2—22no—
294C2#1172773511yescharacteristic
295C2C2×#8926711yescharacteristic
296C2C2×#8927211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1463C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1463D7
hypocenterC7#11814
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
268. C7#11814semidirect

Maximal subgroups

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

subgroupindex
C2×#897582
C7×#14632
#117293162
#117252652
#118147