Finite Group Databasebeta

← #13263420

Subgroups — #13263420

Order 1792.

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

normal subgroups only

This group has 444 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
1#11739827C211yesmaximal, characteristic
2C7×#1459C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725261C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6499C412yes—
7C2×#6432C411yescharacteristic
8C2×C7×C22⋊C8—21no—
9#89984—21no—
10#89984—21no—
11#89979—21no—
12#89746C2212yes—
13#89725—21no—
14#89725—21no—
15C4×C4⋊Dic7C411yescharacteristic
16C7×#324C2212yes—
17C7×#323—21no—
18#89323C2212yes—
19#89320—21no—
20#11564—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×Dic14C2×C412yes—
25C22×C7×C8—41no—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C7×C22⋊C4D411yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C22⋊Dic7—22no—
34#6499—44no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4×Dic7C2×C412yes—
39C2×#1136—41no—
40#6432—41no—
41#6432—41no—
42C7×C22⋊C8—22no—
43C7×C22⋊C8—41no—
44C7⋊#95—21no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C22⋊(C7⋊C8)—22no—
48C22⋊(C7⋊C8)—41no—
49#2547—71no—
50#1465—71no—
51#1459D711yescharacteristic
52#1319—74no—
53C24×C7C22⋊C411yescharacteristic
54C24×C7C22⋊C411yescharacteristic
55C2×C7×D4—22no—
56C2×C7×D4—22no—
57C2×C7×D4—41no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—42no—
63C22×C4×C7—42no—
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—
71C2×Dic14—24no—
72C2×Dic14—42no—
73C2×Dic14—42no—
74C2×C7×C8—42no—
75C2×C7×C8—82no—
76C7×C4⋊C4—41no—
77C7×C22⋊C4—41no—
78C7×C22⋊C4—41no—
79C42×C7—21no—
80C42×C7—21no—
81C22⋊Dic7—44no—
82C22⋊Dic7—44no—
83C4⋊Dic7—42no—
84C4⋊Dic7—42no—
85C4⋊Dic7—41no—
86C4⋊Dic7—41no—
87C4×Dic7—42no—
88#1136—82no—
89C2×C7⋊C8—42no—
90C2×C4⋊Q8—71no—
91C2×#124—72no—
92C2×C4×D4C2×D711yescharacteristic
93#407—141no—
94C2×C22⋊C8—21no—
95#397—141no—
96#397—141no—
97#391—72no—
98#380—141no—
99#380—141no—
100C4×C4⋊C4—71no—
101#324—72no—
102#324C2×D712yes—
103#323—21no—
104#323—141no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7—21no—
108C23×C7—21no—
109C23×C7—21no—
110C23×C7—41no—
111C23×C7—41no—
112C23×C7—41no—
113C23×C7—41no—
114C23×C7#10012yes—
115C23×C7C2×C22⋊C411yescharacteristic
116C7×D4—44no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—22no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—81no—
129C2×C4×C7—81no—
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7#9911yescharacteristic
132C2×C4×C7#13112yes—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137C2×Dic7—42no—
138C2×Dic7—42no—
139Dic14—84no—
140C7×C8—82no—
141C7⋊C8—82no—
142C22×Q8—72no—
143C22×D4C4×D711yescharacteristic
144C23×C4D2811yescharacteristic
145C23×C4C22⋊D711yescharacteristic
146C2×M16—281no—
147C22×C8—41no—
148C4⋊Q8—281no—
149C4⋊Q8—281no—
150#124—284no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4—141no—
154C2×C4⋊C4—141no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4C22×D711yescharacteristic
157C2×C22⋊C4—142no—
158C2×C22⋊C4—142no—
159C2×C22⋊C4D2811yescharacteristic
160C2×C22⋊C4C22⋊D711yescharacteristic
161C2×C42—72no—
162C2×C42C4×D711yescharacteristic
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—142no—
166C22⋊C8—281no—
167#95—141no—
168#95—142no—
169#95—142no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7—22no—
173C22×C7—42no—
174C22×C7—42no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—41no—
178C22×C7—41no—
179C22×C7—41no—
180C22×C7—81no—
181C22×C7—81no—
182C22×C7#40811yescharacteristic
183C22×C7C2×#9911yescharacteristic
184C22×C7C2×#10011yescharacteristic
185C4×C7—21no—
186C4×C7—22no—
187C4×C7—41no—
188C4×C7—41no—
189C4×C7—41no—
190C4×C7#35412yes—
191Dic7—82no—
192Dic7—82no—
193C24(C2×D7)⋊C411yescharacteristic
194C24(C2×D7)⋊C411yescharacteristic
195C2×Q8—144no—
196C2×Q8—282no—
197C2×Q8—282no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—142no—
208C22×C4—142no—
209C22×C4(C2×D7)⋊C411yescharacteristic
210C22×C4(C2×D7)⋊C411yescharacteristic
211C22×C4C2×C4×D711yescharacteristic
212C22×C4C2×D2811yescharacteristic
213C22×C4C2×C22⋊D711yescharacteristic
214M16—562no—
215C2×C8—42no—
216C2×C8—82no—
217C2×C8—282no—
218C4⋊C4—41no—
219C4⋊C4—282no—
220C4⋊C4—282no—
221C4⋊C4—281no—
222C4⋊C4—281no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—284no—
226C22⋊C4—284no—
227C42—21no—
228C42—21no—
229C42—282no—
230C2×C7—21no—
231C2×C7—21no—
232C2×C7—42no—
233C2×C7—81no—
234C2×C7#147111yescharacteristic
235C2×C7C2×#35411yescharacteristic
236C2×C7#213511yescharacteristic
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23#639712yes—
247C23C2×(C2×D7)⋊C411yescharacteristic
248Q8—564no—
249D4—44no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—282no—
264C2×C4—282no—
265C2×C4—282no—
266C2×C4—282no—
267C2×C4—282no—
268C2×C4—282no—
269C2×C4#638011yescharacteristic
270C2×C4#638011yescharacteristic
271C2×C4#646412yes—
272C8—82no—
273C8—562no—
274C7#1156411yescharacteristic, complemented, Sylow
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22C2×#638011yescharacteristic
288C22#8988211yescharacteristic
289C22C2×#639711yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—562no—
296C4—562no—
297C4#8926812yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2#1172767511yescharacteristic
303C2C2×#8926811yescharacteristic
304C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1459C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1459D7
hypocenterC7#11564
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #11725261C2semidirect
274. C7#11564semidirect

Maximal subgroups

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

subgroupindex
#117398272
C7×#14592
#117293562
#117252612
#115647