Finite Group Databasebeta

← #13264387

Subgroups — #13264387

Order 1792.

482 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2548C211yesmaximal, characteristic
2C4×#6410C211yesmaximal, characteristic, complemented
3#11729379C211yesmaximal, characteristic, complemented
4#11725453C214yesmaximal, complemented
5C2×C7×#127C411yescharacteristic
6C2×C7×#124—21no—
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#394C412yes—
9C7×#394C2212yes—
10C7×#390—21no—
11C7×#390—21no—
12C7×#390—21no—
13C4×C7×C4⋊C4C411yescharacteristic
14C2×#6410—21no—
15#89698—21no—
16C4×#1136—21no—
17#89325C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11781—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×C7×D4—21no—
23C22×C7×D4—21no—
24C22×C7×D4C2×C412yes—
25C7×#127—41no—
26C7×#127—41no—
27C7×#124—44no—
28C4×C7×Q8—41no—
29C4×C7×Q8—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4C2311yescharacteristic
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4—22no—
38C2×C42×C7—21no—
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×#1136—22no—
43C7×#95C2×C412yes—
44#6410—24no—
45C22⋊(C7⋊C8)—22no—
46C4⋊(C7⋊C8)—41no—
47#6377—41no—
48#6377—41no—
49C4×C7⋊C8—41no—
50#2548D711yescharacteristic
51C4×#101—71no—
52#1467—71no—
53#1345—74no—
54C24×C7—22no—
55C2×C7×Q8—22no—
56C2×C7×Q8—22no—
57C2×C7×Q8—41no—
58C2×C7×D4—42no—
59C2×C7×D4—42no—
60C2×C7×D4—42no—
61C2×C7×D4—42no—
62C2×C7×D4—42no—
63C2×C7×D4—41no—
64C2×C7×D4—41no—
65C2×C7×D4—42no—
66C2×C7×D4—82no—
67C22×C4×C7—22no—
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—42no—
79C7×C22⋊C4—44no—
80C7×C22⋊C4—44no—
81C7×C22⋊C4—82no—
82C7×C22⋊C4—82no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—42no—
90#1136—24no—
91#1136—42no—
92C2×C7⋊C8—42no—
93C2×C7⋊C8—42no—
94C2×#127Dic711yescharacteristic
95C2×#124—21no—
96C2×C4×Q8C2×D711yescharacteristic
97#432—141no—
98C2×#101—141no—
99C4×M16—141no—
100#394Dic712yes—
101#394C2×D712yes—
102#390—21no—
103#390—21no—
104#390—21no—
105C4×C4⋊C4Dic711yescharacteristic
106#343—72no—
107#324—72no—
108#324—141no—
109C23×C7—42no—
110C23×C7—42no—
111C23×C7—42no—
112C23×C7—42no—
113C23×C7—42no—
114C23×C7—42no—
115C23×C7—42no—
116C23×C7C2×C22⋊C411yescharacteristic
117C7×Q8—44no—
118C7×D4—82no—
119C7×D4—84no—
120C7×D4—84no—
121C7×D4—82no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—22no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7#9911yescharacteristic
140C2×C4×C7#9911yescharacteristic
141C2×C4×C7#10412yes—
142C2×C4×C7AGL(1,ℤ/8)12yes—
143C7⋊C8—44no—
144C7⋊C8—82no—
145C22×Q8C22⋊D711yescharacteristic
146C22×D4—21no—
147C22×D4—21no—
148C22×D4C2×Dic712yes—
149C2×M16—142no—
150#127—41no—
151#127—41no—
152#124—44no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×Dic711yescharacteristic
157C2×C4⋊C4C22⋊D711yescharacteristic
158C2×C4⋊C4C22×D711yescharacteristic
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C42—21no—
164C2×C42C2×Dic711yescharacteristic
165C2×C42C22⋊D711yescharacteristic
166C2×C42C22⋊D711yescharacteristic
167C4⋊C8—281no—
168#101—144no—
169C22⋊C8—142no—
170#97—281no—
171#97—281no—
172C4×C8—281no—
173#95C2×Dic712yes—
174C22×C7—21no—
175C22×C7—21no—
176C22×C7—82no—
177C22×C7—82no—
178C22×C7—82no—
179C22×C7—82no—
180C22×C7—82no—
181C22×C7—82no—
182C22×C7—82no—
183C22×C7C2×#9911yescharacteristic
184C22×C7#41811yescharacteristic
185C22×C7C2×#10411yescharacteristic
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—41no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7—82no—
194C4×C7#35512yes—
195C24—22no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8—41no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—42no—
207C2×D4—82no—
208C22×C4—22no—
209C22×C4C22⋊Dic711yescharacteristic
210C22×C4C22⋊Dic711yescharacteristic
211C22×C4C22⋊Dic711yescharacteristic
212C22×C4C22⋊Dic711yescharacteristic
213C22×C4C22×Dic711yescharacteristic
214C22×C4C2×C22⋊D711yescharacteristic
215C22×C4C2×C22⋊D711yescharacteristic
216M16—144no—
217M16—282no—
218C2×C8—282no—
219C2×C8—282no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C22⋊C4—44no—
225C22⋊C4—44no—
226C22⋊C4—82no—
227C22⋊C4—82no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—42no—
235C2×C7—21no—
236C2×C7—21no—
237C2×C7—162no—
238C2×C7#150711yescharacteristic
239C2×C7#212211yescharacteristic
240C2×C7C2×#35511yescharacteristic
241C23—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23C2×C22⋊Dic711yescharacteristic
249Q8—44no—
250D4—84no—
251D4—82no—
252D4—84no—
253D4—82no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4#640811yescharacteristic
272C2×C4#640811yescharacteristic
273C2×C4#641112yes—
274C2×C4#649512yes—
275C8—284no—
276C8—562no—
277C7#1178111yescharacteristic, complemented, Sylow
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—82no—
286C22—82no—
287C22#8998711yescharacteristic
288C22C2×#640811yescharacteristic
289C22C2×#641111yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4#8933712yes—
299C2—21no—
300C2—21no—
301C2—162no—
302C2#1172942711yescharacteristic
303C2C2×#8933711yescharacteristic
304C2#1172961311yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2548C2
socleC22×C7C2×#99
prime radicalC2×C7×#127C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2548D7
hypocenterC7#11781
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. C4×#6410C2semidirect
3. #11729379C2semidirect
4. #11725453C2semidirect
277. C7#11781semidirect

Maximal subgroups

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

subgroupindex
C7×#25482
C4×#64102
#117293792
#117254532
#117817