Finite Group Databasebeta

← #13249521

Subgroups — #13249521

Order 1792.

694 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 139 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×C7×#376C211yesmaximal, characteristic
2#11739520C211yesmaximal, characteristic
3#11729285C211yesmaximal, characteristic
4C2×#89247C212yesmaximal
5#11725418C212yesmaximal
6C22×C42×C7—21no—
7C22×C42×C7C2211yescharacteristic
8C2×#6487C2211yescharacteristic
9C7×#376—24no—
10C2×C7×#95—21no—
11C2×C7×#95C2212yes—
12#89984C2211yescharacteristic
13#89983—21no—
14#89982—21no—
15C2×C22⋊(C7⋊C8)C2212yes—
16#89705—22no—
17#89701C412yescomplemented
18#89700C412yescomplemented
19#89319—22no—
20#89247—24no—
21#9145—71nomaximal, Sylow
22C23×C4×C7—22no—
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C22×Dic14C2×C411yescharacteristic
27C2×C42×C7—28no—
28C2×C42×C7—24no—
29C2×C42×C7—22no—
30C2×C42×C7—22no—
31C2×C42×C7C2×C412yes—
32C2×C42×C7D412yes—
33C2×C22⋊Dic7—21no—
34C2×C22⋊Dic7—21no—
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×C4⋊Dic7C2×C412yes—
37#6487—22no—
38#6487—22no—
39C2×Dic7⋊C4—22no—
40C2×Dic7⋊C4—21no—
41C22×C7⋊C8—22no—
42C7×#95—24no—
43C7×#95—22no—
44C7×#95D414yes—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C7⋊#95—21no—
49C22⋊(C7⋊C8)—22no—
50C22⋊(C7⋊C8)—22no—
51#2855—71no—
52C2×#376D711yescharacteristic
53#1817—71no—
54C2×#328—72no—
55#1294—72no—
56C24×C7C2×D411yescharacteristic
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—24no—
60C22×C4×C7—28no—
61C22×C4×C7—21no—
62C22×C4×C7—24no—
63C22×C4×C7—21no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—42no—
67C22×C4×C7—44no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7C22⋊C412yes—
71C22×C4×C7C22⋊C412yes—
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D412yes—
75C22×C4×C7#4112yes—
76C22×Dic7—22no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C2×Dic14—22no—
80C2×Dic14—42no—
81C42×C7—216no—
82C42×C7—24no—
83C42×C7—24no—
84C22⋊Dic7—41no—
85C22⋊Dic7—41no—
86C22⋊Dic7—42no—
87C4⋊Dic7—22no—
88C4⋊Dic7—42no—
89Dic7⋊C4—44no—
90Dic7⋊C4—42no—
91C2×C7⋊C8—44no—
92C2×C7⋊C8—42no—
93C2×C22⋊Q8—71no—
94C22×C42—21no—
95C22×C42C2×D711yescharacteristic
96C2×C22⋊C8—72no—
97#391—72no—
98#389—72no—
99#387—142no—
100#385—141no—
101#381—141no—
102#380—71no—
103#376—24no—
104C2×#95—21no—
105C2×#95C2×D712yes—
106#336—142no—
107#328—144no—
108C23×C7—22no—
109C23×C7—22no—
110C23×C7C2×C22⋊C411yescharacteristic
111C23×C7#12011yescharacteristic
112C23×C7#12311yescharacteristic
113C23×C7#13512yes—
114C23×C7#13712yes—
115C2×C4×C7—24no—
116C2×C4×C7—24no—
117C2×C4×C7—22no—
118C2×C4×C7—22no—
119C2×C4×C7—22no—
120C2×C4×C7—22no—
121C2×C4×C7—28no—
122C2×C4×C7—22no—
123C2×C4×C7—22no—
124C2×C4×C7—22no—
125C2×C4×C7—42no—
126C2×C4×C7—42no—
127C2×C4×C7—44no—
128C2×C4×C7—48no—
129C2×C4×C7—48no—
130C2×C4×C7—42no—
131C2×C4×C7—44no—
132C2×C4×C7—42no—
133C2×C4×C7#10414yes—
134C2×C4×C7C4×D412yes—
135C2×C4×C7#12112yes—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—42no—
139C2×Dic7—42no—
140C2×Dic7—42no—
141C2×Dic7—42no—
142C2×Dic7—42no—
143Dic14—82no—
144C7⋊C8—82no—
145C22×Q8—71no—
146C23×C4—22no—
147C23×C4C22⋊D711yescharacteristic
148C23×C4C22⋊D711yescharacteristic
149C23×C4C22×D711yescharacteristic
150C22×C8—142no—
151C22⋊Q8—142no—
152C22⋊Q8—142no—
153C2×C4⋊C4—71no—
154C2×C4⋊C4—72no—
155C2×C4⋊C4—142no—
156C2×C4⋊C4—141no—
157C2×C22⋊C4—141no—
158C2×C22⋊C4—141no—
159C2×C42—24no—
160C2×C42—28no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42C4×D712yes—
164C2×C42D2812yes—
165C22⋊C8—142no—
166C22⋊C8—142no—
167#95—24no—
168#95—22no—
169#95—142no—
170#95—142no—
171#95—142no—
172#95—141no—
173#95C22⋊D714yes—
174C22×C7—21no—
175C22×C7—21no—
176C22×C7—21no—
177C22×C7—21no—
178C22×C7—24no—
179C22×C7—24no—
180C22×C7#38611yescharacteristic
181C22×C7#41012yes—
182C22×C7#41611yescharacteristic
183C22×C7#41911yescharacteristic
184C22×C7C2×#10412yes—
185C22×C7#45212yes—
186C22×C7#48512yes—
187C4×C7—24no—
188C4×C7—22no—
189C4×C7—22no—
190C4×C7—48no—
191C4×C7—42no—
192Dic7—81no—
193Dic7—81no—
194Dic7—82no—
195C24C2×C22⋊D711yescharacteristic
196C2×Q8—142no—
197C2×Q8—282no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—28no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—42no—
208C22×C4—44no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—142no—
212C22×C4—141no—
213C22×C4—141no—
214C22×C4(C2×D7)⋊C412yes—
215C22×C4(C2×D7)⋊C412yes—
216C22×C4C2×C4×D711yescharacteristic
217C22×C4C2×D2811yescharacteristic
218C22×C4#115712yes—
219C22×C4C2×C22⋊D712yes—
220C2×C8—284no—
221C2×C8—282no—
222C4⋊C4—142no—
223C4⋊C4—282no—
224C4⋊C4—282no—
225C4⋊C4—284no—
226C22⋊C4—281no—
227C22⋊C4—282no—
228C22⋊C4—281no—
229C42—216no—
230C42—24no—
231C42—24no—
232C2×C7—22no—
233C2×C7—22no—
234C2×C7#150012yes—
235C2×C7#150612yes—
236C2×C7#187311yescharacteristic
237C2×C7#189611yescharacteristic
238C2×C7#189911yescharacteristic
239C23—22no—
240C23—22no—
241C23C2×(C2×D7)⋊C411yescharacteristic
242C23#649211yescharacteristic
243C23#651312yes—
244C23#651412yes—
245C23#651611yescharacteristic
246Q8—562no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—28no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—48no—
260C2×C4—48no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—282no—
266C2×C4—282no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—282no—
270C2×C4—282no—
271C2×C4—282no—
272C2×C4#637914yes—
273C2×C4C4×C22⋊D712yes—
274C2×C4#649312yes—
275C8—562no—
276C7#914511yescharacteristic, complemented, Sylow
277C22—24no—
278C22—24no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22C2×#637912yes—
284C22#8976812yes—
285C22#8977411yescharacteristic
286C22#8977611yescharacteristic
287C22#8977812yes—
288C22#8998511yescharacteristic
289C22#9001112yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—48no—
294C4—42no—
295C4—562no—
296C4—561no—
297C4—561no—
298C2—22no—
299C2—22no—
300C2#1172718512yes—
301C2#1172718712yes—
302C2#1172928611yescharacteristic
303C2#1172933911yescharacteristic
304C2#1172934911yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#376C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC2×#376D7
hypocenterC7#9145
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
17. #89701C4semidirect
18. #89700C4semidirect
276. C7#9145semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3762
#117395202
#117292852
C2×#892472
#117254182
#91457