Finite Group Databasebeta

← #13249559

Subgroups — #13249559

Order 1792.

586 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 127 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#11739520C211yesmaximal, characteristic
2C2×#89709C211yesmaximal, characteristic
3C7×#1817C211yesmaximal, characteristic
4C2×#89262C212yesmaximal
5#11725481C212yesmaximal
6C22×C42×C7C2211yescharacteristic
7C2×#6487C2211yescharacteristic
8C2×C7×C22⋊C8C2212yes—
9#89984C2211yescharacteristic
10#89983—21no—
11#89982—21no—
12C2×C7⋊#95—21no—
13C2×C7⋊#95—21no—
14C2×C7⋊#95C2212yes—
15#89709—24no—
16#89705—22no—
17#89701C412yescomplemented
18#89700C412yescomplemented
19C7×#336—22no—
20#89262—24no—
21#9153—71nomaximal, Sylow
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7C2311yescharacteristic
25C23×Dic7—22no—
26C22×Dic14C2×C411yescharacteristic
27C22×C7×C8—22no—
28C2×C42×C7—22no—
29C2×C42×C7—22no—
30C2×C42×C7C2×C412yes—
31C2×C42×C7D412yes—
32C2×C22⋊Dic7—21no—
33C2×C22⋊Dic7—21no—
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C412yes—
36#6487—22no—
37#6487—22no—
38C2×Dic7⋊C4—22no—
39C2×Dic7⋊C4—21no—
40C7×C22⋊C8—22no—
41C7×C22⋊C8—22no—
42C7⋊#95—24no—
43C7⋊#95—24no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—21no—
48C7⋊#95—22no—
49C7⋊#95D414yes—
50#2855—71no—
51C2×#383—71no—
52#1817D711yescharacteristic
53C2×#328—72no—
54#1294—72no—
55C24×C7C2×D411yescharacteristic
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7—42no—
63C22×C4×C7—42no—
64C22×C4×C7C22⋊C412yes—
65C22×C4×C7C22⋊C412yes—
66C22×C4×C7C22×C411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D412yes—
69C22×C4×C7#4112yes—
70C22×Dic7—22no—
71C22×Dic7—21no—
72C22×Dic7—21no—
73C22×Dic7—24no—
74C22×Dic7—44no—
75C22×Dic7—44no—
76C22×Dic7—42no—
77C22×Dic7—42no—
78C2×Dic14—22no—
79C2×Dic14—42no—
80C2×C7×C8—44no—
81C2×C7×C8—42no—
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×C22⋊Q8—71no—
92C22×C42C2×D711yescharacteristic
93C2×C22⋊C8C2×D712yes—
94#391—72no—
95#389—72no—
96#387—142no—
97#385—141no—
98#383—144no—
99#381—141no—
100#380—71no—
101C2×#95—72no—
102C2×#95—141no—
103C2×#95—141no—
104#336—22no—
105#328—144no—
106C23×C7—22no—
107C23×C7—22no—
108C23×C7C2×C22⋊C411yescharacteristic
109C23×C7#12011yescharacteristic
110C23×C7#12311yescharacteristic
111C23×C7#13512yes—
112C23×C7#13712yes—
113C2×C4×C7—22no—
114C2×C4×C7—22no—
115C2×C4×C7—22no—
116C2×C4×C7—22no—
117C2×C4×C7—22no—
118C2×C4×C7—22no—
119C2×C4×C7—22no—
120C2×C4×C7—22no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—42no—
127C2×C4×C7C4×D412yes—
128C2×C4×C7#12112yes—
129C2×Dic7—44no—
130C2×Dic7—44no—
131C2×Dic7—41no—
132C2×Dic7—41no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137C2×Dic7—42no—
138C2×Dic7—44no—
139C2×Dic7—84no—
140C2×Dic7—84no—
141Dic14—82no—
142C7×C8—82no—
143C22×Q8—71no—
144C23×C4—142no—
145C23×C4D2811yescharacteristic
146C23×C4D2811yescharacteristic
147C23×C4C22×D711yescharacteristic
148C22×C8—22no—
149C22⋊Q8—142no—
150C22⋊Q8—142no—
151C2×C4⋊C4—71no—
152C2×C4⋊C4—72no—
153C2×C4⋊C4—142no—
154C2×C4⋊C4—141no—
155C2×C22⋊C4—141no—
156C2×C22⋊C4—141no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42C4×D712yes—
160C2×C42C22⋊D712yes—
161C22⋊C8—22no—
162C22⋊C8—22no—
163#95—74no—
164#95—144no—
165#95—144no—
166#95—142no—
167#95—142no—
168#95—142no—
169#95—142no—
170#95—141no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7—21no—
175C22×C7—24no—
176C22×C7—24no—
177C22×C7#38611yescharacteristic
178C22×C7#41012yes—
179C22×C7#41611yescharacteristic
180C22×C7#41911yescharacteristic
181C22×C7#42112yes—
182C22×C7#45212yes—
183C22×C7#48512yes—
184C4×C7—22no—
185C4×C7—22no—
186C4×C7—42no—
187C4×C7—42no—
188Dic7—84no—
189Dic7—81no—
190Dic7—81no—
191Dic7—82no—
192C24C2×D2811yescharacteristic
193C2×Q8—142no—
194C2×Q8—282no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—144no—
204C22×C4—142no—
205C22×C4—141no—
206C22×C4—141no—
207C22×C4—284no—
208C22×C4—284no—
209C22×C4—282no—
210C22×C4—282no—
211C22×C4(C2×D7)⋊C412yes—
212C22×C4(C2×D7)⋊C412yes—
213C22×C4C2×C4×D711yescharacteristic
214C22×C4D4×D712yes—
215C22×C4#115912yes—
216C22×C4C2×C22⋊D711yescharacteristic
217C2×C8—44no—
218C2×C8—42no—
219C4⋊C4—142no—
220C4⋊C4—282no—
221C4⋊C4—284no—
222C4⋊C4—282no—
223C22⋊C4—281no—
224C22⋊C4—281no—
225C22⋊C4—282no—
226C42—24no—
227C42—24no—
228C2×C7—22no—
229C2×C7—22no—
230C2×C7#151512yes—
231C2×C7#152112yes—
232C2×C7#187311yescharacteristic
233C2×C7#189711yescharacteristic
234C2×C7#189911yescharacteristic
235C23—22no—
236C23—22no—
237C23#644511yescharacteristic
238C23#644911yescharacteristic
239C23#646712yes—
240C23#647212yes—
241C23C2×(C2×D7)⋊C411yescharacteristic
242Q8—562no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—284no—
258C2×C4—284no—
259C2×C4—282no—
260C2×C4—282no—
261C2×C4—282no—
262C2×C4—281no—
263C2×C4—281no—
264C2×C4—284no—
265C2×C4—282no—
266C2×C4—282no—
267C2×C4—564no—
268C2×C4—564no—
269C2×C4(C22⋊D7)⋊C412yes—
270C2×C4#650212yes—
271C8—82no—
272C7#915311yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22—24no—
276C22—21no—
277C22—21no—
278C22—24no—
279C22#8949512yes—
280C22#8950512yes—
281C22#8973011yescharacteristic
282C22#8977812yes—
283C22#8988511yescharacteristic
284C22#8989211yescharacteristic
285C22#8991112yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—564no—
291C4—561no—
292C4—562no—
293C4—561no—
294C2—22no—
295C2—22no—
296C2#1172728911yescharacteristic
297C2#1172768511yescharacteristic
298C2#1172772011yescharacteristic
299C2#1172854512yes—
300C2#1172859112yes—
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1817C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#1817D7
hypocenterC7#9153
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #89701C4semidirect
18. #89700C4semidirect
272. C7#9153semidirect

Maximal subgroups

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

subgroupindex
#117395202
C2×#897092
C7×#18172
C2×#892622
#117254812
#91537