Finite Group Databasebeta

← #13247409

Subgroups — #13247409

Order 1792.

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

normal subgroups only

This group has 384 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
1#11739908C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3C4×#6410C211yesmaximal, characteristic
4#11725558C212yesmaximal
5#11725554C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C7×#432C2212yes—
8#90002—21no—
9C2×#6410—21no—
10#89753—21no—
11#89753—21no—
12C4⋊C4×Dic7—21no—
13#89709C411yescharacteristic
14#89709C2211yescharacteristic
15#89708C411yescharacteristic
16C4×C4⋊Dic7C411yescharacteristic
17#89704C411yescharacteristic
18#89704C2211yescharacteristic
19C4×#1136C2212yes—
20C7×#324—21no—
21C7×#324—21no—
22#89325—21no—
23#8774—71nomaximal, Sylow
24C22×C7×Q8D411yescharacteristic
25C4×C7×Q8—22no—
26C4×C7×Q8—22no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7C2311yescharacteristic
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4×Dic7—21no—
36C2×C4×Dic7—21no—
37C2×C4×Dic7—21no—
38C2×#1136—22no—
39C7×C4⋊C8—22no—
40C7×C22⋊C8—22no—
41C7×#97—22no—
42#6410—24no—
43C7⋊#95—21no—
44C7⋊#95—21no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95C2×C411yescharacteristic
51C7⋊#95C2×C411yescharacteristic
52C7⋊#95C2×C411yescharacteristic
53C7⋊#95C2×C411yescharacteristic
54#6377—22no—
55C4×C7⋊C8—22no—
56#2356—71no—
57C4×#101—71no—
58#1467D711yescharacteristic
59#1300—72no—
60#1288—72no—
61C2×C7×Q8—22no—
62C2×C7×Q8—22no—
63C2×C7×Q8—41no—
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×Dic7—21no—
72C22×Dic7—21no—
73C22×Dic7—21no—
74C22×Dic7—21no—
75C2×C7×C8—42no—
76C7×C4⋊C4—22no—
77C7×C4⋊C4—22no—
78C7×C4⋊C4—22no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7#4112yes—
84C42×C7#4112yes—
85C4⋊Dic7—42no—
86C4⋊Dic7—42no—
87C4×Dic7—42no—
88C4×Dic7—42no—
89C4×Dic7—42no—
90#1136—24no—
91#1136—42no—
92C2×C7⋊C8—42no—
93C2×C4×Q8C2×D711yescharacteristic
94#432C2×D712yes—
95C2×#101—141no—
96C4×M16—72no—
97#391—141no—
98#387—141no—
99#387—141no—
100#383—71no—
101#383—71no—
102#382—71no—
103C4×C4⋊C4—71no—
104C4×C4⋊C4—141no—
105#376—71no—
106#376—71no—
107#343—141no—
108#324—21no—
109#324—21no—
110C23×C7C2×C22⋊C411yescharacteristic
111C7×Q8—44no—
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—21no—
120C2×C4×C7—21no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7—41no—
124C2×C4×C7—41no—
125C2×C4×C7#10412yes—
126C2×C4×C7#11711yescharacteristic
127C2×C4×C7#11711yescharacteristic
128C2×C4×C7#12312yes—
129C2×C4×C7#12312yes—
130C2×Dic7—22no—
131C2×Dic7—41no—
132C2×Dic7—41no—
133C2×Dic7—41no—
134C2×Dic7—41no—
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C7×C8—82no—
143C7⋊C8—44no—
144C22×Q8D2811yescharacteristic
145C2×M16—142no—
146C4×Q8—22no—
147C4×Q8—22no—
148C2×C4⋊C4—141no—
149C2×C4⋊C4—141no—
150C2×C4⋊C4D2811yescharacteristic
151C2×C4⋊C4C22⋊D711yescharacteristic
152C2×C4⋊C4C22⋊D711yescharacteristic
153C2×C42—141no—
154C2×C42—141no—
155C2×C42—141no—
156C2×C42C4×D711yescharacteristic
157C2×C42C4×D711yescharacteristic
158C2×C42C22×D711yescharacteristic
159C4⋊C8—22no—
160#101—144no—
161C22⋊C8—22no—
162#97—22no—
163#97—142no—
164C4×C8—142no—
165#95—71no—
166#95—71no—
167#95—71no—
168#95—71no—
169#95—141no—
170#95—141no—
171#95—141no—
172#95—141no—
173#95—141no—
174#95—141no—
175#95—141no—
176C22×C7—21no—
177C22×C7—21no—
178C22×C7#38111yescharacteristic
179C22×C7C2×#10411yescharacteristic
180C22×C7#42111yescharacteristic
181C4×C7—22no—
182C4×C7—22no—
183C4×C7—22no—
184C4×C7—21no—
185C4×C7—21no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—41no—
189Dic7—42no—
190Dic7—81no—
191Dic7—81no—
192Dic7—81no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C22×C4—141no—
197C22×C4—141no—
198C22×C4—141no—
199C22×C4—141no—
200C22×C4(C2×D7)⋊C411yescharacteristic
201C22×C4(C2×D7)⋊C411yescharacteristic
202C22×C4(C2×D7)⋊C411yescharacteristic
203C22×C4(C2×D7)⋊C411yescharacteristic
204C22×C4C2×C4×D711yescharacteristic
205C22×C4C2×D2811yescharacteristic
206C22×C4C2×C22⋊D711yescharacteristic
207M16—144no—
208M16—282no—
209C2×C8—42no—
210C2×C8—282no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—282no—
215C4⋊C4—282no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—282no—
221C42—282no—
222C42—282no—
223C42#115912yes—
224C42#115912yes—
225C2×C7—21no—
226C2×C7—21no—
227C2×C7#182611yescharacteristic
228C2×C7#182711yescharacteristic
229C2×C7#183011yescharacteristic
230C23C2×(C2×D7)⋊C411yescharacteristic
231Q8—44no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—142no—
246C2×C4—281no—
247C2×C4—281no—
248C2×C4—281no—
249C2×C4—281no—
250C2×C4—281no—
251C2×C4—281no—
252C2×C4—281no—
253C2×C4—281no—
254C2×C4—281no—
255C2×C4—281no—
256C2×C4—281no—
257C2×C4#639912yes—
258C2×C4#644011yescharacteristic
259C2×C4#644011yescharacteristic
260C2×C4#644912yes—
261C2×C4#649812yes—
262C8—82no—
263C8—284no—
264C7#877411yescharacteristic, complemented, Sylow
265C22—21no—
266C22—21no—
267C22#8971511yescharacteristic
268C22C2×#639911yescharacteristic
269C22#8991111yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—282no—
279C4—561no—
280C4—561no—
281C4—561no—
282C2—21no—
283C2—21no—
284C2#1172772911yescharacteristic
285C2#1172779311yescharacteristic
286C2#1172785511yescharacteristic
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1467C2
socleC22×C7#381
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1467D7
hypocenterC7#8774
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
264. C7#8774semidirect

Maximal subgroups

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

subgroupindex
#117399082
C7×#14672
C4×#64102
#117255582
#117255542
#87747