Finite Group Databasebeta

← #13272482

Subgroups — #13272482

Order 1792.

420 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 103 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#11739923C211yesmaximal, characteristic
2C7×#1801C211yesmaximal, characteristic
3C4×#6410C211yesmaximal, characteristic
4#11725505C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C7×#423—21no—
8C2×C7×#101C2212yes—
9#90002C2212yes—
10C2×#6410C2212yes—
11#89751—21no—
12#89751—21no—
13#89748C412yes—
14C4×C4⋊Dic7C411yescharacteristic
15#89700—21no—
16#89700—21no—
17C4×#1136—21no—
18C7×#343—21no—
19#89325—21no—
20#13302—71nomaximal, Sylow
21C22×C7×Q8C2311yescharacteristic
22C22×Dic14—21no—
23C2×C7×M16—22no—
24C4×C7×Q8—41no—
25C4×C7×Q8—41no—
26C2×C7×C4⋊C4C2×C411yescharacteristic
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7C2×C412yes—
35C2×Dic7⋊C4—22no—
36C2×Dic7⋊C4—22no—
37C2×C4×Dic7C2×C412yes—
38C2×#1136—22no—
39#6432—41no—
40#6432—41no—
41C7×C4⋊C8—41no—
42C7×C4⋊C8—41no—
43C7×#101—24no—
44#6410—22no—
45#6410Q814yescomplemented
46C7⋊#95—21no—
47C7⋊#95—22no—
48C7⋊#95—22no—
49#6377—41no—
50C4×C7⋊C8—41no—
51#2567—71no—
52#1801D711yescharacteristic
53C4×#101—71no—
54#1394—74no—
55C2×C7×Q8—41no—
56C2×C7×Q8—41no—
57C2×C7×Q8C2×Q812yes—
58C2×C7×Q8#4112yes—
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×Dic7—22no—
67C22×Dic7—22no—
68C2×Dic14—42no—
69C2×Dic14—82no—
70C7×M16—42no—
71C7×M16—42no—
72C2×C7×C8—42no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—41no—
76C42×C7—21no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C4⋊Dic7—24no—
83C4⋊Dic7—41no—
84C4⋊Dic7—41no—
85C4⋊Dic7—42no—
86Dic7⋊C4—82no—
87Dic7⋊C4—82no—
88C4×Dic7—42no—
89#1136—24no—
90#1136—42no—
91C2×C7⋊C8—42no—
92C2×C4⋊Q8—71no—
93C2×C4×Q8C2×D711yescharacteristic
94#423—21no—
95C2×#101—72no—
96C2×#101C2×D712yes—
97C4×M16—141no—
98#395—141no—
99#395—141no—
100#391—72no—
101#389—141no—
102#389—141no—
103#384—72no—
104C4×C4⋊C4—71no—
105#343—21no—
106#343—141no—
107C23×C7C2×C22⋊C411yescharacteristic
108C7×Q8—42no—
109C7×Q8—42no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7#9911yescharacteristic
124C2×C4×C7#9911yescharacteristic
125C2×C4×C7C4×Q812yes—
126C2×C4×C7C22⋊Q812yes—
127C2×C4×C7#12411yescharacteristic
128C2×C4×C7C4⋊Q811yescharacteristic
129C2×Dic7—24no—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135Dic14—84no—
136C7×C8—82no—
137C7⋊C8—44no—
138C22×Q8—141no—
139C22×Q8C22×D711yescharacteristic
140C2×M16—22no—
141C2×M16—142no—
142C4⋊Q8—281no—
143C4⋊Q8—281no—
144C4×Q8—41no—
145C4×Q8—41no—
146C2×C4⋊C4—72no—
147C2×C4⋊C4—141no—
148C2×C4⋊C4—141no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4—142no—
151C2×C4⋊C4C4×D711yescharacteristic
152C2×C4⋊C4D2811yescharacteristic
153C2×C4⋊C4C22⋊D711yescharacteristic
154C2×C42—72no—
155C2×C42C4×D711yescharacteristic
156C2×C42D2811yescharacteristic
157C2×C42C22⋊D711yescharacteristic
158C4⋊C8—41no—
159C4⋊C8—41no—
160#101—24no—
161#101—74no—
162#101—142no—
163#97—281no—
164C4×C8—281no—
165#95—141no—
166#95—142no—
167#95—142no—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7#39111yescharacteristic
171C22×C7C2×#9911yescharacteristic
172C22×C7#41011yescharacteristic
173C4×C7—21no—
174C4×C7—22no—
175C4×C7—21no—
176C4×C7—22no—
177C4×C7—21no—
178C4×C7—41no—
179C4×C7—41no—
180C4×C7—41no—
181C4×C7#35612yes—
182Dic7—44no—
183Dic7—82no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—282no—
187C2×Q8—562no—
188C2×Q8#115912yes—
189C2×Q8Q8×D712yes—
190C22×C4—142no—
191C22×C4—142no—
192C22×C4(C2×D7)⋊C411yescharacteristic
193C22×C4(C2×D7)⋊C411yescharacteristic
194C22×C4(C2×D7)⋊C411yescharacteristic
195C22×C4(C2×D7)⋊C411yescharacteristic
196C22×C4C2×C4×D711yescharacteristic
197C22×C4C2×D2811yescharacteristic
198C22×C4C2×C22⋊D711yescharacteristic
199M16—42no—
200M16—42no—
201M16—144no—
202M16—282no—
203C2×C8—42no—
204C2×C8—282no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—144no—
209C4⋊C4—282no—
210C4⋊C4—281no—
211C4⋊C4—281no—
212C4⋊C4—562no—
213C4⋊C4—562no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—282no—
221C2×C7—21no—
222C2×C7—21no—
223C2×C7#199611yescharacteristic
224C2×C7C2×#35611yescharacteristic
225C2×C7#213411yescharacteristic
226C23C2×(C2×D7)⋊C411yescharacteristic
227Q8—42no—
228Q8—42no—
229Q8—564no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—144no—
244C2×C4—282no—
245C2×C4—282no—
246C2×C4—282no—
247C2×C4—282no—
248C2×C4—282no—
249C2×C4#638011yescharacteristic
250C2×C4#638011yescharacteristic
251C2×C4#645012yes—
252C2×C4#646012yes—
253C2×C4#649911yescharacteristic
254C2×C4#650711yescharacteristic
255C8—82no—
256C8—284no—
257C7#1330211yescharacteristic, complemented, Sylow
258C22—21no—
259C22—21no—
260C22C2×#638011yescharacteristic
261C22#8974611yescharacteristic
262C22#8977811yescharacteristic
263C4—21no—
264C4—21no—
265C4—22no—
266C4—22no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—284no—
272C4—562no—
273C4#8927312yes—
274C2—21no—
275C2—21no—
276C2#1172728311yescharacteristic
277C2C2×#8927311yescharacteristic
278C2#1172790311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC22×Q8C22×D7
FittingC7×#1801C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC22×C7×Q8C23
hypercenter#1801D7
hypocenterC7#13302
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
45. #6410Q8semidirect
257. C7#13302semidirect

Maximal subgroups

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

subgroupindex
#117399232
C7×#18012
C4×#64102
#117255052
#133027