Finite Group Databasebeta

← #13258573

Subgroups — #13258573

Order 1792.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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#11728530C211yesmaximal, characteristic
2#11728269C211yesmaximal, characteristic
3#11728200C211yesmaximal, characteristic
4#11728191C211yesmaximal, characteristic
5C7×#1301C211yesmaximal, characteristic
6#11725543C211yesmaximal, characteristic
7#11725520C211yesmaximal, characteristic
8#90161C2211yescharacteristic
9C7×#431C2211yescharacteristic
10C7×#423C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×Dic7⋊C8—21no—
13C2×Dic7⋊C8—21no—
14#89704C2211yescharacteristic
15#89697C2211yescharacteristic
16C2×C4⋊(C7⋊C8)C2211yescharacteristic
17#89350—21no—
18#89350—21no—
19#89281—21no—
20#89277—21no—
21#89276—21no—
22#89276—21no—
23#10628—71nomaximal, Sylow
24C2×C7×M16—21no—
25C22×C7×C8—21no—
26C2×C42×C7C2311yescharacteristic
27#6489—21no—
28#6487—21no—
29#6487—21no—
30C2×C4×Dic7D411yescharacteristic
31C2×C4×Dic7D411yescharacteristic
32C22×C7⋊C8—21no—
33#6433—21no—
34#6432D411yescharacteristic
35#6432D411yescharacteristic
36C4×Dic14—21no—
37C4×Dic14—21no—
38C7×C4⋊C8—21no—
39C7×C4⋊C8—21no—
40C7×C4⋊C8—21no—
41C7×C4⋊C8—21no—
42C7×C4⋊C8—21no—
43C7×C22⋊C8—21no—
44C4×C7×C8—21no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C22⋊(C7⋊C8)—21no—
48Dic7⋊C8—42no—
49Dic7⋊C8—42no—
50C4⋊(C7⋊C8)—21no—
51C4⋊(C7⋊C8)—21no—
52C4⋊(C7⋊C8)—21no—
53C4×C7⋊C8—21no—
54#1995—71no—
55#1843—71no—
56#1542—71no—
57#1542—71no—
58#1301—71no—
59#1301D711yescharacteristic
60#1274—71no—
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7#4111yescharacteristic
63C22×C4×C7#4111yescharacteristic
64C22×Dic7—21no—
65C22×Dic7—21no—
66C2×Dic14—21no—
67C2×Dic14—21no—
68C7×M16—41no—
69C7×M16—41no—
70C2×C7×C8—41no—
71C2×C7×C8—41no—
72C2×C7×C8—41no—
73C2×C7×C8—41no—
74C2×C7×C8—41no—
75C42×C7C2×D411yescharacteristic
76C42×C7#4111yescharacteristic
77C42×C7#4111yescharacteristic
78C42×C7#4111yescharacteristic
79C22⋊Dic7—41no—
80C4⋊Dic7—21no—
81C4⋊Dic7—21no—
82C4⋊Dic7—21no—
83C4⋊Dic7—21no—
84Dic7⋊C4—41no—
85Dic7⋊C4—41no—
86C4×Dic7—21no—
87C4×Dic7—21no—
88C4×Dic7—41no—
89C4×Dic7SD1612yes—
90C4×Dic7Q1612yes—
91C2×C7⋊C8—41no—
92C2×C7⋊C8—41no—
93C2×C7⋊C8—41no—
94C2×C7⋊C8—41no—
95#533—71no—
96#431—71no—
97#431C2×D711yescharacteristic
98#423C2×D711yescharacteristic
99C2×C4⋊C8—71no—
100C2×C4⋊C8—141no—
101C2×C4⋊C8—141no—
102C2×C4⋊C8C2×D711yescharacteristic
103#376—71no—
104#339—141no—
105#339—141no—
106#333—141no—
107#333—141no—
108#332—141no—
109#332—141no—
110C23×C7#12311yescharacteristic
111C2×C4×C7—41no—
112C2×C4×C7—41no—
113C2×C4×C7#12111yescharacteristic
114C2×C4×C7#12311yescharacteristic
115C2×C4×C7#12311yescharacteristic
116C2×C4×C7#12411yescharacteristic
117C2×C4×C7#12611yescharacteristic
118C2×C4×C7#12611yescharacteristic
119C2×C4×C7C2×SD1611yescharacteristic
120C2×C4×C7C2×Q1611yescharacteristic
121C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C7#13711yescharacteristic
123C2×Dic7—22no—
124C2×Dic7—22no—
125C2×Dic7—41no—
126C2×Dic7—41no—
127C2×Dic7—41no—
128C2×Dic7—41no—
129C2×Dic7—41no—
130C2×Dic7—41no—
131Dic14—81no—
132Dic14—81no—
133C7×C8—81no—
134C7×C8—81no—
135C7×C8—81no—
136C7⋊C8—81no—
137C7⋊C8—81no—
138C2×M16—21no—
139C22×C8—21no—
140C22×C8—141no—
141C4⋊Q8—71no—
142C4⋊Q8—71no—
143#125—141no—
144C22⋊Q8—141no—
145C22⋊Q8—141no—
146C4×Q8—141no—
147C4×Q8—141no—
148#117—141no—
149C2×C42—71no—
150C2×C42—71no—
151C2×C42C22×D711yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—141no—
158C4⋊C8—141no—
159C4⋊C8—141no—
160C4⋊C8—282no—
161C4⋊C8—282no—
162C22⋊C8—21no—
163C22⋊C8—141no—
164C4×C8—21no—
165C4×C8—141no—
166#95—141no—
167#95—141no—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7#39711yescharacteristic
171C22×C7#48311yescharacteristic
172C22×C7#48411yescharacteristic
173C4×C7—21no—
174C4×C7—21no—
175C4×C7—21no—
176C4×C7—21no—
177C4×C7#46011yescharacteristic
178C4×C7#46211yescharacteristic
179C4×C7#48711yescharacteristic
180C4×C7#48911yescharacteristic
181Dic7—42no—
182Dic7—42no—
183Dic7—81no—
184Dic7—81no—
185C2×Q8—141no—
186C2×Q8—141no—
187C22×C4—141no—
188C22×C4—141no—
189C22×C4#115711yescharacteristic
190C22×C4D4×D711yescharacteristic
191C22×C4#116111yescharacteristic
192M16—41no—
193M16—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—281no—
200C2×C8—281no—
201C2×C8—281no—
202C2×C8—281no—
203C4⋊C4—141no—
204C4⋊C4—141no—
205C4⋊C4—141no—
206C4⋊C4—141no—
207C4⋊C4—281no—
208C4⋊C4—281no—
209C22⋊C4—281no—
210C42—72no—
211C42—72no—
212C42—141no—
213C42—141no—
214C42—281no—
215C42#115711yescharacteristic
216C42#115711yescharacteristic
217C42D4×D711yescharacteristic
218C42#115911yescharacteristic
219C2×C7—21no—
220C2×C7—21no—
221C2×C7#207211yescharacteristic
222C2×C7#208011yescharacteristic
223C2×C7#208011yescharacteristic
224C23#645711yescharacteristic
225Q8—561no—
226Q8—561no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—142no—
230C2×C4—142no—
231C2×C4—281no—
232C2×C4—281no—
233C2×C4—281no—
234C2×C4—281no—
235C2×C4—281no—
236C2×C4—281no—
237C2×C4#643911yescharacteristic
238C2×C4#644611yescharacteristic
239C2×C4#644711yescharacteristic
240C2×C4#644811yescharacteristic
241C2×C4#645711yescharacteristic
242C2×C4#646111yescharacteristic
243C2×C4#647411yescharacteristic
244C2×C4D7×SD1611yescharacteristic
245C2×C4#647811yescharacteristic
246C2×C4D7×Q1611yescharacteristic
247C8—81no—
248C8—81no—
249C8—81no—
250C8—561no—
251C8—561no—
252C7#1062811yescharacteristic, complemented, Sylow
253C22—21no—
254C22—21no—
255C22#8944711yescharacteristic
256C22#8963411yescharacteristic
257C22#8965611yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—282no—
263C4—282no—
264C4—561no—
265C4—561no—
266C4#8953411yescharacteristic
267C4#8953711yescharacteristic
268C4#8956411yescharacteristic
269C4#8956511yescharacteristic
270C2—21no—
271C2—21no—
272C2#1172666811yescharacteristic
273C2#1172668911yescharacteristic
274C2#1172679711yescharacteristic
subgroupG/H
centerC2×C4#6448
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1301C2
socleC22×C7#397
prime radicalC23×C7#123
hypercenter#1301D7
hypocenterC7#10628
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
252. C7#10628semidirect

Maximal subgroups

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

subgroupindex
#117285302
#117282692
#117282002
#117281912
C7×#13012
#117255432
#117255202
#106287