Finite Group Databasebeta

← #13254786

Subgroups — #13254786

Order 1792.

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

normal subgroups only

This group has 528 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#11739759C212yesmaximal
2#11735924C211yesmaximal, characteristic, complemented
3C7×#1955C211yesmaximal, characteristic
4#11728183C212yesmaximal, complemented
5#11725466C211yesmaximal, characteristic, complemented
6C2×C4×C7×D4C2211yescharacteristic
7#90161C2212yes—
8C2×C7×C4⋊C8C2211yescharacteristic
9C2×C7×C22⋊C8—22no—
10C2×C7×#97C2211yescharacteristic
11#89990—22no—
12#89878—22no—
13#89791—22no—
14C4×#1142—24no—
15#89780—22no—
16#89743—22no—
17#89697C2212yes—
18#89474—22no—
19#89474—22no—
20#89279—24no—
21#10036—71nomaximal, Sylow
22C22×C7×D4D411yescharacteristic
23C23×C4×C7—21no—
24C22×C7×C8—21no—
25C22×C7×C8D412yes—
26C4×C7×D4—22no—
27C4×C7×D4—22no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C22⋊C4—21no—
30C2×C42×C7C2311yescharacteristic
31C2×#1142—24no—
32#6489—22no—
33#6487—22no—
34#6487—22no—
35#6433—22no—
36#6432D412yes—
37#6432D412yes—
38C4×Dic14—22no—
39C4×Dic14—22no—
40C7×C4⋊C8—22no—
41C7×C22⋊C8—44no—
42C7×#97—22no—
43#6406—24no—
44C22⋊(C7⋊C8)—22no—
45#6392—22no—
46#6392—22no—
47#6391—24no—
48#6384—24no—
49#6382—24no—
50C4⋊(C7⋊C8)—22no—
51C4×C7⋊C8D414yes—
52#3162—71no—
53#3101—72no—
54#1955D711yescharacteristic
55#1481—72no—
56#1275—71no—
57C24×C7—21no—
58C2×C7×D4—22no—
59C2×C7×D4—42no—
60C22×C4×C7—21no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7C2×D411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7#4111yescharacteristic
68C2×Dic14—22no—
69C2×Dic14—22no—
70C2×C7×C8—22no—
71C2×C7×C8—22no—
72C2×C7×C8—41no—
73C2×C7×C8—42no—
74C2×C7×C8SD1614yescomplemented
75C7×C4⋊C4—22no—
76C7×C22⋊C4—42no—
77C42×C7C2×D412yes—
78C42×C7C2×D412yes—
79C22⋊Dic7—42no—
80#1142—48no—
81C4⋊Dic7—22no—
82C4⋊Dic7—22no—
83C4⋊Dic7—22no—
84C4⋊Dic7—22no—
85Dic7⋊C4—42no—
86Dic7⋊C4—42no—
87C4×Dic7—42no—
88C2×C7⋊C8—24no—
89#533—72no—
90C2×C4×D4C2×D711yescharacteristic
91#501—142no—
92#501—142no—
93#483—142no—
94#476—142no—
95#461—142no—
96#450—142no—
97C4×SD16—144no—
98#431—72no—
99#427—142no—
100C2×C4⋊C8C2×D711yescharacteristic
101C2×C22⋊C8—22no—
102C2×#97C2×D711yescharacteristic
103Q8⋊C8—144no—
104C23×C7—22no—
105C23×C7—41no—
106C23×C7—42no—
107C23×C7—41no—
108C23×C7—42no—
109C23×C7#12111yescharacteristic
110C7×D4—24no—
111C7×D4—42no—
112C2×C4×C7—41no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7—42no—
116C2×C4×C7—82no—
117C2×C4×C7—81no—
118C2×C4×C7—81no—
119C2×C4×C7#12012yes—
120C2×C4×C7#12011yescharacteristic
121C2×C4×C7#12112yes—
122C2×C4×C7#12711yescharacteristic
123C2×C4×C7C2×SD1612yes—
124C2×C4×C7#13712yes—
125C2×Dic7—42no—
126C2×Dic7—42no—
127Dic14—44no—
128Dic14—44no—
129C7×C8—24no—
130C7×C8—81no—
131C7⋊C8—44no—
132C22×D4D2811yescharacteristic
133C23×C4—21no—
134C2×SD16—144no—
135C22×C8—21no—
136C22×C8C22⋊D712yes—
137C4⋊Q8—72no—
138C4⋊Q8—72no—
139#125—142no—
140C22⋊Q8—142no—
141C22⋊Q8—142no—
142C4×Q8—142no—
143C4×Q8—142no—
144C4×D4—22no—
145C4×D4—22no—
146#117—142no—
147C2×C4⋊C4D2811yescharacteristic
148C2×C22⋊C4—21no—
149C2×C42C22×D711yescharacteristic
150#107—142no—
151#107—142no—
152#106—144no—
153#106—144no—
154C4⋊C8—22no—
155C4⋊C8—142no—
156#103—144no—
157#102—144no—
158C22⋊C8—44no—
159C22⋊C8—142no—
160#97—22no—
161C4×C8—74no—
162C22×C7—21no—
163C22×C7—21no—
164C22×C7—44no—
165C22×C7—42no—
166C22×C7—82no—
167C22×C7—81no—
168C22×C7—81no—
169C22×C7#39211yescharacteristic
170C22×C7#46112yes—
171C4×C7—22no—
172C4×C7—22no—
173C4×C7—81no—
174C4×C7#44812yes—
175C4×C7#49211yescharacteristic
176C4×C7#49711yescharacteristic
177Dic7—82no—
178Dic7—82no—
179C24—21no—
180C2×Q8—142no—
181C2×Q8—142no—
182C2×D4—22no—
183C2×D4—42no—
184C22×C4—21no—
185C22×C4—42no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—42no—
189C22×C4C2×D2811yescharacteristic
190C22×C4#115711yescharacteristic
191C22×C4C2×C22⋊D711yescharacteristic
192SD16—288no—
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—42no—
196C2×C8—41no—
197C2×C8—144no—
198C2×C8#114214yescomplemented
199C4⋊C4—22no—
200C4⋊C4—142no—
201C4⋊C4—142no—
202C4⋊C4—142no—
203C4⋊C4—142no—
204C4⋊C4—282no—
205C4⋊C4—282no—
206C22⋊C4—42no—
207C22⋊C4—282no—
208C42—282no—
209C42D4×D712yes—
210C42D4×D712yes—
211C2×C7—22no—
212C2×C7—82no—
213C2×C7#201011yescharacteristic
214C2×C7#201311yescharacteristic
215C2×C7#201711yescharacteristic
216C23—22no—
217C23—41no—
218C23—42no—
219C23—41no—
220C23—42no—
221C23#649311yescharacteristic
222Q8—284no—
223Q8—284no—
224D4—24no—
225D4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—82no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—282no—
234C2×C4—282no—
235C2×C4#644512yes—
236C2×C4#644712yes—
237C2×C4C2×#114212yes—
238C2×C4#650011yescharacteristic
239C2×C4#650311yescharacteristic
240C2×C4#651412yes—
241C8—24no—
242C8—81no—
243C8—284no—
244C7#1003611yescharacteristic, complemented, Sylow
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#8973211yescharacteristic
253C22#8979112yes—
254C4—22no—
255C4—22no—
256C4—81no—
257C4—562no—
258C4—562no—
259C4#8981212yes—
260C4#8983211yescharacteristic
261C4#8984811yescharacteristic
262C2—22no—
263C2—82no—
264C2#1172741511yescharacteristic
265C2#1172774711yescharacteristic
266C2#1172776711yescharacteristic
subgroupG/H
centerC2×C4#6503
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1955C2
socleC22×C7#392
prime radicalC22×C7×D4D4
hypercenter#1955D7
hypocenterC7#10036
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #11735924C2semidirect
4. #11728183C2semidirect
5. #11725466C2semidirect
74. C2×C7×C8SD16semidirect
198. C2×C8#1142semidirect
244. C7#10036semidirect

Maximal subgroups

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

subgroupindex
#117397592
#117359242
C7×#19552
#117281832
#117254662
#100367