Finite Group Databasebeta

← #13255131

Subgroups — #13255131

Order 1792.

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

normal subgroups only

This group has 500 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
1C2×#89852C212yesmaximal
2#11731662C211yesmaximal, characteristic
3C7×#1960C211yesmaximal, characteristic
4C2×#89260C212yesmaximal
5#11725436C211yesmaximal, characteristic
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×#6433C2212yes—
8C2×C7×#103—22no—
9C2×C7×#97C2211yescharacteristic
10C7×#382C2211yescharacteristic
11#89852—24no—
12#89852—24no—
13#89755—22no—
14C2×#6382—22no—
15C2×#6381—22no—
16C2×#6377C2212yes—
17#89433—22no—
18#89431—22no—
19#89260—24no—
20#10087—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×C7×C8—21no—
23C7×C4⋊Q8—22no—
24C7×C4⋊Q8—21no—
25C7×C4⋊Q8D412yes—
26C2×C7×C4⋊C4—22no—
27C2×C7×C4⋊C4D412yes—
28C2×C42×C7C2311yescharacteristic
29C2×C4⋊Dic7—22no—
30C2×C4⋊Dic7D412yes—
31C2×C4⋊Dic7D412yes—
32C2×Dic7⋊C4—22no—
33C2×Dic7⋊C4—22no—
34C22×C7⋊C8—22no—
35#6433—22no—
36#6433—22no—
37#6433—22no—
38#6433—22no—
39C7×#103—44no—
40C7×#97—22no—
41C7×#95—22no—
42C7⋊#95—22no—
43C7⋊#95—24no—
44#6382—28no—
45#6381—28no—
46#6377—22no—
47#6377D414yes—
48C2×#501—72no—
49#2822—71no—
50#1960D711yescharacteristic
51C2×#330—72no—
52#1295—71no—
53C2×C7×Q8—22no—
54C2×C7×Q8—42no—
55C2×C7×Q8—42no—
56C2×C7×Q8—41no—
57C22×C4×C7—22no—
58C22×C4×C7—41no—
59C22×C4×C7C2×D412yes—
60C22×C4×C7C2×D411yescharacteristic
61C22×Dic7—22no—
62C22×Dic7—22no—
63C2×C7×C8—22no—
64C2×C7×C8—41no—
65C2×C7×C8—41no—
66C7×C4⋊C4—24no—
67C7×C4⋊C4—42no—
68C7×C4⋊C4—42no—
69C42×C7C2×D411yescharacteristic
70C42×C7C2×D412yes—
71C42×C7#4111yescharacteristic
72C4⋊Dic7—22no—
73C4⋊Dic7—22no—
74C4⋊Dic7—22no—
75C4⋊Dic7—22no—
76C4⋊Dic7—82no—
77Dic7⋊C4—42no—
78Dic7⋊C4—42no—
79Dic7⋊C4—42no—
80Dic7⋊C4—42no—
81C2×C7⋊C8—28no—
82C2×C7⋊C8—24no—
83C2×C4⋊Q8C2×D711yescharacteristic
84C2×#125—72no—
85#501—144no—
86#501—144no—
87C2×#107—142no—
88C2×#106—142no—
89C2×#103—22no—
90C2×#97—72no—
91C2×#97C2×D711yescharacteristic
92#400—142no—
93#398—142no—
94#398—142no—
95#382C2×D711yescharacteristic
96#330—144no—
97C23×C7#12011yescharacteristic
98C7×Q8—44no—
99C7×Q8—82no—
100C2×C4×C7—21no—
101C2×C4×C7—21no—
102C2×C4×C7—24no—
103C2×C4×C7—42no—
104C2×C4×C7—42no—
105C2×C4×C7—44no—
106C2×C4×C7—81no—
107C2×C4×C7—81no—
108C2×C4×C7#12012yes—
109C2×C4×C7#12112yes—
110C2×C4×C7#12111yescharacteristic
111C2×C4×C7#12711yescharacteristic
112C2×Dic7—42no—
113C2×Dic7—42no—
114C2×Dic7—42no—
115C2×Dic7—42no—
116C2×Dic7—44no—
117C7×C8—42no—
118C7⋊C8—28no—
119C22×Q8—21no—
120C22×C8—21no—
121C22×C8—142no—
122C4⋊Q8—21no—
123C4⋊Q8—22no—
124C4⋊Q8D2812yes—
125#125—142no—
126#125—142no—
127#125—142no—
128#125—142no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—72no—
131C2×C4⋊C4—72no—
132C2×C4⋊C4—142no—
133C2×C4⋊C4—142no—
134C2×C4⋊C4—142no—
135C2×C4⋊C4C22⋊D712yes—
136C2×C42C22×D711yescharacteristic
137#107—148no—
138#106—148no—
139#103—44no—
140#97—22no—
141#97—74no—
142#97—142no—
143#95—22no—
144#95—144no—
145#95—142no—
146C22×C7#39211yescharacteristic
147C22×C7#45311yescharacteristic
148C22×C7#45411yescharacteristic
149C22×C7#45614yes—
150C4×C7—22no—
151C4×C7—22no—
152C4×C7—21no—
153C4×C7—21no—
154C4×C7—82no—
155C4×C7—82no—
156Dic7—82no—
157Dic7—82no—
158C2×Q8—22no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—41no—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4—142no—
165C22×C4—142no—
166C22×C4D4×D712yes—
167C22×C4C2×C22⋊D711yescharacteristic
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—148no—
172C2×C8—144no—
173C4⋊C4—24no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—142no—
177C4⋊C4—142no—
178C4⋊C4—142no—
179C4⋊C4—142no—
180C4⋊C4—282no—
181C4⋊C4—282no—
182C4⋊C4—282no—
183C4⋊C4—282no—
184C4⋊C4—562no—
185C42C2×D2811yescharacteristic
186C42#115711yescharacteristic
187C42D4×D712yes—
188C2×C7#166012yes—
189C2×C7#166312yes—
190C2×C7#200512yes—
191C2×C7#200611yescharacteristic
192C23#650011yescharacteristic
193Q8—44no—
194Q8—82no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—44no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—284no—
204C2×C4—282no—
205C2×C4—282no—
206C2×C4—282no—
207C2×C4—282no—
208C2×C4#644512yes—
209C2×C4#644712yes—
210C2×C4#649311yescharacteristic
211C2×C4#650311yescharacteristic
212C8—42no—
213C8—148no—
214C7#1008711yescharacteristic, complemented, Sylow
215C22#8973211yescharacteristic
216C22#8983411yescharacteristic
217C22#8984911yescharacteristic
218C22#8997714yes—
219C4—21no—
220C4—21no—
221C4—22no—
222C4—22no—
223C4—82no—
224C4—82no—
225C4—562no—
226C4—562no—
227C2#1172741811yescharacteristic
228C2#1172810012yes—
229C2#1172900612yes—
230C2#1172908412yes—
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1960C2
socle, prime radicalC23×C7#120
hypercenter#1960D7
hypocenterC7#10087
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
214. C7#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#898522
#117316622
C7×#19602
C2×#892602
#117254362
#100877