Finite Group Databasebeta

← #13256149

Subgroups — #13256149

Order 1792.

560 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 131 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×#89863C212yesmaximal
2#11731788C211yesmaximal, characteristic
3C7×#1956C211yesmaximal, characteristic
4C2×#89251C212yesmaximal
5#11725440C211yesmaximal, characteristic
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C4×Dic14C2212yes—
8C2×C7×#103—22no—
9C2×C4×C7×C8C2211yescharacteristic
10C7×#384C2211yescharacteristic
11#89863—24no—
12#89863—24no—
13#89757—22no—
14#89755—22no—
15#89746—22no—
16C2×#6384—22no—
17C2×#6381—22no—
18C2×C4⋊(C7⋊C8)C2212yes—
19#89251—24no—
20#10237—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×Dic14D412yes—
23C22×C7×C8—21no—
24C7×C4⋊Q8—22no—
25C7×C4⋊Q8—21no—
26C7×C4⋊Q8D412yes—
27C2×C7×C4⋊C4—22no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4D412yes—
30C2×C42×C7C2311yescharacteristic
31C2×C4⋊Dic7—22no—
32C2×C4⋊Dic7D412yes—
33C2×Dic7⋊C4—22no—
34C2×C4×Dic7—22no—
35C22×C7⋊C8—22no—
36C4×Dic14—22no—
37C4×Dic14—22no—
38C4×Dic14—22no—
39C4×Dic14—22no—
40C7×#103—44no—
41C4×C7×C8—22no—
42C7⋊#95—22no—
43C7⋊#95—24no—
44#6384—28no—
45#6381—28no—
46C4⋊(C7⋊C8)—22no—
47C4⋊(C7⋊C8)D414yes—
48C2×#477—72no—
49#2582—71no—
50#1956D711yescharacteristic
51C2×Q8⋊C8—72no—
52#1296—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×D411yescharacteristic
60C22×C4×C7C2×D412yes—
61C22×Dic7—22no—
62C22×Dic7—22no—
63C2×Dic14—22no—
64C2×Dic14—22no—
65C2×Dic14—22no—
66C2×Dic14—22no—
67C2×Dic14—22no—
68C2×Dic14Q1614yes—
69C2×C7×C8—22no—
70C2×C7×C8—41no—
71C2×C7×C8—41no—
72C7×C4⋊C4—24no—
73C7×C4⋊C4—42no—
74C7×C4⋊C4—42no—
75C7×C4⋊C4—42no—
76C7×C4⋊C4—42no—
77C42×C7C2×D411yescharacteristic
78C42×C7C2×D412yes—
79C42×C7#4111yescharacteristic
80C4⋊Dic7—22no—
81C4⋊Dic7—22no—
82C4⋊Dic7—82no—
83Dic7⋊C4—42no—
84Dic7⋊C4—42no—
85C4×Dic7—42no—
86C4×Dic7—42no—
87C2×C7⋊C8—24no—
88C2×C7⋊C8—42no—
89C2×C7⋊C8—42no—
90C2×C4⋊Q8C2×D711yescharacteristic
91C2×C4×Q8—72no—
92#477—144no—
93#477—144no—
94C2×#107—142no—
95C2×C4⋊C8—72no—
96C2×#103—22no—
97C2×#103—142no—
98C2×C4×C8C2×D711yescharacteristic
99#398—142no—
100#391—142no—
101#389—142no—
102#384C2×D711yescharacteristic
103Q8⋊C8—144no—
104C23×C7#12011yescharacteristic
105C7×Q8—44no—
106C7×Q8—82no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—42no—
110C2×C4×C7—44no—
111C2×C4×C7—42no—
112C2×C4×C7—81no—
113C2×C4×C7—81no—
114C2×C4×C7#12012yes—
115C2×C4×C7#12112yes—
116C2×C4×C7#12111yescharacteristic
117C2×C4×C7#12711yescharacteristic
118C2×C4×C7C2×Q1612yes—
119C2×C4×C7#13512yes—
120C2×C4×C7#13712yes—
121C2×C4×C7#13712yes—
122C2×Dic7—24no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126C2×Dic7—42no—
127C2×Dic7—42no—
128Dic14—24no—
129Dic14—24no—
130Dic14—42no—
131Dic14—42no—
132C7×C8—42no—
133C7⋊C8—44no—
134C22×Q8—21no—
135C22×Q8—72no—
136C22×C8—21no—
137C22×C8—142no—
138C4⋊Q8—21no—
139C4⋊Q8—22no—
140C4⋊Q8D2812yes—
141C4×Q8—142no—
142C4×Q8—142no—
143C4×Q8—142no—
144C4×Q8—142no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—72no—
148C2×C4⋊C4—142no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4C22⋊D712yes—
151C2×C42—142no—
152C2×C42C22×D711yescharacteristic
153#107—148no—
154C4⋊C8—74no—
155C4⋊C8—142no—
156#103—44no—
157#103—148no—
158C4×C8—22no—
159#95—144no—
160#95—142no—
161C22×C7#39211yescharacteristic
162C22×C7#45112yes—
163C22×C7#45212yes—
164C22×C7#45311yescharacteristic
165C22×C7#45411yescharacteristic
166C4×C7—21no—
167C4×C7—21no—
168C4×C7—82no—
169C4×C7—82no—
170C4×C7#45112yes—
171C4×C7#45212yes—
172C4×C7#46712yes—
173C4×C7#47012yes—
174Dic7—44no—
175Dic7—82no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—41no—
180C2×Q8—74no—
181C2×Q8—142no—
182C2×Q8—142no—
183C2×Q8—142no—
184C2×Q8—142no—
185C2×Q8—142no—
186C22×C4—22no—
187C22×C4—41no—
188C22×C4—142no—
189C22×C4—142no—
190C22×C4D4×D712yes—
191C22×C4C2×C22⋊D711yescharacteristic
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—144no—
196C2×C8—282no—
197C2×C8—282no—
198C4⋊C4—24no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—142no—
204C4⋊C4—142no—
205C4⋊C4—282no—
206C4⋊C4—282no—
207C4⋊C4—562no—
208C42—282no—
209C42—282no—
210C42C2×D2811yescharacteristic
211C42#115711yescharacteristic
212C42D4×D712yes—
213C2×C7#163011yescharacteristic
214C2×C7#163311yescharacteristic
215C2×C7#163612yes—
216C2×C7#200112yes—
217C2×C7#200611yescharacteristic
218C23#650011yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—144no—
222Q8—144no—
223Q8—282no—
224Q8—282no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—144no—
233C2×C4—282no—
234C2×C4—282no—
235C2×C4—282no—
236C2×C4—282no—
237C2×C4—282no—
238C2×C4#644512yes—
239C2×C4#644712yes—
240C2×C4#647812yes—
241C2×C4#647912yes—
242C2×C4D7×Q1612yes—
243C2×C4#648112yes—
244C2×C4#649311yescharacteristic
245C2×C4#650311yescharacteristic
246C8—42no—
247C8—284no—
248C7#1023711yescharacteristic, complemented, Sylow
249C22#8973211yescharacteristic
250C22#8983411yescharacteristic
251C22#8984911yescharacteristic
252C22#8994512yes—
253C22#8995812yes—
254C4—21no—
255C4—21no—
256C4—82no—
257C4—82no—
258C4—284no—
259C4—562no—
260C4#8958012yes—
261C4#8958212yes—
262C4#8958512yes—
263C4#8958812yes—
264C2#1172741811yescharacteristic
265C2#1172802712yes—
266C2#1172899012yes—
267C2#1172902411yescharacteristic
268C2#1172906111yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1956C2
socle, prime radicalC23×C7#120
hypercenter#1956D7
hypocenterC7#10237
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
248. C7#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#898632
#117317882
C7×#19562
C2×#892512
#117254402
#102377