Finite Group Databasebeta

← C7×#13465 #13190681

Subgroups — C7×#13465 #13190681

Order 1792.

384 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C7×#2809C211yesmaximal, characteristic
2C7×#1857C212yesmaximal
3C7×#1857C211yesmaximal, characteristic
4C7×#1394C211yesmaximal, characteristic
5C7×#1394C212yesmaximal
6C7×#519C2211yescharacteristic
7C7×#428—22no—
8C7×#428—21no—
9C2×C7×#101C2212yes—
10C2×C7×#101C2211yescharacteristic
11C7×#400—21no—
12C7×#398—22no—
13C7×#391C2211yescharacteristic
14C7×#391C2212yes—
15C7×#389—21no—
16C7×#387—22no—
17C7×#339—22no—
18C7×#339—21no—
19#13465C711yesmaximal, characteristic, direct product factor, Sylow
20C22×C7×Q8C2311yescharacteristic
21C2×C7×M16—22no—
22C2×C7×M16—21no—
23C4×C7×Q8—41no—
24C4×C7×Q8—41no—
25C7×#117—22no—
26C7×#117—21no—
27C2×C7×C4⋊C4—22no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4D412yes—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C42×C7D412yes—
34C2×C42×C7D411yescharacteristic
35C7×#107—42no—
36C7×#107—41no—
37C7×#106—42no—
38C7×#106—41no—
39C7×#101—22no—
40C7×#101—21no—
41C7×#101Q814yes—
42C7×#101Q812yes—
43C7×#95—21no—
44C7×#95—22no—
45C7×#95—22no—
46C7×#95—22no—
47C7×#95—22no—
48#2809C2×C711yescharacteristic
49#1857C2×C712yes—
50#1857C2×C711yescharacteristic
51#1394C2×C711yescharacteristic
52#1394C2×C712yes—
53C2×C7×Q8—41no—
54C2×C7×Q8—41no—
55C2×C7×Q8C2×Q812yes—
56C2×C7×Q8C2×Q811yescharacteristic
57C2×C7×Q8#4111yescharacteristic
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7C2×D412yes—
63C22×C4×C7C2×D411yescharacteristic
64C7×M16—24no—
65C7×M16—22no—
66C7×M16—41no—
67C7×M16—42no—
68C2×C7×C8—42no—
69C2×C7×C8—41no—
70C7×C4⋊C4—22no—
71C7×C4⋊C4—21no—
72C7×C4⋊C4—21no—
73C7×C4⋊C4—22no—
74C7×C4⋊C4—42no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—44no—
77C7×C4⋊C4—42no—
78C7×C4⋊C4—81no—
79C7×C4⋊C4—81no—
80C7×C22⋊C4—41no—
81C42×C7—41no—
82C42×C7—42no—
83C42×C7—42no—
84C42×C7—41no—
85#519C22×C711yescharacteristic
86#428—22no—
87#428—21no—
88C2×#101C22×C712yes—
89C2×#101C22×C711yescharacteristic
90#400—21no—
91#398—22no—
92#391C22×C711yescharacteristic
93#391C22×C712yes—
94#389—21no—
95#387—22no—
96#339—22no—
97#339—21no—
98C23×C7#12011yescharacteristic
99C7×Q8—42no—
100C7×Q8—41no—
101C7×Q8—41no—
102C2×C4×C7—22no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—41no—
108C2×C4×C7—41no—
109C2×C4×C7—42no—
110C2×C4×C7—42no—
111C2×C4×C7—42no—
112C2×C4×C7—42no—
113C2×C4×C7—42no—
114C2×C4×C7—41no—
115C2×C4×C7—41no—
116C2×C4×C7—41no—
117C2×C4×C7—42no—
118C2×C4×C7—42no—
119C2×C4×C7C22⋊Q812yes—
120C2×C4×C7C22⋊Q811yescharacteristic
121C2×C4×C7C4⋊Q812yes—
122C2×C4×C7C4⋊Q811yescharacteristic
123C7×C8—44no—
124C7×C8—42no—
125C22×Q8C23×C711yescharacteristic
126C2×M16—22no—
127C2×M16—21no—
128C4×Q8—41no—
129C4×Q8—41no—
130#117—22no—
131#117—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C7×D412yes—
137C2×C4⋊C4C7×D411yescharacteristic
138C2×C42C7×D412yes—
139C2×C42C7×D411yescharacteristic
140#107—42no—
141#107—41no—
142#106—42no—
143#106—41no—
144#101—22no—
145#101—21no—
146#101C7×Q814yes—
147#101C7×Q812yes—
148#95—21no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—22no—
153C22×C7—21no—
154C22×C7—21no—
155C22×C7#39511yescharacteristic
156C22×C7B(4,𝔽2)11yescharacteristic
157C22×C7#45811yescharacteristic
158C4×C7—22no—
159C4×C7—21no—
160C4×C7—22no—
161C4×C7—21no—
162C4×C7—42no—
163C4×C7—82no—
164C4×C7—81no—
165C4×C7—81no—
166C4×C7—81no—
167C4×C7—82no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8C2×C7×Q812yes—
171C2×Q8C2×C7×Q811yescharacteristic
172C2×Q8C7×#4111yescharacteristic
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4C2×C7×D412yes—
178C22×C4C2×C7×D411yescharacteristic
179M16—24no—
180M16—22no—
181M16—41no—
182M16—42no—
183C2×C8—42no—
184C2×C8—41no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C22⋊C4—41no—
196C42—41no—
197C42—42no—
198C42—42no—
199C42—41no—
200C2×C7—21no—
201C2×C7—21no—
202C2×C7#206211yescharacteristic
203C2×C7#220311yescharacteristic
204C2×C7#220411yescharacteristic
205C23C7×#12011yescharacteristic
206Q8—42no—
207Q8—41no—
208Q8—41no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4C7×C22⋊Q812yes—
227C2×C4C7×C22⋊Q811yescharacteristic
228C2×C4C7×C4⋊Q812yes—
229C2×C4C7×C4⋊Q811yescharacteristic
230C8—44no—
231C8—42no—
232C7#1346511yescharacteristic, direct product factor, Sylow
233C22—21no—
234C22—21no—
235C22C7×#39511yescharacteristic
236C22C7×B(4,𝔽2)11yescharacteristic
237C22C7×#45811yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—81no—
246C4—82no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2C7×#206211yescharacteristic
251C2C7×#220311yescharacteristic
252C2C7×#220411yescharacteristic
subgroupG/H
center, socleC22×C7B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C7
prime radicalC23×C7#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
19. #13465C7direct (N × H)
232. C7#13465direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#28092
C7×#18572
C7×#13942
#134657