Finite Group Databasebeta

← C7×#7831 #13185047

Subgroups — C7×#7831 #13185047

Order 1792.

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

normal subgroups only

This group has 350 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×#2100C212yesmaximal
3C7×#2095C211yesmaximal, characteristic
4C7×#1272C211yesmaximal, characteristic
5C7×#1271C212yesmaximal
6C2×C7×#107—21no—
7C2×C7×#103—21no—
8C7×#400—21no—
9C7×#398—22no—
10C7×#391—21no—
11C7×#391C2211yescharacteristic
12C7×#389C2212yes—
13C7×#387—22no—
14C7×#384C2211yescharacteristic
15C7×#340—22no—
16C7×#340—22no—
17C7×#336C2211yescharacteristic
18C7×#336C2212yes—
19#7831C711yesmaximal, characteristic, direct product factor, Sylow
20C22×C7×Q8D411yescharacteristic
21C22×C7×C8—21no—
22C22×C7×C8—22no—
23C2×C7×C4⋊C4—22no—
24C2×C7×C4⋊C4—22no—
25C2×C7×C4⋊C4—21no—
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4D412yes—
29C2×C7×C4⋊C4D412yes—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C42×C7—21no—
32C2×C42×C7C2311yescharacteristic
33C7×#107—42no—
34C7×#103—42no—
35C7×#95—21no—
36C7×#95—22no—
37C7×#95—22no—
38C7×#95—22no—
39C7×#95—22no—
40#2809C2×C711yescharacteristic
41#2100C2×C712yes—
42#2095C2×C711yescharacteristic
43#1272C2×C711yescharacteristic
44#1271C2×C712yes—
45C2×C7×Q8—21no—
46C2×C7×Q8—41no—
47C2×C7×Q8—41no—
48C2×C7×Q8Q1612yes—
49C22×C4×C7—21no—
50C22×C4×C7—21no—
51C22×C4×C7—22no—
52C22×C4×C7—22no—
53C22×C4×C7—41no—
54C22×C4×C7C2×D411yescharacteristic
55C22×C4×C7C2×D412yes—
56C2×C7×C8—22no—
57C2×C7×C8—41no—
58C2×C7×C8—41no—
59C2×C7×C8—42no—
60C2×C7×C8—42no—
61C2×C7×C8—42no—
62C7×C4⋊C4—22no—
63C7×C4⋊C4—22no—
64C7×C4⋊C4—41no—
65C7×C4⋊C4—42no—
66C7×C4⋊C4—41no—
67C7×C4⋊C4—41no—
68C7×C4⋊C4—44no—
69C7×C4⋊C4—42no—
70C7×C4⋊C4—42no—
71C7×C4⋊C4—81no—
72C7×C4⋊C4—81no—
73C42×C7—41no—
74C42×C7—81no—
75C2×#107—21no—
76C2×#103—21no—
77#400—21no—
78#398—22no—
79#391—21no—
80#391C22×C711yescharacteristic
81#389C22×C712yes—
82#387—22no—
83#384C22×C711yescharacteristic
84#340—22no—
85#340—22no—
86#336C22×C711yescharacteristic
87#336C22×C712yes—
88C23×C7#12011yescharacteristic
89C7×Q8—42no—
90C7×Q8—81no—
91C2×C4×C7—21no—
92C2×C4×C7—22no—
93C2×C4×C7—22no—
94C2×C4×C7—21no—
95C2×C4×C7—22no—
96C2×C4×C7—41no—
97C2×C4×C7—41no—
98C2×C4×C7—42no—
99C2×C4×C7—42no—
100C2×C4×C7—42no—
101C2×C4×C7—41no—
102C2×C4×C7—42no—
103C2×C4×C7—42no—
104C2×C4×C7—42no—
105C2×C4×C7—42no—
106C2×C4×C7—81no—
107C2×C4×C7—82no—
108C2×C4×C7C2×Q1611yescharacteristic
109C2×C4×C7#13512yes—
110C2×C4×C7#13711yescharacteristic
111C2×C4×C7#13712yes—
112C7×C8—42no—
113C7×C8—82no—
114C22×Q8C7×D411yescharacteristic
115C22×C8—21no—
116C22×C8—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C7×D412yes—
123C2×C4⋊C4C7×D412yes—
124C2×C4⋊C4C7×D411yescharacteristic
125C2×C42—21no—
126C2×C42C23×C711yescharacteristic
127#107—42no—
128#103—42no—
129#95—21no—
130#95—22no—
131#95—22no—
132#95—22no—
133#95—22no—
134C22×C7#45111yescharacteristic
135C22×C7#45212yes—
136C22×C7#45311yescharacteristic
137C22×C7#45412yes—
138C22×C7#45811yescharacteristic
139C4×C7—21no—
140C4×C7—21no—
141C4×C7—22no—
142C4×C7—22no—
143C4×C7—42no—
144C4×C7—82no—
145C4×C7—82no—
146C4×C7—81no—
147C4×C7—161no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8C7×Q1612yes—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—41no—
157C22×C4C2×C7×D411yescharacteristic
158C22×C4C2×C7×D412yes—
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—42no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C42—41no—
177C42—81no—
178C2×C7#161411yescharacteristic
179C2×C7#161512yes—
180C2×C7#163411yescharacteristic
181C2×C7#163612yes—
182C2×C7#165711yescharacteristic
183C23C7×#12011yescharacteristic
184Q8—42no—
185Q8—81no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—82no—
203C2×C4C2×C7×Q1611yescharacteristic
204C2×C4C7×#13512yes—
205C2×C4C7×#13711yescharacteristic
206C2×C4C7×#13712yes—
207C8—42no—
208C8—82no—
209C7#783111yescharacteristic, direct product factor, Sylow
210C22C7×#45111yescharacteristic
211C22C7×#45212yes—
212C22C7×#45311yescharacteristic
213C22C7×#45412yes—
214C22C7×#45811yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—82no—
222C4—81no—
223C4—161no—
224C2C7×#161411yescharacteristic
225C2C7×#161512yes—
226C2C7×#163411yescharacteristic
227C2C7×#163612yes—
228C2C7×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C7#120
commutator, Frattini, cosocleC2×C42C23×C7
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
19. #7831C7direct (N × H)
209. C7#7831direct (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×#21002
C7×#20952
C7×#12722
C7×#12712
#78317