Finite Group Databasebeta

← C7×#9435 #13186651

Subgroups — C7×#9435 #13186651

Order 1792.

504 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3152C211yesmaximal, characteristic
2C7×#2979C211yesmaximal, characteristic
3C7×#1560C211yesmaximal, characteristic
4C7×#1549C212yesmaximal, complemented
5C7×#1299C212yesmaximal, complemented
6C2×C7×#137—22no—
7C7×#532C2211yescharacteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C7×#497C414yes—
10C7×#494—21no—
11C7×#492—21no—
12C7×#436—22no—
13C7×C8×D4—22no—
14C7×#431C2212yes—
15C7×#423C2212yes—
16C7×#408—22no—
17C4×C7×M16C2211yescharacteristic
18C7×#333—21no—
19C7×#332—22no—
20C7×#332—22no—
21C7×#331—21no—
22#9435C711yesmaximal, characteristic, direct product factor, Sylow
23C2×C7×#41D412yes—
24C22×C7×Q8—21no—
25C7×#137—44no—
26C7×#137—44no—
27C2×C7×Q16—24no—
28C2×C7×SD16—24no—
29C2×C7×M16—21no—
30C2×C7×M16—22no—
31C2×C7×M16—22no—
32C22×C7×C8—22no—
33C7×C4⋊Q8—22no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8C2×C412yes—
36C7×C4⋊Q8D411yescharacteristic
37C7×#127D411yescharacteristic
38C7×#124C2×C412yes—
39C7×#121—22no—
40C4×C7×D4—22no—
41C2×C7×C4⋊C4—22no—
42C2×C42×C7C2311yescharacteristic
43C7×C4⋊C8—22no—
44C7×C4⋊C8—22no—
45C7×C4⋊C8D412yes—
46C7×C4⋊C8D412yes—
47C7×C22⋊C8—24no—
48C7×C22⋊C8—22no—
49C7×#97C2×C412yes—
50C4×C7×C8—21no—
51C4×C7×C8—22no—
52#3152C2×C711yescharacteristic
53#2979C2×C711yescharacteristic
54#1560C2×C711yescharacteristic
55#1549C2×C712yescomplemented
56#1299C2×C712yescomplemented
57C7×#41—42no—
58C7×#41—42no—
59C2×C7×Q8—22no—
60C2×C7×Q8—42no—
61C2×C7×Q8—42no—
62C2×C7×Q8—41no—
63C2×C7×Q8C22⋊C412yes—
64C2×C7×D4—22no—
65C2×C7×D4—22no—
66C2×C7×D4C22⋊C412yes—
67C22×C4×C7—22no—
68C22×C4×C7—41no—
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7#4112yes—
71C7×Q16—48no—
72C7×SD16—48no—
73C7×M16—22no—
74C7×M16—22no—
75C7×M16—82no—
76C7×M16—82no—
77C2×C7×C8—22no—
78C2×C7×C8—22no—
79C2×C7×C8—22no—
80C2×C7×C8—42no—
81C2×C7×C8—82no—
82C7×C4⋊C4—22no—
83C7×C4⋊C4—24no—
84C7×C4⋊C4—42no—
85C7×C22⋊C4—24no—
86C42×C7C22×C411yescharacteristic
87C42×C7C2×D411yescharacteristic
88C42×C7C2×D412yes—
89C2×#137—22no—
90#532C22×C711yescharacteristic
91C2×C4⋊Q8C22×C711yescharacteristic
92#497C4×C714yes—
93#494—21no—
94#492—21no—
95#436—22no—
96C8×D4—22no—
97#431C22×C712yes—
98#423C22×C712yes—
99#408—22no—
100C4×M16C22×C711yescharacteristic
101#333—21no—
102#332—22no—
103#332—22no—
104#331—21no—
105C23×C7—22no—
106C23×C7#12311yescharacteristic
107C7×Q8—42no—
108C7×Q8—44no—
109C7×Q8—81no—
110C7×Q8—81no—
111C7×D4—42no—
112C7×D4—42no—
113C7×D4—42no—
114C7×D4—82no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—22no—
118C2×C4×C7—22no—
119C2×C4×C7—22no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—82no—
124C2×C4×C7C2×C22⋊C411yescharacteristic
125C2×C4×C7C4×D412yes—
126C2×C4×C7#12011yescharacteristic
127C2×C4×C7#12112yes—
128C7×C8—24no—
129C7×C8—42no—
130C7×C8—42no—
131C7×C8—82no—
132C2×#41C7×D412yes—
133C22×Q8—21no—
134#137—44no—
135#137—44no—
136C2×Q16—24no—
137C2×SD16—24no—
138C2×M16—21no—
139C2×M16—22no—
140C2×M16—22no—
141C22×C8—22no—
142C4⋊Q8—22no—
143C4⋊Q8—21no—
144C4⋊Q8C2×C4×C712yes—
145C4⋊Q8C7×D411yescharacteristic
146#127C7×D411yescharacteristic
147#124C2×C4×C712yes—
148#121—22no—
149C4×D4—22no—
150C2×C4⋊C4—22no—
151C2×C42C23×C711yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8C7×D412yes—
155C4⋊C8C7×D412yes—
156C22⋊C8—24no—
157C22⋊C8—22no—
158#97C2×C4×C712yes—
159C4×C8—21no—
160C4×C8—22no—
161C22×C7—21no—
162C22×C7—22no—
163C22×C7—42no—
164C22×C7—44no—
165C22×C7#38611yescharacteristic
166C4×C7—21no—
167C4×C7—22no—
168C4×C7—42no—
169C4×C7—82no—
170C4×C7#45311yescharacteristic
171C4×C7#45311yescharacteristic
172C4×C7#47112yes—
173C4×C7#47312yes—
174#41—42no—
175#41—42no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—41no—
180C2×Q8C7×C22⋊C412yes—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4C7×C22⋊C412yes—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4C2×C7×D411yescharacteristic
187C22×C4C7×#4112yes—
188Q16—48no—
189SD16—48no—
190M16—22no—
191M16—22no—
192M16—82no—
193M16—82no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—42no—
198C2×C8—82no—
199C4⋊C4—22no—
200C4⋊C4—24no—
201C4⋊C4—42no—
202C22⋊C4—24no—
203C42C22×C4×C711yescharacteristic
204C42C2×C7×D411yescharacteristic
205C42C2×C7×D412yes—
206C2×C7—41no—
207C2×C7—82no—
208C2×C7#188711yescharacteristic
209C2×C7#190812yes—
210C23—22no—
211C23C7×#12311yescharacteristic
212Q8—42no—
213Q8—44no—
214Q8—81no—
215Q8—81no—
216D4—42no—
217D4—42no—
218D4—42no—
219D4—82no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—82no—
229C2×C4C2×C7×C22⋊C411yescharacteristic
230C2×C4C4×C7×D412yes—
231C2×C4C7×#12011yescharacteristic
232C2×C4C7×#12112yes—
233C8—24no—
234C8—42no—
235C8—42no—
236C8—82no—
237C7#943511yescharacteristic, direct product factor, Sylow
238C22—21no—
239C22—22no—
240C22—42no—
241C22—44no—
242C22C7×#38611yescharacteristic
243C4—21no—
244C4—22no—
245C4—42no—
246C4—82no—
247C4C7×#45311yescharacteristic
248C4C7×#45311yescharacteristic
249C4C7×#47112yes—
250C4C7×#47312yes—
251C2—41no—
252C2—82no—
253C2C7×#188711yescharacteristic
254C2C7×#190812yes—
subgroupG/H
center, socleC22×C7#386
commutatorC42C22×C4×C7
Frattini, cosocleC2×C42C23×C7
prime radicalC7×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1549C2semidirect
5. C7×#1299C2semidirect
22. #9435C7direct (N × H)
55. #1549C2×C7semidirect
56. #1299C2×C7semidirect
237. C7#9435direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31522
C7×#29792
C7×#15602
C7×#15492
C7×#12992
#94357