Finite Group Databasebeta

← C7×#13428 #13190644

Subgroups — C7×#13428 #13190644

Order 1792.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2734C211yesmaximal, characteristic
2C2×C7×#356C212yesmaximal
3C7×#1886C212yesmaximal
4C7×#1857C211yesmaximal, characteristic
5C7×#1394C211yesmaximal, characteristic
6C2×C7×C4⋊Q8C2212yes—
7C7×#519C2211yescharacteristic
8C7×#428—21no—
9C7×#419—22no—
10C2×C7×#101C2212yes—
11C2×C7×#101C2211yescharacteristic
12C7×#398—21no—
13C7×#395—22no—
14C7×#391C2211yescharacteristic
15C7×#389—21no—
16C7×#387—22no—
17C7×#356—24no—
18C7×#339—21no—
19C7×#339—22no—
20#13428C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8D412yes—
22C22×C7×Q8C2311yescharacteristic
23C2×C7×M16—21no—
24C2×C7×M16—22no—
25C7×C4⋊Q8—22no—
26C7×C4⋊Q8—22no—
27C7×C4⋊Q8—22no—
28C7×C4⋊Q8—22no—
29C4×C7×Q8—41no—
30C4×C7×Q8—41no—
31C7×#117—22no—
32C7×#117—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—22no—
35C2×C7×C4⋊C4—22no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C42×C7D412yes—
40C2×C42×C7D411yescharacteristic
41C7×#107—41no—
42C7×#106—41no—
43C7×#103—42no—
44C7×#103—42no—
45C7×#101—21no—
46C7×#101—22no—
47C7×#101—22no—
48C7×#101D412yes—
49C7×#95—21no—
50C7×#95—22no—
51C7×#95—22no—
52C7×#95—22no—
53#2734C2×C711yescharacteristic
54C2×#356C2×C712yes—
55#1886C2×C712yes—
56#1857C2×C711yescharacteristic
57#1394C2×C711yescharacteristic
58C2×C7×Q8—22no—
59C2×C7×Q8—22no—
60C2×C7×Q8—41no—
61C2×C7×Q8—41no—
62C2×C7×Q8—42no—
63C2×C7×Q8—42no—
64C2×C7×Q8C2×D411yescharacteristic
65C2×C7×Q8#4111yescharacteristic
66C2×C7×Q8#4112yes—
67C22×C4×C7—21no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—22no—
71C22×C4×C7C2×D412yes—
72C22×C4×C7C2×D411yescharacteristic
73C7×M16—22no—
74C7×M16—41no—
75C7×M16—42no—
76C7×M16—42no—
77C2×C7×C8—41no—
78C2×C7×C8—42no—
79C7×C4⋊C4—24no—
80C7×C4⋊C4—22no—
81C7×C4⋊C4—22no—
82C7×C4⋊C4—21no—
83C7×C4⋊C4—21no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—81no—
90C7×C4⋊C4—81no—
91C7×C22⋊C4—41no—
92C42×C7—22no—
93C42×C7—22no—
94C42×C7—41no—
95C42×C7—41no—
96C42×C7—42no—
97C2×C4⋊Q8C22×C712yes—
98#519C22×C711yescharacteristic
99#428—21no—
100#419—22no—
101C2×#101C22×C712yes—
102C2×#101C22×C711yescharacteristic
103#398—21no—
104#395—22no—
105#391C22×C711yescharacteristic
106#389—21no—
107#387—22no—
108#356—24no—
109#339—21no—
110#339—22no—
111C23×C7#12011yescharacteristic
112C7×Q8—41no—
113C7×Q8—41no—
114C7×Q8—42no—
115C7×Q8—44no—
116C7×Q8—82no—
117C2×C4×C7—21no—
118C2×C4×C7—22no—
119C2×C4×C7—21no—
120C2×C4×C7—22no—
121C2×C4×C7—22no—
122C2×C4×C7—24no—
123C2×C4×C7—41no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—41no—
127C2×C4×C7—42no—
128C2×C4×C7—42no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—42no—
133C2×C4×C7—42no—
134C2×C4×C7#12112yes—
135C2×C4×C7#12111yescharacteristic
136C2×C4×C7#12312yes—
137C2×C4×C7#12411yescharacteristic
138C7×C8—42no—
139C7×C8—82no—
140C22×Q8C7×D412yes—
141C22×Q8C23×C711yescharacteristic
142C2×M16—21no—
143C2×M16—22no—
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4⋊Q8—22no—
147C4⋊Q8—22no—
148C4×Q8—41no—
149C4×Q8—41no—
150#117—22no—
151#117—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C7×D411yescharacteristic
158C2×C42C7×D412yes—
159C2×C42C7×D411yescharacteristic
160#107—41no—
161#106—41no—
162#103—42no—
163#103—42no—
164#101—21no—
165#101—22no—
166#101—22no—
167#101C7×D412yes—
168#95—21no—
169#95—22no—
170#95—22no—
171#95—22no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7#39411yescharacteristic
175C22×C7B(4,𝔽2)11yescharacteristic
176C22×C7#45811yescharacteristic
177C4×C7—21no—
178C4×C7—22no—
179C4×C7—22no—
180C4×C7—21no—
181C4×C7—44no—
182C4×C7—42no—
183C4×C7—81no—
184C4×C7—81no—
185C4×C7—81no—
186C4×C7—82no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8C2×C7×D411yescharacteristic
194C2×Q8C7×#4111yescharacteristic
195C2×Q8C7×#4112yes—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4C2×C7×D412yes—
201C22×C4C2×C7×D411yescharacteristic
202M16—22no—
203M16—41no—
204M16—42no—
205M16—42no—
206C2×C8—41no—
207C2×C8—42no—
208C4⋊C4—24no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C22⋊C4—41no—
221C42—22no—
222C42—22no—
223C42—41no—
224C42—41no—
225C42—42no—
226C2×C7—21no—
227C2×C7—21no—
228C2×C7#204411yescharacteristic
229C2×C7#220311yescharacteristic
230C2×C7#220511yescharacteristic
231C23C7×#12011yescharacteristic
232Q8—41no—
233Q8—41no—
234Q8—42no—
235Q8—44no—
236Q8—82no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4C7×#12112yes—
255C2×C4C7×#12111yescharacteristic
256C2×C4C7×#12312yes—
257C2×C4C7×#12411yescharacteristic
258C8—42no—
259C8—82no—
260C7#1342811yescharacteristic, direct product factor, Sylow
261C22—21no—
262C22—21no—
263C22C7×#39411yescharacteristic
264C22C7×B(4,𝔽2)11yescharacteristic
265C22C7×#45811yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—81no—
275C4—81no—
276C2—21no—
277C2—21no—
278C2C7×#204411yescharacteristic
279C2C7×#220311yescharacteristic
280C2C7×#220511yescharacteristic
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
20. #13428C7direct (N × H)
260. C7#13428direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#27342
C2×C7×#3562
C7×#18862
C7×#18572
C7×#13942
#134287