Finite Group Databasebeta

← C7×#9030 #13186246

Subgroups — C7×#9030 #13186246

Order 1792.

484 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2983C211yesmaximal, characteristic
2C7×#2399C211yesmaximal, characteristic
3C4×C7×#101C211yesmaximal, characteristic
4C7×#1491C212yesmaximal
5C7×#1300C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#446—24no—
9C7×#432—21no—
10C7×#432C2212yes—
11C7×#431—21no—
12C2×C7×#101—21no—
13C4×C7×M16C2212yes—
14C7×#398—21no—
15C7×#398C411yescharacteristic
16C7×#398C411yescharacteristic
17C7×#395—21no—
18C7×#395C411yescharacteristic
19C7×#395C411yescharacteristic
20C4×C7×C4⋊C4—21no—
21C4×C7×C4⋊C4—21no—
22C7×#376C2211yescharacteristic
23C7×#343—21no—
24C7×Q8⋊C8—24no—
25#9030C711yesmaximal, characteristic, direct product factor, Sylow
26C22×C7×Q8C2×C411yescharacteristic
27C22×C7×Q8D411yescharacteristic
28C2×C7×M16—22no—
29C4×C7×Q8—22no—
30C4×C7×Q8—22no—
31C4×C7×Q8—22no—
32C4×C7×Q8—22no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4C2×C411yescharacteristic
40C2×C7×C4⋊C4C2×C411yescharacteristic
41C2×C7×C4⋊C4D411yescharacteristic
42C2×C42×C7—21no—
43C2×C42×C7—21no—
44C2×C42×C7D411yescharacteristic
45C2×C42×C7D411yescharacteristic
46C2×C42×C7C2311yescharacteristic
47C7×C4⋊C8—22no—
48C7×C4⋊C8—22no—
49C7×C4⋊C8D414yes—
50C7×#101—24no—
51C7×C22⋊C8—22no—
52C7×#97—22no—
53C7×#97—22no—
54C7×#97—22no—
55C4×C7×C8—22no—
56C4×C7×C8—22no—
57C7×#95—21no—
58C7×#95—21no—
59C7×#95—21no—
60C7×#95—21no—
61C7×#95—21no—
62C7×#95C2×C411yescharacteristic
63C7×#95C2×C411yescharacteristic
64#2983C2×C711yescharacteristic
65#2399C2×C711yescharacteristic
66C4×#101C2×C711yescharacteristic
67#1491C2×C712yes—
68#1300C2×C712yes—
69C2×C7×Q8—22no—
70C2×C7×Q8—22no—
71C2×C7×Q8—22no—
72C2×C7×Q8—41no—
73C2×C7×Q8—42no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22×C411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C7×M16—24no—
86C7×M16—42no—
87C2×C7×C8—24no—
88C2×C7×C8—42no—
89C7×C4⋊C4—22no—
90C7×C4⋊C4—22no—
91C7×C4⋊C4—22no—
92C7×C4⋊C4—22no—
93C7×C4⋊C4—42no—
94C7×C4⋊C4—42no—
95C7×C4⋊C4—42no—
96C7×C4⋊C4—42no—
97C7×C4⋊C4—42no—
98C42×C7—24no—
99C42×C7—21no—
100C42×C7—21no—
101C42×C7—21no—
102C42×C7—21no—
103C42×C7—41no—
104C42×C7—41no—
105C42×C7C2×D412yes—
106C42×C7#4112yes—
107C2×C4×Q8C22×C711yescharacteristic
108C2×C4×Q8C22×C711yescharacteristic
109#446—24no—
110#432—21no—
111#432C22×C712yes—
112#431—21no—
113C2×#101—21no—
114C4×M16C22×C712yes—
115#398—21no—
116#398C4×C711yescharacteristic
117#398C4×C711yescharacteristic
118#395—21no—
119#395C4×C711yescharacteristic
120#395C4×C711yescharacteristic
121C4×C4⋊C4—21no—
122C4×C4⋊C4—21no—
123#376C22×C711yescharacteristic
124#343—21no—
125Q8⋊C8—24no—
126C23×C7C2×C22⋊C411yescharacteristic
127C7×Q8—24no—
128C7×Q8—44no—
129C7×Q8—42no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7#10412yes—
156C2×C4×C7C4×D412yes—
157C2×C4×C7#12011yescharacteristic
158C2×C4×C7#12112yes—
159C2×C4×C7#12311yescharacteristic
160C7×C8—44no—
161C7×C8—44no—
162C22×Q8C2×C4×C711yescharacteristic
163C22×Q8C7×D411yescharacteristic
164C2×M16—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×C4×C711yescharacteristic
175C2×C4⋊C4C2×C4×C711yescharacteristic
176C2×C4⋊C4C2×C4×C711yescharacteristic
177C2×C4⋊C4C7×D411yescharacteristic
178C2×C42—21no—
179C2×C42—21no—
180C2×C42C7×D411yescharacteristic
181C2×C42C7×D411yescharacteristic
182C2×C42C23×C711yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8C7×D414yes—
186#101—24no—
187C22⋊C8—22no—
188#97—22no—
189#97—22no—
190#97—22no—
191C4×C8—22no—
192C4×C8—22no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95C2×C4×C711yescharacteristic
199#95C2×C4×C711yescharacteristic
200C22×C7—21no—
201C22×C7—21no—
202C22×C7#38611yescharacteristic
203C22×C7C2×#10411yescharacteristic
204C22×C7#42111yescharacteristic
205C4×C7—22no—
206C4×C7—22no—
207C4×C7—21no—
208C4×C7—22no—
209C4×C7—42no—
210C4×C7—42no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7—42no—
215C4×C7—81no—
216C4×C7#45612yes—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—42no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4C7×C22⋊C411yescharacteristic
227C22×C4C7×C22⋊C411yescharacteristic
228C22×C4C7×C22⋊C411yescharacteristic
229C22×C4C7×C22⋊C411yescharacteristic
230C22×C4C22×C4×C711yescharacteristic
231C22×C4C2×C7×D411yescharacteristic
232C22×C4C2×C7×D411yescharacteristic
233M16—24no—
234M16—42no—
235C2×C8—24no—
236C2×C8—42no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C42—24no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—41no—
252C42—41no—
253C42C2×C7×D412yes—
254C42C7×#4112yes—
255C2×C7—21no—
256C2×C7—21no—
257C2×C7#187111yescharacteristic
258C2×C7#188611yescharacteristic
259C2×C7#189111yescharacteristic
260C23C2×C7×C22⋊C411yescharacteristic
261Q8—24no—
262Q8—44no—
263Q8—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4C7×#10412yes—
290C2×C4C4×C7×D412yes—
291C2×C4C7×#12011yescharacteristic
292C2×C4C7×#12112yes—
293C2×C4C7×#12311yescharacteristic
294C8—44no—
295C8—44no—
296C7#903011yescharacteristic, direct product factor, Sylow
297C22—21no—
298C22—21no—
299C22C7×#38611yescharacteristic
300C22C2×C7×#10411yescharacteristic
301C22C7×#42111yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4C7×#45612yes—
314C2—21no—
315C2—21no—
316C2C7×#187111yescharacteristic
317C2C7×#188611yescharacteristic
318C2C7×#189111yescharacteristic
subgroupG/H
centerC2×C4×C7#120
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C42C23×C7
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
25. #9030C7direct (N × H)
296. C7#9030direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29832
C7×#23992
C4×C7×#1012
C7×#14912
C7×#13002
#90307