Finite Group Databasebeta

← C7×#9470 #13186686

Subgroups — C7×#9470 #13186686

Order 1792.

598 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2972C211yesmaximal, characteristic
2C7×#2486C211yesmaximal, characteristic
3C7×#1823C212yesmaximal, complemented
4C7×#1799C211yesmaximal, characteristic
5C7×#1289C212yesmaximal, complemented
6C2×C7×#123—21no—
7C2×C4×C7×D4C2211yescharacteristic
8C22×C7×C4⋊C4C2211yescharacteristic
9C7×C8×D4—24no—
10C7×#431—21no—
11C2×C7×#99—21no—
12C2×C7×C22⋊C8—21no—
13C2×C7×C22⋊C8C2212yes—
14C7×#398C412yescomplemented
15C7×#397C412yescomplemented
16C7×#389—21no—
17C7×#381—21no—
18C7×#380—21no—
19C7×#380C2212yes—
20C7×#380C2211yescharacteristic
21C7×#342—21no—
22C7×#340—24no—
23#9470C711yesmaximal, characteristic, direct product factor, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7—21no—
26C23×C4×C7D411yescharacteristic
27C23×C4×C7C2311yescharacteristic
28C22×C7×C8—22no—
29C22×C7×C8D414yes—
30C7×#123—42no—
31C7×#123—42no—
32C4×C7×D4—22no—
33C4×C7×D4—22no—
34C2×C7×C4⋊C4—22no—
35C2×C7×C4⋊C4—22no—
36C2×C7×C4⋊C4—22no—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4—22no—
40C2×C7×C4⋊C4C2×C412yes—
41C2×C7×C4⋊C4C2×C411yescharacteristic
42C2×C7×C22⋊C4—22no—
43C2×C7×C22⋊C4—21no—
44C2×C7×C22⋊C4—22no—
45C2×C7×C22⋊C4C2×C411yescharacteristic
46C2×C7×C22⋊C4D411yescharacteristic
47C2×C42×C7D411yescharacteristic
48C7×C4⋊C8—22no—
49C7×#99—42no—
50C7×C22⋊C8—22no—
51C7×C22⋊C8—22no—
52C7×C22⋊C8—22no—
53C4×C7×C8—22no—
54C7×#95—22no—
55C7×#95—22no—
56C7×#95—22no—
57C7×#95C2×C412yes—
58#2972C2×C711yescharacteristic
59#2486C2×C711yescharacteristic
60#1823C2×C712yescomplemented
61#1799C2×C711yescharacteristic
62#1289C2×C712yescomplemented
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—22no—
66C2×C7×D4—22no—
67C2×C7×D4D812yes—
68C2×C7×D4SD1612yes—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—22no—
72C22×C4×C7—22no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7—42no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—42no—
79C22×C4×C7—42no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22×C411yescharacteristic
84C22×C4×C7C2×D412yes—
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7#4112yes—
87C2×C7×C8—24no—
88C2×C7×C8—44no—
89C2×C7×C8—82no—
90C7×C4⋊C4—22no—
91C7×C4⋊C4—24no—
92C7×C4⋊C4—42no—
93C7×C4⋊C4—44no—
94C7×C4⋊C4—44no—
95C7×C4⋊C4—41no—
96C7×C4⋊C4—41no—
97C7×C22⋊C4—22no—
98C7×C22⋊C4—22no—
99C7×C22⋊C4—44no—
100C7×C22⋊C4—41no—
101C7×C22⋊C4—41no—
102C7×C22⋊C4—42no—
103C7×C22⋊C4—42no—
104C42×C7—21no—
105C42×C7—21no—
106C2×#123—21no—
107C2×C4×D4C22×C711yescharacteristic
108C22×C4⋊C4C22×C711yescharacteristic
109C8×D4—24no—
110#431—21no—
111C2×#99—21no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8C22×C712yes—
114#398C4×C712yescomplemented
115#397C4×C712yescomplemented
116#389—21no—
117#381—21no—
118#380—21no—
119#380C22×C712yes—
120#380C22×C711yescharacteristic
121#342—21no—
122#340—24no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7#10212yes—
130C23×C7C2×C22⋊C411yescharacteristic
131C23×C7#12112yes—
132C23×C7C2×D811yescharacteristic
133C23×C7C2×SD1611yescharacteristic
134C23×C7#13512yes—
135C7×D4—24no—
136C7×D4—24no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—24no—
140C2×C4×C7—22no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—41no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7—42no—
151C2×C4×C7—42no—
152C2×C4×C7—42no—
153C2×C4×C7—42no—
154C2×C4×C7—81no—
155C2×C4×C7—82no—
156C2×C4×C7—82no—
157C2×C4×C7—82no—
158C2×C4×C7—82no—
159C2×C4×C7—82no—
160C2×C4×C7#10212yes—
161C2×C4×C7C4×D412yes—
162C2×C4×C7#12011yescharacteristic
163C2×C4×C7#12311yescharacteristic
164C7×C8—44no—
165C22×D4C7×D411yescharacteristic
166C23×C4—21no—
167C23×C4C7×D411yescharacteristic
168C23×C4C23×C711yescharacteristic
169C22×C8—22no—
170C22×C8C7×D414yes—
171#123—42no—
172#123—42no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×C4×C712yes—
182C2×C4⋊C4C2×C4×C711yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4C2×C4×C711yescharacteristic
187C2×C22⋊C4C7×D411yescharacteristic
188C2×C42C7×D411yescharacteristic
189C4⋊C8—22no—
190#99—42no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C4×C8—22no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95C2×C4×C712yes—
199C22×C7—21no—
200C22×C7—22no—
201C22×C7—21no—
202C22×C7—22no—
203C22×C7—22no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—42no—
207C22×C7—42no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—81no—
211C22×C7#38611yescharacteristic
212C22×C7C2×#10211yescharacteristic
213C22×C7#41611yescharacteristic
214C22×C7#46512yes—
215C22×C7#46612yes—
216C4×C7—21no—
217C4×C7—22no—
218C4×C7—22no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—82no—
222C4×C7—82no—
223C4×C7—162no—
224C4×C7#45812yes—
225C24C7×C22⋊C411yescharacteristic
226C24C2×C7×D411yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4C7×D812yes—
230C2×D4C7×SD1612yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C7×C22⋊C411yescharacteristic
243C22×C4C7×C22⋊C411yescharacteristic
244C22×C4C7×C22⋊C411yescharacteristic
245C22×C4C22×C4×C711yescharacteristic
246C22×C4C2×C7×D412yes—
247C22×C4C2×C7×D411yescharacteristic
248C22×C4C7×#4112yes—
249C2×C8—24no—
250C2×C8—44no—
251C2×C8—82no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—44no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—44no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C2×C7—21no—
269C2×C7—22no—
270C2×C7—21no—
271C2×C7—22no—
272C2×C7—42no—
273C2×C7#189011yescharacteristic
274C2×C7#189311yescharacteristic
275C2×C7#190911yescharacteristic
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23C7×#10212yes—
283C23C2×C7×C22⋊C411yescharacteristic
284C23C7×#12112yes—
285C23C2×C7×D811yescharacteristic
286C23C2×C7×SD1611yescharacteristic
287C23C7×#13512yes—
288D4—24no—
289D4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4C7×#10212yes—
314C2×C4C4×C7×D412yes—
315C2×C4C7×#12011yescharacteristic
316C2×C4C7×#12311yescharacteristic
317C8—44no—
318C7#947011yescharacteristic, direct product factor, Sylow
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C7×#38611yescharacteristic
332C22C2×C7×#10211yescharacteristic
333C22C7×#41611yescharacteristic
334C22C7×#46512yes—
335C22C7×#46612yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—162no—
344C4C7×#45812yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2C7×#189011yescharacteristic
351C2C7×#189311yescharacteristic
352C2C7×#190911yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC22×C7×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1823C2semidirect
5. C7×#1289C2semidirect
14. C7×#398C4semidirect
15. C7×#397C4semidirect
23. #9470C7direct (N × H)
60. #1823C2×C7semidirect
62. #1289C2×C7semidirect
114. #398C4×C7semidirect
115. #397C4×C7semidirect
318. C7#9470direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29722
C7×#24862
C7×#18232
C7×#17992
C7×#12892
#94707