Finite Group Databasebeta

← C7×#14331 #13191547

Subgroups — C7×#14331 #13191547

Order 1792.

1290 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C7×#1445C213yesmaximal, complemented
3C7×#1443C211yesmaximal, characteristic, complemented
4C7×#1440C213yesmaximal
5C7×#1437C213yesmaximal
6C7×#1436C213yesmaximal, complemented
7C4×C7×#95C211yesmaximal, characteristic, complemented
8C22×C7×C4⋊C4C2213yes—
9C22×C7×C22⋊C4C2211yescharacteristic
10C22×C7×C22⋊C4C2213yes—
11C22×C7×C22⋊C4C2213yes—
12C22×C42×C7C2213yes—
13C7×#396C418yescomplemented
14C2×C7×#95C2213yes—
15C2×C7×#95C2213yes—
16C2×C7×#95C2213yes—
17C2×C7×#95C2213yes—
18C2×C7×#95C2213yes—
19C2×C7×#95C2213yes—
20C2×C7×#95C2213yes—
21C2×C7×#95C2211yescharacteristic
22#14331C711yesmaximal, characteristic, direct product factor, Sylow
23C25×C7C2311yescharacteristic
24C23×C4×C7C2313yes—
25C23×C4×C7C2311yescharacteristic
26C23×C4×C7C2313yes—
27C23×C4×C7C2313yes—
28C23×C4×C7C2313yes—
29C23×C4×C7C2311yescharacteristic
30C2×C7×C4⋊C4—43no—
31C2×C7×C4⋊C4—43no—
32C2×C7×C4⋊C4C2×C4112yes—
33C2×C7×C22⋊C4—26no—
34C2×C7×C22⋊C4—26no—
35C2×C7×C22⋊C4—43no—
36C2×C7×C22⋊C4—43no—
37C2×C7×C22⋊C4—43no—
38C2×C7×C22⋊C4—43no—
39C2×C7×C22⋊C4C2×C4112yes—
40C2×C42×C7—26no—
41C2×C42×C7—43no—
42C2×C42×C7—43no—
43C7×#95—26no—
44C7×#95—26no—
45C7×#95—26no—
46C7×#95—43no—
47C7×#95—43no—
48C7×#95—43no—
49C7×#95—43no—
50C7×#95C2×C414yes—
51C2×#396C2×C711yescharacteristic
52#1445C2×C713yescomplemented
53#1443C2×C711yescharacteristic, complemented
54#1440C2×C713yes—
55#1437C2×C713yes—
56#1436C2×C713yescomplemented
57C4×#95C2×C711yescharacteristic, complemented
58C24×C7—23no—
59C24×C7—23no—
60C24×C7—23no—
61C24×C7—23no—
62C24×C7—21no—
63C24×C7—21no—
64C24×C7C22×C412yes—
65C24×C7C2411yescharacteristic
66C22×C4×C7—23no—
67C22×C4×C7—21no—
68C22×C4×C7—23no—
69C22×C4×C7—23no—
70C22×C4×C7—23no—
71C22×C4×C7—23no—
72C22×C4×C7—23no—
73C22×C4×C7—23no—
74C22×C4×C7—23no—
75C22×C4×C7—23no—
76C22×C4×C7—23no—
77C22×C4×C7—23no—
78C22×C4×C7—23no—
79C22×C4×C7—23no—
80C22×C4×C7—23no—
81C22×C4×C7—23no—
82C22×C4×C7—23no—
83C22×C4×C7—23no—
84C22×C4×C7—23no—
85C22×C4×C7—23no—
86C22×C4×C7—23no—
87C22×C4×C7—23no—
88C22×C4×C7—23no—
89C22×C4×C7—23no—
90C22×C4×C7—23no—
91C22×C4×C7—23no—
92C22×C4×C7—23no—
93C22×C4×C7—23no—
94C22×C4×C7—23no—
95C22×C4×C7—21no—
96C22×C4×C7C22×C416yes—
97C22×C4×C7C22×C416yes—
98C22×C4×C7#4116yes—
99C22×C4×C7#4116yes—
100C7×C4⋊C4—412no—
101C7×C22⋊C4—412no—
102C7×C22⋊C4—412no—
103C7×C22⋊C4—44no—
104C42×C7—412no—
105C22×C4⋊C4C22×C713yes—
106C22×C22⋊C4C22×C711yescharacteristic
107C22×C22⋊C4C22×C713yes—
108C22×C22⋊C4C22×C713yes—
109C22×C42C22×C713yes—
110#396C4×C718yescomplemented
111C2×#95C22×C713yes—
112C2×#95C22×C713yes—
113C2×#95C22×C713yes—
114C2×#95C22×C713yes—
115C2×#95C22×C713yes—
116C2×#95C22×C713yes—
117C2×#95C22×C713yes—
118C2×#95C22×C711yescharacteristic
119C23×C7—26no—
120C23×C7—26no—
121C23×C7—22no—
122C23×C7—41no—
123C23×C7—43no—
124C23×C7—43no—
125C23×C7—43no—
126C23×C7—43no—
127C23×C7—43no—
128C23×C7—43no—
129C23×C7—43no—
130C23×C7—43no—
131C23×C7—43no—
132C23×C7C23×C411yescharacteristic
133C23×C7C2×#4113yes—
134C23×C7C2×#4113yes—
135C23×C7H(5,𝔽2)13yes—
136C23×C7H(5,𝔽2)13yes—
137C23×C72−1+411yescharacteristic
138C23×C72−1+411yescharacteristic
139C2×C4×C7—26no—
140C2×C4×C7—26no—
141C2×C4×C7—26no—
142C2×C4×C7—26no—
143C2×C4×C7—26no—
144C2×C4×C7—26no—
145C2×C4×C7—26no—
146C2×C4×C7—26no—
147C2×C4×C7—26no—
148C2×C4×C7—26no—
149C2×C4×C7—26no—
150C2×C4×C7—43no—
151C2×C4×C7—43no—
152C2×C4×C7—43no—
153C2×C4×C7—43no—
154C2×C4×C7—43no—
155C2×C4×C7—43no—
156C2×C4×C7—43no—
157C2×C4×C7—43no—
158C2×C4×C7—43no—
159C2×C4×C7—43no—
160C2×C4×C7—43no—
161C2×C4×C7—43no—
162C2×C4×C7—41no—
163C2×C4×C7—43no—
164C2×C4×C7—43no—
165C2×C4×C7—43no—
166C2×C4×C7—43no—
167C2×C4×C7—43no—
168C2×C4×C7—43no—
169C2×C4×C7—43no—
170C2×C4×C7—43no—
171C2×C4×C7—43no—
172C2×C4×C7#12614yes—
173C25C23×C711yescharacteristic
174C23×C4C23×C713yes—
175C23×C4C23×C711yescharacteristic
176C23×C4C23×C713yes—
177C23×C4C23×C713yes—
178C23×C4C23×C713yes—
179C23×C4C23×C711yescharacteristic
180C2×C4⋊C4—43no—
181C2×C4⋊C4—43no—
182C2×C4⋊C4C2×C4×C7112yes—
183C2×C22⋊C4—26no—
184C2×C22⋊C4—26no—
185C2×C22⋊C4—43no—
186C2×C22⋊C4—43no—
187C2×C22⋊C4—43no—
188C2×C22⋊C4—43no—
189C2×C22⋊C4C2×C4×C7112yes—
190C2×C42—26no—
191C2×C42—43no—
192C2×C42—43no—
193#95—26no—
194#95—26no—
195#95—26no—
196#95—43no—
197#95—43no—
198#95—43no—
199#95—43no—
200#95C2×C4×C714yes—
201C22×C7—42no—
202C22×C7—46no—
203C22×C7—46no—
204C22×C7—81no—
205C22×C7—81no—
206C22×C7—83no—
207C22×C7—83no—
208C22×C7C4×#4113yes—
209C22×C7#51813yes—
210C22×C7#51911yescharacteristic
211C22×C7C2×#12611yescharacteristic
212C22×C7#52913yes—
213C22×C7#53813yes—
214C22×C7#53813yes—
215C22×C7#53913yes—
216C22×C7#53913yes—
217C22×C7#54013yes—
218C22×C7#54013yes—
219C22×C7#54213yes—
220C22×C7#54213yes—
221C4×C7—24no—
222C4×C7—46no—
223C4×C7—46no—
224C4×C7—46no—
225C4×C7—81no—
226C4×C7—83no—
227C24—23no—
228C24—23no—
229C24—23no—
230C24—23no—
231C24—21no—
232C24—21no—
233C24C22×C4×C712yes—
234C24C24×C711yescharacteristic
235C22×C4—23no—
236C22×C4—21no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—23no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—21no—
265C22×C4C22×C4×C716yes—
266C22×C4C22×C4×C716yes—
267C22×C4C7×#4116yes—
268C22×C4C7×#4116yes—
269C4⋊C4—412no—
270C22⋊C4—412no—
271C22⋊C4—412no—
272C22⋊C4—44no—
273C42—412no—
274C2×C7—82no—
275C2×C7C4×#12611yescharacteristic
276C2×C7#233213yes—
277C2×C7#233313yes—
278C2×C7#264311yescharacteristic
279C2×C7#264411yescharacteristic
280C2×C7#264913yes—
281C2×C7#265113yes—
282C23—26no—
283C23—26no—
284C23—22no—
285C23—41no—
286C23—43no—
287C23—43no—
288C23—43no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23C23×C4×C711yescharacteristic
296C23C2×C7×#4113yes—
297C23C2×C7×#4113yes—
298C23C7×H(5,𝔽2)13yes—
299C23C7×H(5,𝔽2)13yes—
300C23C7×2−1+411yescharacteristic
301C23C7×2−1+411yescharacteristic
302C2×C4—26no—
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—43no—
314C2×C4—43no—
315C2×C4—43no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—41no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4C7×#12614yes—
336C7#1433111yescharacteristic, direct product factor, Sylow
337C22—42no—
338C22—46no—
339C22—46no—
340C22—81no—
341C22—81no—
342C22—83no—
343C22—83no—
344C22C4×C7×#4113yes—
345C22C7×#51813yes—
346C22C7×#51911yescharacteristic
347C22C2×C7×#12611yescharacteristic
348C22C7×#52913yes—
349C22C7×#53813yes—
350C22C7×#53813yes—
351C22C7×#53913yes—
352C22C7×#53913yes—
353C22C7×#54013yes—
354C22C7×#54013yes—
355C22C7×#54213yes—
356C22C7×#54213yes—
357C4—24no—
358C4—46no—
359C4—46no—
360C4—46no—
361C4—81no—
362C4—83no—
363C2—82no—
364C2C4×C7×#12611yescharacteristic
365C2C7×#233213yes—
366C2C7×#233313yes—
367C2C7×#264311yescharacteristic
368C2C7×#264411yescharacteristic
369C2C7×#264913yes—
370C2C7×#265113yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#1445C2semidirect
3. C7×#1443C2semidirect
6. C7×#1436C2semidirect
7. C4×C7×#95C2semidirect
13. C7×#396C4semidirect
22. #14331C7direct (N × H)
52. #1445C2×C7semidirect
53. #1443C2×C7semidirect
56. #1436C2×C7semidirect
57. C4×#95C2×C7semidirect
110. #396C4×C7semidirect
336. C7#14331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C7×#14452
C7×#14432
C7×#14402
C7×#14372
C7×#14362
C4×C7×#952
#143317