Finite Group Databasebeta

← C7×#14562 #13191778

Subgroups — C7×#14562 #13191778

Order 1792.

1590 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C2×C7×#389C213yesmaximal, complemented
3C2×C7×#388C213yesmaximal
4C7×#1444C211yesmaximal, characteristic, complemented
5C7×#1443C211yesmaximal, characteristic, complemented
6C7×#1439C213yesmaximal
7C7×#1436C213yesmaximal, complemented
8C22×C7×C4⋊C4C2213yes—
9C22×C7×C4⋊C4C2213yes—
10C22×C7×C4⋊C4C2213yes—
11C22×C7×C22⋊C4C2213yes—
12C22×C7×C22⋊C4C2213yes—
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C42×C7C2213yes—
15C7×#396C418yescomplemented
16C7×#389—212no—
17C7×#388—212no—
18C2×C7×#95C2213yes—
19C2×C7×#95C2213yes—
20C2×C7×#95C2213yes—
21C2×C7×#95C2213yes—
22C2×C7×#95C2211yescharacteristic
23C2×C7×#95C2213yes—
24#14562C711yesmaximal, characteristic, direct product factor, Sylow
25C25×C7C2311yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×C4×C7C2311yescharacteristic
28C23×C4×C7C2313yes—
29C23×C4×C7C2313yes—
30C23×C4×C7C2313yes—
31C23×C4×C7C2313yes—
32C2×C7×C4⋊C4—26no—
33C2×C7×C4⋊C4—26no—
34C2×C7×C4⋊C4—26no—
35C2×C7×C4⋊C4—26no—
36C2×C7×C4⋊C4—26no—
37C2×C7×C4⋊C4—26no—
38C2×C7×C4⋊C4—43no—
39C2×C7×C4⋊C4—43no—
40C2×C7×C4⋊C4C2×C4112yes—
41C2×C7×C22⋊C4—26no—
42C2×C7×C22⋊C4—26no—
43C2×C7×C22⋊C4—26no—
44C2×C7×C22⋊C4—26no—
45C2×C7×C22⋊C4—43no—
46C2×C7×C22⋊C4—43no—
47C2×C7×C22⋊C4C2×C4112yes—
48C2×C42×C7—26no—
49C2×C42×C7—26no—
50C2×C42×C7—43no—
51C7×#95—26no—
52C7×#95—26no—
53C7×#95—26no—
54C7×#95—43no—
55C7×#95C2×C414yes—
56C7×#95D4112yes—
57C2×#396C2×C711yescharacteristic
58C2×#389C2×C713yescomplemented
59C2×#388C2×C713yes—
60#1444C2×C711yescharacteristic, complemented
61#1443C2×C711yescharacteristic, complemented
62#1439C2×C713yes—
63#1436C2×C713yescomplemented
64C24×C7—23no—
65C24×C7—23no—
66C24×C7—23no—
67C24×C7—21no—
68C24×C7—21no—
69C24×C7—23no—
70C24×C7C22×C412yes—
71C24×C7C2411yescharacteristic
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—23no—
96C22×C4×C7—23no—
97C22×C4×C7—23no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7C22×C416yes—
101C22×C4×C7C22×C416yes—
102C22×C4×C7C2×D416yes—
103C22×C4×C7C2×D416yes—
104C22×C4×C7C2×D416yes—
105C22×C4×C7#4116yes—
106C7×C4⋊C4—224no—
107C7×C4⋊C4—412no—
108C7×C4⋊C4—412no—
109C7×C22⋊C4—224no—
110C7×C22⋊C4—412no—
111C7×C22⋊C4—44no—
112C42×C7—412no—
113C22×C4⋊C4C22×C713yes—
114C22×C4⋊C4C22×C713yes—
115C22×C4⋊C4C22×C713yes—
116C22×C22⋊C4C22×C713yes—
117C22×C22⋊C4C22×C713yes—
118C22×C22⋊C4C22×C711yescharacteristic
119C22×C42C22×C713yes—
120#396C4×C718yescomplemented
121#389—212no—
122#388—212no—
123C2×#95C22×C713yes—
124C2×#95C22×C713yes—
125C2×#95C22×C713yes—
126C2×#95C22×C713yes—
127C2×#95C22×C711yescharacteristic
128C2×#95C22×C713yes—
129C23×C7—26no—
130C23×C7—22no—
131C23×C7—26no—
132C23×C7—43no—
133C23×C7—43no—
134C23×C7—43no—
135C23×C7—43no—
136C23×C7—43no—
137C23×C7—43no—
138C23×C7—43no—
139C23×C7—43no—
140C23×C7—41no—
141C23×C7—43no—
142C23×C7C23×C411yescharacteristic
143C23×C7C22×D413yes—
144C23×C7C2×#4113yes—
145C23×C7H(5,𝔽2)13yes—
146C23×C72−1+411yescharacteristic
147C23×C72−1+411yescharacteristic
148C23×C72−1+413yes—
149C2×C4×C7—26no—
150C2×C4×C7—26no—
151C2×C4×C7—26no—
152C2×C4×C7—26no—
153C2×C4×C7—26no—
154C2×C4×C7—26no—
155C2×C4×C7—26no—
156C2×C4×C7—26no—
157C2×C4×C7—26no—
158C2×C4×C7—26no—
159C2×C4×C7—26no—
160C2×C4×C7—26no—
161C2×C4×C7—26no—
162C2×C4×C7—26no—
163C2×C4×C7—26no—
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—43no—
173C2×C4×C7—43no—
174C2×C4×C7—43no—
175C2×C4×C7—43no—
176C2×C4×C7—43no—
177C2×C4×C7—43no—
178C2×C4×C7—43no—
179C2×C4×C7—43no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7C4×D4112yes—
183C25C23×C711yescharacteristic
184C23×C4C23×C711yescharacteristic
185C23×C4C23×C711yescharacteristic
186C23×C4C23×C713yes—
187C23×C4C23×C713yes—
188C23×C4C23×C713yes—
189C23×C4C23×C713yes—
190C2×C4⋊C4—26no—
191C2×C4⋊C4—26no—
192C2×C4⋊C4—26no—
193C2×C4⋊C4—26no—
194C2×C4⋊C4—26no—
195C2×C4⋊C4—26no—
196C2×C4⋊C4—43no—
197C2×C4⋊C4—43no—
198C2×C4⋊C4C2×C4×C7112yes—
199C2×C22⋊C4—26no—
200C2×C22⋊C4—26no—
201C2×C22⋊C4—26no—
202C2×C22⋊C4—26no—
203C2×C22⋊C4—43no—
204C2×C22⋊C4—43no—
205C2×C22⋊C4C2×C4×C7112yes—
206C2×C42—26no—
207C2×C42—26no—
208C2×C42—43no—
209#95—26no—
210#95—26no—
211#95—26no—
212#95—43no—
213#95C2×C4×C714yes—
214#95C7×D4112yes—
215C22×C7—46no—
216C22×C7—46no—
217C22×C7—42no—
218C22×C7—83no—
219C22×C7—81no—
220C22×C7—83no—
221C22×C7—81no—
222C22×C7C2×C4×D413yes—
223C22×C7#51911yescharacteristic
224C22×C7#52013yes—
225C22×C7#53613yes—
226C22×C7#53713yes—
227C22×C7#54113yes—
228C22×C7#54213yes—
229C22×C7D4213yes—
230C22×C7#54713yes—
231C22×C7#54813yes—
232C22×C7#55313yes—
233C22×C7#56011yescharacteristic
234C22×C7#56313yes—
235C4×C7—212no—
236C4×C7—46no—
237C4×C7—46no—
238C4×C7—46no—
239C4×C7—81no—
240C4×C7—81no—
241C24—23no—
242C24—23no—
243C24—23no—
244C24—21no—
245C24—21no—
246C24—23no—
247C24C22×C4×C712yes—
248C24C24×C711yescharacteristic
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—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C716yes—
278C22×C4C22×C4×C716yes—
279C22×C4C2×C7×D416yes—
280C22×C4C2×C7×D416yes—
281C22×C4C2×C7×D416yes—
282C22×C4C7×#4116yes—
283C4⋊C4—224no—
284C4⋊C4—412no—
285C4⋊C4—412no—
286C22⋊C4—224no—
287C22⋊C4—412no—
288C22⋊C4—44no—
289C42—412no—
290C2×C7—82no—
291C2×C7#232313yes—
292C2×C7#236113yes—
293C2×C7#238311yescharacteristic
294C2×C7#267413yes—
295C2×C7#267511yescharacteristic
296C2×C7#272513yes—
297C2×C7#280111yescharacteristic
298C23—26no—
299C23—22no—
300C23—26no—
301C23—43no—
302C23—43no—
303C23—43no—
304C23—43no—
305C23—43no—
306C23—43no—
307C23—43no—
308C23—43no—
309C23—41no—
310C23—43no—
311C23C23×C4×C711yescharacteristic
312C23C22×C7×D413yes—
313C23C2×C7×#4113yes—
314C23C7×H(5,𝔽2)13yes—
315C23C7×2−1+411yescharacteristic
316C23C7×2−1+411yescharacteristic
317C23C7×2−1+413yes—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—26no—
322C2×C4—26no—
323C2×C4—26no—
324C2×C4—26no—
325C2×C4—26no—
326C2×C4—26no—
327C2×C4—26no—
328C2×C4—26no—
329C2×C4—26no—
330C2×C4—26no—
331C2×C4—26no—
332C2×C4—26no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—43no—
341C2×C4—43no—
342C2×C4—43no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—43no—
346C2×C4—43no—
347C2×C4—43no—
348C2×C4—43no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4C4×C7×D4112yes—
352C7#1456211yescharacteristic, direct product factor, Sylow
353C22—46no—
354C22—46no—
355C22—42no—
356C22—83no—
357C22—81no—
358C22—83no—
359C22—81no—
360C22C2×C4×C7×D413yes—
361C22C7×#51911yescharacteristic
362C22C7×#52013yes—
363C22C7×#53613yes—
364C22C7×#53713yes—
365C22C7×#54113yes—
366C22C7×#54213yes—
367C22C7×D4213yes—
368C22C7×#54713yes—
369C22C7×#54813yes—
370C22C7×#55313yes—
371C22C7×#56011yescharacteristic
372C22C7×#56313yes—
373C4—212no—
374C4—46no—
375C4—46no—
376C4—46no—
377C4—81no—
378C4—81no—
379C2—82no—
380C2C7×#232313yes—
381C2C7×#236113yes—
382C2C7×#238311yescharacteristic
383C2C7×#267413yes—
384C2C7×#267511yescharacteristic
385C2C7×#272513yes—
386C2C7×#280111yescharacteristic
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. C2×C7×#389C2semidirect
4. C7×#1444C2semidirect
5. C7×#1443C2semidirect
7. C7×#1436C2semidirect
15. C7×#396C4semidirect
24. #14562C7direct (N × H)
58. C2×#389C2×C7semidirect
60. #1444C2×C7semidirect
61. #1443C2×C7semidirect
63. #1436C2×C7semidirect
120. #396C4×C7semidirect
352. C7#14562direct (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
C2×C7×#3892
C2×C7×#3882
C7×#14442
C7×#14432
C7×#14392
C7×#14362
#145627