Finite Group Databasebeta

← C2×C7×#1828 #13197925

Subgroups — C2×C7×#1828 #13197925

Order 1792.

1554 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#518C211yesmaximal, characteristic
2C22×C7×#99C212yesmaximal
3C7×#1828C218yesmaximal, direct product factor
4C2×C7×#342C214yesmaximal, complemented
5C23×C7×D4C2211yescharacteristic
6C7×#518—24no—
7C7×#518C414yescomplemented
8C7×#518C2214yes—
9C2×C4×C7×D4—24no—
10C2×C7×#117C412yescomplemented
11C22×C7×C22⋊C4C412yescomplemented
12C22×C7×C22⋊C4C2214yes—
13C22×C7×C22⋊C4C2212yes—
14C2×C7×#99—24no—
15C2×C7×#99—24no—
16C2×C7×#99C2218yes—
17C7×#342C22116yescomplemented
18C2×#1828C711yesmaximal, characteristic, direct product factor, Sylow
19C25×C7C2×C411yescharacteristic
20C25×C7C2311yescharacteristic
21C22×C7×D4—24no—
22C22×C7×D4—24no—
23C22×C7×D4C2×C412yes—
24C22×C7×D4D414yes—
25C22×C7×D4D414yes—
26C22×C7×D4C2312yes—
27C23×C4×C7—22no—
28C23×C4×C7—22no—
29C23×C4×C7—24no—
30C23×C4×C7C2×C411yescharacteristic
31C4×C7×D4—216no—
32C4×C7×D4—216no—
33C7×#117—24no—
34C7×#117C2×C418yescomplemented
35C2×C7×C4⋊C4—22no—
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4—24no—
38C2×C7×C22⋊C4—22no—
39C2×C7×C22⋊C4—22no—
40C2×C7×C22⋊C4—22no—
41C2×C7×C22⋊C4—24no—
42C2×C7×C22⋊C4—24no—
43C2×C7×C22⋊C4—24no—
44C2×C7×C22⋊C4—24no—
45C2×C7×C22⋊C4—24no—
46C2×C7×C22⋊C4C2×C414yes—
47C2×C7×C22⋊C4C2×C414yes—
48C2×C7×C22⋊C4C2×C418yescomplemented
49C2×C7×C22⋊C4C2318yes—
50C2×C7×C22⋊C4C2314yes—
51C2×C42×C7—22no—
52C7×#99—216no—
53C2×#518C2×C711yescharacteristic
54C22×#99C2×C712yes—
55#1828C2×C718yesdirect product factor
56C2×#342C2×C714yescomplemented
57C24×C7—22no—
58C24×C7—22no—
59C24×C7—82no—
60C24×C7—82no—
61C24×C7C22⋊C412yes—
62C24×C7C22⋊C412yes—
63C24×C7C22×C412yes—
64C24×C7C22×C411yescharacteristic
65C24×C7C22×C411yescharacteristic
66C24×C7C2×D412yes—
67C24×C7C2×D412yes—
68C24×C7#4114yes—
69C24×C7#4114yes—
70C24×C7C2411yescharacteristic
71C2×C7×D4—28no—
72C2×C7×D4—28no—
73C2×C7×D4—28no—
74C2×C7×D4—28no—
75C2×C7×D4—28no—
76C2×C7×D4—28no—
77C2×C7×D4C22⋊C418yes—
78C2×C7×D4C2×D418yes—
79C22×C4×C7—22no—
80C22×C4×C7—22no—
81C22×C4×C7—24no—
82C22×C4×C7—24no—
83C22×C4×C7—28no—
84C22×C4×C7—24no—
85C22×C4×C7—28no—
86C22×C4×C7—44no—
87C22×C4×C7—44no—
88C22×C4×C7—84no—
89C22×C4×C7—84no—
90C22×C4×C7—88no—
91C22×C4×C7C22⋊C412yes—
92C22×C4×C7C22⋊C412yes—
93C22×C4×C7C22×C412yes—
94C7×C4⋊C4—28no—
95C7×C22⋊C4—24no—
96C7×C22⋊C4—24no—
97C7×C22⋊C4—28no—
98C7×C22⋊C4—24no—
99C7×C22⋊C4—28no—
100C7×C22⋊C4—28no—
101C7×C22⋊C4—44no—
102C7×C22⋊C4—44no—
103C7×C22⋊C4C22×C418yes—
104C42×C7—28no—
105C23×D4C22×C711yescharacteristic
106#518—24no—
107#518C4×C714yescomplemented
108#518C22×C714yes—
109C2×C4×D4—24no—
110C2×#117C4×C712yescomplemented
111C22×C22⋊C4C4×C712yescomplemented
112C22×C22⋊C4C22×C714yes—
113C22×C22⋊C4C22×C712yes—
114C2×#99—24no—
115C2×#99—24no—
116C2×#99C22×C718yes—
117#342C22×C7116yescomplemented
118C23×C7—22no—
119C23×C7—22no—
120C23×C7—24no—
121C23×C7—24no—
122C23×C7—44no—
123C23×C7—48no—
124C23×C7—42no—
125C23×C7—44no—
126C23×C7—84no—
127C23×C7—81no—
128C23×C7—82no—
129C23×C7—84no—
130C23×C7—81no—
131C23×C7—82no—
132C23×C7—82no—
133C23×C7—84no—
134C23×C7C2×C22⋊C411yescharacteristic
135C23×C7C2×C22⋊C414yes—
136C23×C7C2×C22⋊C411yescharacteristic
137C23×C7C2×C22⋊C412yes—
138C23×C7#11712yes—
139C23×C7#11712yes—
140C23×C7#11714yes—
141C23×C7#12314yes—
142C23×C7#12314yes—
143C23×C7#12314yes—
144C23×C7#12314yes—
145C23×C7C23×C411yescharacteristic
146C23×C7C22×D412yes—
147C23×C7C2×#4114yes—
148C7×D4—216no—
149C7×D4—216no—
150C2×C4×C7—24no—
151C2×C4×C7—22no—
152C2×C4×C7—24no—
153C2×C4×C7—22no—
154C2×C4×C7—28no—
155C2×C4×C7—48no—
156C2×C4×C7—48no—
157C2×C4×C7—84no—
158C2×C4×C7—84no—
159C2×C4×C7—88no—
160C2×C4×C7—88no—
161C2×C4×C7—88no—
162C2×C4×C7—88no—
163C2×C4×C7C2×C22⋊C414yes—
164C25C2×C4×C711yescharacteristic
165C25C23×C711yescharacteristic
166C22×D4—24no—
167C22×D4—24no—
168C22×D4C2×C4×C712yes—
169C22×D4C7×D414yes—
170C22×D4C7×D414yes—
171C22×D4C23×C712yes—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—24no—
175C23×C4C2×C4×C711yescharacteristic
176C4×D4—216no—
177C4×D4—216no—
178#117—24no—
179#117C2×C4×C718yescomplemented
180C2×C4⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4C2×C4×C714yes—
192C2×C22⋊C4C2×C4×C714yes—
193C2×C22⋊C4C2×C4×C718yescomplemented
194C2×C22⋊C4C23×C718yes—
195C2×C22⋊C4C23×C714yes—
196C2×C42—22no—
197#99—216no—
198C22×C7—22no—
199C22×C7—28no—
200C22×C7—24no—
201C22×C7—24no—
202C22×C7—42no—
203C22×C7—44no—
204C22×C7—42no—
205C22×C7—44no—
206C22×C7—41no—
207C22×C7—42no—
208C22×C7—41no—
209C22×C7—44no—
210C22×C7—44no—
211C22×C7—44no—
212C22×C7—44no—
213C22×C7—44no—
214C22×C7—44no—
215C22×C7—84no—
216C22×C7—84no—
217C22×C7#38111yescharacteristic
218C22×C7#38112yes—
219C22×C7#38114yes—
220C22×C7#38111yescharacteristic
221C22×C7C22×C22⋊C411yescharacteristic
222C22×C7C2×#11712yes—
223C22×C7C2×#12314yes—
224C4×C7—24no—
225C4×C7—48no—
226C4×C7—88no—
227C24—22no—
228C24—22no—
229C24—82no—
230C24—82no—
231C24C7×C22⋊C412yes—
232C24C7×C22⋊C412yes—
233C24C22×C4×C712yes—
234C24C22×C4×C711yescharacteristic
235C24C22×C4×C711yescharacteristic
236C24C2×C7×D412yes—
237C24C2×C7×D412yes—
238C24C7×#4114yes—
239C24C7×#4114yes—
240C24C24×C711yescharacteristic
241C2×D4—28no—
242C2×D4—28no—
243C2×D4—28no—
244C2×D4—28no—
245C2×D4—28no—
246C2×D4—28no—
247C2×D4C7×C22⋊C418yes—
248C2×D4C2×C7×D418yes—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—84no—
259C22×C4—84no—
260C22×C4—88no—
261C22×C4C7×C22⋊C412yes—
262C22×C4C7×C22⋊C412yes—
263C22×C4C22×C4×C712yes—
264C4⋊C4—28no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4—28no—
268C22⋊C4—24no—
269C22⋊C4—28no—
270C22⋊C4—28no—
271C22⋊C4—44no—
272C22⋊C4—44no—
273C22⋊C4C22×C4×C718yes—
274C42—28no—
275C2×C7—21no—
276C2×C7—24no—
277C2×C7—21no—
278C2×C7—22no—
279C2×C7—22no—
280C2×C7—24no—
281C2×C7—44no—
282C2×C7#182812yesdirect product factor
283C2×C7C2×#38111yescharacteristic
284C23—22no—
285C23—22no—
286C23—24no—
287C23—24no—
288C23—44no—
289C23—48no—
290C23—42no—
291C23—44no—
292C23—84no—
293C23—81no—
294C23—82no—
295C23—84no—
296C23—81no—
297C23—82no—
298C23—82no—
299C23—84no—
300C23C2×C7×C22⋊C411yescharacteristic
301C23C2×C7×C22⋊C414yes—
302C23C2×C7×C22⋊C411yescharacteristic
303C23C2×C7×C22⋊C412yes—
304C23C7×#11712yes—
305C23C7×#11712yes—
306C23C7×#11714yes—
307C23C7×#12314yes—
308C23C7×#12314yes—
309C23C7×#12314yes—
310C23C7×#12314yes—
311C23C23×C4×C711yescharacteristic
312C23C22×C7×D412yes—
313C23C2×C7×#4114yes—
314D4—216no—
315D4—216no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—48no—
322C2×C4—48no—
323C2×C4—84no—
324C2×C4—84no—
325C2×C4—88no—
326C2×C4—88no—
327C2×C4—88no—
328C2×C4—88no—
329C2×C4C2×C7×C22⋊C414yes—
330C7C2×#182811yescharacteristic, direct product factor, Sylow
331C22—22no—
332C22—28no—
333C22—24no—
334C22—24no—
335C22—42no—
336C22—44no—
337C22—42no—
338C22—44no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—44no—
343C22—44no—
344C22—44no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—84no—
349C22—84no—
350C22C7×#38111yescharacteristic
351C22C7×#38112yes—
352C22C7×#38114yes—
353C22C7×#38111yescharacteristic
354C22C22×C7×C22⋊C411yescharacteristic
355C22C2×C7×#11712yes—
356C22C2×C7×#12314yes—
357C4—24no—
358C4—48no—
359C4—88no—
360C2—21no—
361C2—24no—
362C2—21no—
363C2—22no—
364C2—22no—
365C2—24no—
366C2—44no—
367C2C7×#182812yesdirect product factor
368C2C2×C7×#38111yescharacteristic
subgroupG/H
center, socleC22×C7#381
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1828C2direct (N × H)
4. C2×C7×#342C2semidirect
7. C7×#518C4semidirect
10. C2×C7×#117C4semidirect
11. C22×C7×C22⋊C4C4semidirect
17. C7×#342C22semidirect
18. C2×#1828C7direct (N × H)
34. C7×#117C2×C4semidirect
48. C2×C7×C22⋊C4C2×C4semidirect
55. #1828C2×C7direct (N × H)
56. C2×#342C2×C7semidirect
107. #518C4×C7semidirect
110. C2×#117C4×C7semidirect
111. C22×C22⋊C4C4×C7semidirect
117. #342C22×C7semidirect
179. #117C2×C4×C7semidirect
193. C2×C22⋊C4C2×C4×C7semidirect
282. C2×C7#1828direct (N × H)
330. C7C2×#1828direct (N × H)
367. C2C7×#1828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5182
C22×C7×#992
C7×#18282
C2×C7×#3422
C2×#18287