Finite Group Databasebeta

← C2×C7×#1819 #13197902

Subgroups — C2×C7×#1819 #13197902

Order 1792.

3118 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C7×#379C212yesmaximal
3C7×#1819C218yesmaximal, direct product factor
4C2×C7×#342C214yesmaximal, complemented
5C26×C7C2211yescharacteristic
6C24×C4×C7C412yescomplemented
7C22×C7×C22⋊C4—24no—
8C22×C7×C22⋊C4—24no—
9C22×C7×C22⋊C4—24no—
10C22×C7×C22⋊C4C414yescomplemented
11C22×C7×C22⋊C4C412yescomplemented
12C22×C7×C22⋊C4C2214yes—
13C22×C7×C22⋊C4C2212yes—
14C22×C7×C22⋊C4C2214yes—
15C7×#379—24no—
16C7×#379C2218yes—
17C7×#342C22116yescomplemented
18C2×#1819C711yesmaximal, characteristic, direct product factor, Sylow
19C25×C7—28no—
20C25×C7—48no—
21C25×C7C2×C411yescharacteristic
22C25×C7C2×C411yescharacteristic
23C25×C7C2×C412yes—
24C25×C7D414yes—
25C25×C7D414yes—
26C25×C7C2312yes—
27C25×C7C2311yescharacteristic
28C23×C4×C7—24no—
29C23×C4×C7—22no—
30C23×C4×C7—22no—
31C23×C4×C7—24no—
32C23×C4×C7—48no—
33C23×C4×C7C2×C414yes—
34C23×C4×C7C2×C418yescomplemented
35C2×C7×C22⋊C4—216no—
36C2×C7×C22⋊C4—24no—
37C2×C7×C22⋊C4—24no—
38C2×C7×C22⋊C4—24no—
39C2×C7×C22⋊C4—24no—
40C2×C7×C22⋊C4—216no—
41C2×C7×C22⋊C4—216no—
42C2×C7×C22⋊C4—216no—
43C2×C7×C22⋊C4—24no—
44C2×C7×C22⋊C4—416no—
45C2×C7×C22⋊C4C2×C414yes—
46C2×C7×C22⋊C4C2×C418yescomplemented
47C2×C7×C22⋊C4C2318yes—
48C2×C7×C22⋊C4C2314yes—
49C23×C22⋊C4C2×C711yescharacteristic
50C2×#379C2×C712yes—
51#1819C2×C718yesdirect product factor
52C2×#342C2×C714yescomplemented
53C24×C7—28no—
54C24×C7—24no—
55C24×C7—216no—
56C24×C7—28no—
57C24×C7—24no—
58C24×C7—216no—
59C24×C7—216no—
60C24×C7—28no—
61C24×C7—48no—
62C24×C7—44no—
63C24×C7—48no—
64C24×C7—416no—
65C24×C7—44no—
66C24×C7—48no—
67C24×C7—464no—
68C24×C7C22⋊C412yes—
69C24×C7C22⋊C412yes—
70C24×C7C22⋊C418yes—
71C24×C7C22⋊C412yes—
72C24×C7C22⋊C412yes—
73C24×C7C22×C412yes—
74C24×C7C22×C411yescharacteristic
75C24×C7C22×C412yes—
76C24×C7C22×C411yescharacteristic
77C24×C7C2×D418yes—
78C24×C7C2×D412yes—
79C24×C7C2×D412yes—
80C24×C7#4118yes—
81C24×C7C2411yescharacteristic
82C22×C4×C7—24no—
83C22×C4×C7—28no—
84C22×C4×C7—28no—
85C22×C4×C7—24no—
86C22×C4×C7—28no—
87C22×C4×C7—416no—
88C22×C4×C7—48no—
89C22×C4×C7—48no—
90C22×C4×C7—48no—
91C22×C4×C7—416no—
92C22×C4×C7—416no—
93C22×C4×C7—48no—
94C22×C4×C7C22×C418yes—
95C7×C22⋊C4—28no—
96C7×C22⋊C4—216no—
97C7×C22⋊C4—28no—
98C7×C22⋊C4—216no—
99C7×C22⋊C4—432no—
100C7×C22⋊C4—48no—
101C26C22×C711yescharacteristic
102C24×C4C4×C712yescomplemented
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4C4×C714yescomplemented
107C22×C22⋊C4C4×C712yescomplemented
108C22×C22⋊C4C22×C714yes—
109C22×C22⋊C4C22×C712yes—
110C22×C22⋊C4C22×C714yes—
111#379—24no—
112#379C22×C718yes—
113#342C22×C7116yescomplemented
114C23×C7—232no—
115C23×C7—24no—
116C23×C7—24no—
117C23×C7—24no—
118C23×C7—28no—
119C23×C7—24no—
120C23×C7—28no—
121C23×C7—24no—
122C23×C7—28no—
123C23×C7—24no—
124C23×C7—216no—
125C23×C7—216no—
126C23×C7—24no—
127C23×C7—24no—
128C23×C7—216no—
129C23×C7—216no—
130C23×C7—28no—
131C23×C7—48no—
132C23×C7—44no—
133C23×C7—42no—
134C23×C7—44no—
135C23×C7—44no—
136C23×C7—48no—
137C23×C7—416no—
138C23×C7—42no—
139C23×C7—464no—
140C23×C7—432no—
141C23×C7—464no—
142C23×C7—432no—
143C23×C7—416no—
144C23×C7#9918yes—
145C23×C7C2×C22⋊C414yes—
146C23×C7C2×C22⋊C412yes—
147C23×C7C2×C22⋊C411yescharacteristic
148C23×C7C2×C22⋊C414yes—
149C23×C7C2×C22⋊C411yescharacteristic
150C23×C7#11714yes—
151C23×C7#11714yes—
152C23×C7#12318yes—
153C23×C7#12318yes—
154C23×C7C23×C411yescharacteristic
155C23×C7C22×D412yes—
156C23×C7C2×#4114yes—
157C2×C4×C7—28no—
158C2×C4×C7—48no—
159C2×C4×C7—416no—
160C2×C4×C7—416no—
161C2×C4×C7—48no—
162C2×C4×C7—48no—
163C2×C4×C7—416no—
164C2×C4×C7—48no—
165C2×C4×C7—816no—
166C25—28no—
167C25—48no—
168C25C2×C4×C711yescharacteristic
169C25C2×C4×C711yescharacteristic
170C25C2×C4×C712yes—
171C25C7×D414yes—
172C25C7×D414yes—
173C25C23×C712yes—
174C25C23×C711yescharacteristic
175C23×C4—24no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—24no—
179C23×C4—48no—
180C23×C4C2×C4×C714yes—
181C23×C4C2×C4×C718yescomplemented
182C2×C22⋊C4—216no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—216no—
188C2×C22⋊C4—216no—
189C2×C22⋊C4—216no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—416no—
192C2×C22⋊C4C2×C4×C714yes—
193C2×C22⋊C4C2×C4×C718yescomplemented
194C2×C22⋊C4C23×C718yes—
195C2×C22⋊C4C23×C714yes—
196C22×C7—216no—
197C22×C7—216no—
198C22×C7—216no—
199C22×C7—216no—
200C22×C7—28no—
201C22×C7—22no—
202C22×C7—24no—
203C22×C7—22no—
204C22×C7—24no—
205C22×C7—24no—
206C22×C7—24no—
207C22×C7—28no—
208C22×C7—24no—
209C22×C7—44no—
210C22×C7—48no—
211C22×C7—44no—
212C22×C7—432no—
213C22×C7—432no—
214C22×C7—48no—
215C22×C7—48no—
216C22×C7—48no—
217C22×C7#38112yes—
218C22×C7#38114yes—
219C22×C7#38112yes—
220C22×C7C2×#9918yes—
221C22×C7C2×#9914yes—
222C22×C7C22×C22⋊C411yescharacteristic
223C22×C7C2×#11712yes—
224C22×C7C2×#12314yes—
225C4×C7—48no—
226C4×C7—88no—
227C24—28no—
228C24—24no—
229C24—216no—
230C24—28no—
231C24—24no—
232C24—216no—
233C24—216no—
234C24—28no—
235C24—48no—
236C24—44no—
237C24—48no—
238C24—416no—
239C24—44no—
240C24—48no—
241C24—464no—
242C24C7×C22⋊C412yes—
243C24C7×C22⋊C412yes—
244C24C7×C22⋊C418yes—
245C24C7×C22⋊C412yes—
246C24C7×C22⋊C412yes—
247C24C22×C4×C712yes—
248C24C22×C4×C711yescharacteristic
249C24C22×C4×C712yes—
250C24C22×C4×C711yescharacteristic
251C24C2×C7×D418yes—
252C24C2×C7×D412yes—
253C24C2×C7×D412yes—
254C24C7×#4118yes—
255C24C24×C711yescharacteristic
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—416no—
262C22×C4—48no—
263C22×C4—48no—
264C22×C4—48no—
265C22×C4—416no—
266C22×C4—416no—
267C22×C4—48no—
268C22×C4C22×C4×C718yes—
269C22⋊C4—28no—
270C22⋊C4—216no—
271C22⋊C4—28no—
272C22⋊C4—216no—
273C22⋊C4—432no—
274C22⋊C4—48no—
275C2×C7—24no—
276C2×C7—22no—
277C2×C7—22no—
278C2×C7—28no—
279C2×C7—24no—
280C2×C7—44no—
281C2×C7#181914yesdirect product factor
282C2×C7C2×#38111yescharacteristic
283C2×C7C22×#9912yes—
284C23—232no—
285C23—24no—
286C23—24no—
287C23—24no—
288C23—28no—
289C23—24no—
290C23—28no—
291C23—24no—
292C23—28no—
293C23—24no—
294C23—216no—
295C23—24no—
296C23—24no—
297C23—216no—
298C23—216no—
299C23—216no—
300C23—28no—
301C23—48no—
302C23—44no—
303C23—42no—
304C23—44no—
305C23—44no—
306C23—48no—
307C23—416no—
308C23—42no—
309C23—464no—
310C23—432no—
311C23—464no—
312C23—432no—
313C23—416no—
314C23C7×#9918yes—
315C23C2×C7×C22⋊C414yes—
316C23C2×C7×C22⋊C412yes—
317C23C2×C7×C22⋊C411yescharacteristic
318C23C2×C7×C22⋊C414yes—
319C23C2×C7×C22⋊C411yescharacteristic
320C23C7×#11714yes—
321C23C7×#11714yes—
322C23C7×#12318yes—
323C23C7×#12318yes—
324C23C23×C4×C711yescharacteristic
325C23C22×C7×D412yes—
326C23C2×C7×#4114yes—
327C2×C4—28no—
328C2×C4—48no—
329C2×C4—416no—
330C2×C4—416no—
331C2×C4—48no—
332C2×C4—48no—
333C2×C4—416no—
334C2×C4—48no—
335C2×C4—816no—
336C7C2×#181911yescharacteristic, direct product factor, Sylow
337C22—216no—
338C22—216no—
339C22—216no—
340C22—216no—
341C22—28no—
342C22—24no—
343C22—22no—
344C22—24no—
345C22—22no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—28no—
350C22—44no—
351C22—48no—
352C22—44no—
353C22—432no—
354C22—432no—
355C22—48no—
356C22—48no—
357C22—48no—
358C22C7×#38112yes—
359C22C7×#38114yes—
360C22C7×#38112yes—
361C22C2×C7×#9918yes—
362C22C2×C7×#9914yes—
363C22C22×C7×C22⋊C411yescharacteristic
364C22C2×C7×#11712yes—
365C22C2×C7×#12314yes—
366C4—48no—
367C4—88no—
368C2—24no—
369C2—22no—
370C2—22no—
371C2—28no—
372C2—24no—
373C2—44no—
374C2C7×#181914yesdirect product factor
375C2C2×C7×#38111yescharacteristic
376C2C22×C7×#9912yes—
subgroupG/H
center, socleC23×C7C2×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C26×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1819C2direct (N × H)
4. C2×C7×#342C2semidirect
6. C24×C4×C7C4semidirect
10. C22×C7×C22⋊C4C4semidirect
11. C22×C7×C22⋊C4C4semidirect
17. C7×#342C22semidirect
18. C2×#1819C7direct (N × H)
34. C23×C4×C7C2×C4semidirect
46. C2×C7×C22⋊C4C2×C4semidirect
51. #1819C2×C7direct (N × H)
52. C2×#342C2×C7semidirect
102. C24×C4C4×C7semidirect
106. C22×C22⋊C4C4×C7semidirect
107. C22×C22⋊C4C4×C7semidirect
113. #342C22×C7semidirect
181. C23×C4C2×C4×C7semidirect
193. C2×C22⋊C4C2×C4×C7semidirect
281. C2×C7#1819direct (N × H)
336. C7C2×#1819direct (N × H)
374. C2C7×#1819direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C2×C7×#3792
C7×#18192
C2×C7×#3422
C2×#18197