Finite Group Databasebeta

← C2×C7×#1821 #13197908

Subgroups — C2×C7×#1821 #13197908

Order 1792.

1734 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C4⋊C4C211yesmaximal, characteristic
2C2×C7×#407C212yesmaximal
3C7×#1821C218yesmaximal, direct product factor
4C2×C7×#343C214yesmaximal, complemented
5C24×C4×C7C412yes—
6C24×C4×C7C2211yescharacteristic
7C22×C7×M16C2214yes—
8C22×C7×C4⋊C4—22no—
9C22×C7×C4⋊C4—22no—
10C22×C7×C4⋊C4—24no—
11C22×C7×C4⋊C4C414yes—
12C22×C7×C4⋊C4C412yes—
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2214yes—
15C7×#407—24no—
16C7×#407C2218yes—
17C2×C7×C22⋊C8—22no—
18C2×C7×C22⋊C8—22no—
19C7×#343C22116yescomplemented
20C2×#1821C711yesmaximal, characteristic, direct product factor, Sylow
21C25×C7C2×C411yescharacteristic
22C23×C4×C7—28no—
23C23×C4×C7—24no—
24C23×C4×C7—22no—
25C23×C4×C7—22no—
26C23×C4×C7—48no—
27C23×C4×C7C2×C411yescharacteristic
28C23×C4×C7C2×C412yes—
29C23×C4×C7C2×C418yes—
30C23×C4×C7C2×C414yes—
31C23×C4×C7D412yes—
32C23×C4×C7D412yes—
33C23×C4×C7D414yes—
34C23×C4×C7C2312yes—
35C23×C4×C7C2311yescharacteristic
36C2×C7×M16—24no—
37C2×C7×M16—216no—
38C2×C7×M16C2318yes—
39C22×C7×C8—24no—
40C2×C7×C4⋊C4—24no—
41C2×C7×C4⋊C4—28no—
42C2×C7×C4⋊C4—28no—
43C2×C7×C4⋊C4—24no—
44C2×C7×C4⋊C4—28no—
45C2×C7×C4⋊C4—28no—
46C2×C7×C4⋊C4—24no—
47C2×C7×C4⋊C4—24no—
48C2×C7×C4⋊C4C2×C418yes—
49C2×C7×C4⋊C4C2×C414yes—
50C2×C7×C4⋊C4C2314yes—
51C7×C22⋊C8—28no—
52C7×C22⋊C8—28no—
53C23×C4⋊C4C2×C711yescharacteristic
54C2×#407C2×C712yes—
55#1821C2×C718yesdirect product factor
56C2×#343C2×C714yescomplemented
57C24×C7—24no—
58C24×C7—24no—
59C24×C7—24no—
60C24×C7C22⋊C412yes—
61C24×C7C22⋊C411yescharacteristic
62C24×C7C22⋊C411yescharacteristic
63C24×C7C22×C412yes—
64C24×C7C22×C411yescharacteristic
65C22×C4×C7—24no—
66C22×C4×C7—28no—
67C22×C4×C7—28no—
68C22×C4×C7—28no—
69C22×C4×C7—216no—
70C22×C4×C7—28no—
71C22×C4×C7—24no—
72C22×C4×C7—28no—
73C22×C4×C7—28no—
74C22×C4×C7—24no—
75C22×C4×C7—416no—
76C22×C4×C7—48no—
77C22×C4×C7—48no—
78C22×C4×C7—416no—
79C22×C4×C7—48no—
80C22×C4×C7C22⋊C412yes—
81C22×C4×C7C22⋊C414yes—
82C22×C4×C7C22⋊C414yes—
83C22×C4×C7C22⋊C412yes—
84C22×C4×C7C22×C412yes—
85C22×C4×C7C22×C418yes—
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D414yes—
88C22×C4×C7C2×D414yes—
89C22×C4×C7C2×D412yes—
90C22×C4×C7C2×D412yes—
91C22×C4×C7#4118yes—
92C22×C4×C7C2411yescharacteristic
93C7×M16—216no—
94C7×M16—48no—
95C2×C7×C8—28no—
96C2×C7×C8—48no—
97C7×C4⋊C4—216no—
98C7×C4⋊C4—28no—
99C7×C4⋊C4—28no—
100C24×C4C4×C712yes—
101C24×C4C22×C711yescharacteristic
102C22×M16C22×C714yes—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4C4×C712yes—
107C22×C4⋊C4C4×C714yes—
108C22×C4⋊C4C22×C714yes—
109C22×C4⋊C4C22×C712yes—
110#407—24no—
111#407C22×C718yes—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114#343C22×C7116yescomplemented
115C23×C7—232no—
116C23×C7—24no—
117C23×C7—24no—
118C23×C7—22no—
119C23×C7—22no—
120C23×C7—24no—
121C23×C7—22no—
122C23×C7—24no—
123C23×C7—22no—
124C23×C7—24no—
125C23×C7—22no—
126C23×C7—24no—
127C23×C7—22no—
128C23×C7#10014yes—
129C23×C7#10114yes—
130C23×C7C2×C22⋊C411yescharacteristic
131C23×C7C2×C22⋊C412yes—
132C23×C7C2×C22⋊C412yes—
133C23×C7C2×C22⋊C411yescharacteristic
134C23×C7#11714yes—
135C23×C7C23×C411yescharacteristic
136C2×C4×C7—24no—
137C2×C4×C7—24no—
138C2×C4×C7—24no—
139C2×C4×C7—28no—
140C2×C4×C7—28no—
141C2×C4×C7—28no—
142C2×C4×C7—28no—
143C2×C4×C7—28no—
144C2×C4×C7—48no—
145C2×C4×C7—416no—
146C2×C4×C7—416no—
147C2×C4×C7—48no—
148C2×C4×C7—48no—
149C2×C4×C7C2×C22⋊C414yes—
150C2×C4×C7C2×C22⋊C412yes—
151C2×C4×C7#11714yes—
152C2×C4×C7#12318yes—
153C2×C4×C7#12318yes—
154C2×C4×C7C22×D412yes—
155C2×C4×C7C2×#4114yes—
156C7×C8—48no—
157C25C2×C4×C711yescharacteristic
158C23×C4—28no—
159C23×C4—24no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—48no—
163C23×C4C2×C4×C711yescharacteristic
164C23×C4C2×C4×C712yes—
165C23×C4C2×C4×C718yes—
166C23×C4C2×C4×C714yes—
167C23×C4C7×D412yes—
168C23×C4C7×D412yes—
169C23×C4C7×D414yes—
170C23×C4C23×C712yes—
171C23×C4C23×C711yescharacteristic
172C2×M16—24no—
173C2×M16—216no—
174C2×M16C23×C718yes—
175C22×C8—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—28no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—28no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4C2×C4×C718yes—
185C2×C4⋊C4C2×C4×C714yes—
186C2×C4⋊C4C23×C714yes—
187C22⋊C8—28no—
188C22⋊C8—28no—
189C22×C7—216no—
190C22×C7—216no—
191C22×C7—28no—
192C22×C7—28no—
193C22×C7—28no—
194C22×C7—21no—
195C22×C7—22no—
196C22×C7—21no—
197C22×C7—21no—
198C22×C7—22no—
199C22×C7—21no—
200C22×C7—22no—
201C22×C7—22no—
202C22×C7#38112yes—
203C22×C7#38112yes—
204C22×C7C2×#10014yes—
205C22×C7C2×#10012yes—
206C22×C7C2×#10114yes—
207C22×C7C2×#10112yes—
208C22×C7C22×C22⋊C411yescharacteristic
209C22×C7C2×#11712yes—
210C4×C7—24no—
211C4×C7—48no—
212C4×C7#38114yes—
213C4×C7C2×#12314yes—
214C24—24no—
215C24—24no—
216C24—24no—
217C24C7×C22⋊C412yes—
218C24C7×C22⋊C411yescharacteristic
219C24C7×C22⋊C411yescharacteristic
220C24C22×C4×C712yes—
221C24C22×C4×C711yescharacteristic
222C22×C4—24no—
223C22×C4—28no—
224C22×C4—28no—
225C22×C4—28no—
226C22×C4—216no—
227C22×C4—28no—
228C22×C4—24no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4—416no—
233C22×C4—48no—
234C22×C4—48no—
235C22×C4—416no—
236C22×C4—48no—
237C22×C4C7×C22⋊C412yes—
238C22×C4C7×C22⋊C412yes—
239C22×C4C7×C22⋊C414yes—
240C22×C4C7×C22⋊C414yes—
241C22×C4C22×C4×C712yes—
242C22×C4C22×C4×C718yes—
243C22×C4C22×C4×C711yescharacteristic
244C22×C4C2×C7×D414yes—
245C22×C4C2×C7×D414yes—
246C22×C4C2×C7×D412yes—
247C22×C4C2×C7×D412yes—
248C22×C4C7×#4118yes—
249C22×C4C24×C711yescharacteristic
250M16—216no—
251M16—48no—
252C2×C8—28no—
253C2×C8—48no—
254C4⋊C4—216no—
255C4⋊C4—28no—
256C4⋊C4—28no—
257C2×C7—22no—
258C2×C7—22no—
259C2×C7—24no—
260C2×C7—24no—
261C2×C7#182114yesdirect product factor
262C2×C7C2×#38111yescharacteristic
263C2×C7C22×#10011yescharacteristic
264C2×C7C22×#10111yescharacteristic
265C23—232no—
266C23—24no—
267C23—24no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—24no—
273C23—22no—
274C23—24no—
275C23—22no—
276C23—24no—
277C23—22no—
278C23C7×#10014yes—
279C23C7×#10114yes—
280C23C2×C7×C22⋊C411yescharacteristic
281C23C2×C7×C22⋊C412yes—
282C23C2×C7×C22⋊C412yes—
283C23C2×C7×C22⋊C411yescharacteristic
284C23C7×#11714yes—
285C23C23×C4×C711yescharacteristic
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—48no—
295C2×C4—416no—
296C2×C4—416no—
297C2×C4—48no—
298C2×C4—48no—
299C2×C4C2×C7×C22⋊C414yes—
300C2×C4C2×C7×C22⋊C412yes—
301C2×C4C7×#11714yes—
302C2×C4C7×#12318yes—
303C2×C4C7×#12318yes—
304C2×C4C22×C7×D412yes—
305C2×C4C2×C7×#4114yes—
306C8—48no—
307C7C2×#182111yescharacteristic, direct product factor, Sylow
308C22—216no—
309C22—216no—
310C22—28no—
311C22—28no—
312C22—28no—
313C22—22no—
314C22—22no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—21no—
321C22C7×#38112yes—
322C22C7×#38112yes—
323C22C2×C7×#10014yes—
324C22C2×C7×#10012yes—
325C22C2×C7×#10114yes—
326C22C2×C7×#10112yes—
327C22C22×C7×C22⋊C411yescharacteristic
328C22C2×C7×#11712yes—
329C4—24no—
330C4—48no—
331C4C7×#38114yes—
332C4C2×C7×#12314yes—
333C2—22no—
334C2—22no—
335C2—24no—
336C2—24no—
337C2C7×#182114yesdirect product factor
338C2C2×C7×#38111yescharacteristic
339C2C22×C7×#10011yescharacteristic
340C2C22×C7×#10111yescharacteristic
subgroupG/H
center, socleC23×C7C2×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC25×C7C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1821C2direct (N × H)
4. C2×C7×#343C2semidirect
19. C7×#343C22semidirect
20. C2×#1821C7direct (N × H)
55. #1821C2×C7direct (N × H)
56. C2×#343C2×C7semidirect
114. #343C22×C7semidirect
261. C2×C7#1821direct (N × H)
307. C7C2×#1821direct (N × H)
337. C2C7×#1821direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C4⋊C42
C2×C7×#4072
C7×#18212
C2×C7×#3432
C2×#18217