Finite Group Databasebeta

← C2×C7×#1599 #13195326

Subgroups — C2×C7×#1599 #13195326

Order 1792.

1372 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic, complemented
2C2×C7×#450C212yesmaximal
3C2×C7×#394C211yesmaximal, characteristic
4C7×#1599C218yesmaximal, direct product factor
5C2×C7×#328C212yesmaximal, complemented
6C2×C7×#324C211yesmaximal, characteristic, complemented
7C23×C7×D4C2211yescharacteristic
8C22×C7×SD16—22no—
9C7×#544—24no—
10C7×#544—22no—
11C7×#544C2214yescomplemented
12C2×C7×C4⋊Q8—22no—
13C2×C7×#125—22no—
14C2×C7×C22⋊Q8—21no—
15C2×C7×C22⋊Q8C2212yes—
16C2×C7×#117—21no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4—21no—
19C22×C7×C22⋊C4—21no—
20C7×#450—24no—
21C7×#450C2218yes—
22C2×C7×#102—22no—
23C2×C7×C22⋊C8C2212yes—
24C7×#394—22no—
25C7×#394C2214yes—
26C2×C7×#95C2211yescharacteristic
27C7×#328C2218yescomplemented
28C7×#324C2214yescomplemented
29C2×#1599C711yesmaximal, characteristic, direct product factor, Sylow
30C25×C7—21no—
31C22×C7×Q8—21no—
32C22×C7×Q8D412yes—
33C22×C7×D4—22no—
34C22×C7×D4—22no—
35C22×C7×D4—21no—
36C22×C7×D4—44no—
37C22×C7×D4C2312yes—
38C23×C4×C7—21no—
39C23×C4×C7D411yescharacteristic
40C23×C4×C7D411yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C2×C7×SD16—28no—
43C2×C7×SD16—48no—
44C22×C7×C8—22no—
45C7×C4⋊Q8—28no—
46C7×C4⋊Q8—28no—
47C7×#125—28no—
48C7×#125—28no—
49C7×C22⋊Q8—24no—
50C7×C22⋊Q8—24no—
51C7×C22⋊Q8—22no—
52C7×C22⋊Q8—22no—
53C7×C22⋊Q8D414yes—
54C7×C22⋊Q8C2314yes—
55C7×#117—24no—
56C7×#117—24no—
57C2×C7×C4⋊C4—21no—
58C2×C7×C4⋊C4—21no—
59C2×C7×C4⋊C4—21no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4D412yes—
65C2×C7×C4⋊C4D412yes—
66C2×C7×C4⋊C4C2312yes—
67C2×C7×C22⋊C4—22no—
68C2×C7×C22⋊C4—24no—
69C2×C7×C22⋊C4—24no—
70C2×C7×C22⋊C4—44no—
71C2×C7×C22⋊C4—44no—
72C2×C42×C7—22no—
73C7×#102—28no—
74C7×C22⋊C8—22no—
75C7×C22⋊C8C2314yes—
76C7×#95—21no—
77C7×#95C2312yes—
78C2×#544C2×C711yescharacteristic, complemented
79C2×#450C2×C712yes—
80C2×#394C2×C711yescharacteristic
81#1599C2×C718yesdirect product factor
82C2×#328C2×C712yescomplemented
83C2×#324C2×C711yescharacteristic, complemented
84C24×C7—24no—
85C24×C7—22no—
86C24×C7—42no—
87C24×C7—42no—
88C24×C7—42no—
89C24×C7—41no—
90C24×C7—41no—
91C24×C7—42no—
92C24×C7—42no—
93C24×C7C2×D411yescharacteristic
94C2×C7×Q8—24no—
95C2×C7×Q8—22no—
96C2×C7×Q8—44no—
97C2×C7×Q8—82no—
98C2×C7×Q8C2×D414yes—
99C2×C7×D4—28no—
100C2×C7×D4—24no—
101C2×C7×D4—44no—
102C2×C7×D4—44no—
103C2×C7×D4—48no—
104C2×C7×D4—44no—
105C2×C7×D4—42no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—22no—
114C22×C4×C7—42no—
115C22×C4×C7—42no—
116C22×C4×C7—42no—
117C22×C4×C7—42no—
118C22×C4×C7—42no—
119C22×C4×C7SD1614yescomplemented
120C22×C4×C7C2×D412yes—
121C22×C4×C7C2×D412yes—
122C22×C4×C7C2×D412yes—
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2411yescharacteristic
126C7×SD16—416no—
127C2×C7×C8—24no—
128C2×C7×C8—44no—
129C7×C4⋊C4—24no—
130C7×C4⋊C4—24no—
131C7×C4⋊C4—24no—
132C7×C4⋊C4—28no—
133C7×C4⋊C4—24no—
134C7×C4⋊C4—24no—
135C7×C4⋊C4—22no—
136C7×C4⋊C4—24no—
137C7×C4⋊C4—24no—
138C7×C4⋊C4C2×D414yes—
139C7×C22⋊C4—24no—
140C7×C22⋊C4—24no—
141C7×C22⋊C4—48no—
142C7×C22⋊C4—48no—
143C42×C7—28no—
144C23×D4C22×C711yescharacteristic
145C22×SD16—22no—
146#544—24no—
147#544—22no—
148#544C22×C714yescomplemented
149C2×C4⋊Q8—22no—
150C2×#125—22no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8C22×C712yes—
153C2×#117—21no—
154C22×C4⋊C4C22×C711yescharacteristic
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157#450—24no—
158#450C22×C718yes—
159C2×#102—22no—
160C2×C22⋊C8C22×C712yes—
161#394—22no—
162#394C22×C714yes—
163C2×#95C22×C711yescharacteristic
164#328C22×C718yescomplemented
165#324C22×C714yescomplemented
166C23×C7—22no—
167C23×C7—22no—
168C23×C7—24no—
169C23×C7—42no—
170C23×C7—44no—
171C23×C7—48no—
172C23×C7—48no—
173C23×C7—42no—
174C23×C7—42no—
175C23×C7—42no—
176C23×C7—42no—
177C23×C7—42no—
178C23×C7—44no—
179C23×C7—84no—
180C23×C7—84no—
181C23×C7—82no—
182C23×C7—82no—
183C23×C7—82no—
184C23×C7—82no—
185C23×C7#12011yescharacteristic
186C23×C7#12011yescharacteristic
187C23×C7C2×SD1612yes—
188C23×C7#13712yes—
189C23×C7C22×D411yescharacteristic
190C7×Q8—44no—
191C7×Q8—82no—
192C7×Q8—84no—
193C7×D4—28no—
194C7×D4—44no—
195C7×D4—48no—
196C2×C4×C7—22no—
197C2×C4×C7—22no—
198C2×C4×C7—24no—
199C2×C4×C7—24no—
200C2×C4×C7—24no—
201C2×C4×C7—24no—
202C2×C4×C7—24no—
203C2×C4×C7—22no—
204C2×C4×C7—42no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—44no—
208C2×C4×C7—42no—
209C2×C4×C7—44no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7—42no—
213C2×C4×C7—42no—
214C2×C4×C7—81no—
215C2×C4×C7—84no—
216C2×C4×C7#12012yes—
217C2×C4×C7C2×SD1614yescomplemented
218C2×C4×C7C22×D412yes—
219C7×C8—44no—
220C25—21no—
221C22×Q8—21no—
222C22×Q8C7×D412yes—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—21no—
226C22×D4—44no—
227C22×D4C23×C712yes—
228C23×C4—21no—
229C23×C4C7×D411yescharacteristic
230C23×C4C7×D411yescharacteristic
231C23×C4C23×C711yescharacteristic
232C2×SD16—28no—
233C2×SD16—48no—
234C22×C8—22no—
235C4⋊Q8—28no—
236C4⋊Q8—28no—
237#125—28no—
238#125—28no—
239C22⋊Q8—24no—
240C22⋊Q8—24no—
241C22⋊Q8—22no—
242C22⋊Q8—22no—
243C22⋊Q8C7×D414yes—
244C22⋊Q8C23×C714yes—
245#117—24no—
246#117—24no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4C7×D412yes—
255C2×C4⋊C4C7×D412yes—
256C2×C4⋊C4C23×C712yes—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4—44no—
262C2×C42—22no—
263#102—28no—
264C22⋊C8—22no—
265C22⋊C8C23×C714yes—
266#95—21no—
267#95C23×C712yes—
268C22×C7—24no—
269C22×C7—24no—
270C22×C7—21no—
271C22×C7—21no—
272C22×C7—21no—
273C22×C7—21no—
274C22×C7—44no—
275C22×C7—44no—
276C22×C7—44no—
277C22×C7—82no—
278C22×C7—82no—
279C22×C7—88no—
280C22×C7—88no—
281C22×C7—82no—
282C22×C7—82no—
283C22×C7#44812yes—
284C22×C7#44812yes—
285C22×C7#45412yes—
286C22×C7B(4,𝔽2)12yes—
287C22×C7C2×#12011yescharacteristic
288C22×C7C22×SD1611yescharacteristic
289C22×C7C2×#13711yescharacteristic
290C4×C7—24no—
291C4×C7—22no—
292C4×C7—22no—
293C4×C7—44no—
294C4×C7—42no—
295C4×C7—44no—
296C4×C7—82no—
297C24—24no—
298C24—22no—
299C24—42no—
300C24—42no—
301C24—42no—
302C24—41no—
303C24—41no—
304C24—42no—
305C24—42no—
306C24C2×C7×D411yescharacteristic
307C2×Q8—24no—
308C2×Q8—22no—
309C2×Q8—44no—
310C2×Q8—82no—
311C2×Q8C2×C7×D414yes—
312C2×D4—28no—
313C2×D4—24no—
314C2×D4—44no—
315C2×D4—44no—
316C2×D4—48no—
317C2×D4—44no—
318C2×D4—42no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4C7×SD1614yescomplemented
333C22×C4C2×C7×D412yes—
334C22×C4C2×C7×D412yes—
335C22×C4C2×C7×D412yes—
336C22×C4C2×C7×D411yescharacteristic
337C22×C4C2×C7×D412yes—
338C22×C4C24×C711yescharacteristic
339SD16—416no—
340C2×C8—24no—
341C2×C8—44no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—28no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4C2×C7×D414yes—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—48no—
355C22⋊C4—48no—
356C42—28no—
357C2×C7—21no—
358C2×C7—21no—
359C2×C7—22no—
360C2×C7—84no—
361C2×C7#159914yesdirect product factor
362C2×C7C2×#44811yescharacteristic
363C2×C7C2×#45411yescharacteristic
364C2×C7C2×B(4,𝔽2)11yescharacteristic
365C23—22no—
366C23—22no—
367C23—24no—
368C23—42no—
369C23—44no—
370C23—42no—
371C23—42no—
372C23—48no—
373C23—48no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—44no—
378C23—82no—
379C23—84no—
380C23—84no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C7×#12011yescharacteristic
385C23C7×#12011yescharacteristic
386C23C2×C7×SD1612yes—
387C23C7×#13712yes—
388C23C22×C7×D411yescharacteristic
389Q8—44no—
390Q8—82no—
391Q8—84no—
392D4—28no—
393D4—44no—
394D4—48no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—81no—
414C2×C4—84no—
415C2×C4C7×#12012yes—
416C2×C4C2×C7×SD1614yescomplemented
417C2×C4C22×C7×D412yes—
418C8—44no—
419C7C2×#159911yescharacteristic, direct product factor, Sylow
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—24no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—88no—
432C22—82no—
433C22—82no—
434C22—88no—
435C22C7×#44812yes—
436C22C7×#44812yes—
437C22C7×#45412yes—
438C22C7×B(4,𝔽2)12yes—
439C22C2×C7×#12011yescharacteristic
440C22C22×C7×SD1611yescharacteristic
441C22C2×C7×#13711yescharacteristic
442C4—24no—
443C4—22no—
444C4—22no—
445C4—44no—
446C4—42no—
447C4—44no—
448C4—82no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—84no—
453C2C7×#159914yesdirect product factor
454C2C2×C7×#44811yescharacteristic
455C2C2×C7×#45411yescharacteristic
456C2C2×C7×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#544C2semidirect
4. C7×#1599C2direct (N × H)
5. C2×C7×#328C2semidirect
6. C2×C7×#324C2semidirect
11. C7×#544C22semidirect
27. C7×#328C22semidirect
28. C7×#324C22semidirect
29. C2×#1599C7direct (N × H)
78. C2×#544C2×C7semidirect
81. #1599C2×C7direct (N × H)
82. C2×#328C2×C7semidirect
83. C2×#324C2×C7semidirect
119. C22×C4×C7SD16semidirect
148. #544C22×C7semidirect
164. #328C22×C7semidirect
165. #324C22×C7semidirect
217. C2×C4×C7C2×SD16semidirect
332. C22×C4C7×SD16semidirect
361. C2×C7#1599direct (N × H)
416. C2×C4C2×C7×SD16semidirect
419. C7C2×#1599direct (N × H)
453. C2C7×#1599direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5442
C2×C7×#4502
C2×C7×#3942
C7×#15992
C2×C7×#3282
C2×C7×#3242
C2×#15997