Finite Group Databasebeta

← C2×C7×#1608 #13195319

Subgroups — C2×C7×#1608 #13195319

Order 1792.

1136 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#543C211yesmaximal, characteristic
2C2×C7×#483C212yesmaximal, complemented
3C2×C7×#397C211yesmaximal, characteristic
4C7×#1608C218yesmaximal, direct product factor
5C2×C7×#328C212yesmaximal, complemented
6C2×C7×#323C211yesmaximal, characteristic
7C7×#543—24no—
8C7×#543—22no—
9C7×#543C2214yes—
10C2×C7×C22⋊Q8—22no—
11C2×C7×C22⋊Q8—21no—
12C2×C7×C22⋊Q8—22no—
13C2×C7×C22⋊Q8C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4—21no—
16C22×C7×C22⋊C4—21no—
17C22×C7×C22⋊C4C2211yescharacteristic
18C7×#483—24no—
19C7×#483C2218yescomplemented
20C2×C7×#106—22no—
21C2×C7×#103—22no—
22C2×C7×C22⋊C8C2212yes—
23C7×#397—22no—
24C7×#397C2214yes—
25C2×C7×#95—21no—
26C2×C7×#95C2211yescharacteristic
27C7×#328C2218yescomplemented
28C7×#323C2214yes—
29C2×#1608C711yesmaximal, characteristic, direct product factor, Sylow
30C25×C7D411yescharacteristic
31C22×C7×Q8—21no—
32C22×C7×Q8D412yes—
33C23×C4×C7—21no—
34C23×C4×C7—21no—
35C23×C4×C7—21no—
36C23×C4×C7—21no—
37C23×C4×C7D411yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C22×C7×C8—22no—
40C7×C22⋊Q8—28no—
41C7×C22⋊Q8—28no—
42C7×C22⋊Q8—24no—
43C7×C22⋊Q8—28no—
44C7×C22⋊Q8—24no—
45C7×C22⋊Q8—22no—
46C7×C22⋊Q8—22no—
47C7×C22⋊Q8—28no—
48C7×C22⋊Q8D414yes—
49C7×C22⋊Q8C2314yes—
50C2×C7×C4⋊C4—21no—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4D412yes—
57C2×C7×C4⋊C4C2312yes—
58C2×C7×C22⋊C4—22no—
59C2×C7×C22⋊C4—24no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—24no—
62C2×C7×C22⋊C4—22no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—44no—
66C2×C7×C22⋊C4D412yes—
67C2×C7×C22⋊C4C2312yes—
68C7×#106—28no—
69C7×#103—28no—
70C7×C22⋊C8—22no—
71C7×C22⋊C8C2314yes—
72C7×#95—24no—
73C7×#95—21no—
74C7×#95C2312yes—
75C2×#543C2×C711yescharacteristic
76C2×#483C2×C712yescomplemented
77C2×#397C2×C711yescharacteristic
78#1608C2×C718yesdirect product factor
79C2×#328C2×C712yescomplemented
80C2×#323C2×C711yescharacteristic
81C24×C7—21no—
82C24×C7—21no—
83C24×C7—22no—
84C24×C7—42no—
85C24×C7—42no—
86C24×C7SD1614yes—
87C24×C7C2×D411yescharacteristic
88C24×C7C2×D412yes—
89C2×C7×Q8—24no—
90C2×C7×Q8—22no—
91C2×C7×Q8—44no—
92C2×C7×Q8—82no—
93C2×C7×Q8C2×D414yes—
94C22×C4×C7—22no—
95C22×C4×C7—21no—
96C22×C4×C7—22no—
97C22×C4×C7—24no—
98C22×C4×C7—24no—
99C22×C4×C7—21no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—42no—
103C22×C4×C7—42no—
104C22×C4×C7—42no—
105C22×C4×C7—42no—
106C22×C4×C7—41no—
107C22×C4×C7—41no—
108C22×C4×C7—42no—
109C22×C4×C7—42no—
110C22×C4×C7—42no—
111C22×C4×C7—82no—
112C22×C4×C7—82no—
113C22×C4×C7C2×D412yes—
114C22×C4×C7C2×D412yes—
115C22×C4×C7C2×D411yescharacteristic
116C22×C4×C7C2×D412yes—
117C22×C4×C7C2411yescharacteristic
118C2×C7×C8—24no—
119C2×C7×C8—44no—
120C7×C4⋊C4—24no—
121C7×C4⋊C4—28no—
122C7×C4⋊C4—24no—
123C7×C4⋊C4—22no—
124C7×C4⋊C4—24no—
125C7×C4⋊C4—24no—
126C7×C4⋊C4—42no—
127C7×C4⋊C4C2×D414yes—
128C7×C22⋊C4—28no—
129C7×C22⋊C4—24no—
130C7×C22⋊C4—24no—
131C7×C22⋊C4—24no—
132C7×C22⋊C4—24no—
133C7×C22⋊C4—48no—
134#543—24no—
135#543—22no—
136#543C22×C714yes—
137C2×C22⋊Q8—22no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8C22×C712yes—
141C22×C4⋊C4C22×C711yescharacteristic
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4C22×C711yescharacteristic
145#483—24no—
146#483C22×C718yescomplemented
147C2×#106—22no—
148C2×#103—22no—
149C2×C22⋊C8C22×C712yes—
150#397—22no—
151#397C22×C714yes—
152C2×#95—21no—
153C2×#95C22×C711yescharacteristic
154#328C22×C718yescomplemented
155#323C22×C714yes—
156C23×C7—22no—
157C23×C7—22no—
158C23×C7—22no—
159C23×C7—24no—
160C23×C7—22no—
161C23×C7—24no—
162C23×C7—48no—
163C23×C7—42no—
164C23×C7—42no—
165C23×C7—42no—
166C23×C7—42no—
167C23×C7—84no—
168C23×C7—81no—
169C23×C7—81no—
170C23×C7#12011yescharacteristic
171C23×C7#12011yescharacteristic
172C23×C7C2×SD1612yes—
173C23×C7C2×SD1614yes—
174C23×C7#13712yes—
175C23×C7C22×D411yescharacteristic
176C7×Q8—44no—
177C7×Q8—82no—
178C7×Q8—84no—
179C2×C4×C7—24no—
180C2×C4×C7—24no—
181C2×C4×C7—22no—
182C2×C4×C7—24no—
183C2×C4×C7—42no—
184C2×C4×C7—41no—
185C2×C4×C7—41no—
186C2×C4×C7—42no—
187C2×C4×C7—44no—
188C2×C4×C7—44no—
189C2×C4×C7—42no—
190C2×C4×C7—42no—
191C2×C4×C7—42no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—42no—
196C2×C4×C7—81no—
197C2×C4×C7—84no—
198C2×C4×C7—84no—
199C2×C4×C7—84no—
200C2×C4×C7—82no—
201C2×C4×C7—82no—
202C2×C4×C7#12012yes—
203C2×C4×C7C22×D412yes—
204C7×C8—44no—
205C25C7×D411yescharacteristic
206C22×Q8—21no—
207C22×Q8C7×D412yes—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4C7×D411yescharacteristic
213C23×C4C23×C711yescharacteristic
214C22×C8—22no—
215C22⋊Q8—28no—
216C22⋊Q8—28no—
217C22⋊Q8—24no—
218C22⋊Q8—28no—
219C22⋊Q8—24no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222C22⋊Q8—28no—
223C22⋊Q8C7×D414yes—
224C22⋊Q8C23×C714yes—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C7×D412yes—
232C2×C4⋊C4C23×C712yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—24no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—44no—
241C2×C22⋊C4C7×D412yes—
242C2×C22⋊C4C23×C712yes—
243#106—28no—
244#103—28no—
245C22⋊C8—22no—
246C22⋊C8C23×C714yes—
247#95—24no—
248#95—21no—
249#95C23×C712yes—
250C22×C7—24no—
251C22×C7—24no—
252C22×C7—21no—
253C22×C7—21no—
254C22×C7—21no—
255C22×C7—21no—
256C22×C7—24no—
257C22×C7—44no—
258C22×C7—48no—
259C22×C7—42no—
260C22×C7—42no—
261C22×C7—82no—
262C22×C7—84no—
263C22×C7#44812yes—
264C22×C7#44812yes—
265C22×C7#45512yes—
266C22×C7#45812yes—
267C22×C7C2×#12011yescharacteristic
268C22×C7C22×SD1611yescharacteristic
269C22×C7C2×#13711yescharacteristic
270C4×C7—22no—
271C4×C7—22no—
272C4×C7—42no—
273C4×C7—44no—
274C4×C7—44no—
275C4×C7—82no—
276C4×C7—82no—
277C24—21no—
278C24—21no—
279C24—22no—
280C24—42no—
281C24—42no—
282C24C7×SD1614yes—
283C24C2×C7×D411yescharacteristic
284C24C2×C7×D412yes—
285C2×Q8—24no—
286C2×Q8—22no—
287C2×Q8—44no—
288C2×Q8—82no—
289C2×Q8C2×C7×D414yes—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4C2×C7×D412yes—
310C22×C4C2×C7×D412yes—
311C22×C4C2×C7×D411yescharacteristic
312C22×C4C2×C7×D412yes—
313C22×C4C24×C711yescharacteristic
314C2×C8—24no—
315C2×C8—44no—
316C4⋊C4—24no—
317C4⋊C4—28no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—42no—
323C4⋊C4C2×C7×D414yes—
324C22⋊C4—28no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C22⋊C4—48no—
330C2×C7—21no—
331C2×C7—21no—
332C2×C7—22no—
333C2×C7—44no—
334C2×C7#160814yesdirect product factor
335C2×C7C2×#44811yescharacteristic
336C2×C7C2×#45511yescharacteristic
337C2×C7C2×#45811yescharacteristic
338C23—22no—
339C23—22no—
340C23—22no—
341C23—24no—
342C23—22no—
343C23—24no—
344C23—48no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—81no—
350C23—81no—
351C23—84no—
352C23C7×#12011yescharacteristic
353C23C7×#12011yescharacteristic
354C23C2×C7×SD1612yes—
355C23C2×C7×SD1614yes—
356C23C7×#13712yes—
357C23C22×C7×D411yescharacteristic
358Q8—44no—
359Q8—82no—
360Q8—84no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—84no—
380C2×C4—84no—
381C2×C4—84no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4C7×#12012yes—
385C2×C4C22×C7×D412yes—
386C8—44no—
387C7C2×#160811yescharacteristic, direct product factor, Sylow
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—24no—
394C22—24no—
395C22—44no—
396C22—42no—
397C22—42no—
398C22—48no—
399C22—82no—
400C22—84no—
401C22C7×#44812yes—
402C22C7×#44812yes—
403C22C7×#45512yes—
404C22C7×#45812yes—
405C22C2×C7×#12011yescharacteristic
406C22C22×C7×SD1611yescharacteristic
407C22C2×C7×#13711yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—82no—
414C4—82no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2C7×#160814yesdirect product factor
420C2C2×C7×#44811yescharacteristic
421C2C2×C7×#45511yescharacteristic
422C2C2×C7×#45811yescharacteristic
subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC25×C7D4
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
2. C2×C7×#483C2semidirect
4. C7×#1608C2direct (N × H)
5. C2×C7×#328C2semidirect
19. C7×#483C22semidirect
27. C7×#328C22semidirect
29. C2×#1608C7direct (N × H)
76. C2×#483C2×C7semidirect
78. #1608C2×C7direct (N × H)
79. C2×#328C2×C7semidirect
146. #483C22×C7semidirect
154. #328C22×C7semidirect
334. C2×C7#1608direct (N × H)
387. C7C2×#1608direct (N × H)
419. C2C7×#1608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5432
C2×C7×#4832
C2×C7×#3972
C7×#16082
C2×C7×#3282
C2×C7×#3232
C2×#16087