Finite Group Databasebeta

← C2×C7×#1677 #13196322

Subgroups — C2×C7×#1677 #13196322

Order 1792.

810 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#486C211yesmaximal, characteristic, complemented
2C2×C7×#476C211yesmaximal, characteristic, complemented
3C2×C7×#459C211yesmaximal, characteristic
4C2×C7×C8×D4C211yesmaximal, characteristic, complemented
5C7×#1677C218yesmaximal, direct product factor
6C2×C7×#334C211yesmaximal, characteristic, complemented
7C2×C7×#333C211yesmaximal, characteristic, complemented
8C2×C7×#331C211yesmaximal, characteristic, complemented
9C22×C7×D8—21no—
10C23×C7×C8—21no—
11C2×C7×C4⋊Q8C2211yescharacteristic
12C2×C7×#127C2211yescharacteristic
13C2×C4×C7×D4C2211yescharacteristic
14C7×#486—22no—
15C7×#486C2214yescomplemented
16C7×#476—22no—
17C7×#476C2214yescomplemented
18C7×#459—22no—
19C7×#459C2214yes—
20C7×C8×D4—22no—
21C7×C8×D4C2214yescomplemented
22C2×C7×#106—21no—
23C2×C7×C4⋊C8C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×C4⋊C8C2211yescharacteristic
26C2×C7×#102—21no—
27C2×C7×#102—21no—
28C2×C7×#102—21no—
29C2×C7×#102—21no—
30C2×C7×C22⋊C8—21no—
31C2×C4×C7×C8C2211yescharacteristic
32C7×#334C2214yescomplemented
33C7×#333C2214yescomplemented
34C7×#331C2214yescomplemented
35C2×#1677C711yesmaximal, characteristic, direct product factor, Sylow
36C22×C7×Q8—21no—
37C22×C7×D4—21no—
38C22×C7×D4—21no—
39C22×C7×D4—21no—
40C22×C7×D4D411yescharacteristic
41C23×C4×C7—21no—
42C2×C7×D8—24no—
43C2×C7×D8—44no—
44C22×C7×C8—21no—
45C22×C7×C8—21no—
46C22×C7×C8—21no—
47C22×C7×C8—24no—
48C22×C7×C8—44no—
49C22×C7×C8D411yescharacteristic
50C22×C7×C8D411yescharacteristic
51C7×C4⋊Q8—21no—
52C7×C4⋊Q8—21no—
53C7×C4⋊Q8—21no—
54C7×C4⋊Q8C2312yes—
55C7×#127—21no—
56C7×#127—21no—
57C7×#127—21no—
58C7×#127C2312yes—
59C4×C7×D4—21no—
60C4×C7×D4—21no—
61C4×C7×D4D412yes—
62C4×C7×D4C2312yes—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4D411yescharacteristic
66C2×C7×C22⋊C4—21no—
67C2×C42×C7C2311yescharacteristic
68C7×#106—24no—
69C7×C4⋊C8—21no—
70C7×C4⋊C8—21no—
71C7×C4⋊C8—21no—
72C7×C4⋊C8C2312yes—
73C7×C4⋊C8C2312yes—
74C7×C4⋊C8C2312yes—
75C7×#102—24no—
76C7×#102—24no—
77C7×#102—24no—
78C7×#102—24no—
79C7×C22⋊C8—24no—
80C4×C7×C8D412yes—
81C4×C7×C8C2312yes—
82C2×#486C2×C711yescharacteristic, complemented
83C2×#476C2×C711yescharacteristic, complemented
84C2×#459C2×C711yescharacteristic
85C2×C8×D4C2×C711yescharacteristic, complemented
86#1677C2×C718yesdirect product factor
87C2×#334C2×C711yescharacteristic, complemented
88C2×#333C2×C711yescharacteristic, complemented
89C2×#331C2×C711yescharacteristic, complemented
90C24×C7—21no—
91C24×C7—41no—
92C2×C7×Q8—22no—
93C2×C7×Q8—41no—
94C2×C7×Q8—82no—
95C2×C7×D4—21no—
96C2×C7×D4—22no—
97C2×C7×D4—22no—
98C2×C7×D4—22no—
99C2×C7×D4—22no—
100C2×C7×D4—41no—
101C2×C7×D4—41no—
102C2×C7×D4—41no—
103C2×C7×D4—42no—
104C2×C7×D4—42no—
105C2×C7×D4—42no—
106C2×C7×D4—42no—
107C2×C7×D4—82no—
108C2×C7×D4SD1614yes—
109C2×C7×D4C2×D412yes—
110C22×C4×C7—21no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—42no—
114C22×C4×C7—42no—
115C22×C4×C7—41no—
116C22×C4×C7C2×D411yescharacteristic
117C22×C4×C7C2×D411yescharacteristic
118C22×C4×C7#4111yescharacteristic
119C7×D8—48no—
120C2×C7×C8—22no—
121C2×C7×C8—22no—
122C2×C7×C8—22no—
123C2×C7×C8—22no—
124C2×C7×C8—22no—
125C2×C7×C8—48no—
126C2×C7×C8—42no—
127C2×C7×C8—42no—
128C2×C7×C8—42no—
129C2×C7×C8C2×D412yes—
130C2×C7×C8C2×D412yes—
131C7×C4⋊C4—21no—
132C7×C4⋊C4—22no—
133C7×C4⋊C4—22no—
134C7×C4⋊C4—41no—
135C7×C4⋊C4—41no—
136C7×C4⋊C4C2×D412yes—
137C7×C22⋊C4—22no—
138C7×C22⋊C4—22no—
139C42×C7C2×D411yescharacteristic
140C42×C7C2×D411yescharacteristic
141C42×C7#4111yescharacteristic
142C42×C7C2411yescharacteristic
143C22×D8—21no—
144C23×C8—21no—
145C2×C4⋊Q8C22×C711yescharacteristic
146C2×#127C22×C711yescharacteristic
147C2×C4×D4C22×C711yescharacteristic
148#486—22no—
149#486C22×C714yescomplemented
150#476—22no—
151#476C22×C714yescomplemented
152#459—22no—
153#459C22×C714yes—
154C8×D4—22no—
155C8×D4C22×C714yescomplemented
156C2×#106—21no—
157C2×C4⋊C8C22×C711yescharacteristic
158C2×C4⋊C8C22×C711yescharacteristic
159C2×C4⋊C8C22×C711yescharacteristic
160C2×#102—21no—
161C2×#102—21no—
162C2×#102—21no—
163C2×#102—21no—
164C2×C22⋊C8—21no—
165C2×C4×C8C22×C711yescharacteristic
166#334C22×C714yescomplemented
167#333C22×C714yescomplemented
168#331C22×C714yescomplemented
169C23×C7—22no—
170C23×C7—24no—
171C23×C7—42no—
172C23×C7—42no—
173C23×C7—42no—
174C23×C7—82no—
175C23×C7—82no—
176C23×C7—82no—
177C23×C7#12111yescharacteristic
178C7×Q8—82no—
179C7×Q8—82no—
180C7×D4—22no—
181C7×D4—24no—
182C7×D4—42no—
183C7×D4—42no—
184C7×D4—42no—
185C7×D4—42no—
186C7×D4—82no—
187C7×D4—82no—
188C7×D4—82no—
189C7×D4—82no—
190C7×D4C2×SD1614yes—
191C2×C4×C7—22no—
192C2×C4×C7—22no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—42no—
196C2×C4×C7—44no—
197C2×C4×C7—42no—
198C2×C4×C7—82no—
199C2×C4×C7#12111yescharacteristic
200C2×C4×C7#12111yescharacteristic
201C2×C4×C7#12111yescharacteristic
202C2×C4×C7C2×SD1612yes—
203C2×C4×C7#13512yes—
204C2×C4×C7#13512yes—
205C2×C4×C7AGL(1,ℤ/8)12yes—
206C2×C4×C7C22×D411yescharacteristic
207C2×C4×C7C22×D411yescharacteristic
208C2×C4×C7C2×#4111yescharacteristic
209C7×C8—22no—
210C7×C8—22no—
211C7×C8—42no—
212C7×C8—42no—
213C7×C8—42no—
214C22×Q8—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C7×D411yescharacteristic
219C23×C4—21no—
220C2×D8—24no—
221C2×D8—44no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—24no—
226C22×C8—44no—
227C22×C8C7×D411yescharacteristic
228C22×C8C7×D411yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C23×C712yes—
233#127—21no—
234#127—21no—
235#127—21no—
236#127C23×C712yes—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4C7×D412yes—
240C4×D4C23×C712yes—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C7×D411yescharacteristic
244C2×C22⋊C4—21no—
245C2×C42C23×C711yescharacteristic
246#106—24no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8C23×C712yes—
251C4⋊C8C23×C712yes—
252C4⋊C8C23×C712yes—
253#102—24no—
254#102—24no—
255#102—24no—
256#102—24no—
257C22⋊C8—24no—
258C4×C8C7×D412yes—
259C4×C8C23×C712yes—
260C22×C7—24no—
261C22×C7—48no—
262C22×C7—42no—
263C22×C7—42no—
264C22×C7—82no—
265C22×C7—82no—
266C22×C7—82no—
267C22×C7—164no—
268C22×C7#46312yes—
269C22×C7#46512yes—
270C22×C7#47212yes—
271C22×C7C2×#12111yescharacteristic
272C4×C7—21no—
273C4×C7—21no—
274C4×C7—42no—
275C4×C7—82no—
276C4×C7#46312yes—
277C4×C7#46512yes—
278C4×C7C22×SD1611yescharacteristic
279C4×C7C2×#13511yescharacteristic
280C4×C7C2×#13511yescharacteristic
281C4×C7C2×AGL(1,ℤ/8)11yescharacteristic
282C24—21no—
283C24—41no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—82no—
287C2×D4—21no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—82no—
300C2×D4C7×SD1614yes—
301C2×D4C2×C7×D412yes—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4C2×C7×D411yescharacteristic
309C22×C4C2×C7×D411yescharacteristic
310C22×C4C7×#4111yescharacteristic
311D8—48no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—48no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8C2×C7×D412yes—
322C2×C8C2×C7×D412yes—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C2×C7×D412yes—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C42C2×C7×D411yescharacteristic
332C42C2×C7×D411yescharacteristic
333C42C7×#4111yescharacteristic
334C42C24×C711yescharacteristic
335C2×C7—44no—
336C2×C7—162no—
337C2×C7#167714yesdirect product factor
338C2×C7C2×#46311yescharacteristic
339C2×C7C2×#46511yescharacteristic
340C2×C7C2×#47211yescharacteristic
341C23—22no—
342C23—24no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—82no—
347C23—82no—
348C23—82no—
349C23C7×#12111yescharacteristic
350Q8—82no—
351Q8—82no—
352D4—22no—
353D4—24no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—42no—
358D4—82no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4C2×C7×SD1614yes—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—82no—
371C2×C4C7×#12111yescharacteristic
372C2×C4C7×#12111yescharacteristic
373C2×C4C7×#12111yescharacteristic
374C2×C4C2×C7×SD1612yes—
375C2×C4C7×#13512yes—
376C2×C4C7×#13512yes—
377C2×C4C7×AGL(1,ℤ/8)12yes—
378C2×C4C22×C7×D411yescharacteristic
379C2×C4C22×C7×D411yescharacteristic
380C2×C4C2×C7×#4111yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C7C2×#167711yescharacteristic, direct product factor, Sylow
387C22—24no—
388C22—42no—
389C22—42no—
390C22—48no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—164no—
395C22C7×#46312yes—
396C22C7×#46512yes—
397C22C7×#47212yes—
398C22C2×C7×#12111yescharacteristic
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4C7×#46312yes—
404C4C7×#46512yes—
405C4C22×C7×SD1611yescharacteristic
406C4C2×C7×#13511yescharacteristic
407C4C2×C7×#13511yescharacteristic
408C4C2×C7×AGL(1,ℤ/8)11yescharacteristic
409C2—44no—
410C2—162no—
411C2C7×#167714yesdirect product factor
412C2C2×C7×#46311yescharacteristic
413C2C2×C7×#46511yescharacteristic
414C2C2×C7×#47211yescharacteristic
subgroupG/H
center, socleC23×C7#121
commutator, Frattini, cosocleC42C24×C7
prime radicalC2×C7×#459C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#486C2semidirect
2. C2×C7×#476C2semidirect
4. C2×C7×C8×D4C2semidirect
5. C7×#1677C2direct (N × H)
6. C2×C7×#334C2semidirect
7. C2×C7×#333C2semidirect
8. C2×C7×#331C2semidirect
15. C7×#486C22semidirect
17. C7×#476C22semidirect
21. C7×C8×D4C22semidirect
32. C7×#334C22semidirect
33. C7×#333C22semidirect
34. C7×#331C22semidirect
35. C2×#1677C7direct (N × H)
82. C2×#486C2×C7semidirect
83. C2×#476C2×C7semidirect
85. C2×C8×D4C2×C7semidirect
86. #1677C2×C7direct (N × H)
87. C2×#334C2×C7semidirect
88. C2×#333C2×C7semidirect
89. C2×#331C2×C7semidirect
149. #486C22×C7semidirect
151. #476C22×C7semidirect
155. C8×D4C22×C7semidirect
166. #334C22×C7semidirect
167. #333C22×C7semidirect
168. #331C22×C7semidirect
337. C2×C7#1677direct (N × H)
386. C7C2×#1677direct (N × H)
411. C2C7×#1677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4862
C2×C7×#4762
C2×C7×#4592
C2×C7×C8×D42
C7×#16772
C2×C7×#3342
C2×C7×#3332
C2×C7×#3312
C2×#16777