Finite Group Databasebeta

← C2×#11739166 #14225896

Subgroups — C2×#11739166 #14225896

Order 1792.

2050 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90407C211yesmaximal, characteristic
2C2×D7×#125C211yesmaximal, characteristic, complemented
3C2×C7×#490C211yesmaximal, characteristic, complemented
4C2×#89843C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6#11739166C2116yesmaximal, direct product factor
7C2×#89549C212yesmaximal, complemented
8C2×#89546C212yesmaximal, complemented
9C2×#89535C212yesmaximal, complemented
10C2×#89538C212yesmaximal, complemented
11C2×#89477C211yesmaximal, characteristic, complemented
12C2×#89474C211yesmaximal, characteristic, complemented
13C22×#1159—21no—
14C2×C7×#127C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×#6501—21no—
17C2×#6501C2212yes—
18C2×#6499—21no—
19C2×D4×Dic7—21no—
20C2×D4×Dic7C2212yes—
21#90407—24no—
22#90407C2218yes—
23D7×#125—24no—
24D7×#125C2218yescomplemented
25C2×D7×C4⋊C4—21no—
26C2×D7×C4⋊C4—21no—
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×#6453C2211yescharacteristic
30C2×#6453C2211yescharacteristic
31C2×#6452—21no—
32C2×#6452—21no—
33C2×C42×D7C2211yescharacteristic
34C2×#6433C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#490C2218yescomplemented
37C2×C7×#102C2212yes—
38C2×C7×#102C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6406C2212yes—
41C2×#6406C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6391C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89843C2218yescomplemented
47#89837C2218yescomplemented
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89549C22116yescomplemented
52#89546C22116yescomplemented
53#89538C22116yescomplemented
54#89535C22116yescomplemented
55#89477C2218yescomplemented
56#89474C2218yescomplemented
57C2×#3234—71nomaximal, Sylow
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4C2312yes—
61C22×C22⋊D7—22no—
62C23×Dic7—22no—
63C2×#1159—28no—
64C2×#1159—48no—
65C22×C4×D7—21no—
66C22×C4×D7—21no—
67C22×C4×D7D411yescharacteristic
68C22×C4×D7D411yescharacteristic
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—21no—
71C22×C7×C8C2312yes—
72C7×#127—22no—
73C7×#127C2314yes—
74C7×#125—22no—
75C7×#125C2314yes—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C42×C7C2311yescharacteristic
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83#6501—24no—
84#6501—28no—
85#6501C2318yes—
86#6499—28no—
87D4×Dic7—24no—
88D4×Dic7—28no—
89D4×Dic7C2318yes—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7—21no—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2312yes—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—21no—
102C2×C4×Dic7D411yescharacteristic
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7C2311yescharacteristic
105C22×C7⋊C8C2312yes—
106D7×C4⋊C4—22no—
107D7×C4⋊C4—22no—
108D7×C4⋊C4—28no—
109D7×C4⋊C4—28no—
110D7×C4⋊C4C2314yes—
111D7×C4⋊C4C2314yes—
112#6453—22no—
113#6453—22no—
114#6453C2314yes—
115#6453C2314yes—
116#6452—28no—
117#6452—28no—
118C42×D7D414yes—
119C42×D7C2314yes—
120#6433—22no—
121#6433C2314yes—
122#6432—22no—
123#6432C2314yes—
124C7×#102C2318yes—
125C7×#102C2318yes—
126C7×#97C2314yes—
127#6406C2318yes—
128#6406C2318yes—
129(C2×D7)⋊C8C2318yes—
130#6392C2318yes—
131#6391C2318yes—
132Dic7⋊C8C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135#6377C2314yes—
136C2×#532—71no—
137C22×#125—71no—
138#3234—716no—
139C2×#501—71no—
140C2×#501—71no—
141C2×#490—71no—
142C2×#490D711yescharacteristic, complemented
143C2×#481—72no—
144C2×#480—72no—
145C2×#478—72no—
146C2×#478—72no—
147C2×#432—71no—
148C24×C7—22no—
149C23×D7C2×D411yescharacteristic
150C2×C7×D4—22no—
151C2×C7×D4—24no—
152C2×C7×D4—24no—
153C2×C7×D4—28no—
154C2×C7×D4—44no—
155C2×C7×D4—44no—
156C2×C7×D4C2414yes—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C2×C22⋊D7—28no—
163C2×C22⋊D7—48no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—22no—
167C22×Dic7—28no—
168C22×Dic7—48no—
169C22×Dic7C2×D411yescharacteristic
170C22×Dic7C2×D411yescharacteristic
171C22×Dic7C2×D411yescharacteristic
172#1159—432no—
173C2×C4×D7—24no—
174C2×C4×D7—24no—
175C2×C4×D7—24no—
176C2×C4×D7—24no—
177C2×C4×D7—42no—
178C2×C4×D7—44no—
179C2×C4×D7—44no—
180C2×C4×D7C2×D412yes—
181C2×C4×D7C2×D414yes—
182C2×C4×D7C2×D414yes—
183C2×C4×D7C2412yes—
184C2×Dic14—24no—
185C2×Dic14—44no—
186C2×C7×C8—24no—
187C2×C7×C8C2414yes—
188C7×C4⋊C4—24no—
189C7×C4⋊C4—24no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4C2412yes—
193C7×C4⋊C4C2412yes—
194C42×C7C2×D412yes—
195C42×C7C2412yes—
196C22⋊Dic7—28no—
197C22⋊Dic7—28no—
198C4⋊Dic7—22no—
199C4⋊Dic7—24no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—24no—
203C4⋊Dic7—24no—
204C4⋊Dic7C2412yes—
205C4⋊Dic7C2412yes—
206C4⋊Dic7C2414yes—
207Dic7⋊C4—24no—
208Dic7⋊C4—24no—
209Dic7⋊C4—24no—
210Dic7⋊C4—24no—
211Dic7⋊C4—24no—
212Dic7⋊C4—24no—
213C4×Dic7C2×D412yes—
214C4×Dic7C2×D414yes—
215C4×Dic7C2×D414yes—
216C4×Dic7C2412yes—
217C2×C7⋊C8—24no—
218C2×C7⋊C8C2414yes—
219C22×#41—141no—
220#532—78no—
221#532—144no—
222C2×C4⋊Q8—71no—
223C2×#127C2×D711yescharacteristic
224C2×#125—78no—
225C2×#125—71no—
226C2×#125—71no—
227C2×#125—71no—
228C2×#125—141no—
229C2×#125—141no—
230C2×#125—144no—
231C2×#125C2×D711yescharacteristic
232C2×#124—141no—
233C2×#121—72no—
234C2×#121—141no—
235C2×C4×D4—72no—
236C2×C4×D4—141no—
237C22×C4⋊C4—71no—
238C22×C4⋊C4—71no—
239C22×C4⋊C4—141no—
240C22×C4⋊C4—141no—
241C22×C42—71no—
242#501—78no—
243#501—78no—
244#490—78no—
245#490C2×D718yescomplemented
246#481—716no—
247#480—716no—
248#478—716no—
249#478—716no—
250#432—78no—
251C2×#107—72no—
252C2×#107—72no—
253C2×#106—72no—
254C2×#106—72no—
255C2×C4⋊C8—72no—
256C2×#102—72no—
257C2×#102—72no—
258C2×#102C2×D712yes—
259C2×#102C2×D712yes—
260C2×C22⋊C8—72no—
261C2×#97—71no—
262C2×#97C2×D711yescharacteristic
263C23×C7—24no—
264C23×C7—44no—
265C23×C7—44no—
266C23×C7—44no—
267C23×C7C22×D411yescharacteristic
268C22×D7—22no—
269C22×D7—22no—
270C22×D7AGL(1,ℤ/8)14yes—
271C22×D7C22×D412yes—
272C7×D4—28no—
273C7×D4—48no—
274C7×D4—48no—
275C7×D4—44no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7C22×D412yes—
283C2×C4×C7C22×D412yes—
284C2×C4×C7C22×D411yescharacteristic
285C2×C4×C72−1+414yes—
286C2×C4×C7C2511yescharacteristic
287C22⋊D7—416no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—24no—
294C2×Dic7—416no—
295C2×Dic7—44no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7C22×D412yes—
299C2×Dic7C22×D412yes—
300C2×Dic7C22×D412yes—
301C4×D7—28no—
302C4×D7—24no—
303C4×D7—24no—
304C4×D7—44no—
305C4×D7—48no—
306C4×D7—48no—
307Dic14—48no—
308C7×C8—24no—
309C7⋊C8—24no—
310C2×#41—148no—
311C2×#41—288no—
312C22×Q8—141no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—142no—
316C22×D4C22×D712yes—
317C23×C4—71no—
318C23×C4—71no—
319C23×C4—71no—
320C23×C4—141no—
321C23×C4—141no—
322C23×C4—142no—
323C22×C8—72no—
324C22×C8C22×D712yes—
325C4⋊Q8—74no—
326C4⋊Q8—142no—
327#127—22no—
328#127C22×D714yes—
329#125—22no—
330#125—74no—
331#125—74no—
332#125—74no—
333#125—148no—
334#125—148no—
335#125—142no—
336#125—142no—
337#125—142no—
338#125C22×D714yes—
339#124—148no—
340#121—78no—
341#121—144no—
342#121—148no—
343C4×D4—78no—
344C4×D4—144no—
345C4×D4—148no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—72no—
351C2×C4⋊C4—74no—
352C2×C4⋊C4—74no—
353C2×C4⋊C4—142no—
354C2×C4⋊C4—142no—
355C2×C4⋊C4—148no—
356C2×C4⋊C4—148no—
357C2×C4⋊C4—141no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4—141no—
360C2×C4⋊C4—141no—
361C2×C4⋊C4—141no—
362C2×C4⋊C4—141no—
363C2×C4⋊C4—141no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4C22×D711yescharacteristic
367C2×C4⋊C4C22×D711yescharacteristic
368C2×C22⋊C4—142no—
369C2×C22⋊C4—142no—
370C2×C42—71no—
371C2×C42—71no—
372C2×C42—71no—
373C2×C42—74no—
374C2×C42—74no—
375C2×C42C22×D711yescharacteristic
376#107—78no—
377#107—78no—
378#106—78no—
379#106—78no—
380C4⋊C8—78no—
381#102—78no—
382#102—78no—
383#102C22×D718yes—
384#102C22×D718yes—
385C22⋊C8—78no—
386#97—74no—
387#97C22×D714yes—
388C22×C7—44no—
389C22×C7—44no—
390C22×C7—44no—
391C22×C7—88no—
392C22×C7#53612yes—
393C22×C7C2×AGL(1,ℤ/8)12yes—
394C22×C7#57512yes—
395C22×C7C23×D411yescharacteristic
396C2×D7—22no—
397C2×D7—28no—
398C2×D7—22no—
399C2×D7C2×AGL(1,ℤ/8)14yes—
400C4×C7—22no—
401C4×C7—22no—
402C4×C7—42no—
403C4×C7—42no—
404C4×C7#53612yes—
405C4×C7C2×2−1+412yes—
406Dic7—22no—
407Dic7—22no—
408Dic7—22no—
409Dic7—44no—
410Dic7—42no—
411Dic7—42no—
412C24—22no—
413C24—71no—
414#41—2832no—
415C2×Q8—144no—
416C2×Q8—284no—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—28no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—148no—
424C2×D4—288no—
425C2×D4C23×D714yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—71no—
429C22×C4—71no—
430C22×C4—71no—
431C22×C4—72no—
432C22×C4—74no—
433C22×C4—72no—
434C22×C4—74no—
435C22×C4—144no—
436C22×C4—144no—
437C22×C4—144no—
438C22×C4—148no—
439C22×C4—144no—
440C22×C4—142no—
441C22×C4—141no—
442C22×C4—141no—
443C22×C4—282no—
444C22×C4—284no—
445C22×C4—284no—
446C22×C4—288no—
447C22×C4D4×D711yescharacteristic
448C22×C4D4×D711yescharacteristic
449C22×C4C23×D711yescharacteristic
450C2×C8—24no—
451C2×C8—74no—
452C2×C8—144no—
453C2×C8C23×D714yes—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—72no—
459C4⋊C4—72no—
460C4⋊C4—74no—
461C4⋊C4—144no—
462C4⋊C4—144no—
463C4⋊C4—144no—
464C4⋊C4—144no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—144no—
468C4⋊C4—144no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—142no—
472C4⋊C4—144no—
473C4⋊C4C23×D712yes—
474C4⋊C4C23×D712yes—
475C22⋊C4—148no—
476C22⋊C4—148no—
477C42—74no—
478C42—72no—
479C42—74no—
480C42—72no—
481C42D4×D712yes—
482C42C23×D712yes—
483C2×C7—84no—
484C2×C7#323414yescomplemented
485C2×C7C2×#53611yescharacteristic
486C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
487C2×C7C2×#57511yescharacteristic
488D7—24no—
489C23—24no—
490C23—44no—
491C23—44no—
492C23—44no—
493C23—74no—
494C23—72no—
495C23—142no—
496C23—142no—
497C23C2×D4×D711yescharacteristic
498Q8—288no—
499D4—28no—
500D4—48no—
501D4—48no—
502D4—44no—
503D4—2816no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—72no—
511C2×C4—72no—
512C2×C4—72no—
513C2×C4—148no—
514C2×C4—142no—
515C2×C4—142no—
516C2×C4—142no—
517C2×C4—144no—
518C2×C4—144no—
519C2×C4—144no—
520C2×C4—142no—
521C2×C4—142no—
522C2×C4—284no—
523C2×C4—288no—
524C2×C4—288no—
525C2×C4—2816no—
526C2×C4—282no—
527C2×C4—284no—
528C2×C4—282no—
529C2×C4C2×D4×D712yes—
530C2×C4C2×D4×D712yes—
531C2×C4C2×D4×D711yescharacteristic
532C2×C4#655414yes—
533C2×C4C24×D711yescharacteristic
534C8—24no—
535C8—144no—
536C7C2×#323411yescharacteristic, complemented, Sylow
537C22—44no—
538C22—44no—
539C22—44no—
540C22—74no—
541C22—88no—
542C22—142no—
543C22—148no—
544C22—142no—
545C22#9036612yes—
546C22D7×AGL(1,ℤ/8)12yes—
547C22#9046412yes—
548C22C22×D4×D711yescharacteristic
549C4—22no—
550C4—22no—
551C4—42no—
552C4—42no—
553C4—142no—
554C4—142no—
555C4—142no—
556C4—284no—
557C4—282no—
558C4—282no—
559C4#9036612yes—
560C4C2×#655412yes—
561C2—84no—
562C2—144no—
563C2#1173916614yesdirect product factor
564C2C2×#9036611yescharacteristic
565C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
566C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#490C2
socleC23×C7C22×D4
prime radicalC2×#90407C2
hypercenterC2×#490D7
hypocenterC7C2×#3234
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. C2×D7×#125C2semidirect
3. C2×C7×#490C2semidirect
4. C2×#89843C2semidirect
5. C2×#89837C2semidirect
6. #11739166C2direct (N × H)
7. C2×#89549C2semidirect
8. C2×#89546C2semidirect
9. C2×#89535C2semidirect
10. C2×#89538C2semidirect
11. C2×#89477C2semidirect
12. C2×#89474C2semidirect
24. D7×#125C22semidirect
36. C7×#490C22semidirect
46. #89843C22semidirect
47. #89837C22semidirect
51. #89549C22semidirect
52. #89546C22semidirect
53. #89538C22semidirect
54. #89535C22semidirect
55. #89477C22semidirect
56. #89474C22semidirect
142. C2×#490D7semidirect
245. #490C2×D7semidirect
484. C2×C7#3234semidirect
536. C7C2×#3234semidirect
563. C2#11739166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904072
C2×D7×#1252
C2×C7×#4902
C2×#898432
C2×#898372
#117391662
C2×#895492
C2×#895462
C2×#895352
C2×#895382
C2×#894772
C2×#894742
C2×#32347