Finite Group Databasebeta

← C2×#11739423 #14225902

Subgroups — C2×#11739423 #14225902

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×#90416C211yesmaximal, characteristic
2C2×D7×#125C211yesmaximal, characteristic, complemented
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89839C211yesmaximal, characteristic, complemented
6#11739423C2116yesmaximal, direct product factor
7C2×#89663C212yesmaximal, complemented
8C2×#89654C212yesmaximal, complemented
9C2×#89643C212yesmaximal, complemented
10C2×#89635C212yesmaximal, complemented
11C2×#89485C211yesmaximal, characteristic, complemented
12C2×#89477C211yesmaximal, characteristic, complemented
13C22×#1161—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×#6510—21no—
17#90416—24no—
18#90416C2218yes—
19D7×#125—24no—
20D7×#125C2218yescomplemented
21C2×#6458—21no—
22C2×#6458C2212yes—
23C2×#6456—21no—
24C2×#6456C2212yes—
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×#6437C2211yescharacteristic
34C2×C42×D7C2211yescharacteristic
35C2×#6433C2211yescharacteristic
36C7×#501C2218yescomplemented
37C2×C7×#107C2212yes—
38C2×C7×#106C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6395C2212yes—
41C2×#6395C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×Dic7⋊C8C2212yes—
44#89852C2218yescomplemented
45#89839C2218yescomplemented
46C2×#6383C2212yes—
47C2×#6383C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89663C22116yescomplemented
52#89654C22116yescomplemented
53#89643C22116yescomplemented
54#89635C22116yescomplemented
55#89485C2218yescomplemented
56#89477C2218yescomplemented
57C2×#3234—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C2×#1161—28no—
60C2×#1161—48no—
61C22×D28—22no—
62C22×D28—21no—
63C22×D28—21no—
64C22×D28C2312yes—
65C22×C4×D7—21no—
66C22×C4×D7—21no—
67C22×C4×D7—22no—
68C22×C4×D7D411yescharacteristic
69C22×C4×D7D411yescharacteristic
70C22×C4×D7C2311yescharacteristic
71C22×C7×C8C2312yes—
72C7×C4⋊Q8—22no—
73C7×C4⋊Q8C2314yes—
74C7×#125—22no—
75C7×#125C2314yes—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2312yes—
82C2×C42×C7C2311yescharacteristic
83#6510—28no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7C2311yescharacteristic
99C22×C7⋊C8C2312yes—
100#6458—24no—
101#6458—28no—
102#6458C2318yes—
103#6456—24no—
104#6456—28no—
105#6456C2318yes—
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—
118#6437—22no—
119#6437C2314yes—
120C42×D7D414yes—
121C42×D7C2314yes—
122#6433—22no—
123#6433C2314yes—
124C7×#107C2318yes—
125C7×#106C2318yes—
126C7×#97C2314yes—
127#6395C2318yes—
128#6395C2318yes—
129(C2×D7)⋊C8C2318yes—
130Dic7⋊C8C2318yes—
131#6383C2318yes—
132#6383C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135#6377C2314yes—
136C2×#532—71no—
137C22×#125—71no—
138#3234—716no—
139C2×#501—71no—
140C2×#501D711yescharacteristic, complemented
141C2×#490—71no—
142C2×#490—71no—
143C2×#481—72no—
144C2×#480—72no—
145C2×#478—72no—
146C2×#478—72no—
147C2×#432—71no—
148C23×D7—22no—
149C23×D7C2×D411yescharacteristic
150C2×C7×Q8—24no—
151C2×C7×Q8—44no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2411yescharacteristic
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163#1161—432no—
164C2×D28—28no—
165C2×D28—28no—
166C2×D28—22no—
167C2×D28—24no—
168C2×D28—24no—
169C2×D28—44no—
170C2×D28—44no—
171C2×D28—48no—
172C2×D28C2414yes—
173C2×C4×D7—24no—
174C2×C4×D7—24no—
175C2×C4×D7—24no—
176C2×C4×D7—24no—
177C2×C4×D7—28no—
178C2×C4×D7—42no—
179C2×C4×D7—48no—
180C2×C4×D7—44no—
181C2×C4×D7—44no—
182C2×C4×D7C2×D412yes—
183C2×C4×D7C2×D414yes—
184C2×C4×D7C2×D414yes—
185C2×C4×D7C2412yes—
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⋊C4—24no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4C2412yes—
195C7×C4⋊C4C2414yes—
196C7×C4⋊C4C2412yes—
197C42×C7C2×D412yes—
198C42×C7C2412yes—
199(C2×D7)⋊C4—28no—
200(C2×D7)⋊C4—28no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—24no—
204C4⋊Dic7—24no—
205C4⋊Dic7C2412yes—
206C4⋊Dic7C2412yes—
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⋊Q8C2×D711yescharacteristic
223C2×#127—71no—
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#501C2×D718yescomplemented
244#490—78no—
245#490—78no—
246#481—716no—
247#480—716no—
248#478—716no—
249#478—716no—
250#432—78no—
251C2×#107—72no—
252C2×#107C2×D712yes—
253C2×#106—72no—
254C2×#106C2×D712yes—
255C2×C4⋊C8—72no—
256C2×#102—72no—
257C2×#102—72no—
258C2×#102—72no—
259C2×#102—72no—
260C2×C22⋊C8—72no—
261C2×#97—71no—
262C2×#97C2×D711yescharacteristic
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—22no—
266C22×D7—24no—
267C22×D7—44no—
268C22×D7—44no—
269C22×D7—44no—
270C22×D7AGL(1,ℤ/8)14yes—
271C22×D7C22×D412yes—
272C7×Q8—48no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—24no—
278C2×C4×C7—44no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7C22×D412yes—
282C2×C4×C7C22×D412yes—
283C2×C4×C7C22×D411yescharacteristic
284C2×C4×C72−1+414yes—
285C2×C4×C7C2511yescharacteristic
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7C22×D412yes—
294C2×Dic7C22×D412yes—
295C2×Dic7C22×D412yes—
296D28—28no—
297D28—48no—
298D28—48no—
299D28—416no—
300D28—44no—
301C4×D7—28no—
302C4×D7—24no—
303C4×D7—24no—
304C4×D7—44no—
305C4×D7—416no—
306C4×D7—48no—
307C4×D7—48no—
308C7×C8—24no—
309C7⋊C8—24no—
310C2×#41—148no—
311C2×#41—288no—
312C22×Q8—21no—
313C22×D4—72no—
314C22×D4—142no—
315C22×D4—141no—
316C22×D4—141no—
317C23×C4—71no—
318C23×C4—71no—
319C23×C4—71no—
320C23×C4—142no—
321C23×C4—141no—
322C23×C4—141no—
323C22×C8—72no—
324C22×C8C22×D712yes—
325C4⋊Q8—22no—
326C4⋊Q8C22×D714yes—
327#127—74no—
328#127—142no—
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—21no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
366C2×C4⋊C4C22×D711yescharacteristic
367C2×C4⋊C4C22×D712yes—
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#107C22×D718yes—
378#106—78no—
379#106C22×D718yes—
380C4⋊C8—78no—
381#102—78no—
382#102—78no—
383#102—78no—
384#102—78no—
385C22⋊C8—78no—
386#97—74no—
387#97C22×D714yes—
388C22×C7#53612yes—
389C22×C7C2×AGL(1,ℤ/8)12yes—
390C22×C7#57512yes—
391C22×C7C23×D411yescharacteristic
392C2×D7—22no—
393C2×D7—28no—
394C2×D7—22no—
395C2×D7—44no—
396C2×D7—44no—
397C2×D7—44no—
398C2×D7—88no—
399C2×D7C2×AGL(1,ℤ/8)14yes—
400C4×C7—22no—
401C4×C7—22no—
402C4×C7—44no—
403C4×C7—42no—
404C4×C7—42no—
405C4×C7#53612yes—
406C4×C7C2×2−1+412yes—
407Dic7—22no—
408Dic7—22no—
409Dic7—22no—
410Dic7—42no—
411Dic7—42no—
412C24—71no—
413C24—142no—
414#41—2832no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×D4—74no—
418C2×D4—148no—
419C2×D4—144no—
420C2×D4—142no—
421C2×D4—144no—
422C2×D4—148no—
423C2×D4—284no—
424C2×D4—284no—
425C2×D4—288no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—71no—
430C22×C4—71no—
431C22×C4—71no—
432C22×C4—72no—
433C22×C4—74no—
434C22×C4—72no—
435C22×C4—74no—
436C22×C4—148no—
437C22×C4—144no—
438C22×C4—144no—
439C22×C4—144no—
440C22×C4—144no—
441C22×C4—141no—
442C22×C4—141no—
443C22×C4—282no—
444C22×C4—288no—
445C22×C4—284no—
446C22×C4—284no—
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—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—72no—
461C4⋊C4—72no—
462C4⋊C4—144no—
463C4⋊C4—144no—
464C4⋊C4—144no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—144no—
468C4⋊C4—144no—
469C4⋊C4—144no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4C23×D712yes—
473C4⋊C4C23×D712yes—
474C4⋊C4C23×D714yes—
475C22⋊C4—148no—
476C22⋊C4—148no—
477C42—74no—
478C42—72no—
479C42—74no—
480C42—72no—
481C42D4×D712yes—
482C42C23×D712yes—
483C2×C7#323414yescomplemented
484C2×C7C2×#53611yescharacteristic
485C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
486C2×C7C2×#57511yescharacteristic
487D7—24no—
488D7—84no—
489C23—74no—
490C23—72no—
491C23—142no—
492C23—142no—
493C23—144no—
494C23—284no—
495C23—284no—
496C23—284no—
497C23C2×D4×D711yescharacteristic
498Q8—48no—
499D4—148no—
500D4—288no—
501D4—288no—
502D4—2816no—
503D4—284no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—72no—
513C2×C4—72no—
514C2×C4—72no—
515C2×C4—148no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—142no—
519C2×C4—144no—
520C2×C4—144no—
521C2×C4—142no—
522C2×C4—142no—
523C2×C4—284no—
524C2×C4—2816no—
525C2×C4—288no—
526C2×C4—288no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4C2×D4×D712yes—
530C2×C4C2×D4×D712yes—
531C2×C4C2×D4×D711yescharacteristic
532C2×C4#655114yes—
533C2×C4C24×D711yescharacteristic
534C8—24no—
535C8—144no—
536C7C2×#323411yescharacteristic, complemented, Sylow
537C22—74no—
538C22—142no—
539C22—148no—
540C22—142no—
541C22—284no—
542C22—284no—
543C22—284no—
544C22—568no—
545C22#9041512yes—
546C22D7×AGL(1,ℤ/8)12yes—
547C22#9046812yes—
548C22C22×D4×D711yescharacteristic
549C4—22no—
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—142no—
555C4—142no—
556C4—142no—
557C4—282no—
558C4—282no—
559C4#9041512yes—
560C4C2×#655112yes—
561C2—144no—
562C2—564no—
563C2#1173942314yesdirect product factor
564C2C2×#9041511yescharacteristic
565C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
566C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#501C2
socleC23×C7C22×D4
prime radicalC2×#90416C2
hypercenterC2×#501D7
hypocenterC7C2×#3234
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
2. C2×D7×#125C2semidirect
3. C2×C7×#501C2semidirect
4. C2×#89852C2semidirect
5. C2×#89839C2semidirect
6. #11739423C2direct (N × H)
7. C2×#89663C2semidirect
8. C2×#89654C2semidirect
9. C2×#89643C2semidirect
10. C2×#89635C2semidirect
11. C2×#89485C2semidirect
12. C2×#89477C2semidirect
20. D7×#125C22semidirect
36. C7×#501C22semidirect
44. #89852C22semidirect
45. #89839C22semidirect
51. #89663C22semidirect
52. #89654C22semidirect
53. #89643C22semidirect
54. #89635C22semidirect
55. #89485C22semidirect
56. #89477C22semidirect
140. C2×#501D7semidirect
243. #501C2×D7semidirect
483. C2×C7#3234semidirect
536. C7C2×#3234semidirect
563. C2#11739423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904162
C2×D7×#1252
C2×C7×#5012
C2×#898522
C2×#898392
#117394232
C2×#896632
C2×#896542
C2×#896432
C2×#896352
C2×#894852
C2×#894772
C2×#32347