Finite Group Databasebeta

← C2×#11739427 #14225919

Subgroups — C2×#11739427 #14225919

Order 1792.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90382C211yesmaximal, characteristic
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89861C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6#11739427C2116yesmaximal, direct product factor
7C2×#89647C212yesmaximal, complemented
8C2×#89654C212yesmaximal
9C2×#89642C212yesmaximal, complemented
10C2×#89634C212yesmaximal, complemented
11C2×#89486C211yesmaximal, characteristic, complemented
12C2×#89477C211yesmaximal, characteristic, complemented
13C22×Q8×D7—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×#6507—21no—
17D7×C4⋊Q8—24no—
18D7×C4⋊Q8C2218yescomplemented
19#90382—24no—
20#90382C2218yes—
21C2×#6461—21no—
22C2×#6460C2211yescharacteristic
23C2×#6458C2211yescharacteristic
24C2×#6457—21no—
25C2×#6456—21no—
26C2×#6456C2211yescharacteristic
27C2×#6455—21no—
28C2×D7×C4⋊C4—21no—
29C2×D7×C4⋊C4C2212yes—
30C2×#6451—21no—
31C2×#6451C2212yes—
32C2×#6450C2211yescharacteristic
33C2×#6438C2211yescharacteristic
34C2×C42×D7C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#501C2218yescomplemented
37C2×C7×#107C2212yes—
38C2×C7×#106C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6395C2212yes—
41C2×(C2×D7)⋊C8C2212yes—
42C2×#6390C2212yes—
43C2×Dic7⋊C8C2212yes—
44#89861C2218yescomplemented
45#89837C2218yescomplemented
46C2×#6384C2212yes—
47C2×#6383C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89654C22116yes—
52#89647C22116yescomplemented
53#89642C22116yescomplemented
54#89634C22116yescomplemented
55#89486C2218yescomplemented
56#89477C2218yescomplemented
57C2×#3238—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C2×Q8×D7—28no—
60C2×Q8×D7—48no—
61C22×D28—21no—
62C22×D28C2311yescharacteristic
63C22×C4×D7—22no—
64C22×C4×D7—21no—
65C22×C4×D7D411yescharacteristic
66C22×C4×D7D411yescharacteristic
67C22×C4×D7C2311yescharacteristic
68C22×Dic14—21no—
69C22×Dic14—22no—
70C22×Dic14C2311yescharacteristic
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⋊C4C2312yes—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C42×C7C2311yescharacteristic
83#6507—28no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—21no—
87C2×(C2×D7)⋊C4—21no—
88C2×(C2×D7)⋊C4—21no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7C2312yes—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7C2311yescharacteristic
99C22×C7⋊C8C2312yes—
100#6461—28no—
101#6460—22no—
102#6460C2314yes—
103#6458—22no—
104#6458C2314yes—
105#6457—28no—
106#6456—28no—
107#6456—22no—
108#6456C2314yes—
109#6455—28no—
110D7×C4⋊C4—24no—
111D7×C4⋊C4—28no—
112D7×C4⋊C4C2318yes—
113#6451—24no—
114#6451—28no—
115#6451C2318yes—
116#6450—22no—
117#6450C2314yes—
118#6438—22no—
119#6438C2314yes—
120C42×D7D414yes—
121C42×D7C2314yes—
122#6432—22no—
123#6432C2314yes—
124C7×#107C2318yes—
125C7×#106C2318yes—
126C7×#97C2314yes—
127#6395C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6390C2318yes—
130Dic7⋊C8C2318yes—
131#6384C2318yes—
132#6383C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135#6377C2314yes—
136C22×C4⋊Q8—71no—
137C2×#529—71no—
138#3238—716no—
139C2×#501—71no—
140C2×#501D711yescharacteristic, complemented
141C2×#489—71no—
142C2×#489—71no—
143C2×#483—72no—
144C2×#480—72no—
145C2×#477—72no—
146C2×#476—72no—
147C2×#432—71no—
148C23×D7—21no—
149C23×D7C2×D411yescharacteristic
150C2×C7×Q8—24no—
151C2×C7×Q8—44no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2411yescharacteristic
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163Q8×D7—432no—
164C2×D28—24no—
165C2×D28—24no—
166C2×D28—21no—
167C2×D28—44no—
168C2×D28C2412yes—
169C2×C4×D7—24no—
170C2×C4×D7—24no—
171C2×C4×D7—24no—
172C2×C4×D7—28no—
173C2×C4×D7—24no—
174C2×C4×D7—48no—
175C2×C4×D7—44no—
176C2×C4×D7C2×D412yes—
177C2×C4×D7C2×D414yes—
178C2×C4×D7C2×D414yes—
179C2×C4×D7C2412yes—
180C2×Dic14—24no—
181C2×Dic14—24no—
182C2×Dic14—21no—
183C2×Dic14—28no—
184C2×Dic14—48no—
185C2×Dic14—44no—
186C2×Dic14C2412yes—
187C2×C7×C8—24no—
188C2×C7×C8C2414yes—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—24no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—24no—
195C7×C4⋊C4C2412yes—
196C7×C4⋊C4C2414yes—
197C7×C4⋊C4C2412yes—
198C42×C7C2×D412yes—
199C42×C7C2412yes—
200(C2×D7)⋊C4—24no—
201(C2×D7)⋊C4—24no—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—24no—
204(C2×D7)⋊C4—24no—
205C4⋊Dic7—22no—
206C4⋊Dic7—24no—
207C4⋊Dic7—24no—
208C4⋊Dic7C2414yes—
209Dic7⋊C4—24no—
210Dic7⋊C4—28no—
211Dic7⋊C4—28no—
212C4×Dic7—24no—
213C4×Dic7C2×D412yes—
214C4×Dic7C2×D414yes—
215C4×Dic7C2×D414yes—
216C4×Dic7C2412yes—
217C2×C7⋊C8—24no—
218C2×C7⋊C8C2414yes—
219C23×Q8—141no—
220C2×C4⋊Q8—78no—
221C2×C4⋊Q8—72no—
222C2×C4⋊Q8—71no—
223C2×C4⋊Q8—141no—
224C2×C4⋊Q8—144no—
225C2×C4⋊Q8—141no—
226C2×C4⋊Q8C2×D711yescharacteristic
227#529—78no—
228#529—144no—
229C2×#126—141no—
230C2×#125C2×D711yescharacteristic
231C2×#124—71no—
232C2×#123—141no—
233C2×C22⋊Q8—71no—
234C2×#121—71no—
235C2×C4×Q8—71no—
236C2×C4×D4—71no—
237C2×C4×D4—141no—
238C2×#117—141no—
239C22×C4⋊C4—72no—
240C22×C4⋊C4—141no—
241C22×C42—71no—
242#501—78no—
243#501C2×D718yescomplemented
244#489—78no—
245#489—78no—
246#483—716no—
247#480—716no—
248#477—716no—
249#476—716no—
250#432—78no—
251C2×#107—72no—
252C2×#107C2×D712yes—
253C2×#106—72no—
254C2×#106C2×D712yes—
255C2×C4⋊C8—72no—
256C2×#103—72no—
257C2×#103—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—22no—
267C22×D7—42no—
268C22×D7—42no—
269C22×D7—42no—
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—24no—
277C2×C4×C7—22no—
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—24no—
290C2×Dic7—42no—
291C2×Dic7—44no—
292C2×Dic7#13714yes—
293C2×Dic7C22×D412yes—
294C2×Dic7C22×D412yes—
295C2×Dic7C22×D412yes—
296D28—24no—
297D28—48no—
298D28—42no—
299C4×D7—28no—
300C4×D7—24no—
301C4×D7—24no—
302C4×D7—28no—
303C4×D7—416no—
304C4×D7—48no—
305Dic14—24no—
306Dic14—416no—
307Dic14—48no—
308Dic14—42no—
309C7×C8—24no—
310C7⋊C8—24no—
311C22×Q8—21no—
312C22×Q8—71no—
313C22×Q8—142no—
314C22×Q8—148no—
315C22×Q8—141no—
316C22×Q8—288no—
317C22×D4—71no—
318C22×D4—141no—
319C23×C4—71no—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—141no—
323C23×C4—142no—
324C22×C8—72no—
325C22×C8C22×D712yes—
326C4⋊Q8—22no—
327C4⋊Q8—78no—
328C4⋊Q8—74no—
329C4⋊Q8—144no—
330C4⋊Q8—148no—
331C4⋊Q8—148no—
332C4⋊Q8—142no—
333C4⋊Q8C22×D714yes—
334#126—148no—
335#125—22no—
336#125C22×D714yes—
337#124—74no—
338#124—142no—
339#123—148no—
340C22⋊Q8—74no—
341C22⋊Q8—142no—
342#121—74no—
343#121—142no—
344C4×Q8—74no—
345C4×Q8—142no—
346C4×D4—74no—
347C4×D4—142no—
348C4×D4—148no—
349#117—148no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—72no—
354C2×C4⋊C4—78no—
355C2×C4⋊C4—144no—
356C2×C4⋊C4—148no—
357C2×C4⋊C4—142no—
358C2×C4⋊C4—142no—
359C2×C4⋊C4—141no—
360C2×C4⋊C4—141no—
361C2×C4⋊C4—141no—
362C2×C4⋊C4C22×D712yes—
363C2×C4⋊C4C22×D711yescharacteristic
364C2×C4⋊C4C22×D711yescharacteristic
365C2×C22⋊C4—141no—
366C2×C22⋊C4—141no—
367C2×C22⋊C4—141no—
368C2×C22⋊C4—141no—
369C2×C22⋊C4—141no—
370C2×C42—71no—
371C2×C42—71no—
372C2×C42—71no—
373C2×C42—74no—
374C2×C42—74no—
375C2×C42—141no—
376C2×C42C22×D711yescharacteristic
377#107—78no—
378#107C22×D718yes—
379#106—78no—
380#106C22×D718yes—
381C4⋊C8—78no—
382#103—78no—
383#103—78no—
384#102—78no—
385#102—78no—
386C22⋊C8—78no—
387#97—74no—
388#97C22×D714yes—
389C22×C7#53612yes—
390C22×C7C2×AGL(1,ℤ/8)12yes—
391C22×C7C2×#13712yes—
392C22×C7C23×D411yescharacteristic
393C2×D7—22no—
394C2×D7—28no—
395C2×D7—22no—
396C2×D7—42no—
397C2×D7—42no—
398C2×D7—42no—
399C2×D7—84no—
400C2×D7C2×AGL(1,ℤ/8)14yes—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—44no—
404C4×C7—42no—
405C4×C7—42no—
406C4×C7#53612yes—
407C4×C7C2×2−1+412yes—
408Dic7—22no—
409Dic7—22no—
410Dic7—42no—
411Dic7—44no—
412Dic7C2×#13714yes—
413C24—71no—
414C24—141no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—72no—
418C2×Q8—148no—
419C2×Q8—141no—
420C2×Q8—144no—
421C2×Q8—144no—
422C2×Q8—284no—
423C2×Q8—288no—
424C2×Q8—2832no—
425C2×D4—72no—
426C2×D4—144no—
427C2×D4—141no—
428C2×D4—144no—
429C2×D4—284no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—71no—
434C22×C4—71no—
435C22×C4—71no—
436C22×C4—74no—
437C22×C4—72no—
438C22×C4—74no—
439C22×C4—72no—
440C22×C4—144no—
441C22×C4—144no—
442C22×C4—144no—
443C22×C4—148no—
444C22×C4—144no—
445C22×C4—141no—
446C22×C4—142no—
447C22×C4—284no—
448C22×C4—288no—
449C22×C4D4×D711yescharacteristic
450C22×C4D4×D711yescharacteristic
451C22×C4C23×D711yescharacteristic
452C2×C8—24no—
453C2×C8—74no—
454C2×C8—144no—
455C2×C8C23×D714yes—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—74no—
463C4⋊C4—148no—
464C4⋊C4—148no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—142no—
468C4⋊C4—144no—
469C4⋊C4C23×D714yes—
470C4⋊C4C23×D712yes—
471C4⋊C4C23×D712yes—
472C22⋊C4—144no—
473C22⋊C4—144no—
474C22⋊C4—144no—
475C22⋊C4—144no—
476C22⋊C4—144no—
477C42—74no—
478C42—72no—
479C42—74no—
480C42—72no—
481C42—144no—
482C42D4×D712yes—
483C42C23×D712yes—
484C2×C7#323814yescomplemented
485C2×C7C2×#53611yescharacteristic
486C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
487C2×C7C22×#13711yescharacteristic
488D7—24no—
489D7—82no—
490C23—74no—
491C23—72no—
492C23—142no—
493C23—142no—
494C23—142no—
495C23—282no—
496C23—282no—
497C23—282no—
498C23C2×D4×D711yescharacteristic
499Q8—48no—
500Q8—144no—
501Q8—288no—
502Q8—2816no—
503Q8—282no—
504D4—144no—
505D4—288no—
506D4—282no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—74no—
516C2×C4—72no—
517C2×C4—72no—
518C2×C4—72no—
519C2×C4—148no—
520C2×C4—148no—
521C2×C4—142no—
522C2×C4—142no—
523C2×C4—144no—
524C2×C4—144no—
525C2×C4—142no—
526C2×C4—144no—
527C2×C4—288no—
528C2×C4—2816no—
529C2×C4—282no—
530C2×C4—284no—
531C2×C4C2×D4×D712yes—
532C2×C4C2×D4×D712yes—
533C2×C4C2×D4×D711yescharacteristic
534C2×C4#655114yes—
535C2×C4C24×D711yescharacteristic
536C8—24no—
537C8—144no—
538C7C2×#323811yescharacteristic, complemented, Sylow
539C22—74no—
540C22—142no—
541C22—148no—
542C22—142no—
543C22—282no—
544C22—282no—
545C22—282no—
546C22—564no—
547C22#9041512yes—
548C22D7×AGL(1,ℤ/8)12yes—
549C22D7×#13712yes—
550C22C22×D4×D711yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—42no—
556C4—74no—
557C4—142no—
558C4—142no—
559C4—284no—
560C4—282no—
561C4#9041512yes—
562C4C2×#655112yes—
563C2—144no—
564C2—562no—
565C2#1173942714yesdirect product factor
566C2C2×#9041511yescharacteristic
567C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#501C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
hypercenterC2×#501D7
hypocenterC7C2×#3238
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
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#501C2semidirect
4. C2×#89861C2semidirect
5. C2×#89837C2semidirect
6. #11739427C2direct (N × H)
7. C2×#89647C2semidirect
9. C2×#89642C2semidirect
10. C2×#89634C2semidirect
11. C2×#89486C2semidirect
12. C2×#89477C2semidirect
18. D7×C4⋊Q8C22semidirect
36. C7×#501C22semidirect
44. #89861C22semidirect
45. #89837C22semidirect
52. #89647C22semidirect
53. #89642C22semidirect
54. #89634C22semidirect
55. #89486C22semidirect
56. #89477C22semidirect
140. C2×#501D7semidirect
243. #501C2×D7semidirect
484. C2×C7#3238semidirect
538. C7C2×#3238semidirect
565. C2#11739427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#903822
C2×C7×#5012
C2×#898612
C2×#898372
#117394272
C2×#896472
C2×#896542
C2×#896422
C2×#896342
C2×#894862
C2×#894772
C2×#32387