Finite Group Databasebeta

← C2×#11739135 #14225914

Subgroups — C2×#11739135 #14225914

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×#90371C211yesmaximal, characteristic
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89827C211yesmaximal, characteristic, complemented
6#11739135C2116yesmaximal, direct product factor
7C2×#89577C212yesmaximal, complemented
8C2×#89566C212yesmaximal, complemented
9C2×#89546C212yesmaximal
10C2×#89533C212yesmaximal, complemented
11C2×#89477C211yesmaximal, characteristic, complemented
12C2×#89474C211yesmaximal, characteristic, complemented
13C22×Q8×D7—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#124C2211yescharacteristic
16C2×#6509C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×#6507—21no—
19C2×#6501C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21D7×C4⋊Q8—24no—
22D7×C4⋊Q8C2218yescomplemented
23#90371—24no—
24#90371C2218yes—
25C2×D7×C4⋊C4—21no—
26C2×D7×C4⋊C4C2212yes—
27C2×#6451—21no—
28C2×#6451C2212yes—
29C2×#6446—21no—
30C2×(C22⋊D7)⋊C4—21no—
31C2×#6442—21no—
32C2×#6440—21no—
33C2×C42×D7C2211yescharacteristic
34C2×#6433C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#489C2218yescomplemented
37C2×C7×#103C2212yes—
38C2×C7×#102C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6409C2212yes—
41C2×#6406C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6391C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89852C2218yescomplemented
47#89827C2218yescomplemented
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89577C22116yescomplemented
52#89566C22116yescomplemented
53#89546C22116yes—
54#89533C22116yescomplemented
55#89477C2218yescomplemented
56#89474C2218yescomplemented
57C2×#3238—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×Q8C2311yescharacteristic
60C22×C7×D4C2311yescharacteristic
61C22×C22⋊D7—21no—
62C23×Dic7—21no—
63C2×Q8×D7—28no—
64C2×Q8×D7—48no—
65C22×C4×D7—22no—
66C22×C4×D7D411yescharacteristic
67C22×C4×D7D411yescharacteristic
68C22×C4×D7C2311yescharacteristic
69C22×Dic14—21no—
70C22×Dic14—22no—
71C22×C7×C8C2312yes—
72C7×C4⋊Q8—22no—
73C7×C4⋊Q8C2314yes—
74C7×#124—22no—
75C7×#124C2314yes—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2312yes—
78C2×C7×C22⋊C4—21no—
79C2×C7×C22⋊C4—21no—
80C2×C42×C7C2311yescharacteristic
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7—21no—
83#6509—22no—
84#6509C2314yes—
85Q8×Dic7—22no—
86Q8×Dic7C2314yes—
87#6507—28no—
88#6501—22no—
89#6501C2314yes—
90D4×Dic7—22no—
91D4×Dic7C2314yes—
92C2×(C2×D7)⋊C4—21no—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2312yes—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7D411yescharacteristic
106C2×C4×Dic7C2311yescharacteristic
107C22×C7⋊C8C2312yes—
108D7×C4⋊C4—24no—
109D7×C4⋊C4—28no—
110D7×C4⋊C4C2318yes—
111#6451—24no—
112#6451—28no—
113#6451C2318yes—
114#6446—28no—
115(C22⋊D7)⋊C4—28no—
116#6442—28no—
117#6440—28no—
118C42×D7D414yes—
119C42×D7C2314yes—
120#6433—22no—
121#6433C2314yes—
122#6432—22no—
123#6432C2314yes—
124C7×#103C2318yes—
125C7×#102C2318yes—
126C7×#97C2314yes—
127#6409C2318yes—
128#6406C2318yes—
129(C2×D7)⋊C8C2318yes—
130#6392C2318yes—
131#6391C2318yes—
132Dic7⋊C8C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135#6377C2314yes—
136C22×C4⋊Q8—71no—
137C2×#529—71no—
138#3238—716no—
139C2×#501—71no—
140C2×#501—71no—
141C2×#489—71no—
142C2×#489D711yescharacteristic, complemented
143C2×#483—72no—
144C2×#480—72no—
145C2×#477—72no—
146C2×#476—72no—
147C2×#432—71no—
148C24×C7—21no—
149C23×D7C2×D411yescharacteristic
150C2×C7×Q8—24no—
151C2×C7×Q8—21no—
152C2×C7×Q8—24no—
153C2×C7×Q8—44no—
154C2×C7×Q8C2412yes—
155C2×C7×D4—21no—
156C2×C7×D4—24no—
157C2×C7×D4C2412yes—
158C22×C4×C7—21no—
159C22×C4×C7—22no—
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C2×C22⋊D7—24no—
164C2×C22⋊D7—44no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—22no—
168C22×Dic7—24no—
169C22×Dic7—44no—
170C22×Dic7C2×D411yescharacteristic
171C22×Dic7C2×D411yescharacteristic
172C22×Dic7C2×D411yescharacteristic
173Q8×D7—432no—
174C2×C4×D7—24no—
175C2×C4×D7—24no—
176C2×C4×D7—24no—
177C2×C4×D7—28no—
178C2×C4×D7—48no—
179C2×C4×D7C2×D412yes—
180C2×C4×D7C2×D414yes—
181C2×C4×D7C2×D414yes—
182C2×C4×D7C2412yes—
183C2×Dic14—24no—
184C2×Dic14—28no—
185C2×Dic14—48no—
186C2×Dic14—44no—
187C2×C7×C8—24no—
188C2×C7×C8C2414yes—
189C7×C4⋊C4—24no—
190C7×C4⋊C4—22no—
191C7×C4⋊C4C2414yes—
192C7×C22⋊C4—24no—
193C7×C22⋊C4—24no—
194C42×C7C2×D412yes—
195C42×C7C2412yes—
196C22⋊Dic7—24no—
197C22⋊Dic7—24no—
198(C2×D7)⋊C4—24no—
199C4⋊Dic7—22no—
200C4⋊Dic7—24no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—24no—
204C4⋊Dic7C2414yes—
205C4⋊Dic7C2412yes—
206C4⋊Dic7C2412yes—
207Dic7⋊C4—24no—
208Dic7⋊C4—24no—
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×#125—71no—
231C2×#124C2×D711yescharacteristic
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#501—78no—
244#489—78no—
245#489C2×D718yescomplemented
246#483—716no—
247#480—716no—
248#477—716no—
249#476—716no—
250#432—78no—
251C2×#107—72no—
252C2×#107—72no—
253C2×#106—72no—
254C2×#106—72no—
255C2×C4⋊C8—72no—
256C2×#103—72no—
257C2×#103C2×D712yes—
258C2×#102—72no—
259C2×#102C2×D712yes—
260C2×C22⋊C8—72no—
261C2×#97—71no—
262C2×#97C2×D711yescharacteristic
263C23×C7—22no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7C22×D411yescharacteristic
268C22×D7—22no—
269C22×D7—22no—
270C22×D7AGL(1,ℤ/8)14yes—
271C22×D7C22×D412yes—
272C7×Q8—24no—
273C7×Q8—48no—
274C7×Q8—42no—
275C7×D4—24no—
276C7×D4—42no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—24no—
281C2×C4×C7—42no—
282C2×C4×C7—44no—
283C2×C4×C7C22×D412yes—
284C2×C4×C7C22×D412yes—
285C2×C4×C7C22×D411yescharacteristic
286C2×C4×C72−1+414yes—
287C2×C4×C7C2511yescharacteristic
288C22⋊D7—48no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—24no—
294C2×Dic7—44no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—48no—
298C2×Dic7#13714yes—
299C2×Dic7C22×D412yes—
300C2×Dic7C22×D412yes—
301C2×Dic7C22×D412yes—
302C4×D7—28no—
303C4×D7—24no—
304C4×D7—24no—
305C4×D7—28no—
306C4×D7—416no—
307Dic14—416no—
308Dic14—48no—
309C7×C8—24no—
310C7⋊C8—24no—
311C22×Q8—21no—
312C22×Q8—142no—
313C22×Q8—148no—
314C22×Q8—141no—
315C22×Q8—288no—
316C22×Q8C22×D711yescharacteristic
317C22×D4—141no—
318C22×D4C22×D711yescharacteristic
319C23×C4—71no—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—142no—
323C23×C4—141no—
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—74no—
336#125—142no—
337#124—22no—
338#124C22×D714yes—
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—72no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—71no—
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⋊C4—141no—
363C2×C4⋊C4—141no—
364C2×C4⋊C4C22×D712yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
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#107—78no—
379#106—78no—
380#106—78no—
381C4⋊C8—78no—
382#103—78no—
383#103C22×D718yes—
384#102—78no—
385#102C22×D718yes—
386C22⋊C8—78no—
387#97—74no—
388#97C22×D714yes—
389C22×C7—42no—
390C22×C7—42no—
391C22×C7—42no—
392C22×C7—84no—
393C22×C7#53612yes—
394C22×C7C2×AGL(1,ℤ/8)12yes—
395C22×C7C2×#13712yes—
396C22×C7C23×D411yescharacteristic
397C2×D7—22no—
398C2×D7—28no—
399C2×D7—22no—
400C2×D7C2×AGL(1,ℤ/8)14yes—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—42no—
404C4×C7—44no—
405C4×C7#53612yes—
406C4×C7C2×2−1+412yes—
407Dic7—22no—
408Dic7—22no—
409Dic7—44no—
410Dic7—42no—
411Dic7—42no—
412Dic7C2×#13714yes—
413C24—21no—
414C24—71no—
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8—24no—
418C2×Q8—44no—
419C2×Q8—148no—
420C2×Q8—144no—
421C2×Q8—284no—
422C2×Q8—288no—
423C2×Q8—2832no—
424C2×Q8C23×D712yes—
425C2×D4—21no—
426C2×D4—24no—
427C2×D4—144no—
428C2×D4—284no—
429C2×D4C23×D712yes—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—71no—
433C22×C4—71no—
434C22×C4—71no—
435C22×C4—74no—
436C22×C4—72no—
437C22×C4—74no—
438C22×C4—72no—
439C22×C4—144no—
440C22×C4—144no—
441C22×C4—148no—
442C22×C4—144no—
443C22×C4—144no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—142no—
447C22×C4—288no—
448C22×C4—284no—
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—22no—
458C4⋊C4—74no—
459C4⋊C4—72no—
460C4⋊C4—72no—
461C4⋊C4—148no—
462C4⋊C4—148no—
463C4⋊C4—144no—
464C4⋊C4—144no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—142no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—144no—
471C4⋊C4C23×D714yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
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—82no—
485C2×C7#323814yescomplemented
486C2×C7C2×#53611yescharacteristic
487C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
488C2×C7C22×#13711yescharacteristic
489D7—24no—
490C23—22no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—74no—
495C23—72no—
496C23—142no—
497C23—142no—
498C23C2×D4×D711yescharacteristic
499Q8—24no—
500Q8—48no—
501Q8—42no—
502Q8—288no—
503Q8—2816no—
504D4—24no—
505D4—42no—
506D4—288no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—74no—
514C2×C4—72no—
515C2×C4—72no—
516C2×C4—72no—
517C2×C4—148no—
518C2×C4—148no—
519C2×C4—142no—
520C2×C4—142no—
521C2×C4—144no—
522C2×C4—144no—
523C2×C4—142no—
524C2×C4—142no—
525C2×C4—144no—
526C2×C4—2816no—
527C2×C4—288no—
528C2×C4—284no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4C2×D4×D712yes—
532C2×C4C2×D4×D712yes—
533C2×C4C2×D4×D711yescharacteristic
534C2×C4#655414yes—
535C2×C4C24×D711yescharacteristic
536C8—24no—
537C8—144no—
538C7C2×#323811yescharacteristic, complemented, Sylow
539C22—42no—
540C22—42no—
541C22—42no—
542C22—74no—
543C22—84no—
544C22—142no—
545C22—142no—
546C22—148no—
547C22#9036612yes—
548C22D7×AGL(1,ℤ/8)12yes—
549C22D7×#13712yes—
550C22C22×D4×D711yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—74no—
556C4—142no—
557C4—142no—
558C4—284no—
559C4—282no—
560C4—282no—
561C4#9036612yes—
562C4C2×#655412yes—
563C2—82no—
564C2—144no—
565C2#1173913514yesdirect product factor
566C2C2×#9036611yescharacteristic
567C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#489D7
hypocenterC7C2×#3238
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89852C2semidirect
5. C2×#89827C2semidirect
6. #11739135C2direct (N × H)
7. C2×#89577C2semidirect
8. C2×#89566C2semidirect
10. C2×#89533C2semidirect
11. C2×#89477C2semidirect
12. C2×#89474C2semidirect
22. D7×C4⋊Q8C22semidirect
36. C7×#489C22semidirect
46. #89852C22semidirect
47. #89827C22semidirect
51. #89577C22semidirect
52. #89566C22semidirect
54. #89533C22semidirect
55. #89477C22semidirect
56. #89474C22semidirect
142. C2×#489D7semidirect
245. #489C2×D7semidirect
485. C2×C7#3238semidirect
538. C7C2×#3238semidirect
565. C2#11739135direct (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×#903712
C2×C7×#4892
C2×#898522
C2×#898272
#117391352
C2×#895772
C2×#895662
C2×#895462
C2×#895332
C2×#894772
C2×#894742
C2×#32387