Finite Group Databasebeta

← C2×#11738512 #14225917

Subgroups — C2×#11738512 #14225917

Order 1792.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90248C211yesmaximal, characteristic
3C2×C7×#476C211yesmaximal, characteristic, complemented
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89780C211yesmaximal, characteristic, complemented
6#11738512C2116yesmaximal, direct product factor
7C2×#89634C212yesmaximal, complemented
8C2×#89628C212yesmaximal, complemented
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89607C211yesmaximal, characteristic, complemented
11C2×#89546C212yesmaximal
12C2×#89537C212yesmaximal, complemented
13C22×Q8×D7—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6507—21no—
17C2×#6501C2211yescharacteristic
18C2×#6499C2211yescharacteristic
19C2×C4×C22⋊D7—21no—
20C2×#6489—21no—
21D7×C4⋊Q8—24no—
22D7×C4⋊Q8C2218yescomplemented
23#90248—24no—
24#90248C2218yes—
25C2×#6460C2211yescharacteristic
26C2×D7×C4⋊C4—21no—
27C2×D7×C4⋊C4C2212yes—
28C2×#6453C2211yescharacteristic
29C2×#6451—21no—
30C2×#6451C2212yes—
31C2×#6446—21no—
32C2×#6442—21no—
33C2×C42×D7C2211yescharacteristic
34C2×#6432C2211yescharacteristic
35C2×C4×Dic14C2211yescharacteristic
36C7×#476C2218yescomplemented
37C2×C7×#106C2212yes—
38C2×C7×C4⋊C8C2211yescharacteristic
39C2×C7×#102C2212yes—
40C2×#6406C2212yes—
41C2×(C2×D7)⋊C8C2212yes—
42C2×#6392C2212yes—
43C2×#6390C2212yes—
44C2×#6389C2212yes—
45#89863C2218yescomplemented
46#89780C2218yescomplemented
47C2×#6384C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89634C22116yescomplemented
52#89628C22116yescomplemented
53#89622C2218yescomplemented
54#89607C2218yescomplemented
55#89546C22116yes—
56#89537C22116yescomplemented
57C2×#3238—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C22×C22⋊D7—21no—
62C2×Q8×D7—28no—
63C2×Q8×D7—48no—
64C22×C4×D7—22no—
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—
74C4×C7×D4—22no—
75C4×C7×D4C2314yes—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2312yes—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C22⋊C4—21no—
80C2×C42×C7C2311yescharacteristic
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84#6507—28no—
85#6501—22no—
86#6501C2314yes—
87#6499—22no—
88#6499C2314yes—
89C4×C22⋊D7—28no—
90C2×(C2×D7)⋊C4—21no—
91#6489—28no—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2312yes—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7D411yescharacteristic
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7C2311yescharacteristic
105C22×C7⋊C8C2312yes—
106#6460—22no—
107#6460C2314yes—
108D7×C4⋊C4—24no—
109D7×C4⋊C4—28no—
110D7×C4⋊C4C2318yes—
111#6453—22no—
112#6453C2314yes—
113#6451—24no—
114#6451—28no—
115#6451C2318yes—
116#6446—28no—
117#6442—28no—
118C42×D7D414yes—
119C42×D7C2314yes—
120#6432—22no—
121#6432C2314yes—
122C4×Dic14—22no—
123C4×Dic14C2314yes—
124C7×#106C2318yes—
125C7×C4⋊C8C2314yes—
126C7×#102C2318yes—
127#6406C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6392C2318yes—
130#6390C2318yes—
131#6389C2318yes—
132#6384C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135C4⋊(C7⋊C8)C2314yes—
136C22×C4⋊Q8—71no—
137C2×#529—71no—
138#3238—716no—
139C2×#501—72no—
140C2×#489—72no—
141C2×#483—72no—
142C2×#480—72no—
143C2×#477—71no—
144C2×#477—71no—
145C2×#476—71no—
146C2×#476D711yescharacteristic, complemented
147C2×#432—71no—
148C24×C7—21no—
149C23×D7C2×D411yescharacteristic
150C2×C7×Q8—24no—
151C2×C7×Q8—44no—
152C2×C7×D4—21no—
153C2×C7×D4—22no—
154C2×C7×D4—22no—
155C2×C7×D4C2412yes—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—24no—
159C22×C4×C7—44no—
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×Dic7C2×D411yescharacteristic
169C22×Dic7C2×D411yescharacteristic
170C22×Dic7C2×D411yescharacteristic
171Q8×D7—432no—
172C2×C4×D7—24no—
173C2×C4×D7—24no—
174C2×C4×D7—22no—
175C2×C4×D7—22no—
176C2×C4×D7—28no—
177C2×C4×D7—48no—
178C2×C4×D7C2×D412yes—
179C2×C4×D7C2×D414yes—
180C2×C4×D7C2×D414yes—
181C2×C4×D7C2412yes—
182C2×Dic14—22no—
183C2×Dic14—22no—
184C2×Dic14—21no—
185C2×Dic14—24no—
186C2×Dic14—28no—
187C2×Dic14—48no—
188C2×Dic14—44no—
189C2×Dic14C2412yes—
190C2×C7×C8—24no—
191C2×C7×C8C2414yes—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4C2414yes—
196C7×C4⋊C4C2412yes—
197C7×C22⋊C4—24no—
198C42×C7C2×D412yes—
199C42×C7C2412yes—
200C22⋊Dic7—24no—
201C22⋊Dic7—24no—
202C22⋊Dic7—24no—
203(C2×D7)⋊C4—24no—
204C4⋊Dic7—21no—
205C4⋊Dic7—22no—
206C4⋊Dic7—24no—
207C4⋊Dic7—24no—
208C4⋊Dic7—24no—
209C4⋊Dic7C2414yes—
210C4⋊Dic7C2412yes—
211Dic7⋊C4—24no—
212Dic7⋊C4—24no—
213Dic7⋊C4—28no—
214Dic7⋊C4—28no—
215C4×Dic7—24no—
216C4×Dic7C2×D412yes—
217C4×Dic7C2×D414yes—
218C4×Dic7C2×D414yes—
219C4×Dic7C2412yes—
220C2×C7⋊C8—24no—
221C2×C7⋊C8C2414yes—
222C23×Q8—141no—
223C2×C4⋊Q8—78no—
224C2×C4⋊Q8—72no—
225C2×C4⋊Q8—71no—
226C2×C4⋊Q8—141no—
227C2×C4⋊Q8—144no—
228C2×C4⋊Q8—141no—
229C2×C4⋊Q8C2×D711yescharacteristic
230#529—78no—
231#529—144no—
232C2×#126—141no—
233C2×#125—71no—
234C2×#124—71no—
235C2×#123—141no—
236C2×C22⋊Q8—71no—
237C2×#121—71no—
238C2×C4×Q8—71no—
239C2×C4×D4—141no—
240C2×C4×D4C2×D711yescharacteristic
241C2×#117—141no—
242C22×C4⋊C4—72no—
243C22×C4⋊C4—141no—
244C22×C42—71no—
245#501—716no—
246#489—716no—
247#483—716no—
248#480—716no—
249#477—78no—
250#477—78no—
251#476—78no—
252#476C2×D718yescomplemented
253#432—78no—
254C2×#107—72no—
255C2×#107—72no—
256C2×#106—72no—
257C2×#106C2×D712yes—
258C2×C4⋊C8—71no—
259C2×C4⋊C8C2×D711yescharacteristic
260C2×#103—72no—
261C2×#103—72no—
262C2×#102—72no—
263C2×#102C2×D712yes—
264C2×C22⋊C8—72no—
265C2×#97—72no—
266C23×C7—22no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7C22×D411yescharacteristic
271C22×D7—22no—
272C22×D7—22no—
273C22×D7AGL(1,ℤ/8)14yes—
274C22×D7C22×D412yes—
275C7×Q8—48no—
276C7×D4—22no—
277C7×D4—22no—
278C7×D4—42no—
279C2×C4×C7—22no—
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—44no—
283C2×C4×C7—42no—
284C2×C4×C7—48no—
285C2×C4×C7#13714yes—
286C2×C4×C7C22×D412yes—
287C2×C4×C7C22×D411yescharacteristic
288C2×C4×C7C22×D412yes—
289C2×C4×C72−1+412yes—
290C2×C4×C72−1+412yes—
291C2×C4×C7C2511yescharacteristic
292C22⋊D7—48no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—24no—
299C2×Dic7—42no—
300C2×Dic7—44no—
301C2×Dic7—42no—
302C2×Dic7C22×D412yes—
303C2×Dic7C22×D412yes—
304C2×Dic7C22×D412yes—
305C4×D7—28no—
306C4×D7—24no—
307C4×D7—28no—
308C4×D7—22no—
309C4×D7—22no—
310C4×D7—416no—
311Dic14—22no—
312Dic14—22no—
313Dic14—416no—
314Dic14—48no—
315Dic14—42no—
316C7×C8—24no—
317C7⋊C8—24no—
318C22×Q8—21no—
319C22×Q8—71no—
320C22×Q8—142no—
321C22×Q8—148no—
322C22×Q8—141no—
323C22×Q8—288no—
324C22×D4—141no—
325C22×D4C22×D711yescharacteristic
326C23×C4—21no—
327C23×C4—71no—
328C23×C4—71no—
329C23×C4—71no—
330C23×C4—142no—
331C22×C8—72no—
332C22×C8C22×D712yes—
333C4⋊Q8—22no—
334C4⋊Q8—78no—
335C4⋊Q8—74no—
336C4⋊Q8—148no—
337C4⋊Q8—144no—
338C4⋊Q8—148no—
339C4⋊Q8—142no—
340C4⋊Q8C22×D714yes—
341#126—148no—
342#125—74no—
343#125—142no—
344#124—74no—
345#124—142no—
346#123—148no—
347C22⋊Q8—74no—
348C22⋊Q8—142no—
349#121—74no—
350#121—142no—
351C4×Q8—74no—
352C4×Q8—142no—
353C4×D4—22no—
354C4×D4—148no—
355C4×D4C22×D714yes—
356#117—148no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—72no—
359C2×C4⋊C4—71no—
360C2×C4⋊C4—78no—
361C2×C4⋊C4—144no—
362C2×C4⋊C4—148no—
363C2×C4⋊C4—142no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4—141no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4C22×D712yes—
371C2×C4⋊C4C22×D711yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—141no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C42—71no—
378C2×C42—71no—
379C2×C42—71no—
380C2×C42—74no—
381C2×C42—74no—
382C2×C42—141no—
383C2×C42C22×D711yescharacteristic
384#107—78no—
385#107—78no—
386#106—78no—
387#106C22×D718yes—
388C4⋊C8—74no—
389C4⋊C8C22×D714yes—
390#103—78no—
391#103—78no—
392#102—78no—
393#102C22×D718yes—
394C22⋊C8—78no—
395#97—78no—
396C22×C7—42no—
397C22×C7—42no—
398C22×C7—42no—
399C22×C7—84no—
400C22×C7#53612yes—
401C22×C7C2×AGL(1,ℤ/8)12yes—
402C22×C7C2×#13712yes—
403C22×C7C23×D411yescharacteristic
404C2×D7—22no—
405C2×D7—28no—
406C2×D7—22no—
407C2×D7C2×AGL(1,ℤ/8)14yes—
408C4×C7—22no—
409C4×C7—44no—
410C4×C7—42no—
411C4×C7#53612yes—
412C4×C7C2×#13714yes—
413C4×C7C2×2−1+411yescharacteristic
414C4×C7C2×2−1+411yescharacteristic
415Dic7—22no—
416Dic7—22no—
417Dic7—22no—
418Dic7—42no—
419Dic7—44no—
420Dic7—42no—
421C24—21no—
422C24—71no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—72no—
426C2×Q8—148no—
427C2×Q8—141no—
428C2×Q8—144no—
429C2×Q8—142no—
430C2×Q8—142no—
431C2×Q8—284no—
432C2×Q8—288no—
433C2×Q8—2832no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—144no—
438C2×D4—284no—
439C2×D4C23×D712yes—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—44no—
444C22×C4—71no—
445C22×C4—71no—
446C22×C4—71no—
447C22×C4—74no—
448C22×C4—72no—
449C22×C4—74no—
450C22×C4—72no—
451C22×C4—144no—
452C22×C4—148no—
453C22×C4—144no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—142no—
459C22×C4—288no—
460C22×C4D4×D711yescharacteristic
461C22×C4D4×D711yescharacteristic
462C22×C4C23×D711yescharacteristic
463C2×C8—24no—
464C2×C8—74no—
465C2×C8—144no—
466C2×C8C23×D714yes—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—74no—
471C4⋊C4—72no—
472C4⋊C4—148no—
473C4⋊C4—148no—
474C4⋊C4—144no—
475C4⋊C4—144no—
476C4⋊C4—144no—
477C4⋊C4—144no—
478C4⋊C4—142no—
479C4⋊C4—141no—
480C4⋊C4—144no—
481C4⋊C4C23×D714yes—
482C4⋊C4C23×D712yes—
483C22⋊C4—24no—
484C22⋊C4—144no—
485C22⋊C4—144no—
486C22⋊C4—144no—
487C22⋊C4—144no—
488C42—74no—
489C42—72no—
490C42—74no—
491C42—72no—
492C42—144no—
493C42D4×D712yes—
494C42C23×D712yes—
495C2×C7—82no—
496C2×C7#323814yescomplemented
497C2×C7C2×#53611yescharacteristic
498C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
499C2×C7C22×#13711yescharacteristic
500D7—24no—
501C23—22no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—74no—
506C23—72no—
507C23—142no—
508C23—142no—
509C23C2×D4×D711yescharacteristic
510Q8—48no—
511Q8—142no—
512Q8—142no—
513Q8—288no—
514Q8—2816no—
515Q8—282no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—288no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—72no—
527C2×C4—72no—
528C2×C4—72no—
529C2×C4—148no—
530C2×C4—142no—
531C2×C4—142no—
532C2×C4—142no—
533C2×C4—148no—
534C2×C4—144no—
535C2×C4—142no—
536C2×C4—142no—
537C2×C4—142no—
538C2×C4—142no—
539C2×C4—144no—
540C2×C4—2816no—
541C2×C4—284no—
542C2×C4—282no—
543C2×C4—282no—
544C2×C4#647814yes—
545C2×C4C2×D4×D712yes—
546C2×C4C2×D4×D712yes—
547C2×C4C2×D4×D711yescharacteristic
548C2×C4#655112yes—
549C2×C4#655412yes—
550C2×C4C24×D711yescharacteristic
551C8—24no—
552C8—144no—
553C7C2×#323811yescharacteristic, complemented, Sylow
554C22—42no—
555C22—42no—
556C22—42no—
557C22—74no—
558C22—84no—
559C22—142no—
560C22—148no—
561C22—142no—
562C22#9031912yes—
563C22C2×#647812yes—
564C22D7×AGL(1,ℤ/8)12yes—
565C22C22×D4×D711yescharacteristic
566C4—22no—
567C4—44no—
568C4—42no—
569C4—142no—
570C4—142no—
571C4—142no—
572C4—284no—
573C4—282no—
574C4—282no—
575C4#9031912yes—
576C4C2×#647814yes—
577C4C2×#655111yescharacteristic
578C4C2×#655411yescharacteristic
579C2—82no—
580C2—144no—
581C2#1173851214yesdirect product factor
582C2C2×#9031911yescharacteristic
583C2C22×#647811yescharacteristic
584C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#476C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#476D7
hypocenterC7C2×#3238
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#476C2semidirect
4. C2×#89863C2semidirect
5. C2×#89780C2semidirect
6. #11738512C2direct (N × H)
7. C2×#89634C2semidirect
8. C2×#89628C2semidirect
9. C2×#89622C2semidirect
10. C2×#89607C2semidirect
12. C2×#89537C2semidirect
22. D7×C4⋊Q8C22semidirect
36. C7×#476C22semidirect
45. #89863C22semidirect
46. #89780C22semidirect
51. #89634C22semidirect
52. #89628C22semidirect
53. #89622C22semidirect
54. #89607C22semidirect
56. #89537C22semidirect
146. C2×#476D7semidirect
252. #476C2×D7semidirect
496. C2×C7#3238semidirect
553. C7C2×#3238semidirect
581. C2#11738512direct (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×#902482
C2×C7×#4762
C2×#898632
C2×#897802
#117385122
C2×#896342
C2×#896282
C2×#896222
C2×#896072
C2×#895462
C2×#895372
C2×#32387