Finite Group Databasebeta

← C2×#11740966 #14232512

Subgroups — C2×#11740966 #14232512

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic, complemented
3#11740966C2116yesmaximal, direct product factor
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89851C211yesmaximal, characteristic, complemented
6C2×#89811C212yesmaximal, complemented
7C2×#89807C212yesmaximal, complemented
8C2×#89784C211yesmaximal, characteristic, complemented
9C2×#89780C211yesmaximal, characteristic, complemented
10C2×C4×#1141C211yesmaximal, characteristic, complemented
11C2×#89740C212yesmaximal, complemented
12C2×#89736C212yesmaximal, complemented
13C22×C7×#41—21no—
14C7×#547—24no—
15C7×#547C2218yescomplemented
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#123—22no—
18C2×C7×C22⋊Q8—21no—
19C2×C7×#121C2212yes—
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C22×C7×C4⋊C4C2212yes—
23C2×#6501—21no—
24C22×#1141C2211yescharacteristic
25C2×#6493C2212yes—
26C2×#6489C2212yes—
27C22×#1136C2212yes—
28#90254—24no—
29#90254C2218yescomplemented
30C2×#6455—21no—
31C2×#6448—22no—
32C2×C4×D28C2211yescharacteristic
33C2×#6432C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2212yes—
36C2×C22⋊(C7⋊C8)C2212yes—
37#89859C2218yescomplemented
38#89851C2218yescomplemented
39#89811C22116yescomplemented
40#89807C22116yescomplemented
41C4×#1141C2218yescomplemented
42#89784C2218yescomplemented
43#89780C2218yescomplemented
44#89740C22116yescomplemented
45C2×#6383C2211yescharacteristic
46C2×#6383C2212yes—
47#89736C22116yescomplemented
48C2×#6382C2212yes—
49C2×#6382C2212yes—
50C2×#6382C2212yes—
51C2×#6381C2211yescharacteristic
52C2×#6381C2212yes—
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3354—71nomaximal, Sylow
56C2×C7×#41—28no—
57C2×C7×#41—48no—
58C22×C7×Q8—21no—
59C22×C7×D4—22no—
60C22×C7×D4D411yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—22no—
63C23×C4×C7—21no—
64C23×C4×C7C2312yes—
65C22×C22⋊D7—22no—
66C22×D28C2311yescharacteristic
67C22×C4×D7—21no—
68C22×Dic14—21no—
69C7×C4⋊Q8—22no—
70C7×C4⋊Q8C2314yes—
71C7×#123—216no—
72C7×C22⋊Q8—28no—
73C7×#121—24no—
74C7×#121C2318yes—
75C4×C7×D4—22no—
76C4×C7×D4D414yes—
77C4×C7×D4C2314yes—
78C4×C7×D4C2314yes—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4D411yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C4⋊C4C2318yes—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4D412yes—
89C2×C42×C7C2311yescharacteristic
90C2×C22⋊Dic7—22no—
91#6501—28no—
92C2×#1141—24no—
93C2×#1141C2314yes—
94#6493—24no—
95#6493C2318yes—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—22no—
98#6489—24no—
99#6489C2318yes—
100C2×C4⋊Dic7—21no—
101C2×C4⋊Dic7C2312yes—
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4×Dic7—22no—
104C2×#1136—28no—
105C2×#1136C2318yes—
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2312yes—
108C22×C7⋊C8C2311yescharacteristic
109#6455—28no—
110#6448—216no—
111C4×D28—22no—
112C4×D28C2314yes—
113#6432—22no—
114#6432C2314yes—
115#6406C2318yes—
116#6406C2314yes—
117C22⋊(C7⋊C8)C2318yes—
118#6383C2318yes—
119#6383C2314yes—
120#6382C2318yes—
121#6382C2318yes—
122#6382C2318yes—
123#6381C2318yes—
124#6381C2314yes—
125C4⋊(C7⋊C8)C2314yes—
126C4×C7⋊C8C2314yes—
127C2×#555—71no—
128C2×#547D711yescharacteristic, complemented
129#3354—716no—
130C2×#498—71no—
131C2×#481—72no—
132C2×#482—72no—
133C2×#476—71no—
134C2×#474—71no—
135C2×#469—72no—
136C2×C4×D8—71no—
137C2×#436—71no—
138C2×#428—72no—
139C24×C7—21no—
140C24×C7C2×D412yes—
141C23×D7—21no—
142C7×#41—432no—
143C2×C7×Q8—24no—
144C2×C7×Q8—44no—
145C2×C7×D4—28no—
146C2×C7×D4—24no—
147C2×C7×D4—21no—
148C2×C7×D4—22no—
149C2×C7×D4—22no—
150C2×C7×D4—48no—
151C2×C7×D4C2×D414yes—
152C2×C7×D4C2412yes—
153C22×C4×C7—24no—
154C22×C4×C7—24no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—28no—
158C22×C4×C7—24no—
159C22×C4×C7—48no—
160C22×C4×C7—44no—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D414yes—
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2414yes—
166C22×C4×C7C2411yescharacteristic
167C2×C22⋊D7—28no—
168C2×C22⋊D7—84no—
169C22×Dic7—21no—
170C22×Dic7—22no—
171C2×D28—22no—
172C2×D28—22no—
173C2×D28—21no—
174C2×D28C2412yes—
175C2×C4×D7—24no—
176C2×C4×D7—44no—
177C2×Dic14—24no—
178C2×Dic14—82no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—22no—
181C7×C4⋊C4—28no—
182C7×C4⋊C4—24no—
183C7×C4⋊C4C2×D414yes—
184C7×C4⋊C4C2412yes—
185C7×C4⋊C4C2414yes—
186C7×C22⋊C4—24no—
187C7×C22⋊C4—28no—
188C7×C22⋊C4C2×D418yes—
189C42×C7C2×D412yes—
190C42×C7C2412yes—
191C22⋊Dic7—28no—
192#1141—28no—
193(C2×D7)⋊C4—24no—
194(C2×D7)⋊C4—28no—
195C4⋊Dic7—22no—
196C4⋊Dic7—24no—
197C4⋊Dic7—21no—
198C4⋊Dic7C2414yes—
199C4⋊Dic7C2412yes—
200C4×Dic7—28no—
201#1136—216no—
202C2×C7⋊C8—24no—
203C2×C7⋊C8—22no—
204C2×C7⋊C8#4114yescomplemented
205C2×C7⋊C8C2412yes—
206C2×C7⋊C8C2414yes—
207C2×C7⋊C8C2412yes—
208C22×#41—21no—
209C22×D8—71no—
210C22×M16—72no—
211#555—78no—
212#555—144no—
213#547—24no—
214#547C2×D718yescomplemented
215C2×C4⋊Q8—71no—
216C2×C4⋊Q8C2×D711yescharacteristic
217C2×#124—142no—
218C2×#123—22no—
219C2×C22⋊Q8—21no—
220C2×#121—72no—
221C2×#121—141no—
222C2×#121C2×D712yes—
223C2×C4×D4—71no—
224C2×C4×D4C2×D711yescharacteristic
225C2×C4×D4C2×D711yescharacteristic
226C2×#117—72no—
227C2×#117—141no—
228C22×C4⋊C4C2×D712yes—
229#498—78no—
230#482—716no—
231#481—716no—
232#476—78no—
233#474—78no—
234#469—716no—
235C4×D8—78no—
236#436—78no—
237#428—716no—
238C2×#107—72no—
239C2×#107—71no—
240C2×#106—72no—
241C2×#106—72no—
242C2×#106—72no—
243C2×C4⋊C8—71no—
244C2×#102—71no—
245C2×#102—72no—
246C2×#102—71no—
247C2×#102—72no—
248C2×C22⋊C8—72no—
249C2×C4×C8—71no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—22no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7C22×D414yes—
258C23×C7C22×D411yescharacteristic
259C22×D7—22no—
260C22×D7—42no—
261C22×D7—42no—
262C22×D7—42no—
263C7×Q8—48no—
264C7×D4—28no—
265C7×D4—22no—
266C7×D4—22no—
267C7×D4—416no—
268C7×D4—42no—
269C2×C4×C7—24no—
270C2×C4×C7—22no—
271C2×C4×C7—28no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—22no—
275C2×C4×C7—24no—
276C2×C4×C7—416no—
277C2×C4×C7—42no—
278C2×C4×C7—44no—
279C2×C4×C7—48no—
280C2×C4×C7AGL(1,ℤ/8)14yes—
281C2×C4×C7C22×D414yes—
282C2×C4×C7C22×D412yes—
283C2×C4×C7C22×D411yescharacteristic
284C2×C4×C7C22×D412yes—
285C2×C4×C7C2×#4112yes—
286C2×C4×C72−1+412yes—
287C2×C4×C7C2511yescharacteristic
288C22⋊D7—88no—
289C2×Dic7—22no—
290C2×Dic7—24no—
291C2×Dic7—42no—
292C2×Dic7—44no—
293D28—22no—
294D28—22no—
295D28—42no—
296C4×D7—48no—
297Dic14—84no—
298C7⋊C8—24no—
299C7⋊C8—22no—
300C7⋊C8C2×#4114yescomplemented
301C2×#41—28no—
302C2×#41—48no—
303C22×Q8—21no—
304C22×Q8—141no—
305C22×D4—22no—
306C22×D4—71no—
307C22×D4—142no—
308C22×D4C22⋊D711yescharacteristic
309C22×D4C22×D711yescharacteristic
310C23×C4—22no—
311C23×C4—21no—
312C23×C4—141no—
313C23×C4C22×D712yes—
314C2×D8—74no—
315C2×D8—144no—
316C2×M16—78no—
317C2×M16—148no—
318C22×C8—71no—
319C22×C8—72no—
320C22×C8—71no—
321C4⋊Q8—22no—
322C4⋊Q8—74no—
323C4⋊Q8—142no—
324C4⋊Q8C22×D714yes—
325#124—1416no—
326#123—216no—
327C22⋊Q8—28no—
328#121—24no—
329#121—78no—
330#121—148no—
331#121—144no—
332#121C22×D718yes—
333C4×D4—22no—
334C4×D4—74no—
335C4×D4—142no—
336C4×D4C22⋊D714yes—
337C4×D4C22×D714yes—
338C4×D4C22×D714yes—
339#117—78no—
340#117—144no—
341#117—148no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—72no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4C22⋊D711yescharacteristic
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C4⋊C4C22×D712yes—
351C2×C4⋊C4C22×D718yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—142no—
355C2×C22⋊C4—142no—
356C2×C22⋊C4—141no—
357C2×C22⋊C4C22⋊D712yes—
358C2×C42—142no—
359C2×C42C22×D711yescharacteristic
360#107—74no—
361#107—78no—
362#106—78no—
363#106—78no—
364#106—78no—
365C4⋊C8—74no—
366#102—74no—
367#102—78no—
368#102—74no—
369#102—78no—
370C22⋊C8—78no—
371C4×C8—74no—
372C22×C7—24no—
373C22×C7—24no—
374C22×C7—24no—
375C22×C7—48no—
376C22×C7—42no—
377C22×C7—42no—
378C22×C7—42no—
379C22×C7—84no—
380C22×C7#54712yes—
381C22×C7C2×AGL(1,ℤ/8)12yes—
382C22×C7#57712yes—
383C22×C7C23×D411yescharacteristic
384C2×D7—42no—
385C2×D7—42no—
386C2×D7—42no—
387C2×D7—84no—
388C4×C7—24no—
389C4×C7—22no—
390C4×C7—42no—
391C4×C7—44no—
392C4×C7#54712yes—
393C4×C7C2×AGL(1,ℤ/8)14yes—
394C4×C7C22×#4111yescharacteristic
395C4×C7C2×2−1+411yescharacteristic
396Dic7—42no—
397Dic7—44no—
398C24—21no—
399C24—141no—
400C24C2×C22⋊D712yes—
401#41—432no—
402C2×Q8—24no—
403C2×Q8—44no—
404C2×Q8—144no—
405C2×Q8—562no—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—48no—
412C2×D4—72no—
413C2×D4—148no—
414C2×D4—142no—
415C2×D4—142no—
416C2×D4—141no—
417C2×D4—564no—
418C2×D4C2×C22⋊D714yes—
419C2×D4C23×D712yes—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—28no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—48no—
427C22×C4—44no—
428C22×C4—141no—
429C22×C4—142no—
430C22×C4—144no—
431C22×C4—284no—
432C22×C4C2×C22⋊D714yes—
433C22×C4C2×C22⋊D712yes—
434C22×C4C2×C22⋊D711yescharacteristic
435C22×C4C2×C22⋊D711yescharacteristic
436C22×C4C23×D714yes—
437C22×C4C23×D711yescharacteristic
438D8—148no—
439M16—1416no—
440C2×C8—74no—
441C2×C8—72no—
442C2×C8—72no—
443C2×C8—74no—
444C2×C8—144no—
445C2×C8—142no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—28no—
449C4⋊C4—24no—
450C4⋊C4—74no—
451C4⋊C4—72no—
452C4⋊C4—141no—
453C4⋊C4—142no—
454C4⋊C4—144no—
455C4⋊C4C2×C22⋊D714yes—
456C4⋊C4C23×D712yes—
457C4⋊C4C23×D714yes—
458C22⋊C4—24no—
459C22⋊C4—28no—
460C22⋊C4—148no—
461C22⋊C4—148no—
462C22⋊C4—144no—
463C22⋊C4C2×C22⋊D718yes—
464C42—148no—
465C42C2×C22⋊D712yes—
466C42C23×D712yes—
467C2×C7—44no—
468C2×C7—82no—
469C2×C7#335414yescomplemented
470C2×C7C2×#54711yescharacteristic
471C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
472C2×C7C2×#57711yescharacteristic
473D7—82no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—142no—
482C23—282no—
483C23—282no—
484C23—282no—
485C23C22×C22⋊D714yes—
486C23C22×C22⋊D711yescharacteristic
487Q8—48no—
488Q8—564no—
489D4—28no—
490D4—22no—
491D4—22no—
492D4—416no—
493D4—42no—
494D4—142no—
495D4—142no—
496D4—282no—
497D4—568no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—28no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—416no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—48no—
509C2×C4—142no—
510C2×C4—144no—
511C2×C4—282no—
512C2×C4—284no—
513C2×C4—288no—
514C2×C4#649514yes—
515C2×C4D7×#4112yes—
516C2×C4#655412yes—
517C2×C4C22×C22⋊D714yes—
518C2×C4C22×C22⋊D712yes—
519C2×C4C22×C22⋊D712yes—
520C2×C4C22×C22⋊D711yescharacteristic
521C2×C4C24×D711yescharacteristic
522C8—74no—
523C8—144no—
524C8—142no—
525C7C2×#335411yescharacteristic, complemented, Sylow
526C22—24no—
527C22—24no—
528C22—24no—
529C22—48no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—282no—
535C22—282no—
536C22—282no—
537C22—564no—
538C22C2×#649512yes—
539C22#9051512yes—
540C22#9052812yes—
541C22C23×C22⋊D711yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—44no—
546C4—282no—
547C4—284no—
548C4C2×#649514yes—
549C4#9051512yes—
550C4C2×D7×#4111yescharacteristic
551C4C2×#655411yescharacteristic
552C2—44no—
553C2—82no—
554C2—562no—
555C2#1174096614yesdirect product factor
556C2C22×#649511yescharacteristic
557C2C2×#9051511yescharacteristic
558C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3354
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C7×#547C2semidirect
2. C2×#90254C2semidirect
3. #11740966C2direct (N × H)
4. C2×#89859C2semidirect
5. C2×#89851C2semidirect
6. C2×#89811C2semidirect
7. C2×#89807C2semidirect
8. C2×#89784C2semidirect
9. C2×#89780C2semidirect
10. C2×C4×#1141C2semidirect
11. C2×#89740C2semidirect
12. C2×#89736C2semidirect
15. C7×#547C22semidirect
29. #90254C22semidirect
37. #89859C22semidirect
38. #89851C22semidirect
39. #89811C22semidirect
40. #89807C22semidirect
41. C4×#1141C22semidirect
42. #89784C22semidirect
43. #89780C22semidirect
44. #89740C22semidirect
47. #89736C22semidirect
128. C2×#547D7semidirect
204. C2×C7⋊C8#41semidirect
214. #547C2×D7semidirect
300. C7⋊C8C2×#41semidirect
469. C2×C7#3354semidirect
525. C7C2×#3354semidirect
555. C2#11740966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#902542
#117409662
C2×#898592
C2×#898512
C2×#898112
C2×#898072
C2×#897842
C2×#897802
C2×C4×#11412
C2×#897402
C2×#897362
C2×#33547