Finite Group Databasebeta

← C2×#11740965 #14232500

Subgroups — C2×#11740965 #14232500

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic
2C2×#90233C211yesmaximal, characteristic, complemented
3#11740965C2116yesmaximal, direct product factor
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89850C211yesmaximal, characteristic, complemented
6C2×#89814C212yesmaximal, complemented
7C2×#89807C212yesmaximal, complemented
8C2×C4×#1142C211yesmaximal, characteristic, complemented
9C2×#89784C211yesmaximal, characteristic, complemented
10C2×#89779C211yesmaximal, characteristic, complemented
11C2×#89742C212yesmaximal, complemented
12C2×#89736C212yesmaximal, complemented
13C22×C7×#41—21no—
14C7×#547—24no—
15C7×#547C2218yes—
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×#6499—21no—
24C22×#1142C2211yescharacteristic
25C2×#6489C2212yes—
26C2×#6487C2212yes—
27C22×#1136C2212yes—
28#90233—24no—
29#90233C2218yescomplemented
30C2×#6450—21no—
31C2×#6442—22no—
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C2×#6406C2212yes—
35C2×#6406C2211yescharacteristic
36C2×C22⋊(C7⋊C8)C2212yes—
37#89866C2218yescomplemented
38#89850C2218yescomplemented
39#89814C22116yescomplemented
40#89807C22116yescomplemented
41C4×#1142C2218yescomplemented
42#89784C2218yescomplemented
43#89779C2218yescomplemented
44#89742C22116yescomplemented
45C2×#6384C2211yescharacteristic
46C2×#6384C2212yes—
47#89736C22116yescomplemented
48C2×#6382C2211yescharacteristic
49C2×#6382C2212yes—
50C2×#6381C2212yes—
51C2×#6381C2212yes—
52C2×#6381C2212yes—
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3353—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×Dic14—21no—
66C22×Dic14C2311yescharacteristic
67C7×C4⋊Q8—22no—
68C7×C4⋊Q8C2314yes—
69C7×#123—216no—
70C7×C22⋊Q8—28no—
71C7×#121—24no—
72C7×#121C2318yes—
73C4×C7×D4—22no—
74C4×C7×D4D414yes—
75C4×C7×D4C2314yes—
76C4×C7×D4C2314yes—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—24no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2312yes—
83C2×C7×C4⋊C4C2318yes—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4D412yes—
87C2×C42×C7C2311yescharacteristic
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90#6499—28no—
91C2×#1142—24no—
92C2×#1142C2314yes—
93#6489—24no—
94#6489C2318yes—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2312yes—
98#6487—24no—
99#6487C2318yes—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—22no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—22no—
104C2×#1136—28no—
105C2×#1136C2318yes—
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2312yes—
108C22×C7⋊C8C2311yescharacteristic
109#6450—28no—
110#6442—216no—
111#6432—22no—
112#6432C2314yes—
113C4×Dic14—22no—
114C4×Dic14C2314yes—
115#6406C2318yes—
116#6406C2314yes—
117C22⋊(C7⋊C8)C2318yes—
118#6384C2318yes—
119#6384C2314yes—
120#6382C2318yes—
121#6382C2314yes—
122#6381C2318yes—
123#6381C2318yes—
124#6381C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C4×C7⋊C8C2314yes—
127C2×#556—71no—
128C2×#547D711yescharacteristic
129#3353—716no—
130C2×#500—71no—
131C2×#484—72no—
132C2×#482—72no—
133C2×#475—71no—
134C2×#474—71no—
135C2×#468—72no—
136C2×C4×SD16—71no—
137C2×#436—71no—
138C2×#428—72no—
139C24×C7—21no—
140C24×C7C2×D412yes—
141C7×#41—432no—
142C2×C7×Q8—24no—
143C2×C7×Q8—44no—
144C2×C7×D4—28no—
145C2×C7×D4—24no—
146C2×C7×D4—21no—
147C2×C7×D4—22no—
148C2×C7×D4—22no—
149C2×C7×D4—48no—
150C2×C7×D4C2×D414yes—
151C2×C7×D4C2412yes—
152C22×C4×C7—24no—
153C22×C4×C7—24no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—28no—
157C22×C4×C7—24no—
158C22×C4×C7—48no—
159C22×C4×C7—44no—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D414yes—
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2414yes—
165C22×C4×C7C2411yescharacteristic
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—22no—
169C2×Dic14—22no—
170C2×Dic14—22no—
171C2×Dic14—21no—
172C2×Dic14—24no—
173C2×Dic14—44no—
174C2×Dic14C2412yes—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—28no—
178C7×C4⋊C4—24no—
179C7×C4⋊C4C2×D414yes—
180C7×C4⋊C4C2412yes—
181C7×C4⋊C4C2414yes—
182C7×C22⋊C4—24no—
183C7×C22⋊C4—28no—
184C7×C22⋊C4C2×D418yes—
185C42×C7C2×D412yes—
186C42×C7C2412yes—
187C22⋊Dic7—28no—
188C22⋊Dic7—28no—
189#1142—28no—
190C4⋊Dic7—21no—
191C4⋊Dic7—22no—
192C4⋊Dic7—24no—
193C4⋊Dic7C2412yes—
194C4⋊Dic7C2414yes—
195Dic7⋊C4—24no—
196Dic7⋊C4—28no—
197C4×Dic7—24no—
198C4×Dic7—28no—
199#1136—216no—
200C2×C7⋊C8—24no—
201C2×C7⋊C8—22no—
202C2×C7⋊C8#4114yescomplemented
203C2×C7⋊C8C2412yes—
204C2×C7⋊C8C2414yes—
205C2×C7⋊C8C2412yes—
206C22×#41—21no—
207C22×SD16—71no—
208C22×M16—72no—
209#556—78no—
210#556—144no—
211#547—24no—
212#547C2×D718yes—
213C2×C4⋊Q8—71no—
214C2×C4⋊Q8C2×D711yescharacteristic
215C2×#126—142no—
216C2×#124—141no—
217C2×#123—22no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—72no—
220C2×#121C2×D712yes—
221C2×C4×Q8—71no—
222C2×C4×Q8—141no—
223C2×C4×D4C2×D711yescharacteristic
224C2×C4×D4C2×D711yescharacteristic
225C2×#117—72no—
226C22×C4⋊C4C2×D712yes—
227#500—78no—
228#484—716no—
229#482—716no—
230#475—78no—
231#474—78no—
232#468—716no—
233C4×SD16—78no—
234#436—78no—
235#428—716no—
236C2×#107—72no—
237C2×#107—72no—
238C2×#107—72no—
239C2×#106—72no—
240C2×#106—71no—
241C2×C4⋊C8—71no—
242C2×#103—72no—
243C2×#103—71no—
244C2×#102—71no—
245C2×#102—72no—
246C2×C22⋊C8—72no—
247C2×C4×C8—71no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—22no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7C22×D414yes—
256C23×C7C22×D411yescharacteristic
257C7×Q8—48no—
258C7×D4—28no—
259C7×D4—22no—
260C7×D4—22no—
261C7×D4—416no—
262C7×D4—42no—
263C2×C4×C7—24no—
264C2×C4×C7—22no—
265C2×C4×C7—28no—
266C2×C4×C7—24no—
267C2×C4×C7—24no—
268C2×C4×C7—22no—
269C2×C4×C7—24no—
270C2×C4×C7—416no—
271C2×C4×C7—42no—
272C2×C4×C7—44no—
273C2×C4×C7—48no—
274C2×C4×C7AGL(1,ℤ/8)14yes—
275C2×C4×C7C22×D414yes—
276C2×C4×C7C22×D412yes—
277C2×C4×C7C22×D411yescharacteristic
278C2×C4×C7C22×D412yes—
279C2×C4×C7C2×#4112yes—
280C2×C4×C72−1+412yes—
281C2×C4×C7C2511yescharacteristic
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—24no—
285C2×Dic7—42no—
286C2×Dic7—44no—
287C2×Dic7—42no—
288Dic14—22no—
289Dic14—22no—
290Dic14—42no—
291Dic14—48no—
292C7⋊C8—24no—
293C7⋊C8—22no—
294C7⋊C8C2×#4114yescomplemented
295C2×#41—28no—
296C2×#41—48no—
297C22×Q8—21no—
298C22×Q8—71no—
299C22×Q8—141no—
300C22×D4—22no—
301C22×D4C22⋊D711yescharacteristic
302C22×D4C22×D711yescharacteristic
303C23×C4—22no—
304C23×C4—21no—
305C23×C4C22×D712yes—
306C2×SD16—74no—
307C2×SD16—144no—
308C2×M16—78no—
309C2×M16—148no—
310C22×C8—71no—
311C22×C8—72no—
312C22×C8—71no—
313C4⋊Q8—22no—
314C4⋊Q8—74no—
315C4⋊Q8—142no—
316C4⋊Q8C22×D714yes—
317#126—1416no—
318#124—148no—
319#123—216no—
320C22⋊Q8—28no—
321C22⋊Q8—78no—
322C22⋊Q8—144no—
323#121—24no—
324#121C22×D718yes—
325C4×Q8—74no—
326C4×Q8—148no—
327C4×Q8—142no—
328C4×D4—22no—
329C4×D4C22⋊D714yes—
330C4×D4C22×D714yes—
331C4×D4C22×D714yes—
332#117—78no—
333#117—144no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—71no—
338C2×C4⋊C4—72no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4C22⋊D711yescharacteristic
343C2×C4⋊C4C22×D711yescharacteristic
344C2×C4⋊C4C22×D712yes—
345C2×C4⋊C4C22×D718yes—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—142no—
349C2×C22⋊C4—142no—
350C2×C22⋊C4C22⋊D712yes—
351C2×C42—142no—
352C2×C42—141no—
353C2×C42C22×D711yescharacteristic
354#107—78no—
355#107—78no—
356#107—78no—
357#106—74no—
358#106—78no—
359C4⋊C8—74no—
360#103—74no—
361#103—78no—
362#102—74no—
363#102—78no—
364C22⋊C8—78no—
365C4×C8—74no—
366C22×C7—24no—
367C22×C7—24no—
368C22×C7—24no—
369C22×C7—48no—
370C22×C7—42no—
371C22×C7—42no—
372C22×C7—42no—
373C22×C7—84no—
374C22×C7#54712yes—
375C22×C7C2×AGL(1,ℤ/8)12yes—
376C22×C7#57812yes—
377C22×C7C23×D411yescharacteristic
378C4×C7—24no—
379C4×C7—22no—
380C4×C7—42no—
381C4×C7—44no—
382C4×C7#54712yes—
383C4×C7C2×AGL(1,ℤ/8)14yes—
384C4×C7C22×#4111yescharacteristic
385C4×C7C2×2−1+411yescharacteristic
386Dic7—42no—
387Dic7—44no—
388Dic7—42no—
389C24—21no—
390C24C2×C22⋊D712yes—
391#41—432no—
392C2×Q8—24no—
393C2×Q8—44no—
394C2×Q8—72no—
395C2×Q8—141no—
396C2×Q8—144no—
397C2×Q8—142no—
398C2×Q8—142no—
399C2×Q8—284no—
400C2×D4—28no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—48no—
406C2×D4C2×C22⋊D714yes—
407C2×D4C23×D712yes—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—28no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—48no—
415C22×C4—44no—
416C22×C4—141no—
417C22×C4—142no—
418C22×C4—141no—
419C22×C4C2×C22⋊D714yes—
420C22×C4C2×C22⋊D712yes—
421C22×C4C2×C22⋊D711yescharacteristic
422C22×C4C2×C22⋊D711yescharacteristic
423C22×C4C23×D714yes—
424C22×C4C23×D711yescharacteristic
425SD16—148no—
426M16—1416no—
427C2×C8—74no—
428C2×C8—72no—
429C2×C8—72no—
430C2×C8—74no—
431C2×C8—144no—
432C2×C8—142no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—28no—
436C4⋊C4—24no—
437C4⋊C4—72no—
438C4⋊C4—74no—
439C4⋊C4—144no—
440C4⋊C4—148no—
441C4⋊C4—141no—
442C4⋊C4—142no—
443C4⋊C4—144no—
444C4⋊C4C2×C22⋊D714yes—
445C4⋊C4C23×D712yes—
446C4⋊C4C23×D714yes—
447C22⋊C4—24no—
448C22⋊C4—28no—
449C22⋊C4—148no—
450C22⋊C4—148no—
451C22⋊C4C2×C22⋊D718yes—
452C42—148no—
453C42—144no—
454C42C2×C22⋊D712yes—
455C42C23×D712yes—
456C2×C7—44no—
457C2×C7—82no—
458C2×C7#335314yescomplemented
459C2×C7C2×#54711yescharacteristic
460C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
461C2×C7C2×#57811yescharacteristic
462C23—24no—
463C23—24no—
464C23—24no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23C22×C22⋊D714yes—
470C23C22×C22⋊D711yescharacteristic
471Q8—48no—
472Q8—142no—
473Q8—142no—
474Q8—288no—
475Q8—282no—
476D4—28no—
477D4—22no—
478D4—22no—
479D4—416no—
480D4—42no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—28no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—416no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—142no—
493C2×C4—144no—
494C2×C4—142no—
495C2×C4—284no—
496C2×C4—282no—
497C2×C4—282no—
498C2×C4#649514yes—
499C2×C4D7×#4112yes—
500C2×C4#655412yes—
501C2×C4C22×C22⋊D714yes—
502C2×C4C22×C22⋊D712yes—
503C2×C4C22×C22⋊D712yes—
504C2×C4C22×C22⋊D711yescharacteristic
505C2×C4C24×D711yescharacteristic
506C8—74no—
507C8—144no—
508C8—142no—
509C7C2×#335311yescharacteristic, complemented, Sylow
510C22—24no—
511C22—24no—
512C22—24no—
513C22—48no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22C2×#649512yes—
519C22#9051512yes—
520C22#9052912yes—
521C22C23×C22⋊D711yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—44no—
526C4—284no—
527C4—282no—
528C4—282no—
529C4C2×#649514yes—
530C4#9051512yes—
531C4C2×D7×#4111yescharacteristic
532C4C2×#655411yescharacteristic
533C2—44no—
534C2—82no—
535C2#1174096514yesdirect product factor
536C2C22×#649511yescharacteristic
537C2C2×#9051511yescharacteristic
538C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3353
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
2. C2×#90233C2semidirect
3. #11740965C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89850C2semidirect
6. C2×#89814C2semidirect
7. C2×#89807C2semidirect
8. C2×C4×#1142C2semidirect
9. C2×#89784C2semidirect
10. C2×#89779C2semidirect
11. C2×#89742C2semidirect
12. C2×#89736C2semidirect
29. #90233C22semidirect
37. #89866C22semidirect
38. #89850C22semidirect
39. #89814C22semidirect
40. #89807C22semidirect
41. C4×#1142C22semidirect
42. #89784C22semidirect
43. #89779C22semidirect
44. #89742C22semidirect
47. #89736C22semidirect
202. C2×C7⋊C8#41semidirect
294. C7⋊C8C2×#41semidirect
458. C2×C7#3353semidirect
509. C7C2×#3353semidirect
535. C2#11740965direct (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×#902332
#117409652
C2×#898662
C2×#898502
C2×#898142
C2×#898072
C2×C4×#11422
C2×#897842
C2×#897792
C2×#897422
C2×#897362
C2×#33537